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SFUSD Mathematics Core Curriculum, Grade 1, Unit 1.11: Numbers Greater Than 20, 2014–2015

SFUSD Mathematics Core Curriculum Development Project

2014–2015

Creating meaningful transformation in mathematics education

Developing learners who are independent, assertive constructors of their own understanding

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Grade 1

1.11 Numbers Greater than 20

Number of Days

Lesson Reproducibles Number of Copies

Materials

Note: Counters and base-10 blocks will be used throughout this unit.

1 Entry Task What’s Missing? (2 pages) EM Master p 110 Continuing Scroll (2 pages) HW: 1-120 Number Chart

1 per student 1 per student 1 per student

Number chart (pocket chart or poster);

5 Lesson Series 1 Day 1 HW: Groups of 10 (2 pages) EM Journal p 81 Mats EM Master p 339 Base-10 Exchange Day 2 HW: Tens and Ones (2 pages) Number Bond Worksheet Day 3 HW: Groups of 10 (2 pages) Number Bond Worksheet EM Journal Activity Sheets 7 and 8, Animal Weights Day 4 HW: Tens and Ones (2 pages) Ten and One Tables (2 pages) Day 5 HW: Different Ways (3 pages)

1 per student EM Journal 1 per pair 1 per student 1 per student 1 per student 1 per student EM Journal 1 per student 1 per student 1 per student

Base-10 blocks in bags, base-10 sorting mats, 0 to 9 digit cards, white boards, number dice, animal weight cards from Everyday Math, construction paper

1 Apprentice Task Model Problem - Fishy Math Fish Apprentice Task - Pet Store Apprentice Task HW - Monkeys at the Zoo

1 per student 1 per student 1 per student 1 per student

counters or other types of manipulative, dice

5 Lesson Series 2 Day 1 Classwork: Write the Numbers (3 pages) Day 1 HW: Quick Tens (2 pages) Comparison Cards (2 pages, double sided) Day 2 Classwork: Place Value Charts (3 pages) Day 2 HW: Place Value Charts (2 pages)

1 per student 1 per student 1 per student 1 per student 1 per student

coins - dimes and pennies Visual Guides (print on Cardstock)

● Day 1 Visuals ● Place Value Charts ● Day 3 Visuals

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Day 3 Classwork: Quick Tens (2 pages) Day 3 HW: Numbers in Order (2 pages) Day 4 Classwork: Comparisons (2 pages) Day 4 HW: Comparisons (2 pages) Day 5 Classwork: Comparisons (2 pages) Day 5 HW: Comparisons (2 pages)

1 per student 1 per student 1 per student 1 per student 1 per student 1 per student

● Alligator (print double sided)

● Groups of frogs

1 Expert Task Expert Task WS Expert Task Silly Symbols Game Board Expert Task Game Recording Sheet Expert Task HW

1 per student 1 per pair 1 per student 1 per student

Expert Task Game Symbols - copy 5 sheets for the whole class; counters (100 per pair) in a brown bag

5 Lesson Series 3 Day 1 HW: Number Grids (2 pages) Day 1 Classwork: More/Less EM Master p. 258 Number Grid Pieces EM Journal Activity Sheet 16 Number Grid Shapes EM Journal Activity p. 180 Number Grid Puzzles EM Journal Activity Sheet 15 Number Grid Day 2 HW: EM Homelink 9.3 Number Grid Puzzles Day 3 Classwork: Adding on a Number Line (2 pages) Day 3 Classwork: Adding and Subtracting Tens (2 pages) Day 4 Classwork: EM SRB Number Grid Game EM Master p 249 Number Grid Day 4 HW: EM Homelink 9.1 Number Grid Hunt Day 5 Classwork: Solve Using Quick Tens Day 5 HW: Solve Using Pictures (2 pages)

1 per student 1 per student 1 per pair EM Journal EM Journal EM Journal EM homelink 1 per student 1 per student EM SRB 1 per pair EM homelink 1 per student 1 per student

Number Grid Poster Student Number Grids Transparency for lesson series 3 day 1-4 copies +10 and -10 number lines

2 Milestone Task Milestone Task (3 pages) Milestone HW: Subtracting Sets of Ten

1 per student 1 per student

Base-10 Blocks: ones and tens

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Unit Overview

Big Idea

Quantities up to 120 may be compared, counted, and represented in multiple ways, including grouping, place value, pictures, words, number line locations, and symbols. Numbers are made up of digits in the same way that words are made up of letters.

