also cc.k.cc.3, cc.k.cc.4b, cc.k.cc.5 practice practice€¦ · · 2013-06-10houghton mifflin...

New York City Implementation Guide NYC37

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Chapter 1 27

Lesson 1.1

Hands On • Model and Count 1 and 2Instructional Time: 1 day

Common Core Standard CC.K.CC.4a Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

Also CC.K.CC.3, CC.K.CC.4b, CC.K.CC.5

Lesson Objective

Model and count 1 and 2 with objects.

Essential Question

How can you show and count 1 and 2 with objects?

Materials

• MathBoard • Animated Math Models

• two-color counters • iTools: Counters

Engage Approximately 5 min.

This activity reviews prerequisite skills, establishing a common conceptual foundation for the lesson. Use evidence of students’ understanding to decide how deeply to discuss.

Teach and Talk Approximately

20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use fi ve frames to show and count to 1 and 2. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting objects to develop sound mathematical practices by asking these questions. • What do you do fi rst?• How do you know how many counters

to put down?• Could you use a different kind of object

than a counter to help you count? Why?

Practice Share and Show Approximately 10 min.

Use the checked exercises as a diagnostic assessment. If students answer either exercise incorrectly, use RtI (Response to Intervention).

More Practice/Problem Solving Approximately 10 min.

Students can continue to practice once they understand how to model objects by using 1 or 2 counters in a fi ve frame. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.

Summarize Approximately 5 min.

Essential Question

How can you show and count 1 and 2 with objects?Possible answer: I can show 1 with one counter and 2 with two counters.

EngageThis activity reviews prerequisite skills,

1 ENGAGE

how deeply to discuss.

Teach and Talk2 TEACH and TALK

Practice 3 PRACTICE

especially rich.

Summarize 4 SUMMARIZE

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NYC38 New York City Implementation Guide

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28 Chapter 1

Lesson 1.2

Count and Write 1 and 2Instructional Time: 1 day

Common Core StandardCC.K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Also CC.K.CC.4a, CC.K.CC.4b, CC.K.CC.4c, CC.K.CC.5

Lesson Objective

Represent 1 and 2 objects with number names and written numerals.

Essential Question

How can you count and write 1 and 2 with words and numbers?

Materials

• Mathboard • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count objects up to 2 and trace 1 and 2 as numerals and words. As students work through Listen and Draw, gauge their level of under-standing to make better decisions about how to progress through instruction.Build on students’ understanding of 1 and 2 to develop sound mathematical practices by asking these questions.

• How would you describe the shape of each number?

• What parts of your face could you count using the number 1?

• What parts of your face could you count using the number 2?




Students can continue to practice once they understand if a picture shows 1 or 2 objects. The H.O.T. problem, exercises 7, 8, and 10, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 1 and 2 with words and numbers?Possible answer: I can draw pictures of one heart and two hearts. I can write the numbers 1 and 2 under the pictures. I can also use letters to spell the number words.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE

especially rich.



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Chapter 1 29

Lesson 1.3


Common Core StandardCC.K.CC.4a Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.


Lesson Objective

Model and count 3 and 4 with objects.

Essential Question

How can you show and count 3 and 4 with objects?

Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use fi ve frames to model and count 3 and 4. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting whole numbers to develop sound mathematical practices by asking these questions. • How do you know where to put each

counter?• How do you know you have counted

correctly?• What would happen if you forgot to put

a counter on an object?




Students can continue to practice once they understand how to model and count 3 and 4 using counters. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 3 and 4 with objects?Possible answer: I can show 3 with three counters and 4 with four counters.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE

especially rich.






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30 Chapter 1

Lesson 1.4


Common Core StandardCC.K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).


Lesson Objective


Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count up to 4 objects and trace 3 and 4 as numerals and words. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting objects to develop sound mathematical practices by asking these questions. • How do you know when to stop

counting?• How can you make sure you don’t

accidentally count the same object twice?

• What are some other things you could count using the numbers 3 or 4?



More Practice Approximately 10 min.

Students can continue to practice once they understand the concepts of the numbers 3 and 4. The H.O.T. problem and exercises 7, 8, and 10 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 3 and 4 with words and numbers? Possible answer: I can draw pictures of three counters and four counters. I can write the numbers 3 and 4 under the pictures. I can also use letters to write the number words.


1 ENGAGE



Practice 3 PRACTICE

making them especially rich.







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Chapter 1 31

Lesson 1.5

Hands On • Model and Count 5Instructional Time: 1 day

Common Core StandardCC.K.CC.4a Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.


Lesson Objective

Model and count 5 with objects.

Essential Question

How can you show and count 5 with objects?

Materials

• MathBoard • HMH Mega Math• two-color counters • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use fi ve frames to show and count to 5. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the number 5 to develop sound mathematical practices by asking these questions. • What do you do fi rst?• How do you arrange your counters in

the frame?• How do you know there are fi ve

counters?


Use the checked exercise as a diagnostic assessment. If students answer the exercise incorrectly, use RtI (Response to Intervention).


Students can continue to practice once they understand how to model groups of up to 5 objects using counters. The H.O.T. problem, exercises 4, 5, and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 5 with objects? Possible answer: I can show 5 with counters and a full fi ve frame or I can draw fi ve objects.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE

especially rich.






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32 Chapter 1

Lesson 1.6

Count and Write 5Instructional Time: 1 day

Common Core StandardCC.K.CC.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

Also CC.K.CC.3, CC.K.CC.4a, CC.K.CC.5

Lesson Objective

Represent 5 objects with a number name and a written numeral.

Essential Question

How can you count and write 5 with words and numbers?

Materials

• MathBoard • HMH Mega Math• Animated Math

Models • iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count objects to 5 and trace the number 5 using numerals and words. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting objects to develop sound mathematical practices by asking these questions. • What do you say when you point

to each apple?• What are some different ways you

can arrange 5 objects?• If I put those apples in a straight line,

would there still be 5 of them?




Students can continue to practice once they understand how to count and identify groups up to 5. The H.O.T. problem, exercises 3, 5, and 6, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 5 with words and numbers? Possible answer: I can draw fi ve circles. I can write the number 5 and I can write fi ve with letters.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE








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Chapter 1 33

Lesson 1.7

Hands On: Algebra • Ways to Make 5Instructional Time: 1 day

Common Core StandardCC.K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.

Also CC.K.CC.5

Lesson Objective

Use objects or drawings to decompose 5 into pairs in more than one way.

Essential Question

How can you use two sets of objects to show 5 in more than one way?

Materials

• MathBoard • connecting cubes• two-color counters • iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to show the number 5 using two sets of numbers. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting whole numbers up to 5 to develop sound mathematical practices by asking these questions.

• How do you know that every group has 5?

• When you change the color of your counters, what happens to the numbers you write down?

• Is there another way you could solve that problem? How?




Students can continue to practice once they understand how to put together numbers to make 5. The H.O.T. problem, exercises 3 and 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use two sets of objects to show 5 in more than one way? Possible answer: I can pair fi ve objects to make sets of 1 and 4, 2 and 3, 3 and 2, 4 and 1, 5 and 0, and 0 and 5.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE







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34 Chapter 1

Lesson 1.8

Hands On • Count and Order to 5Instructional Time: 1 day

Common Core StandardCC.K.CC.4c Understand that each successive number name refers to a quantity that is one larger.

Also CC.K.CC.3, CC.K.CC.5

Lesson Objective

Know that each successive number refers to a quantity that is one larger.

Essential Question

How do you know that the order of numbers is the same as a set of objects that is one larger?

Materials


• connecting cubes • iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to build sets in order from 1 to 5. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting to 5 to develop sound mathematical practices by asking these questions. • How is each number different than the

one that comes before it?• How is each number different from the

one that comes after it?• What happens to the amounts of cubes

as you count forward?




Students can continue to practice once they understand how to show and count objects in order to 5. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How do you know that the order of numbers is the same as a set of objects that is one larger? Possible answer: I can use the counting order of numbers to 5. Each number is one greater or one less than the next number.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE

especially rich.







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Chapter 1 35

Lesson 1.9

Problem Solving • Understand 0Instructional Time: 1 day


Also CC.K.CC.4a, CC.K.CC.4b

Lesson Objective

Solve problems by using the strategy make a model.

Essential Question

How can you solve problems using the strategy make a model?

Materials





20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to model and discuss the concept of the number zero. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of whole numbers to develop sound mathematical practices by asking these questions.

• What are some things our classroom has zero of?

• How could you show zero in a picture?• What are some other words that mean

almost the same thing as zero?



On Your Own Approximately 10 min.

Students can continue to practice once they understand what the number zero represents. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy make a model? Possible answer: I can use counters to show the objects in a problem. I can put them in and take them away. Then I count how many are left.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE







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36 Chapter 1

Lesson 1.10

Identify and Write 0Instructional Time: 1 day


Also CC.K.CC.4a, CC.K.CC.4b

Lesson Objective


Essential Question

How can you identify and write 0 with words and numbers?

Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to recognize zero and trace zero as a numeral and word. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting zero objects to develop sound mathematical practices by asking these questions. • How is zero different from the other

numbers you have learned?• Can you use counters to count zero?

Why not?• How could you change that picture so

that it no longer shows zero?




Students can continue to practice once they understand how to count a number of objects. The H.O.T. problem, exercises 5, 6, and 8, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify and write 0 with words and numbers? Possible answer: I can show no objects, or I can show a counter and take it away to show 0 or none, or I can write the number 0. I can write the word zero.


1 ENGAGE

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Practice 3 PRACTICE

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Chapter 2 39

Lesson 2.1

Hands On • Same NumberInstructional Time: 1 day

Common Core Standard CC.K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.


Lesson Objective

Use matching and counting strategies to compare sets with the same number of objects.

Essential Question

How can you use matching and counting to compare sets with the same number of objects?

Materials





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to compare and match the number of counters in two sets using fi ve frames. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of numbers 1 through 5 to develop sound mathematical practices by asking these questions. • How do you decide whether to use

matching or counting to see if two groups have the same number?

• How would you be able to tell if two groups did not have the same number?

• Can two groups have the same number if the objects are arranged differently? Why?




Students can continue to practice once they understand matching a number of objects. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use matching and counting to compare sets with the same number of objects? Possible answer: I can draw lines to match the objects from each set to see if they have a match. I can count to see if each set has the same number of objects.


1 ENGAGE

deeply to discuss.


Practice 3 PRACTICE

especially rich.






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40 Chapter 2

Lesson 2.2

Hands On • Greater ThanInstructional Time: 1 day



Lesson Objective

Use matching and counting strategies to compare sets when the number of objects in one set is greater than the number of objects in the other set.

Essential Question

How can you compare sets when the number of objects in one set is greater than the number of objects in the other set?