Unit Objectives

Students will ● understand the order of the counting numbers and their relative magnitudes ● use a number line and number grid to build understanding of numbers and their relation to other numbers ● unitize a group of ten ones as a whole unit: a ten ● compose and decompose numbers from 11 to 19 into ten ones and some further ones ● think of whole numbers between 10 and 100 in terms of tens and ones ● explore the idea that decade numbers (e.g., 10, 20, 30, 40) are groups of tens with no ones left over ● compare two numbers by examining the amount of tens and ones in each number using words, models and symbols greater than (>), less than (<)

and equal to (=) ● create concrete models, drawings and place value strategies to add and subtract within 100 (Students should not be exposed to the standard

algorithm of carrying or borrowing in first grade) ● use place value understanding and properties of operations to add and subtract ● mentally add ten more and ten less than any number less than 100 ● use concrete models, drawings and place value strategies to subtract multiples of 10 from decade numbers (e.g., 30, 40, 50)

Unit Description

In this unit students will extend the counting sequence to 120. Students will develop, discuss, and use efficient, accurate, and generalizable methods to add/subtract within 100 and add/subtract multiples of 10. They will compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They will think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they will understand the order of the counting numbers. Common Misconceptions Often when students learn to use an aid (Pac Man, bird, alligator, etc.) for knowing which comparison sign (<, >, = ) to use, the students don’t associate the real meaning and name with the sign. The use of the learning aids must be accompanied by the connection to the names: < Less Than, > Greater Than, and = Equal To. More importantly, students need to begin to develop the understanding of what it means for one number to be greater than another. In Grade 1, it means that this number has more tens, or the same number of tens, but with more ones, making it greater. Additionally, the symbols are shortcuts for writing down this relationship. Finally, students need to begin to understand that both inequality symbols (<, >) can create true statements about any two numbers where one is greater/smaller than the other, (15 < 28 and 28 >15). Note Standard 1.NBT.1 states that students will count to 120, starting at any number less than 120. This is a change from the previous standard that students will

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count to 100. Everyday Math materials, e.g. Number Grid Poster and student number grids, go up to 110. Adapted number grids to 120 are available in “Resources”.

Games to use throughout the unit (found in Everyday Math, Teacher’s Guide to Games):

● Base 10 Exchange page 38 ● Digit Discovery page 64

Shown for 3 digits, can be adapted for 2 digits ● Ones, Tens, Hundreds Game page 136 ● Rolling for 50 page 153 ● Tens and Ones Trading Game page 169 ● Top It page 175

Can be used in many different ways, depending on focus

Possible Read-Alouds or additions to classroom libraries: ● 1 2 3 Peas Keith Baker ● Chicka Chicka 1 2 3 Bill Martin, Jr. ● The Cheerios Book Barbara Barbeiri McGrath ● 98, 99, 100! Ready or Not, Here I Come! Teddy Slater ● 100 Ways to Get to 100 Jerry Palotta ● Tally O’Malley Stuart Murphy ● Domino Addition Lynetta Long ● Count on Pablo Barbara Derubertis ● Caps for Sale Esphyr Slobodkina ● Let’s Count Tana Hoban ● The Warlord’s Beads Virginia Walton Pilegard ● Anno’s Counting Book Mitsumasa Anno ● 26 Letters and 99 Cents Tana Hoban ● 100 Hungry Ants Elinor J. Pinczes ● One Grain of Rice: A Mathematical Folktale Demi ● Anno’s Magic Seed Mitsumasa Anno ● Equal Shmequal Virgina Kroll ● A Collection For Kate Barbara Derubertis ● A Million Dots Andrew Clements ● A Million Fish . . . More or Less Pat McKissack

CCSS-M Content Standards

Extend the counting sequence. 1 NBT 1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. Understand place value. 1 NBT 2a,b,c Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 1 NBT 3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Use place value understanding and properties of operations to add and subtract. 1 NBT 4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1 NBT 5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1 NBT 6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Progression of Mathematical Ideas

Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

In Kindergarten, students worked with numbers 11–19 to gain foundations for place value. They composed and decomposed numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and recorded each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); and understood that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. By the end of Kindergarten students counted to 100.

In first grade, students count and work with numbers to 120 and learn to view ten ones as a unit called ten. They learn that the numbers 11 through 19 are a group of ten and some ones and that the two digits of a two-digit number represent amounts of tens and ones (67 is 6 tens and 7 ones). They understand that the digit in the tens place is more important for determining the size of a two-digit number and use this understanding to compare two two-digit numbers, using the symbols >, =, and <. Students in this grade also learn to mentally find 10 more or 10 less than a given two-digit number without having to count by ones. They learn to compute differences of two-digit numbers for limited cases. (For example 70-40 can be viewed as 7 tens minus 4 tens.)

Students will continue their understanding of base-10 system, expanding to numbers greater than 100, to 1000. They will gain understanding of three digit numbers, e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Students will count within 1000; skip-count by 5s, 10s, and 100s. Students will also compare three-digit numbers based on the meaning of the hundreds, tens, and ones. Students will fluently add and subtract to 100, and add and subtract within 1000 using concrete models or drawings and strategies based on place value.

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Unit Design All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both formative and summative assessments of student learning. The tasks are designed to address four central questions: Entry Task: What do you already know? Apprentice Task: What sense are you making of what you are learning? Expert Task: How can you apply what you have learned so far to a new situation? Milestone Task: Did you learn what was expected of you from this unit?

1 Day 5 Days 1 Day 5 Days 1 Day 5 Days 2 Days

Total Days: 20

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Entry Task What is Missing?

Apprentice Task Fishy Store

Expert Task Silly Symbols

Milestone Task What Do You Know?

CCSS-M Standards

1 NBT 1; 1 NBT 2a,b,c; 1 NBT 4

1 NBT 2a,b,c; 1 NBT 4

1 NBT 1; 1 NBT 2a,b,c; 1 NBT 3 1 NBT 1; 1 NBT 2a,b,c; 1 NBT 3; 1 NBT 4; 1 NBT 5; 1 NBT 6

Brief Description of Task

Students will fill in missing numbers in a number grid (1 to 120). Students will fill in missing numbers with +1 and -1, and +10 and -10, for a given number on the number grid.

The task will focus on students’ knowledge of place values: tens and one. Students will also compose and decompose numbers with tens and ones.

Students will divide a bag of objects into four piles (without counting). They will then count the objects in each pile, using a variety of counting strategies. After counting and recording, students will then compare the amounts using is greater than >, is less than <, and is equal to =.

Students will independently apply the skills acquired in this unit to a variety of problems. This culminating task is scheduled for two days.

Source Adapted from Everyday Math and Math-Drills.com

Adapted Georgia Department of Education and EngageNY

Adapted Georgia Department of Education Adapted from EngageNY 50 Leveled Math Problems by Linda Dacey K-5teacherresources.com

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

1.NBT.2, 1.NBT.4

1.NBT.1, 1.NBT.2, 1.NBT.3, 1.NBT.4, 1.NBT.5, 1.NBT.1, 1.NBT.4, 1.NBT.5, 1.NBT.6

Brief Description of Lessons

This lesson series starts with introducing place value and building numbers with tens and ones base 10 blocks. Students will learn to compose and decompose numbers into tens and ones. Students will extend their place value understanding to include 100. By the end of the lesson series, students will use their knowledge of composing and decomposing numbers into tens and ones to add together two numbers using base 10 blocks.

This lesson series starts with practicing the term “greater than” and “less than” with 1 and 10 (+/- 1 & +/- 10). Students will learn the term “equal to” addition to “greater than” and “less than” to compare two numbers. By the end of the lesson series, students will be able to represent and compare numbers with relation symbols (>, =, <) and words (“greater than”, “less than”, and “equal to”.

In this lesson series students extend their understanding of their skill with tens and ones. For example, they mentally find 10 more, 10 less, 1 more, and 1 less. They then add pairs of two-digit numbers in which the ones digits have a sum less than 10, recording their work using various methods based on place value.

Sources

This lesson series is based on Everyday Math lessons 5.1, 5.3, 8.3, and 9.4 and Engage NY module 4 place value, as well as Mrs.T’s classroom on Pinterest and images from Pinterest.

from Engageny.org Lesson Module 4

This lesson series is adopted from EngageNY, module 6 and Everyday Mathematics lessons, 9.2, 9.3, and TLSBooks.com

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Entry Task

What is Missing?

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will be able to fill in the missing

numbers on a number chart up to 120 recognizing and extending sequencing patterns .

● Students will be able to complete grids displaying one less, one more, ten less, and ten more than a number as well as identifying the central number. They will be able to justify their numbers on the number grid.

CCSS-M Standards Addressed: 1.NBT.1, 1.NBT.4, 1.NBT.5 Potential Misconceptions

● Students may transpose numbers (21 for 12) or write the numbers incorrectly (backwards).