Materials

• MathBoard • iTools: Counters• two-color counters • Animated Math

Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to model two numbers using counters and determine which set of counters has more. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the counting order to 5 to develop sound mathematical practices by asking these questions. • How does putting objects in a

fi ve frame help you compare?• What is a different way you could

fi nd out which set has more?• Suppose there were two groups of

children. How could we tell which group had more children?




Students can continue to practice once they understand how to use matching and counting to compare. The H.O.T. problem, exercises 3 and 4, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you compare sets when the number of objects in one set is greater than the number of objects in the other set? Possible answer: I can use matching to see which set has more objects. I can count the number of objects in each set and compare the two numbers.


1 ENGAGE



Practice 3 PRACTICE








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Chapter 2 41

Lesson 2.3

Hands On • Less ThanInstructional Time: 1 day



Lesson Objective

Use matching and counting strategies to compare sets when the number of objects in one set is less than the number of objects in the other set.

Essential Question

How can you compare sets when the number of objects in one set is less than the number of objects in the other set?

Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count numbers using fi ve frames and to determine which number has less. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting and matching numbers to 5 to develop sound mathematical practices by asking these questions. • How does putting objects in a fi ve frame

help you see which group has less?• What is a different way you could fi nd

out which set has less?• When you use counting to compare sets,

how do you know which set has less?




Students can continue to practice once they understand using fi ve frames to count and compare. The H.O.T. problem and exercises 3 and 4 require higher order thinking skills and critical reasoning, making them especially rich


Essential Question

How can you compare sets when the number of objects in one set is less than the number of objects in the other set?Possible answer: I can match the objects in each set. I can count and compare the numbers to see which is less.


1 ENGAGE



Practice 3 PRACTICE

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42 Chapter 2

Lesson 2.4

Problem Solving • Compare by Matching Sets to 5Instructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. Use the extra time on Day 1 to complete the H.O.T. problem and Go Deeper in addition to Unlock the Problem and Try Another Problem. Use classroom objects to further compare numbers of objects and have students describe how they are different. Use the extra time on Day 2 to complete the Extend the Math Activity. Then have students create their own sets of numbers and compare with a partner. Have volunteers describe how their sets are different. Also explore the On Your Own problems with students, using connecting cubes to model the problems before drawing their answers on the Student Edition page.



Lesson Objective

Make a model to solve problems using a matching strategy.

Essential Question

How can you make a model to solve problems using a matching strategy?

Materials

• MathBoard • iTools: Algebra• connecting cubes • iTools: Counters• Animated Math Models




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and model a number less than the number of objects shown using cubes. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of matching numbers to develop sound mathematical practices by asking these questions. • How do you know your answer

is correct?• What would be another correct

answer to this problem?• How are your cube trains different?




Students can continue to practice once they understand the concept of identifying more or less of something. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential QuestionHow can you make a model to solve problems using a matching strategy?Possible answer: I can use objects or drawings to show how many are in each set. Then I can draw lines to match.


1 ENGAGE

Practice 3 PRACTICE


Summarize Essential Question

4 SUMMARIZE







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Chapter 2 43

Lesson 2.5

Compare by Counting Sets to 5Instructional Time: 1 day


Also CC.K.CC.3, CC.K.CC.5, CC.K.CC.7

Lesson Objective

Use a counting strategy to compare sets of objects.

Essential Question

How can you use a counting strategy to compare sets of objects?

Materials

• MathBoard • iTools: Algebra• Animated Math





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to determine which set of objects is greater or less than the other set of objects. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting and matching to 5 to develop sound mathematical practices by asking these questions. • What did you do fi rst? Why?• Can counting always tell you which set

has more and which set has less? Why?• How could you use counters to help you

solve the problem?




Students can continue to practice once they understand how to identify a number that is greater or less than another number. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use a counting strategy to compare sets of objects? Possible answer: I can count the objects in each set to see whether the number of objects in one set is greater than, less than, or the same as the number of objects in another set.


1 ENGAGE



Practice 3 PRACTICE







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46 Chapter 3

Lesson 3.1


Common Core Standard CC.K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Also CC.K.CC.3, CC.K.CC.4a, CC.K.CC.4b, CC.K.CC.4c

Lesson Objective


Essential Question

How can you show and count 6 objects?

Materials


Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count objects to 6 and model the number 6 by placing counters in a ten frame. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of the number 5 to develop sound mathematical practices by asking these questions.

• How are 6 objects different from 5 objects?

• How does using the ten frame help you see when there are 6 objects?

• What are some different ways you could arrange 6 counters?




Students can continue to practice once they understand how to arrange the number 6 in a ten frame. The H.O.T. problem, exercise 2, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 6 objects? Possible answer: I can use one more than 5 counters. I can put out counters and count them one at a time: 1, 2, 3, 4, 5, 6.


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Chapter 3 47

Lesson 3.2


Common Core Standard CC.K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

Also CC.K.CC.4a, CC.K.CC.4b, CC.K.CC.5

Lesson Objective


Essential Question


Materials


• iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count objects to 6 and trace the numeral and word form of the number 6. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of having one more of something to develop sound mathematical practices by asking these questions. • What does it mean if a person is

6 years old?• What is the difference between a person

who is 6 years old and a person who is 5 years old?

• How could Christy use a picture to show her age?




Students can continue to practice once they understand how to identify groups of 6. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 6 with words and numbers? Possible answer: I can count from 1 to 6. I can write the number 6 and the word six.


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48 Chapter 3

Lesson 3.3




Lesson Objective


Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to model a set of 7 using counters. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of one more and one less to develop sound mathematical practices by asking these questions. • What does each counter stand for?• What is a different way you could

have drawn your picture?• How could you check to see if a

classmate’s drawing was correct?




Students can continue to practice once they understand how to show 7 on a ten frame. The H.O.T. problem, exercise 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 7 objects? Possible answer: I can make sets with 7 counters. I can draw a set of 7 counters.


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Chapter 3 49

Lesson 3.4




Lesson Objective


Essential Question


Materials

• MathBoard • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count objects to 7 and trace the number 7 as a numeral and in word form. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the counting order to develop sound mathematical practices by asking these questions. • Where are other places it would make

sense to write the number 7?• How can you tell that the two groups

on the page show the same number?• How can you tell from looking at the

pictures that 7 is more than 5?




Students can continue to practice once they understand how to recognize groups of 7. The H.O.T. problem and exercises 4, 5, and 6 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 7 with words and numbers? Possible answer: I can count from 1 to 7. I can write the number 7 and the word seven.


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50 Chapter 3

Lesson 3.5




Lesson Objective


Essential Question


Materials


Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to model 7 objects and then add 1 more object to make 8. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the counting order to develop sound mathematical practices by asking these questions. • If you start counting from a different

starting place, is the total number the same? Why?

• How is your drawing different from a classmate’s? How is it the same?

• How can you arrange 8 in neat rows?




Students can continue to practice once they understand how to make 8 using fi ve and ten frames. The H.O.T. problem, exercise 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 8 objects?Possible answer: I can use counters and count until I have 8; I can draw eight objects.


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Chapter 3 51

Lesson 3.6




Lesson Objective


Essential Question


Materials





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count sets of objects to 8 and trace the number 8 as a numeral and in word form. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of matching groups to develop sound mathematical practices by asking these questions. • How could you use counters to check

that both groups have 8 objects?• How could you recognize a group of

8 without counting each object?• What might come in a box of 8?




Students can continue to practice once they understand how to recognize groups of 8. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 8 with words and numbers? Possible answer: I can count from 1 to 8; I can write 8 as a number and a word.


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52 Chapter 3

Lesson 3.7




Lesson Objective


Essential Question


Materials





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to model 8 objects and then add one more to make 9 objects. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of adding one more to develop sound mathematical practices by asking these questions. • What does each counter stand for?• What other objects could I have used to

show Daniel’s prizes? Why? • What is a different story these counters

could show?




Students can continue to practice once they understand how to show 9 using fi ve and ten frames. The H.O.T. problem, exercise 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 9 objects? Possible answer: I can use nine counters and count as I put down each one. I can also draw pictures of nine objects.


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Chapter 3 53

Lesson 3.8




Lesson Objective


Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count sets of objects to 9 and trace the number 9 as a numeral and in word form. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the counting order to 9 to develop sound mathematical practices by asking these questions. • How can you show 9 in four rows?• How many more than 5 is 9? How can

you tell?• How could you show the same number

of ducks with counters?




Students can continue to practice once they understand how to count groups of objects. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 9 with words and numbers? Possible answer: I can count from 1 to 9. I can draw nine objects. I can write the number 9. I can also write nine.


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54 Chapter 3

Lesson 3.9

Problem Solving • Numbers to 9Instructional Time: 1 day



Lesson Objective

Solve problems by using the strategy draw a picture.

Essential Question

How can you solve problems using the strategy draw a picture?

Materials

• MathBoard • HMH Mega Math• iTools: Counters




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to draw a number of fl ags one greater than the number of fl ags shown. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting numbers through 9 to develop sound mathematical practices by asking these questions. • How could you draw matching lines to

check your work?• How can you tell when a number is one

greater than another number?• What is another way to fi nd the number

of fl ags on the blue tent?




Students can continue to practice once they understand the concept of comparing sets. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy draw a picture? Possible answer: I can draw a row of objects. I can draw another row of objects that has a greater or lesser number in it than the fi rst row. Then I can count the objects in that row.


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Chapter 4 57

Lesson 4.1



Also CC.K.CC.3, CC.K.CC.4a, CC.K.CC.4b

Lesson Objective


Essential Question


Materials





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use counters to model 9 in a ten frame and then to use counters to model 10 in a ten frame. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of modeling and counting numbers through 10 to develop sound mathematical practices by asking these questions. • What are all the possible numbers you

could show using a ten frame?• What are some ways to describe 10?• How are 5 and 10 alike? How are they

different?




Students can continue to practice once they understand how to model and count 10 using a ten frame. The H.O.T. problem, exercise 3, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 10 objects?Possible answer: I can show and count 10 counters. My counters will fi ll a ten frame.


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58 Chapter 4

Lesson 4.2




Lesson Objective


Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count 10 objects and then practice writing the numeral and word form of the number 10. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting to 10 to develop sound mathematical practices by asking these questions.• How could Jimmy check his work using

a ten frame?• How many fi ngers do you have? How

can you tell?• Does Jimmy have more than 8 cubes?

How can you tell?




Students can continue to practice once they understand how to identify sets of 10 and write the number 10. The H.O.T. problem, exercises 7, 8, and 9, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 10 with words and numbers?Possible answer: I can draw 10 objects or show 10 counters. I can write the number 10 or write the word ten.


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Chapter 4 59

Lesson 4.3

Hands On: Algebra • Ways to Make 10Instructional Time: 1 day

Common Core Standard CC.K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Also CC.K.CC.5

Lesson Objective

Use a drawing to make 10 from a given number.