● When showing + 10 or - 10, students may count by ones (going down)

● Students may lose count when wrapping around at the end of each line of the number grid .

● Students may have difficulty understanding that the word ten represents 10 things.

● Students and adults tend to include the word “and” when reading whole numbers in the hundreds and higher. The word “and” is not used when reading or saying numbers unless the number includes a decimal or fraction. Ex: 119 is read, one hundred nineteen; NOT one hundred and nineteen. 101 is read: one hundred one, NOT one hundred and one.

Launch: Students will sit in a circle for routine skip counting by 1s beginning with one student and Stop/Count at 63 and count by 10s beginning at 63. If number pocket chart is available, select a number and remove all the numbers on its sides. For example, 36 is selected and 35, 37, 26, and 46 is removed. If using a number poster, cover surrounding numbers with post-its. Model for student to identify the number (35) missing on the left is 1 less than the number 36 and number (37) on the right is 1 more than the number 36. Model the number (26) above is 10 less than the number 36 and the number (46) below is 10 more than the number 36. (Note: You can always model with the number of the day/number of days in school). During: Part 1: Students are given a number chart with numbers missing up to 120 in which students are to fill in with the correct numbers. This page will be the start of a number scroll which will be an activity they can work on throughout the rest of the school year. Students will use Math Master P. 110 to extend the scroll. Part 2: Students are given sets of grids in which numbers are missing. The grids will include: 3 tiles going across to assess one less and one more and the central number; three tiles going down to assess 10 less and 10 more; and a T-shape combination of the two.. Closure/Extension: Display a copy of 120 grid on document camera. Select students to individually fill in missing numbers. Class can give a thumbs up or thumbs down. Students should make any necessary corrections before continuing to the next page of their scroll. Partners should check each others’ scroll for each page. Display Part 2 grids on document camera and select child to fill in missing numbers and justify their numbers by using the big number chart. Homework: Students will be given a 1-120 chart which they will cut and make into a number line using tape.

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What is Missing?

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 6. Attend to precision. Structures for Student Learning: Academic Language Support:

Vocabulary: less than, more than, above, below Sentence frames: ___ is 1 less than ___. ___ is 1 more than. ___ is 10 less than ___. ___ is 10 more than ___.

Differentiation Strategies: For students having difficulty, allow them to use a 120 number grid for support. Participation Structures (group, partners, individual, other): Counting to 120 in whole group and is a good indication of struggling students. Students have partners check each page before they work independently on completing each page of the scroll.

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Lesson Series #1

Lesson Series Overview: This lesson series starts with introducing place value and building numbers with tens and ones base 10 blocks. Students will learn to compose and decompose numbers into tens and ones. Students will extend their place value understanding to include 100. By the end of the lesson series, students will use their knowledge of composing and decomposing numbers into tens and ones to add together two numbers using base 10 blocks. CCSS-M Standards Addressed: 1.NBT.2a,b,c, 1.NBT.4 Time: 5 days

Lesson Overview – Day 1 Resources

Description of Lesson: Base 10 Exchange In this lesson teacher will introduce the language of base 10 blocks- digits, ones, tens and hundreds and the tool of the 10’s and 1’s mat. Teacher may show numbers using base-ten blocks to model a number. Teacher can show using labeled base 10 blocks- see example to the right. Teacher may want to give the analogy of- Numbers are made up of digits in the same way that words are made up of letters. Launch:

● Teacher will start by modeling the labeled base 10 blocks to show how the numbers are made up of digits and build on each other. Class will count by 1’s and 10’s to 100.

● Place 4 cubes (ones) on the overhead projector or document camera. Keep the cubes available for students to see for approximately 5 seconds. Cover them up and have students tell you how many cubes were visible.

● Repeat the process with 9 cubes. Ask the students about the strategies they are using to count the cubes and discuss why these strategies are effective.

● Next, show students 22 cubes scattered or piled closely together. Ask students if they were able to determine how many cubes were displayed. Most students will not be able to count the cubes within 5 seconds. Discuss why this number is more difficult and possible strategies that would make this number easier to count. If the conversation does not lead into grouping by 10’s, present the idea of grouping into groups of ten. Discuss how this idea could have helped them count faster. Teacher may use a base 10 mat on the document camera/overhead projector

● Show students the number 34 with the cubes scattered. How can we make this number easier to count? Allow the students to come up and demonstrate how to make groups of ten by moving the cubes. This completes the idea that we have created a set of ten. Continue this concept with the remaining cubes. Now go back and count the amount by how many groups of ten first then how many ones are left. Allow

Materials needed: Base 10 blocks in bags (each bag should have 20 1’s and 10 10’s) and base 10 sorting mats (enough for each child), 0 to 9 digit cards (enough for each partnership). Homework: Groups of 10

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students to discuss the benefit of grouping objects when counting. During:

● Introduce the 10’s and 1’s mat and give each student a mat and a bag of base 10 blocks to use. ● Teacher will use number cards 0 to 9 to make 2 digit numbers. Children will build the 2 digit numbers

using the base 10 blocks. ● Teacher will then exchange the digits and have students build the number with the digits in the new

order. (Example 48 becomes 84.) ● As children demonstrate understanding of the concept, teacher may excuse partners to work together

with their blocks, mats and shared deck of 0-9 cards to practice building numbers. ● Teacher may ask students questions like, Which number is larger/smaller? How do you know? How

many groups of ten are in your number? How many ones are in your number? What happens when you move the digits?

Closure/Extensions:

● Teacher may close by having students come up to the document camera to demonstrate the skill. ● Teacher may revisit the labeled base 10 blocks on the document camera. ● Teacher may close with a 100’s read aloud.

Interventions:

● Children with less number sense may benefit from working with smaller numbers or have guided practice with the teacher/ more advanced peer for this lesson.

● Children with less number sense may benefit from building numbers with linker cubes or pony beads and pipe cleaners (if available.)

● Notes: Students need to have multiple experiences counting numbers up to 99 and representing these numbers using tens and ones. Students may have trouble with the teens-11 to 19 and may benefit from additional practice. If students have a regular calendar routine from the beginning of the year that includes counting the days and grouping them by 10’s and 1’s, they will be better prepared for place value concepts.


Description of Lesson: Base 10 Recording and Exchange Game In this lesson teacher will review the language of base 10 blocks- digits, ones, tens and hundreds and the tool of the 10’s and 1’s mat. Teacher may show numbers using base-ten blocks to model a number. Teacher can show using labeled base 10 blocks- see from yesterday. Teacher may give the analogy of- Numbers are made up of digits in the same way that words are made up of letters.

Materials needed: White boards to record on, base 10 blocks in bags (each bag should have 20 1’s and 10 10’s) and base 10 sorting mats (enough for each child), number dice.

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Launch: ● Teacher will start by reviewing the labeled base 10 blocks to show how the numbers are made up of

digits and build on each other. Class will count by 1’s and 10’s to 100. During: Part 1

● Teacher will inform class that today they will learn a way to write/ represent (to support ELL’s make sure you discuss the meaning of the word represent) this information.

● Teacher will show how to draw using vertical l and dots ⦁ to represent 10’s and 1’s. ● Teacher will place 3 base 10 blocks and 4 cubes (ones) on a 10’s and 1’s mat on the overhead projector

or document camera. Model this with a few different numbers and representations. ● Once the students understand how to represent the numbers with vertical lines and dots, continue to

show numbers with base 10 blocks and have them practice writing this on their own white boards using the vertical line and dot notation.

During: Part 2 ● Teacher will introduce the game, Base 10 Exchange and explain/model the directions. 1. Players take turns putting base-10 blocks on their 10’s and 1’s Mats (Math Journal 1, page 81 or Math

Masters, page 318) according to the roll of the die. 2. Players use Math Masters, page 339 to tell how many base-10 blocks correspond to each dice roll. 3. Whenever possible, they exchange 10 cubes for 1 long. 4. The first player to get to 100 wins. (10 tens) 5. Teacher will have students work with a partner to play the game.

Closure/Extensions: Teacher may choose to close with a read aloud, like Chicka Chicka 123. Interventions:

● Some students may need additional practice with notations of line and dots for 10’s and 1’s. This may need more direct instruction so students are not spending time drawing out 10 separate boxes for the lines.

● Some students may benefit from working in a small group during the game with the teacher if their number/digit knowledge is less proficient.