Essential Question

How can you use a drawing to make 10 from a given number?

Materials


• red and blue connecting cubes

• HMH Mega Math

• Number and Symbol Tiles (back) (see eTeacher Resources)

• iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to make 10 in different ways. As students work through Listen and Draw, gauge their level of understanding

to make better decisions about how to progress through instruction.Build on students’ understanding of making 10 to develop sound mathematical practices by asking these questions.• If your classmate’s cube train looks

different than yours, does that mean one of them is wrong? Why not?

• How do you know if your cube train is the right length?

• Would it be a correct answer to the problem to show a cube train with four red and four blue cubes? Why not?




Students can continue to practice once they understand how to model numbers through 10 using connecting cubes. The H.O.T. problem, exercises 4 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use a drawing to make 10 from a given number? Possible answer: I can make cube trains using ten red and blue cubes. Then I can draw to show the cube trains.


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60 Chapter 4

Lesson 4.4

Count and Order to 10Instructional Time: 1 day

Common Core Standard CC.K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Also CC.K.CC.4c

Lesson Objective

Count forward to 10 from a given number.

Essential Question

How can you count forward to 10 from a given number?

Materials


Models • iTools: Number

Line




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count the numbers 1 to 10 in order. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting numbers 1 to 10 to develop sound mathematical practices by asking these questions. • How do you know what number to

write in each blank?• What happens to the numbers as you

move to the right?• Choose two numbers. Which one is

greater? How do you know?




Students can continue to practice once they understand how to count and order numbers up to 10. The H.O.T. problem and exercise 3 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count forward to 10 from a given number? Possible answer: I know the counting order, so I know what number to start with after the number I am given. I keep counting in order to 10.


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Chapter 4 61

Lesson 4.5

Problem Solving • Compare by Matching Sets to 10Instructional Time: 1 day



Lesson Objective


Essential Question


Materials

• MathBoard • crayons• connecting cubes • iTools: Counters




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use two groups of connecting cubes to determine which cube train has more cubes and which cube train has less. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of using cubes to model numbers in a problem to develop sound mathematical practices by asking these questions. • What does each cube stand for?• What does the total number of

cubes stand for?• Could you solve the same problem

using counters? How?




Students can continue to practice once they understand how to model and compare numbers through 10 using connecting cubes. The H.O.T. problem and the exercise on the On Your Own page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy make a model? Possible answer: I can build cube trains and compare them by matching.


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62 Chapter 4

Lesson 4.6

Compare by Counting Sets of 10Instructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. On Day 1 give students connecting cubes to model the number of objects in each set for problems 1 through 6. Have students arrange the cubes to show the number in different ways and compare to see which has more. Ask for student volunteers to act out the H.O.T. Problem and Go Deeper and repeat with different numbers of boys and girls. Use the extra time on Day 2 to complete the Extend the Math Activity and Problem Solving page.Common Core Standard CC.K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.


Lesson Objective

Use counting strategies to compare sets of objects.

Essential Question

How can you use counting strategies to compare sets of objects?

Materials

• MathBoard • iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count sets of

objects and then determine which set has the greater number of objects. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting and comparing numbers to 10 to develop sound mathematical practices by asking these questions. • When you count a group of objects,

how can you check your answer?• How can counting on your fi ngers help

you know which number is greater?• What are some other ways to compare

numbers to see which is greater?




Students can continue to practice once they understand how to count two sets of objects and determine which number is greater. The H.O.T. problem, exercises 4 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use counting strategies to compare sets of objects? Possible answer: I can count the number of objects in each set, write the numbers, and decide which number is greater or less than the other.


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Chapter 4 63

Lesson 4.7

Compare Two NumbersInstructional Time: 1 day

Common Core Standard CC.K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.

Lesson Objective

Compare two numbers between 1 and 10.

Essential Question

How can you compare two numbers between 1 and 10?

Materials





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to compare the numbers 7 and 8 and determine which number is greater and which number is less. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of the counting order of numbers 1 to 10 to develop sound mathematical practices by asking these questions.

• How could you draw a picture to help you compare two numbers?

• How could you use counters to help you compare two numbers?

• How could you fi nd a greater number than 8?




Students can continue to practice once they understand how to use the counting order to compare two numbers between 1 and 10. The H.O.T. problem, exercises 7, 8 and 10, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you compare two numbers between 1 and 10? Possible answer: I can think about the counting order to see which number is greater or which is less.


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66 Chapter 5

Lesson 5.1

Addition: Add ToInstructional Time: 1 day

Common Core Standard CC.K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Lesson Objective

Use expressions to represent addition within 5.

Essential Question

How can you show addition as adding to?

Materials

• MathBoard




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to add by putting two groups together, then fi nd how many there are now. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of adding by putting groups together to develop sound mathematical practices by asking these questions.

• How can you put counters on the children to help you add?

• What math story could you tell about the children?

• How can you use your fi ngers to show the problem?




Students can continue to practice once they understand the concept of adding two groups together. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show addition as adding to?Possible answer: I can count and write how many are in each group. Then I can count and write how many there are now.


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Chapter 5 67

Lesson 5.2

Hands On • Addition: Put TogetherInstructional Time: 1 day


Lesson Objective

Use expressions to represent addition.

Essential Question

How can you show addition as putting together?

Materials

• MathBoard • two-color counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use counters to represent an addition word problem. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of adding by putting 2 groups together to develop sound mathematical practices by asking these questions.

• What does each of the numbers stand for?

• How did you fi nd out how many counters there were in all?

• What if Ryan had 2 red counters? How would the numbers change?




Students can continue to practice once they understand the concept of putting two sets of counters together to add them. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show addition as putting together? Possible answer: I can count how many objects in each set and write the numbers with a plus symbol between them. Then I can count all of the objects to fi nd how many in all.


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68 Chapter 5

Lesson 5.3

Problem Solving • Act Out Addition ProblemsInstructional Time: 1 day


Also CC.K.OA.2, CC.K.OA.5

Lesson Objective

Solve problems by using the strategy act it out.

Essential Question

How can you solve problems using the strategy act it out?

Materials





20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to write an addition sentence to represent an addition word problem. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of addition sentences to develop sound mathematical practices by asking these questions.• What does the fi rst number 2 stand

for? What does the second number 2 stand for?

• How can you check to make sure the addition sentence is correct?

• How could you put counters on the children to help you add?




Students can continue to practice once they understand the concepts of acting out addition problems and writing addition sentences to solve them. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy act it out? Possible answer: I can act out an addition word problem. I can count the people or objects in both sets to fi nd how many in all.


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Chapter 5 69

Lesson 5.4

Hands On: Algebra • Model and Draw Addition ProblemsInstructional Time: 1 day

Common Core Standard CC.K.OA.5 Fluently add and subtract within 5.


Lesson Objective

Use objects and drawings to solve addition word problems within 5.

Essential Question

How can you use objects and drawings to solve addition word problems?

Materials

• MathBoard • HMH Mega Math• connecting cubes • iTools: Counters• Animated Math Models




20 min.

Listen and DrawRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to model an addition word problem. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of modeling and drawing addition problems to develop sound mathematical practices by asking these questions.

• What do the parts of your picture stand for?

• How did you use your picture to solve the addition problem?

• What does each part of the addition sentence stand for?




Students can continue to practice once they understand the concept of modeling and drawing to solve an addition word problem. The H.O.T. problem and exercises 3 and 4 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use objects and drawings to solve addition word problems? Possible answer: I can show how many are in each set and then put them together. I can complete the addition sentence to match what I did with the objects using numbers and symbols.


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70 Chapter 5

Lesson 5.5

Algebra • Write Addition Sentences for 10Instructional Time: 1 day

Common Core Standard CC.K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.


Lesson Objective

Use a drawing to fi nd 10 from a given number and record the equation.

Essential Question

How can you use a drawing to fi nd the number that makes a ten from a given number?

Materials


• iTools: Counters • HMH Mega Math




20 min.

Listen and DrawRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to add to make 10. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of addition to develop sound mathematical practices by asking these questions.• How did you know how many blue

cubes to draw?• What does each part of the addition

sentence stand for?• How can you go back and check

your answer?




Students can continue to practice once they understand the concept of drawing and writing addition sentences to show making 10. The H.O.T. problem, exercises 4 though 6, and the exercises on the Problem solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use a drawing to fi nd the number that makes a ten from a given number? Possible answer: I can draw the number of objects I am given. Then I can draw more objects until I have 10 of them. I can count how many more I needed to draw and write that number in the addition sentence.


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Chapter 5 71

Lesson 5.6

Algebra • Write Addition SentencesInstructional Time: 1 day

Common Core Standard CC.K.OA.5 Fluently add and subtract within 5.


Lesson Objective

Solve addition word problems within 5 and record the equation.

Essential Question

How can you solve addition word problems and complete the addition sentence?

Materials





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to fi nd the unknown addend in an addition sentence. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of addition sentences to develop sound mathematical practices by asking these questions.

• How do you know you are correct about the number of fi sh that swam over?

• What does each part of the addition sentence stand for?

• What other math story could you tell using the same addition sentence?




Students can continue to practice once they understand the concept of fi nding the missing addend in an addition sentence. The H.O.T. problem, and exercises 4 through 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve addition word problems and complete the addition sentence?Possible answer: I can see how many objects are being added to the fi rst set to make the number of objects in all. I can fi ll in that missing number to complete the addition sentence.


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72 Chapter 5

Lesson 5.7Algebra • Write More Addition Sentences Instructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. On Day 1 have students use connecting cubes to model the problem in the Listen and Draw section. Have them show which group of connecting cubes represents the missing number. Have students use the same strategy in the Share and Show and More Practice sections. On Day 2, use the extra time to explore the H.O.T. and Go Deeper problems and have students use connecting cubes to model 3 1 6 5 9 as well as 6 1 3 5 9 from exercise 5. After students compare the two addition sentences, have them break apart the groups of 3 and 6 connecting cubes into groups of different numbers that also equal 9.Common Core Standard CC.K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Also CC.K.OA.1

Lesson Objective

Solve addition word problems within 10 and record the equation.

Essential Question

How can you solve addition word problems and complete the addition sentence?

Materials

• MathBoard • HMH Mega Math• Animated Math • iTools: Counters

Models




20 min.

Listen and Draw • Activity to Build Conceptual Understanding

Remember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to fi nd the missing number in an addition sentence. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of writing addition sentences to solve problems to develop sound mathematical practices by asking these questions.• How did you know how many birds

were there to start?• How did circling the bird who came

help you solve the problem?• Could you solve this problem using

counters? How?




Students can continue to practice once they understand the concept of fi nding the missing addend in an addition sentence. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve addition word problems and complete the addition sentence? Possible answer: I can fi nd how many objects there are at the start. Then I can fi ll in that unknown number to complete the addition sentence.


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Chapter 5 73

Lesson 5.8

Hands On: Algebra • Number Pairs to 5 Instructional Time: 1 day

Common Core Standard CC.K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.


Lesson Objective

Decompose numbers within 5 into pairs in more than one way and record each decomposition with an equation.

Essential Question

How can you model and write addition sentences for number pairs for sums to 5?

Materials

• MathBoard • iTools: Counters• connecting cubes • Animated Math

Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to fi nd two different number pairs that make 3. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of writing addition sentences to develop sound mathematical practices by asking these questions.• Why is there more than one addition

sentence that is equal to 3?• How did using cubes help you solve

the problem? • What cube train is described by your

fi rst addition sentence?• What cube train is described by your

second addition sentence?




Students can continue to practice once they understand the concept of writing addition sentences using different number pairs. The H.O.T. problem and the exercises on the Problem solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you model and write addition sentences for number pairs for sums to 5?Possible answer: I can make two sets of cubes in different colors until I have the number in all. Then I can use the numbers to write the addition sentence.


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74 Chapter 5

Lesson 5.9

Hands On: Algebra • Number Pairs for 6 and 7Instructional Time: 1 day



Lesson Objective

Decompose 6 and 7 into pairs in more than one way and record each decomposition with an equation.

Essential Question

How can you model and write addition sentences for number pairs for each sum of 6 and 7?

Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to model addition word problems for 6 and 7. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of addition sentences to develop sound mathematical practices by asking these questions.• How did you decide how to color each

cube train? • Is there another way Leslie could have

made a six-cube train? Why?• Why is an addition sentence a good way

to tell about Leslie’s cube train?




Students can continue to practice once they understand the concept of using connecting cubes to model number pairs for 6. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you model and write addition sentences for number pairs for each sum of 6 and 7? Possible answer: I can make a set of cubes in one color and make a set in a different color until I have 6 or 7. Then I can fi ll in the numbers I used to write the addition sentence.


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Chapter 5 75

Lesson 5.10

Hands On: Algebra • Number Pairs for 8Instructional Time: 1 day



Lesson Objective

Decompose 8 into pairs in more than one way and record each decomposition with an equation.

Essential Question

How can you model and write addition sentences for number pairs for sums of 8?

Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to model the addition in the problem. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of modeling number sentences to develop sound mathematical practices by asking these questions.• How did using cubes help you solve the

problem? • How did you know how many cubes of

each color to use?• How can you check to make sure the

addition sentence is correct?




Students can continue to practice once they understand the concept of completing addition sentences using different number pairs for 8. The H.O.T. problem and the exercises on the Problem solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you model and write addition sentences for number pairs for sums of 8?Possible answer: I can make a set of cubes in one color and make a set in a different color until I have 8. Then I can fi ll in the numbers I used to write the addition sentence.


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76 Chapter 5

Lesson 5.11




Lesson Objective


Essential Question


Materials

• MathBoard • iTools: Counters• connecting cubes • Animated Math

Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to to use connecting cubes to match the number pair for 9 in the addition sentence. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of addition problems to develop sound mathematical practices by asking these questions.• How is this problem like other problems

you have solved? How is it different?• How could you make your cube train

in a different way and use the same addition sentence?

• If you used 4 orange cubes and 5 green cubes, could you keep the addition sentence shown or would you have to write a new addition sentence? Why?




Students can continue to practice once they understand the concept of writing pairs of numbers to complete addition sentences for 9. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you model and write addition sentences for number pairs for sums of 9?Possible answer: I can make a set of cubes in one color and make a set in a different color that make 9 in all. Then I can fi ll in the numbers I used to write the addition sentence.


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Chapter 5 77

Lesson 5.12




Lesson Objective


Essential Question


Materials

• MathBoard • HMH Mega Math• connecting cubes • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to to use connecting cubes to match the number pair for 10 in the addition sentence. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of number pairs to develop sound mathematical practices by asking these questions.• How is this problem similar to other

problems you have solved? How is it different?

• How can you use the objects to solve the problem?

• What is the other correct answer to the problem? How do you know?




Students can continue to practice once they understand the concept of writing addition sentences to show different number pairs for 10. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you model and write addition sentences for number pairs for sums of 10? Possible answer: I can use some cubes in one color and then add cubes that are a different color until I have 10. Then I can fi ll in the numbers I used to write the addition sentence.


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80 Chapter 6

Lesson 6.1

Subtraction: Take FromInstructional Time: 1 day

Common Core StandardCC.K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Lesson Objective

Use expressions to represent subtraction within 5.

Essential Question

How can you show subtraction as taking from?

Materials

• MathBoard • iTools: Counters• two-color counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and write numbers that represent the groups in a subtraction story. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of subtraction as taking from to develop sound mathematical practices by asking these questions.• How did you know what number to use

for the starting number?• How did you know how many to take

away?• What is another story you could tell for

“3 take away 1”?




Students can continue to practice once they understand the concept of subtraction as taking away from. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show subtraction as taking from? Possible answer: I can write the number in all and write the number that is taken away. I can also write the number for how many are left.

Engage This activity reviews prerequisite skills,

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Chapter 6 81

Lesson 6.2

Hands On • Subtraction: Take ApartInstructional Time: 1 day

Common Core StandardCC.K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Lesson Objective

Use expressions to represent subtraction.

Essential Question

How can you show subtraction as taking apart?

Materials

• MathBoard• two-color counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use counters to model the subtraction problem 7 minus 2 equals 5. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of subtraction as taking away to develop sound mathematical practices by asking these questions.• How does the picture help you subtract?• How did you know what number to

start with?• How did you know what number to take

away?




Students can continue to practice once they understand the concept of subtraction as taking apart. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show subtraction as taking apart?Possible answer: I can use two-color counters to show one color is taken apart. I can write the number in all and write the number that is taken apart. Then I can write the number that shows the other color of counter.


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82 Chapter 6

Lesson 6.3

Problem Solving • Act Out Subtraction ProblemsInstructional Time: 1 day

Common Core StandardCC.K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.


Lesson Objective

Solve problems by using the strategy act it out.

Essential Question

How can you solve problems using the strategy act it out?

Materials

• MathBoard• iTools: Counters




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to write a subtraction sentence to represent a subtraction word problem. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the parts of a subtraction sentence to develop sound mathematical practices by asking these questions.• Look at the subtraction sentence. Which

child in the picture does the 1 stand for? How do you know?

• Which children in the picture does the 2 stand for? How do you know?

• How could we act out 3 minus 2?




Students can continue to practice once they understand the subtraction concepts. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy act it out? Possible answer: I can act it out to see how many there are in all. I can see how many are being taken from or are leaving. Then I can count to see how many are left.


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Chapter 6 83

Lesson 6.4

Hands On: Algebra • Model and Draw Subtraction ProblemsInstructional Time: 1 day

Common Core StandardCC.K.OA.5 Fluently add and subtract within 5.


Lesson Objective

Use objects and drawings to solve subtraction word problems within 5.

Essential Question

How can you use objects and drawings to solve subtraction word problems?

Materials • MathBoard• connecting cubes• two-color

counters

• Animated Math Models

• HMH Mega Math• iTools: Counters




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to model and solve a subtraction word problem. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of modeling subtraction problems to develop sound mathematical practices by asking these questions.• Which part of the subtraction sentence

stands for the yellow cubes? How do you know?

• Which part of the subtraction sentence stands for the red cubes? How do you know?

• How can you use the model to check that your subtraction sentence is true?




Students can continue to practice once they understand the concept of taking apart cube trains to model subtraction. The H.O.T. problem and exercises 3 and 4 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use objects and drawings to solve subtraction word problems? Possible answer: I can make a cube train to show the number in all. I can use one color of cubes for how many to take apart and another color for the rest. I can count the rest to fi nd how many are left. I can draw and color the cubes and complete a subtraction sentence.


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84 Chapter 6

Lesson 6.5

Algebra • Write Subtraction SentencesInstructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. On Day 1 have students use counters to model the word problem in the Listen and Draw section. Have them show the set then move counters away to show the number of fi sh left in the set. Then have students tell how many counters they moved away. Encourage students to use counters in the same way as they complete the exercises in the Share and Show, More Practice, and H.O.T. problem sections. Explore the Go Deeper section by explaining to students the meaning of the parts of a subtraction word problem. On Day 2, explore the Extend the Math and Problem Solving sections by describing subtraction as taking a certain number from a set.Common Core StandardCC.K.OA.5 Fluently add and subtract within 5.


Lesson Objective

Solve subtraction word problems within 5 and record the equation.

Essential Question

How can you solve subtraction word problems and complete the equation?

Materials





20 min.

Listen and Draw • Activity to Build Conceptual Understanding

Remember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to write a subtraction sentence to solve the subtraction word problem. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of subtraction sentences to develop sound mathematical practices by asking these questions.• What do you do fi rst when you write a

subtraction sentence? Why?• What do you do next? Why?• How does crossing out the fi sh that

swims away help you solve the subtraction problem?




Students can continue to practice once they understand the concept of subtraction as taking a certain number from a set. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve subtraction word problems and complete the equation? Possible answer: I can look for how many are in the set and how many there are now. I can show how many are taken from the set. I can complete a subtraction sentence to show how I solved the problem.


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Chapter 6 85

Lesson 6.6

Algebra • Write More Subtraction SentencesInstructional Time: 1 day

Common Core StandardCC.K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Also CC.K.OA.1

Lesson Objective

Solve subtraction word problems within 5 and record the equation.

Essential Question

How can you solve subtraction word problems and complete the equation?

Materials


• iTools: Counters • HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to fi nd the starting number in a subtraction sentence. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of subtraction to develop sound mathematical practices by asking these questions.

• Why did you cross out one of the birds?• How did you know how many birds we

started with?• How did you know how many birds

were left?• What if one more bird fl ew away? What

subtraction sentence would we use to show that? Why?




Students can continue to practice once they understand how to solve subtraction word problems by fi nding the unknown starting number. The H.O.T. problem, exercises 5 and 6, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve subtraction word problems and complete the equation?Possible answer: I can look to see how many are taken from the set and how many are left. I can fi nd the starting number by counting all of the objects in the set.


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86 Chapter 6

Lesson 6.7

Hands On: Algebra · Addition and SubtractionInstructional Time: 1 day

Common Core StandardCC.K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Also CC.K.OA.1

Lesson Objective

Understand addition as putting together or adding to and subtraction as taking apart or taking from to solve word problems.

Essential Question

How can you solve word problems using addition and subtraction?

Materials

• MathBoard• connecting cubes• Number and

Symbol Tiles (front) (see eTeacher Resources)

• iTools: Counters• Animated Math

Models• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use number and symbol tiles and connecting cubes to match addition and subtraction word problems. As students work through Listen and Draw,

gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of addition and subtraction to develop sound mathematical practices by asking these questions.• How are these two sentences alike?