Homework: Tens and Ones Some resources adapted from EngageNY


Description of Lesson: Number Bonds with Base Tens In this lesson the teacher will introduce the language of number bonds. The term "number bond" is used to refer to a pictorial representation of part-part-whole relationships, often found in the Singapore mathematics curriculum. Number bonds consist of a minimum of 3 circles that are connected by lines. The “whole” is written in the first circle and its “parts” are written in the adjoining circles. Number bonds are used to build deeper

Materials needed: white boards, number cards 0 to 9, base 10 blocks, dice (optional)

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understanding of math facts. Launch:

● Teacher will start by reviewing the notation work of 10’s and 1’s from yesterday. Teacher may use the overhead/document camera to have students practice notation of 2 digit numbers. Teacher will show a number or tell a number riddle. (Example: I have 6 groups of 10 and 3 ones. What is my number?) Students will write their answers on a white using lines and dots as 10’s and 1’s.

● Teacher will introduce the language of number bonds and show what that means. (Part plus part = total). Teacher will model with the number 22, base 10 blocks and a number bond outline.

● Teacher may repeat this thinking with a few different 2-digit numbers. During:

● Teacher will model with students how to play the number bond game, then students will work with a partner or independently play the game.

● Directions- 1. Turn over 2 digits and make a number. 2. Build the number using base 10 blocks. 3. Record the number with notation and number bonds on the worksheet. 4. Repeat!

Closure/Extensions: Teacher may close with a read aloud about 100. Interventions: Teacher may choose to use dice instead of cards, if smaller numbers are easier for students to use. Notes: Wikipedia says, “the term "number bond" is sometimes derided as a piece of unnecessary new mathematical jargon, adding an element of pointless abstraction or incomprehensibility for those not familiar with it (such as children's parents) to a subject even as simple as primary school addition. The term has been used at least since the 1920s and formally entered the primary curriculum in Singapore in the early 1970s. In the U.K. the phrase came into widespread classroom use from the late 1990s when the National Numeracy Strategy brought in an emphasis on in-classroom discussion of strategies for developing mental arithmetic in its "numeracy hour".

Number bond worksheets Homework: Groups of 10


Description of Lesson: Place Value Adding 2 digit numbers In this lesson the teacher will introduce the concept of adding 2 digit numbers to create a new number using animal card pictures and stories and base 10 blocks. Students will have to exchange 1’s for 10’s to come up with the answers and will record this information using notation and number bonds. Launch:

● Teacher will review the term number bond from yesterday and show this on the overhead/document

Materials needed: whiteboards, animal weight cards-1 per partnership, recording worksheet Homework: Tens and Ones

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camera. ● Teacher will lead the students in a conversation with a few different number riddles. I have 4 groups of

10 and 7 ones. What is my number? Students may write their answers on a whiteboard using lines and dots for 10’s and 1’s, number bonds or the number itself.

During: ● Teacher will inform students that today they are going to be zookeepers and check how much animals

weigh when they are weighed together. (Teacher will explain that lb stands for pounds which means how heavy an object is.)

● Teacher will present the animal card pictures and have students see/say how much the various animals weigh. A _______ weighs _____ pounds.

● Teacher will work with a partner to turn over 2 cards and model a number story using the 2 animals. For example: The zookeeper needs to weigh the animals. She weighed the koala and the fox. How much do they weigh together? They weighed _______ pounds together.

● Teacher and partner will model counting out the base 10 blocks for the koala and then the fox. Then they will model how to combine those two amounts and exchange the blocks to have as many groups of 10 as possible and the fewest amount of 1’s.

● Teacher and partner will record this combined amount on the worksheet from yesterday. ● Teacher may repeat as needed with another partner. ● When students are ready, they will go and work with a partner to tell, make and record animal weight

number stories. Closure/Extension:

● Teacher may have partners share out a number story. ● Teacher may close with a read aloud about 100.

Intervention: ● Some students may need additional practice in a small group with the teacher or with using smaller

numbers. ● Students who are ready for a challenge may try using the heavier animals.

Notes: ● Teacher may want to write the language stem for students to use when they share how much the

animals weigh.

NOTE: This lesson works best if the animal cards are either colored on the pound side or (better) copied so they are one sided. Teacher should remove the cheetah, porpoise and penguin cards as these animals are too heavy for the purposes of this game and the standards addressed.