How are they different?• Why was addition used for the fi rst

part of the problem? • Why was subtraction used for the

second part of the problem?




Students can continue to practice once they understand the concept of generating addition and subtraction word problems and solving them using connecting cubes. The H.O.T. problem, exercises 3 and 4, and the exercises on the Problem solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve word problems using addition and subtraction? Possible answer: I can use addition to solve problems when sets are put together and I need to fi nd out how many in all. I can use subtraction to fi nd out how many are left when some are being taken away or taken apart from a set.


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Chapter 7 89

Lesson 7.1


Common Core StandardCC.K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 5 10 1 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Also CC.K.CC.3, CC.K.CC.4a, CC.K.CC.4b, CC.K.CC.5

Lesson Objective

Use objects to decompose the numbers 11 and 12 into ten ones and some further ones.

Essential Question

How can you use objects to show 11 and 12 as ten ones and some more ones?

Materials

• MathBoard • HMH Mega Math

• two-color counters • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use ten frames and counters to model and count 11 and 12. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of

modeling numbers in a ten frame to develop sound mathematical practices by asking these questions.• How does a ten frame make it easier to

count 11 and 12?• How are the numbers 11 and 12 alike?

How are they different?• What other story could you model using

11 or 12 counters?




Students can continue to practice once they understand how to show the number 11 in a ten frame and tell how many tens and ones they drew. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use objects to show 11 and 12 as ten ones and some more ones? Possible answer: I can use counters to fi ll a ten frame and place one more below to show 11; I can use counters to fi ll a ten frame and place two more below to show 12.


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90 Chapter 7

Lesson 7.2



Also CC.K.CC.4a, CC.K.CC.4b, CC.K.CC.4c, CC.K.CC.5, CC.K.NBT.1

Lesson Objective


Essential Question


Materials

• MathBoard• Animated Math

Models





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count up to 12 objects and write 11 and 12 as numerals and words. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting objects to develop sound mathematical practices by asking these questions.

• How do the written numbers 11 and 12 look alike? How do they look different?

• How does arranging the cubes in a row of 10 and another row help you count them?

• If someone ate a donut out of Kerri’s box, how should she change the number written on the box? Why?




Students can continue to practice once they understand how to count to and write the numbers 11 and 12. The H.O.T. problem, Exercise 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 11 and 12 with words and numbers? Possible answer: I can count 11 objects, write the number 11 and the word eleven, and write 10 ones and 1 one. I can count 12 objects, write the number 12 and the word twelve, and write 10 ones and 2 ones.


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Chapter 7 91

Lesson 7.3Hands On · Model and Count 13 and 14Instructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. On Day 1 have students complete the Teach and Talk section by using counters and a ten frame to model the numbers 13 and 14. In the Share and Show and More Practice sections, have students model 13 and 14 by fi lling a ten frame and then adding ones. Guide students through the HOT Problem and Go Deeper sections by helping them understand the concept of comparing sets to decide which set has more. On Day 2, use the extra time to have students explore the Extend the Math and Problem Solving sections. Help students fi nd out how many different ways they can make the number 13 or 14 using connecting cubes.Common Core StandardCC.K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 5 10 1 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.


Lesson Objective Use objects to decompose the numbers 13 and 14 into ten ones and some further ones.

Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use counters and a ten frame to model and count 13 and 14. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of adding one more to develop sound mathematical practices by asking these questions.• How are 13 and 14 similar to other

numbers you have learned? How are they different?

• Why does using a ten frame make it easier to solve this problem?

• How did you change your model to go from 14 to 13? Why did you do that?




Students can continue to practice once they understand how to show and count 13 and 14. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use objects to show 13 and 14 as ten ones and some more ones?Possible answer: I can use counters to fi ll a ten frame and place three more below to show 13; I can use counters to fi ll a ten frame and place four more below to show 14.

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92 Chapter 7

Lesson 7.4

Count and Write 13 and 14Common Core StandardInstructional Time: 1 day

CC.K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).


Lesson Objective


Essential Question


Materials


Models





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count up to 14 objects and write 13 and 14 as numerals and words. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting objects to develop sound mathematical practices by asking these questions.

• Look at the picture. What do you think the 3 in 13 stands for? Why?

• What do you think the 4 in 14 stands for? Why?

• How could you count 13 or 14 using a ten frame?




Students can continue to practice once they understand the concepts of counting and writing the numbers 13 and 14. The H.O.T. problem, Exercise 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 13 and 14 with words and numbers? Possible answer: I can count 13 objects, write the number 13 and the word thirteen, and write that 10 ones and 3 ones is 13. I can count 14 objects, write the number 14 and the word fourteen, and write that 10 ones and 4 ones is 14.


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Chapter 7 93

Lesson 7.5

Hands On • Model, Count, and Write 15Instructional Time: 1 day



Lesson Objective

Use objects to decompose 15 into ten ones and some further ones and represent 15 with a number name and a written numeral.

Essential Question

How can you use objects to show 15 as ten ones and some more ones and show 15 as a number?

Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use a ten frame and counters to model and count 15. As students work through Listen and Draw,

gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of ten and some more to develop sound mathematical practices by asking these questions.• What do you notice about each row in

the ten frame?• How many more than 10 is 15? How do

you know?• How could you tell just by looking that

the model has 15 counters, without counting each one?




Students can continue to practice once they understand how to show and count 15. The H.O.T. problem, Exercise 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use objects to show 15 as ten ones and some more ones and show 15 as a number? Possible answer: I can use counters to fi ll a ten frame to show 10 ones and place fi ve more ones below it to show 15. I can show 15 by writing a 1 and a 5 right next to it.


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94 Chapter 7

Lesson 7.6

Problem Solving • Use Numbers to 15Instructional Time: 1 day



Lesson Objective


Essential Question


Materials

• MathBoard• iTools:

Counters


• HMH Mega Math




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to solve a word problem by drawing a picture. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting whole numbers to 15 to develop sound mathematical practices by asking these questions.• What did you draw fi rst? Why?• What did you draw next? Why?• How do you know your answer

makes sense?


Use the checked exercise as a diagnostic assessment. If students answer the exercise incorrectly, use RtI (Response to Intervention).Students can continue to practice once they understand how to solve a word problem by drawing a picture. Have students solve the H.O.T. problem by looking at their drawing and determining how many girls are in the class. This problem requires higher order thinking skills and critical reasoning, making it especially rich.


Essential Question

How can you solve problems using the strategy draw a picture? Possible answer: I can fi nd out what information I have and draw pictures to solve the problem.


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Chapter 7 95

Lesson 7.7




Lesson Objective


Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use ten frames and counters to model and count 16 and 17. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of modeling numbers greater than 10 on a ten frame to develop sound mathematical practices by asking these questions.• How do you know there are more than

15 counters on your frames?• On which day did Ann have more

peaches, Monday or Tuesday? How do you know?

• How does knowing how many counters are in each ten frame help you know the total number?






Essential Question

How can you use objects to show 16 and 17 as ten ones and some more ones?Possible answer: I can use counters to fi ll one ten frame and show six or seven more in another ten frame to show 16 or 17.


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96 Chapter 7

Lesson 7.8




Lesson Objective


Essential Question


Materials


Models





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count up to 17 objects and write 16 and 17 as numerals and words. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the composition of teen numbers to develop sound mathematical practices by asking these questions.• What do you think the 6 in 16 stands

for? Why?• What do you think the 7 in 17 stands

for? Why?• Why did putting the counters in a row

of 10 and another row make it easier to count them?




Students can continue to practice once they understand the concepts of counting and writing the numbers 16 and 17. The H.O.T. problem, Exercise 6, and those on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 16 and 17 with words and numbers? Possible answer: I can count 16 objects, write the number 16 and the word sixteen, and write that 10 ones and 6 ones is 16. I can count 17 objects, write the number 17 and the word seventeen, and write that 10 ones and 7 ones is 17.


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Chapter 7 97

Lesson 7.9




Lesson Objective


Essential Question


Materials






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use ten frames and counters to model word problems for the numbers 18 and 19. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of counting objects to develop sound mathematical practices by asking these questions.• How are 18 and 19 like other numbers

you have learned recently? How are they different?

• How are 18 and 19 like each other? How are they different?

• What is the difference between 8 and 18? What is the difference between 9 and 19?






Essential Question

How can you use objects to show 18 and 19 as ten ones and some more ones? Possible answer: I can use counters to fi ll one ten frame and place eight more in another ten frame to show 18; I can use my counters to fi ll one ten frame and place nine more in another ten frame to show 19.


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98 Chapter 7

Lesson 7.10




Lesson Objective


Essential Question


Materials



• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count objects up to 19 and write 18 and 19 as numerals and words. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of writing teen numbers to develop sound mathematical practices by asking these questions.• What do you know about writing teen

numbers?• How are all the teen numbers the same?

How are they different?• How old was Taryn last year? How do

you know?




Students can continue to practice once they understand the concepts of writing the numbers 18 and 19. The H.O.T. problem, Exercise 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 18 and 19 with words and numbers? Possible answer: I can count 18 objects, write the number 18 and the word eighteen, and write 10 ones and 8 ones. I can count 19 objects, write the number 19 and the word nineteen, and write 10 ones and 9 ones.


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Chapter 8 101

Lesson 8.1


Common Core StandardCC.K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Also CC.K.CC.3, CC.K.CC.4a, CC.K.CC.4b

Lesson Objective


Essential Question


Materials


• connecting cubes • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to model a set of 20 using connecting cubes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of using counters and a ten frame to model numbers to develop sound mathematical practices by asking these questions.

• How is 20 similar to the teen numbers? How is it different?

• Why is it easier to count grapes in ten frames than in a bunch?

• When you’re counting objects, why is it important to know how many groups of 10 there are?




Students can continue to practice once they understand the concept of how to show and count 20. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show and count 20 objects? Possible answer: I can use cubes to fi ll two ten frames to show 20. I can make two ten-cube trains to show 20.


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102 Chapter 8

Lesson 8.2




Lesson Objective


Essential Question


Materials



• HMH Mega Math




20 min.

Remember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count sets of objects to 20 and write the number 20 as a numeral and in word form. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of writing numbers to develop sound mathematical practices by asking these questions.

• What do you think the 2 in 20 might stand for? Why do you think that?

• What number could you write to show how many fi ngers and toes you have? Why?

• Would it make sense to have 20 students in a classroom? Why or why not?

• Would it make sense to have 20 students on a see-saw? Why or why not?




Students can continue to practice once they understand how to recognize groups of 20. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count and write 20 with words and numbers? Possible answer: I can count from 1 to 20. I can draw two ten-cube trains to show 20. I can show that two fi lled ten frames show 20. I can write the number 20 and the number word twenty. I can write that 10 and 10 more make 20.