Description of Lesson: Decomposing Numbers in Pictures In this lesson the teacher will have students practice composing numbers starting with the most blocks possible, using only 1’s, and ending with students using the least amount of 1’s. Students should be able to decompose numbers, but may not really understand all the ways that a number can be decomposed. In this lesson, the teacher will model how a number can be composed step by step from all 1’s to the least amount

Materials needed: base 10 blocks, worksheets with 3 or 4 recording spaces, construction paper cut into rectangles and squares (optional)

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of 1’s. Launch: Teacher will model with a number, see example of the number 47, and build it with 10’s and 1’s with the students. Teacher may want to take a picture of the process or build it using construction paper strip and blocks (see poster). During: ● Students will then choose a number (or teacher can give them a number) and they will make and model this

using base 10 blocks, drawings or construction paper version of 10’s and 1’s. ● As students finish their worksheet/picture poster, they may decorate the number to emphasize that the

number stays the same regardless of the groupings. Closure/Extension: Students may share their number posters with a partner or group. Intervention: Teacher has the choice of 2 different worksheets, with either 3 or 4 recording spaces. Notes: Teacher may want to use the language of the fastest way to create a number so the students have to use tens and one and then the slowest way where they use just ones. Teacher may encourage students to show a fancy way where they can get creative and use tens and ones in different ways. Just the language of the slow way and fast way helps them understand there is more than one way to create a number.

(from Pinterest Mrs T’s classroom)

Homework: Different Ways

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Apprentice Task

Fishy Store



Math Objectives: ● Students will decompose two-digit

number into tens and ones. ● Students will add a two-digit number

and a one-digit number to compose ten.

● Students will use drawings and/or manipulatives to show their understanding of the problem.

CCSS-M Standards Addressed: 1.NBT.2a,b,c, 1.NBT.4 Potential Misconceptions Students cannot come up with the correct number of cages. Students cannot find the addend to make ten. Students cannot show their mathematical reasoning in written form.

Launch: Part I of this task will be completed as a whole group activity. The class will work through the problem solving steps below and engage in mathematical conversations to solve this task.

• Use the 3-Read Protocol (from the Math Teaching Toolkit) to introduce this problem. 46 fish have arrived at the aquarium. You need to put the fish into fish tanks. Each fish tank must have ten fish. How many fish tanks do you need? How many more fish do you need in the last tank to make it ten? Use pictures, words, and numbers to show your math thinking. “Draw the number in three different ways: as base 10, number bonds, and in the place value chart” Have the students solve the problem with a partner. Students should work through the problems using the fish cut outs or manipulatives first. It is important to encourage students to work with manipulatives prior to pencil paper because they can easily rearrange the manipulatives to develop a solution. Have the students use math language to explain their thinking. Example: I drew four squares to show my tanks. Next I drew 10 fish in each tank. I knew that ten fish would fit in each tank because I handed them out one by one and ran out of fish. After students finished working on the problem, invite students to share how they come up with the solution. During: Students will now work independently to create their own problem to solve. Each student will roll two dice to create a 2-digit number and choose an animal to use. The 2-digit number identifies how many animals for the problem. Example: A student rolls 62 and chooses a mouse. Their problem will have 62 mice. Each student will write a story about their animal being delivered to the pet store using the provided template. They will have to separate the animals into cages making sure each cage has ten animals. Ask them what will happen to the 2, what needs to be done to the 2 in order for it to go into a tank? Tell students to show representation of their number using the number-bonds. Guide and observe students as they work independently on their own problem. The teacher should remind the students to use pictures, words, and numbers to explain their solutions and justify their thinking. Closure/Extension: After ample work time, have students share their ideas. Discuss the similar plans and the unique plans. This is an open-ended question and will have different combinations of responses.

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Fishy Store


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. Students engage in mathematical conversations to solve math problems. 6. Attend to precision. Students communicate about each task using the prescribed problem solving steps. Structures for Student Learning: Academic Language Support: Vocabulary:

● tens, ones ● Aquarium, tanks

Sentence frames: ● I add ________ to ________ to make ten. ● ___ + ___ + ___ + ___ + ___ equals to ____

Differentiation Strategies: Have students highlight the questions in the problem. Extension Present this problem to the students: You have 54 starfish. How many different ways can you arrange these creatures and always have the same number of starfish in each aquarium. Students can create their own scenarios for others to solve. Intervention Provide students with paper fish and rectangles to represent the aquariums. Allow students to work with a partner. Create a closed activity workmat giving students a structure to complete his/her word problem. Participation Structures (group, partners, individual, other): Whole group, pair, individual

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Lesson Series #2

Lesson Series Overview: Students will practice the term “greater than” and “less than” with 1 and 10 (+/- 1 & +/- 10). Students will learn the terms “equal to”, “greater than”, and “less than” to compare two numbers. By the end of the lesson series, students will be able to represent and compare numbers with relation symbols (>, =, <) and words (“greater than”, “less than”, and “equal to”.) CCSS-M Standards Addressed: 1.NBT.1, 1.NBT.2a, b c,, 1.NBT.3, 1.NBT.4, 1.NBT.5, Time: 5 days