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Chapter 8 103

Lesson 8.3

Count and Order to 20Instructional Time: 1 day

Common Core StandardCC.K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Also CC.K.CC.4c

Lesson Objective

Count forward to 20 from a given number.

Essential Question

How can you count forward to 20 from a given number?

Materials

• MathBoard• connecting cubes• iTools: Counters


• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to order and compare numbers to 20. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of one more and one less to develop sound mathematical practices by asking these questions.

• Is there a way to solve the problem without making a model? How would you do that?

• Which of your cube trains is longer, the one on the left or the one on the right? Why did the whole class answer this the same way?

• If you drew a cube train over every number, what would your picture look like?




Students can continue to practice once they understand how to count and order to 20. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count forward to 20 from a given number? Possible answer: I can start at any number and count forward by ones until I get to 20.


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104 Chapter 8

Lesson 8.4

Problem Solving • Compare Numbers to 20Instructional Time: 1 day

Common Core StandardCC.K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

Also CC.K.CC.3

Lesson Objective


Essential Question


Materials



• HMH Mega Math




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use connecting cubes to model and compare two numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of matching sets to develop sound mathematical practices by asking these questions.• How do you show “greater than” with

cubes? • How do you show “less than” with

cubes?• What are two ways you could describe

the number 16?• Are there any other ways to describe 16?




Students can continue to practice once they understand the concept of comparing sets. Have them use connecting cubes to model and compare the numbers indicated in the H.O.T. problem. This exercise requires higher order thinking skills and critical reasoning, making it especially rich.


Essential Question

How can you solve problems using the strategy make a model? Possible answer: I can make a model so that I can match or count objects to solve the problem.

•


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Chapter 8 105

Lesson 8.5

Count to 50 by OnesInstructional Time: 1 day

Common Core StandardCC.K.CC.1 Count to 100 by ones and by tens.

Also CC.K.CC.2

Lesson Objective

Know the count sequence when counting to 50 by ones.

Essential Question

How does the order of numbers help you to count to 50 by ones?

Materials

• MathBoard


This activity reviews prerequisite skills, establishing a common conceptual foundation for the lesson. Use evidence of students’ understanding to decidehow deeply to discuss.


20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count to 50 using a fi fty chart. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting by ones to develop sound mathematical practices by asking these questions.

• What other patterns do you see in this chart?

• When you’re counting in order, where do you go after you reach the end of a row?

• How could you use the chart to fi nd a number that is one greater than 26?




Students can continue to practice once they understand the concept of counting forward to 50 starting at any number on the fi fty chart. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How does the order of numbers help you count to 50 by ones?Possible answer: When I know the counting order, I know what number to say after each number. If I start with 1 and say each number in counting order, I can count from 1 to 50.


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106 Chapter 8

Lesson 8.6

Count to 100 by OnesInstructional Time: 1 day


Also CC.K.CC.2

Lesson Objective

Know the count sequence when counting to 100 by ones.

Essential Question

How does the order of numbers help you to count to 100 by ones?

Materials


Models

• iTools: Number Chart




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count from 1 to 100 using a hundred chart. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting on a number chart to develop sound mathematical practices by asking these questions.

• What patterns do you see on this chart?• Brandon said the next number after 56

was 66. What did he do wrong?• How can you use this chart to fi nd a

number that is one greater than another number?




Students can continue to practice once they understand the concept of counting forward from 1 to 100. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How does the order of numbers help you to count to 100 by ones? Possible answer: When I know the order of numbers, I can start counting from any number and count by ones to 100.


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Chapter 8 107

Lesson 8.7

Count to 100 by TensInstructional Time: 1 day


Lesson Objective

Know the count sequence when counting to 100 by tens.

Essential Question

How can you count to 100 by tens on a hundred chart?

Materials


Models





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to count the numbers that end in 0 in order on the hundred chart. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting whole numbers to develop sound mathematical practices by asking these questions.

• Why do you think this is called counting by tens?

• How is counting by tens like counting by ones? How is it different?

• How could you use counting by tens to count your fi ngers and toes?




Students can continue to practice once they understand the concept of counting by tens using a chart. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you count to 100 by tens on a hundred chart? Possible answer: I can fi nd 10 on the hundred chart. Then I can look down that column and say each number to count by tens.


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108 Chapter 8

Lesson 8.8

Count by TensInstructional Time: 1 day


Lesson Objective

Use sets of tens to count to 100.

Essential Question

How can you use sets of tens to count to 100?

Materials


Models





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use cube towers of 10 each to count by tens. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of counting by tens to develop sound mathematical practices by asking these questions.

• Could Caden count his cubes by ones? How long would that take?

• If each cube tower had 9 cubes, could you still count the towers by tens? Why not?

• What pattern do you see on this page?




Students can continue to practice once they understand the concept of using sets of 10 to count by tens. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use sets of tens to count to 100? Possible answer: I can count each set of ten until I get to 100; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.


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Chapter 9 111

Lesson 9.1

Identify and Name CirclesInstructional Time: 1 day

Common Core StandardCC.K.G.2 Correctly name shapes regardless of their orientations or overall size.

Also CC.K.G.3

Lesson Objective

Identify and name two-dimensional shapes including circles.

Essential Question

How can you identify and name circles?

Materials

• MathBoard• two-dimensional

shapes

• HMH Mega Math• iTools: Geometry




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and sort the circles in a group of two-dimensional shapes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of shapes to develop sound mathematical practices by asking these questions.

• Can circles be different sizes? Different colors?

• How are all circles alike?• Do you see any circles in the classroom?

How do you know they are circles?• Which letter of the alphabet looks like a

circle? How do you know?


Use the checked exercise as a diagnostic assessment. If students answer the exercise incorrectly, see RtI (Response to Intervention).


Students can continue to practice once they understand the concept of circles. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify and name circles? Possible answer: I know that a circle is round and fl at.


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112 Chapter 9

Lesson 9.2

Describe CirclesInstructional Time: 1 day

Common Core StandardCC.K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).

Also CC.K.G.2, CC.K.G.5

Lesson Objective

Describe attributes of circles.

Essential Question

How can you describe circles?

Materials

• MathBoard• iTools: Geometry

• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to recognize and describe the attributes of a circle. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of circles to develop sound mathematical practices by asking these questions.

• What words in the problem helped you solve it?

• Why do you think tracing a cup makes a circle?

• What could you draw a picture of using circles?




Students can continue to practice once they understand these geometry concepts. The H.O.T. problem, exercise 3, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you describe circles? Possible answer: A circle is a fl at shape that is round and curved.

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Chapter 9 113

Lesson 9.3

Identify and Name SquaresInstructional Time: 1 day


Also CC.K.G.3

Lesson Objective

Identify and name two-dimensional shapes including squares.

Essential Question

How can you identify and name squares?

Materials


shapes

• iTools: Geometry• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and sort the squares in a group of two-dimensional shapes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of shapes to develop sound mathematical practices by asking these questions.

• What squares do you see in the classroom? How do you know?

• What objects in the classroom are not shaped like squares? How do you know?

• Is every shape with corners a square? Why or why not?




Students can continue to practice once they understand the concept of squares. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify and name squares? Possible answer: I know that a square is a shape with four vertices and four straight sides that match.


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114 Chapter 9

Lesson 9.4

Describe SquaresInstructional Time: 1 day



Lesson Objective

Describe attributes of squares.

Essential Question

How can you describe squares?

Materials

• MathBoard• two-color

counters





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to recognize and describe the attributes of a square. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of squares to develop sound mathematical practices by asking these questions.

• What word in the problem helped you solve it?

• How did that word help you solve the problem?

• Would a square still be a square if you fl ipped it upside down? Why?


Use the checked exercises as a diagnostic assessment. If students answer either exercise incorrectly, see RtI (Response to Intervention).


Students can continue to practice once they understand these geometry concepts. The H.O.T. problem, exercise 3, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you describe squares? Possible answer: A square is a shape that has four sides of equal length and four square vertices.


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Chapter 9 115

Lesson 9.5

Identify and Name TrianglesInstructional Time: 1 day


Also CC.K.G.3

Lesson Objective

Identify and name two-dimensional shapes including triangles.

Essential Question

How can you identify and name triangles?

Materials


shapes





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and sort the triangles in a group of two-dimensional shapes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of shapes to develop sound mathematical practices by asking these questions.

• How did you know how to sort the shapes?

• What are some ways triangles can be different from one another? What do they all have in common?

• Do any of the shapes in the “not triangles” column have 3 sides? Why not?




Students can continue to practice once they understand the concept of triangles. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify and name triangles? Possible answer: I know that a triangle is a shape with three straight sides.


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116 Chapter 9

Lesson 9.6

Describe TrianglesInstructional Time: 1 day



Lesson Objective

Describe attributes of triangles.

Essential Question

How can you describe triangles?

Materials

• MathBoard • iTools: Geometry

• two-color counters • HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to recognize and describe the attributes of triangles. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of triangles to develop sound mathematical practices by asking these questions.• What number in the problem helped

you solve it? How?• How do you know the picture on your

page is a triangle?• How could you tell someone to draw

a triangle without saying the word “triangle”?




Students can continue to practice once they understand how many vertices and sides make up a triangle. The H.O.T. problem and exercise 3 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you describe triangles? Possible answer: A triangle is a shape that has three sides and three vertices.


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Lesson 9.7

Identify and Name RectanglesInstructional Time: 1 day


Also CC.K.G.3

Lesson Objective

Identify and name two-dimensional shapes including rectangles.

Essential Question

How can you identify and name rectangles?

Materials


shapes





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and sort the rectangles in a group of two-dimensional shapes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of shapes to develop sound mathematical practices by asking these questions.

• What object could you trace to make a rectangle on your paper?

• What rectangles do you see in the classroom? How do you know?

• Does it matter if a rectangle is long and skinny or short and fat? Why can those both be rectangles?




Students can continue to practice once they understand the concept of rectangles. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify and name rectangles? Possible answer: I know that a rectangle is a shape with four straight sides and four square vertices.


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118 Chapter 9

Lesson 9.8

Describe RectanglesInstructional Time: 1 day



Lesson Objective

Describe attributes of rectangles.

Essential Question

How can you describe rectangles?

Materials


• two-color counters • iTools: Geometry




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to recognize and describe the attributes of rectangles. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of rectangles to develop sound mathematical practices by asking these questions.

• What do you think each page in Chuck’s book is shaped like? Why do you think that?

• What are some ways rectangles can look different?

• In what ways will all the stamps in Chuck’s book be alike?




Students can continue to practice once they understand these geometry concepts. The H.O.T. problem, exercise 3, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you describe rectangles? Possible answer: I know that a rectangle is a shape that has four straight sides and four square vertices.


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Chapter 9 119

Lesson 9.9

Identify and Name HexagonsInstructional Time: 1 day


Also CC.K.G.3

Lesson Objective

Identify and name two-dimensional shapes including hexagons.

Essential Question

How can you identify and name hexagons?

Materials


shapes





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and sort the hexagons in a group of two-dimensional shapes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of shapes to develop sound mathematical practices by asking these questions.

• How could you tell someone how to draw a hexagon without saying the word “hexagon”?

• How can hexagons look different from one another? How do they all have to be the same?

• How could you tell if a shape block was a hexagon block if you had your eyes closed?




Students can continue to practice once they understand the concept of polygons. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify and name hexagons? Possible answer: I know a hexagon is a shape with six straight sides.


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120 Chapter 9

Lesson 9.10

Describe HexagonsInstructional Time: 1 day



Lesson Objective

Describe attributes of hexagons.

Essential Question

How can you describe hexagons?

Materials

• MathBoard • iTools: Geometry

• two-color counters • HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to recognize and describe the attributes of hexagons. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of identifying hexagons to develop sound mathematical practices by asking these questions.

• Which words in the problem helped you solve it? Why?

• What is a riddle you could tell about a hexagon?

• How could you make a hexagon out of straws?




Students can continue to practice once they understand the concept of hexagons. The H.O.T. problem, exercise 3, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you describe hexagons? Possible answer: A hexagon is a shape with six sides and six vertices.


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Chapter 9 121

Lesson 9.11

Hands On: Algebra • Compare Two-Dimensional ShapesInstructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. On Day 1 give students extra time to color the shapes in the Listen and Draw section using what they’ve learned about polygons. Have students use what they know to sort shapes with similar and different attributes in Share and Show. On Day 2, use the extra time to explore the complete More Practice and Go Deeper problem. Have students use their knowledge of shapes to fi nd how shapes are alike and different for Go Deeper and the Problem Solving page.Common Core StandardCC.K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).

Also CC.K.G.2

Lesson Objective

Use the words alike and different to compare two-dimensional shapes by attributes.

Essential Question

How can you use the words alike and different to compare two-dimensional shapes?

Materials


shapes• Animated Math

Models

• iTools: Geometry• iTools: Counters

• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to sort shapes by their attributes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of sorting shapes to develop sound mathematical practices by asking these questions.• What words in the problem helped you

solve it? Why?• What do the red and green shapes have

in common? How are they different?• What is a different way Erica could color

her shapes?




Students can continue to practice once they understand how to determine if shapes are alike or different. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use the words alike and different to compare two-dimensional shapes?Possible answer: I can choose a number of sides or vertices and make a set of shapes with that number and label it alike. I can put all the other shapes in another set and label it different.

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122 Chapter 9

Lesson 9.12

Problem Solving • Draw to Join ShapesInstructional Time: 1 day

Common Core StandardCC.K.G.6 Compose simple shapes to form larger shapes.

Lesson Objective


Essential Question


Materials


• pattern blocks • HMH Mega Math




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to put together and take apart shapes. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of

triangles to develop sound mathematical practices by asking these questions.• How did you fi gure out how to arrange

the triangles?• Can you make any other shape using

green triangles? How?• Do you think you could make a shape by

putting squares together? What might it look like?




Students can continue to practice once they understand how to make new shapes. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy draw a picture? Possible answer: I can join different shapes to form new shapes, and then draw the shapes to solve the problem.


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Lesson 10.1

Hands On • Three-Dimensional ShapesInstructional Time: 1 day


Lesson Objective

Analyze and compare three-dimensional shapes by attributes.

Essential Question

How can you show which shapes stack, roll,or slide?

Materials• MathBoard• three-dimensional

shapes• Three- Dimensional

Shapes (see eTeacher Resources)

• iTools: Counters• iTools: Geometry• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to compare and sort three-dimensional shapes that stack and do not stack. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the attributes of shapes to develop sound mathematical practices by asking these questions. • How do you know if your blocks are

stacked?• What happens if you try to stack

spheres?• What happens if you try to stack cones?

PracticeShare and Show Approximately 10 min.



Students can continue to practice once they understand when shapes roll, slide, or stack. The H.O.T. problem, exercises 4 and 5, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you show which shapes stack, roll, or slide? Possible answer: I can use solid shapes to show that shapes with a fl at surface stack and slide, while shapes with a curved surface roll.


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Summarize4 SUMMARIZE

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126 Chapter 10

Lesson 10.2

Hands On • Identify, Name, and Describe SpheresInstructional Time: 1 day



Lesson Objective

Identify, name, and describe three- dimensional shapes, including spheres.

Essential Question

How can you identify, name, and describe spheres?

Materials • MathBoard• three-dimensional

shapes• Three-Dimensional






20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to identify and sort spheres using three-dimensional shapes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of three-dimensional shapes to develop sound mathematical practices by asking these questions. • What sports can you think of that use an

object shaped like a sphere?• What fruits can you think of that are

shaped like a sphere?• How could you tell you were holding a

sphere if you had your eyes closed?




Students can continue to practice once they understand how to describe the surfaces of shapes. The H.O.T. problem, exercise 3, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify, name, and describe spheres? Possible answer: I know that spheres are shapes that have curves and no fl at surfaces. I know that a ball is a sphere.


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Lesson 10.3

Hands On • Identify, Name, and Describe CubesInstructional Time: 1 day

Common Core Standard CC.K.G.2 Correctly name shapes regardless of their orientations or overall size.

Also CC.K.G.3, CC.K.G.4, CC.K.G.5

Lesson Objective

Identify, name, and describe three- dimensional shapes, including cubes.

Essential Question

How can you identify, name, and describe cubes?

Materials

• MathBoard• three-dimensional







20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use three-dimensional shapes to help them distinguish cubes and describe their attributes. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of squares to develop sound mathematical practices by asking these questions. • How is a cube different from a square?• Would a cube be a good shape for a

bowling ball? Why or why not?




Students can continue to practice once they understand how to describe cubes based on their surfaces. The H.O.T. problem, exercise 3, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify, name, and describe cubes? Possible answer: I know that cubes are shapes that have six fl at surfaces.


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128 Chapter 10

Lesson 10.4

Hands On • Identify, Name, and Describe CylindersInstructional Time: 1 day



Lesson Objective

Identify, name, and describe three- dimensional shapes, including cylinders.

Essential Question

How can you identify, name, and describe cylinders?

Materials • MathBoard• three-dimensional







20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use three-dimensional shapes to help them identify and describe the attributes of cylinders. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of the attributes of other two-dimensional shapes to develop sound mathematical practices by asking these questions. • How could you tell you were holding

a cylinder block if you had your eyes closed?

• How is a cylinder like a circle? How is it different?




Students can continue to practice once they understand how to describe the surfaces of a cylinder. The H.O.T. problem, exercise 3, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify, name, and describe cylinders?Possible answer: I know that a cylinder has a curved surface and two fl at surfaces. Some cylinders are cans and tubes.


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Lesson 10.5

Hands On • Identify, Name, and Describe ConesInstructional Time: 1 day



Lesson Objective

Identify, name, and describe three- dimensional shapes, including cones.

Essential Question

How can you identify, name, and describe cones?

Materials

• MathBoard• three-dimensional







20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use three-dimensional shapes to identify and describe the attributes of a cone. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of other three-dimensional shapes and their attributes to develop sound mathematical practices by asking these questions. • What objects can you think of that are

shaped like cones?• How are the two ends of a cone

different?• How do a cone and a cylinder roll

differently?




Students can continue to practice once they understand how to describe the surfaces of a cylinder. The H.O.T. problem and exercise 3 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you identify, name, and describe cones? Possible answer: Cones are shapes that have a curved surface, a fl at surface, and a point. Some cones are party hats or ice cream cones.


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130 Chapter 10

Lesson 10.6

Problem Solving • Two- and Three-Dimensional ShapesInstructional Time: 1 day

Note: The instructional time for this lesson can also be 2 days. On Day 1, have students work through Unlock the Problem, Try Another Problem, and Share and Show. Discuss with students how to identify the different attributes of two- and three-dimensional shapes. Use the extra time to work on Go Deeper and discuss with students what two-dimensional shapes they can see on three-dimensional shapes. Use the extra time on Day 2 to complete the On Your Own exercises and explore the Cross-Curricular activities.

Common Core StandardCC.K.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

Lesson Objective

Solve problems by using the strategy use logical reasoning.

Essential Question

How can you solve problems using the strategy use logical reasoning?

Materials • MathBoard• two-dimensional

shapes• three-dimensional

shapes

• Plane Shapes• Three-Dimensional


• iTools: Geometry

•




20 min.

Unlock the Problem • Activity to Build Conceptual Understanding

Remember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use sorting mats to distinguish between two-dimensional and three-dimensional shapes. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of two- and three-dimensional shapes to develop sound mathematical practices by asking these questions. • What are some differences between fl at

and solid shapes?• What material might you use to make a

fl at shape? Why?• What material might you use to make a

solid shape? Why?




Students can continue to practice once they understand how to identify fl at and solid shapes. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy use logical reasoning? Possible answer: I can look at the shapes to fi nd whether they are fl at or solid shapes. I can look at the surfaces to tell what kind of fl at or solid shape they are.


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Lesson 10.7

Above and BelowInstructional Time: 1 day

Common Core Standard CC.K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, beside, in front of, behind, and next to.

Lesson Objective

Use the terms above and below to describe shapes in the environment.

Essential Question

How can you use the terms above and below to describe shapes in the environment?

Materials

• MathBoard• connecting cubes





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use the strategy “act it out” to better understand the terms above and below. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of two- and three-dimensional shapes and their attributes to develop sound mathematical practices by asking these questions. • Which words in the problem helped you

solve it? Why?• What else could you say about where

objects are in the picture?• Draw a new object on the picture. How

can you describe where it is?




Students can continue to practice once they understand how to locate and identify shapes in terms of above and below. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use the terms above and below to describe shapes in the environment?Possible answer: I can say that a shape is above, or higher than, another object. I can say that a shape is below, or lower than, another object.

•


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132 Chapter 10

Lesson 10.8

Beside and Next ToInstructional Time: 1 day

Common Core StandardCC.K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Lesson Objective

Use the terms beside and next to to describe shapes in the environment.

Essential Question

How can you use the terms beside and next to to describe shapes in the environment?

Materials

• MathBoard• iTools: Geometry





20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use real-world objects to better understand the terms beside and next to. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of three-dimensional shapes to develop sound mathematical practices by asking these questions. • How could you draw a picture to help

you solve the problem?• Which words that Coach said helped you

know which ball to get?• How did you know that the tennis ball

could not be the right answer?




Students can continue to practice once they understand how to identify objects using the terms beside and next to. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use the terms beside and next to to describe shapes in the environment? Possible answer: I can use beside or next to to tell about the location of shapes like boxes, balls, cones, and cans. When something is beside or next to me, it is at the side of me.

•


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Lesson 10.9

In Front Of and BehindInstructional Time: 1 day

Common Core Standard CC.K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Lesson Objective

Use the terms in front of and behind to describe shapes in the environment.

Essential Question

How can you use the terms in front of and behind to describe shapes in the environment?

Materials

• MathBoard




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use real-world situations to better understand the terms in front of and behind. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of other position words to develop sound mathematical practices by asking these questions.

• How did you know how to solve the problem?

• What words do you know that can tell where things are?

• What question could you ask a classmate to answer about the picture?




Students can continue to practice once they understand how to identify and describe shapes using in front of and behind. The H.O.T. problem and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you use the terms in front of and behind to describe shapes in the environment? Possible answer: I can use the words in front of and behind to tell the locationof shapes like boxes, balls, cones, andcans. When something is in front of an object, it comes before the object in aline. When it is behind, it comes afterthe object.


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136 Chapter 11

Lesson 11.1

Hands On • Compare LengthsInstructional Time: 1 day

Common Core Standard CC.K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of”the attribute, and describe the difference.

Also CC.K.MD.1

Lesson Objective

Directly compare the lengths of two objects.

Essential Question

How can you compare the lengths of two objects?

Materials


• connecting cubes • iTools: Counters• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to compare two objects to better understand the concepts of longer than and shorter than. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of object comparisons to develop sound mathematical practices by asking these questions.

• What are other pairs of objects you could compare the length of?

• How would you fi nd out which onewas longer and which was shorter?

• Why is it important for the objects to start at the same place when you are measuring them?




Students can continue to practice once they understand how to draw or construct an object that is longer or shorter than another object. The H.O.T. problem, exercises 5 and 6, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you compare the lengths of two objects? Possible answer: I can put two objects one under the other, starting at the same place. I can see if one object is shorter than, longer than, or about the same length as the other object.


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Lesson 11.2

Hands On • Compare HeightsInstructional Time: 1 day


Also CC.K.MD.1

Lesson Objective

Directly compare the heights of two objects.

Essential Question

How can you compare the heights of two objects?

Materials


• Animated Math Modules




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use pictures and real-world scenarios to better understand the concept of height. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of longer than, shorter than, and about the same length as to develop sound mathematical practices by asking these questions. • Which objects in the classroom are taller

than your chair?• Which objects in the classroom are

shorter than your chair?• How do you know?




Students can continue to practice once they understand the concepts of taller than and shorter than. The H.O.T. problem, exercise 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you compare the heights of two objects? Possible answer: I can put two things side by side, starting at the same place. I can see if one object is shorter than, taller than, or about the same height as the other object.

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138 Chapter 11

Lesson 11.3

Problem Solving • Direct ComparisonInstructional Time: 1 day

Common Core StandardCC.K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of”the attribute, and describe the difference.

Also CC.K.MD.1

Lesson Objective


Essential Question


Materials

• MathBoard • classroom objects




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use drawings and real-world objects to learn about comparing lengths and heights. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.

Build on students’ understanding of length and height to develop sound mathematical practices by asking these questions. • What kinds of objects would it make

sense to measure on this page?• What kinds of objects would be

impossible to measure on this page?• Why is it important to make your

drawing exactly the same size asyour object?


Use the checked exercise as a diagnostic assessment. If students answer the exercise incorrectly, see RtI (Response to Intervention).Students can continue to practice once they understand how to align and compare objects. Guide them through the H.O.T. problem on page 475. This exercise requires higher order thinking skills and critical reasoning, making it especially rich.


Essential Question

How can you solve problems using the strategy draw a picture? Possible answer: I can draw two objects that start on the same line to fi nd which one is longer than, shorter than, or about the same length, or to fi nd which one is taller than, shorter than, or about the same height.


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Lesson 11.4

Hands On • Compare WeightsInstructional Time: 1 day


Also CC.K.MD.1

Lesson Objective

Directly compare the weights of two objects.

Essential Question

How can you compare the weights of two objects?

Materials


• classroom objects • HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use the strategy “act it out” to better understand how to compare weights. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of how to compare length and height to develop sound mathematical practices by asking these questions.

• How does acting out the problem help you solve it?

• How does it feel to carry something very heavy?

• How does it feel to carry something very light?

• What are two objects that might have about the same weight? How could you test your guess?




Students can continue to practice once they understand the concepts of the terms lighter and heavier. The H.O.T. problem, exercises 5 and 6, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you compare the weights oftwo objects? Possible answer: I can hold two objects, one in each hand. I can see which onefeels heavier and which one feels lighter.


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deeply to discuss.


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Lesson 11.5

Length, Height, and WeightInstructional Time: 1 day

Common Core StandardCC.K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

Lesson Objective

Describe several measurable attributes of a single object.

Essential Question

How can you describe several ways tomeasure one object?

Materials

• MathBoard • red and blue crayons




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use real-world situations to discuss the various ways to measure an object. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of length, height, and weight to develop sound mathematical practices by asking these questions.

• What have you learned recently that helped you solve this problem?

• What are some ways you could measure a real cat?

• Can you think of something with a small length but a big height?

• Can you think of something with a big length but a small height?




Students can continue to practice once they understand that any given object has various measurable attributes. The H.O.T. problem, exercises 5 and 6, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you describe several ways to measure one object? Possible answer: I can measure the length of an object by going from side to side. I can measure the height of an object by going from bottom to top. I can measure the weight of an object by holding it to see if it is heavy or light.


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Lesson 12.1

Hands On: Algebra • Classify and Count by ColorInstructional Time: 1 day

Common Core Standard CC.K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Lesson Objective

Classify and count objects by color.

Essential Question

How can you classify and count objects by color?

Materials


shapes• iTools: Counters


• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use drawings and objects to understand the concept of classifying by color. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of color descriptions to develop sound mathematical practices by asking these questions.

• How did you decide where to put each shape?

• What if you chose different colors to put in the clouds? How would your chart look different?

• Is color the only way you can sort something? How else could you sort objects?




Students can continue to practice once they understand the concept of sorting shapes by color. The H.O.T. problem, exercises 2, 3, and 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you classify and count objects by color? Possible answer: I can choose a color and put all objects of that color in one category and put all objects that are not that color in another category. I can count how many objects are in each category.

•


1 ENGAGE

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Lesson 12.2

Hands On: Algebra • Classify and Count by ShapeInstructional Time: 1 day

Common Core StandardCC.K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Lesson Objective

Classify and count objects by shape.

Essential Question

How can you classify and count objects by shape?

Materials



Models

• iTools: Geometry• iTools: Counters• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use graphic organizers to understand the process of sorting by shape. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of two-dimensional shapes to develop sound mathematical practices by asking these questions.

• How are your categories different?• How did you know what category to

put each shape in?• How could you have solved the problem

differently?




Students can continue to practice once they understand the concept of classifying objects by their shapes. The H.O.T. problem, exercises 2, 3, and 4, and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you classify and count objects by shape?Possible answer: I can sort and classify objects that are alike by shape into categories. I can count how many objects are in each category.


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Lesson 12.3

Hands On: Algebra • Classify and Count by SizeInstructional Time: 1 day

Common Core StandardCC.K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Lesson Objective

Classify and count objects by size.

Essential Question

How can you classify and count objectsby size?

Materials



Models

• iTools: Counters• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use a graphic organizer to sort objects by size. As s tudents work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of sorting objects by color and shape to develop sound mathematical practices by asking these questions.

• What words in the problem gave you a clue about how you could sort Yoriko’s shapes?

• What information do you need to sort objects?

• Could you sort shapes into more than two groups? Explain.




Students can continue to practice once they understand how to put objects into categories based on their size. The H.O.T. problem and exercises 2 and 3 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you classify and count objectsby size? Possible answer: I can place objects that are small in one category and things that are big in another category. I can count how many objects are in each category.


1 ENGAGE

deeply to discuss.


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Lesson 12.4

Hands On • Make a Concrete GraphInstructional Time: 1 day


Lesson Objective

Make a graph to count objects that have been classifi ed into categories.

Essential Question

How can you make a graph to count objects that have been classifi ed into categories?

Materials

• MathBoard• connecting cubes• two-dimensional

shapes


• iTools: Graphs• HMH Mega Math




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to use a graph to classify and count objects by color. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of classifying objects by a given attribute to develop sound mathematical practices by asking these questions.

• How does the graph make it easier to count how many of each color?

• How did you fi gure out which color truck Tony had more of?

• Why is it important to place the cubes starting in the box farthest to the left?




Students can continue to practice once they understand how graphs can show which of two categories has more of something. The H.O.T. problem, exercises 4, 5, and 6, and the exercise on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you make a graph to count objects that have been classifi ed into categories? Possible answer: I can sort and classify the objects by category. Then I can move them by category onto a graph and draw them.I can count how many are in each category.


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Lesson 12.5

Read a GraphInstructional Time: 1 day


Lesson Objective

Read a graph to count objects that have been classifi ed into categories.

Essential Question

How can you read a graph to count objects that have been classifi ed into categories?

Materials


• two-color counters • iTools: Graphs• Animated Math Models




20 min.

Listen and Draw • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to read a graph to understand which of two categories has more of a given thing. As students work through Listen and Draw, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of what graphs show to develop sound mathematical practices by asking these questions.

• How did you solve the problem?• When you’re counting the counters, why

don’t you count the one on the outside of the chart?

• If Heather found another yellow counter, how would the graph and numbers change?




Students can continue to practice once they understand how to count the objects in each category of a graph. The H.O.T. problem and the exercises on the Problem Solving page require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you read a graph to count objects that have been classifi ed into categories? Possible answer: I can count how many are on each row to see how many are in each category.


1 ENGAGE

deeply to discuss.


Practice3 PRACTICE

especially rich.


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Lesson 12.6

Problem Solving • Sort and CountInstructional Time: 1 day


Lesson Objective

Solve problems by using the strategy use logical reasoning.

Essential Question

How can you solve problems using the strategy use logical reasoning?

Materials


• HMH Mega Math




20 min.

Unlock the Problem • Activity to Build Conceptual UnderstandingRemember, this is the core instruction for this lesson, in which conceptual development is key. The goal of this activity is for students to understand and use information presented in a sorting mat. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction.Build on students’ understanding of fi nding the total number of a given object to develop sound mathematical practices by asking these questions.

• What does each number in your addition sentence stand for?

• If Steven found another red shape, how would the picture and addition sentence change?

• How else could Steven have sorted his shapes?




Students can continue to practice once they understand how to fi nd the total number of objects in two sets. The H.O.T. problem and exercises 1 and 2 require higher order thinking skills and critical reasoning, making them especially rich.


Essential Question

How can you solve problems using the strategy use logical reasoning?Possible answer: I can sort and classify the information I have and then use logical reasoning to fi nd an answer.

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also cc.k.cc.3, cc.k.cc.4b, cc.k.cc.5 practice practice€¦ · · 2013-06-10houghton mifflin...

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