Description of Lesson: Students will practice the term “greater than” and “less than” with 1 and 10 (+/- 1 & +/- 10). Math Talk: Lee has 4 and buys 10 more. Kiana has 17 pencils and loses 10 of them. Who has more pencils now? (Turn and Talk and share their thinking on the chart paper or students can work on a paper and come back to whole group to discuss). Note: This problem gives students a chance to add and subtract 10 using their own methods. At this point in the year, students should feel quite comfortable adding and subtracting 10 with numbers within 20. (Sample Guiding Questions and Responses) 1. Greater (more) than and less than with ones (In a circle with lapboard or whole group) Teacher (T): Ask student(s), “draw symbol to express number 15”. (l …..) T: “How many tens and ones are there?” (1 tens and 5 ones) T: “Show me 1 more than 15.” (Add one more circle or dot.) “What number is it now? Say it in a whole sentence.” Students (S): “1 more than 15 is 16.” T: Draw 15 and 16 in the place value chart. “Look at the chart. What changed and what didn’t? Turn and talk to your partner about why it is so.” (Ones changed from 5 to 6 because we only added 1 more. / 6 is 1 more than 5…) ← “Great thinking class!” 2. Greater than and less than with tens Display the words “greater than, less than, and “equal to” T: Now, how can you show 10 greater than 15? The words “greater than” is like “more than”. Say it in a sentence. (10 greater than 15 is 25.) T: I’m about to write the new number on the place value chart to show 10 greater than 15. Talk to your partner

Number Eating Song “Chomp Chomp!” http://www.teachertube.com/viewVideo.php?video_id=256262 Modified from engageny.org Lesson Module 4 (From page 55) http://www.engageny.org/sites/default/files/resource/attachments/g1-m4-full_module.pdf Visual aids included in this lesson series:

Day 1 Visuals Place Value Charts Day 3 Visuals Alligator (print double sided) Groups of frogs

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about what you think will change and what will remain the same. (The tens changed from 1 ten to 2 tens because we added 10 more. Ones didn’t changed because we added only tens.” T: We added 10 more to 15 to get 25. (Complete the second place value chart with 2 and 5.) *Repeat process with place value chart and symbols until students feel comfortable with the concept. Sequence Example:

● 1 more/10 more than 14 ● 1 less/10 less than 16 ● 1 more/1 less than 36 ● 10 more/10 less than 38 ● 1 more/1 less than 32 ● 10 more/10 less than 53 ● 1 more than 69 & 1 less than 70

3. Independent Practice: Invite students to solve In Class worksheet, Write the Numbers (2 pages). 4. Closure in Group Discussion Possible Guiding Question at the closing of this activity: - Which digit changed when you went from _____ to _____? - What happened to the digits when you went from _____ to _____? - (Do you remember what is the “digit”?) Exit Slip: 3rd page of worksheet Notes: - Students may need to review how to express the numbers in symbols. - The term “greater than” is not used right away in this class. The term is introduced to later part of this lesson. Sentence Frames 1 greater/less than _____ is _____. 10 greater/less than _____ is _____. Ones changed from _____ to _____ because we added/subtracted only 1. Tens changed from _____ to _____ because we added/subtracted only 10.

Classwork: Write the Numbers (3 pages) HW: Quick Tens (2 pages)


Description of Lesson: Compare two quantities, and identify the greater or lesser of the two given numbers. Math Talk: Lisa has 3 boxes of 10 crayons and 5 extra crayons. Sally has 19 crayons. Sally says she has more crayons, but Lisa disagrees. Who is right? (Turn and Talk and share their thinking on the chart paper or students can work on a paper and come back to whole group to discuss). - Provide/display place value chart so that students can use it on the personal whiteboard.

Materials: (T/S) Personal whiteboards or use In class visual place value chart from Day 1 visual.

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Activity: Beep Counting by Ones Say a series of four numbers but replace one of the numbers with the word beep (e.g., 1, 2, 3, beep). When signaled, students say the number that was replaced by the word beep in the sequence. Scaffold number sequences, beginning with easy sequences and moving to more complex ones. Choose sequences that count forward and backward by ones and tens within 40. * Suggested sequence type: 5, 6, 7, beep; 10, 9, 8, beep; 21, 20, 19, beep; 13, 14, 15 beep; 0, 1, 2, beep; 19, 18, 17, beep; 4, 3, 2, beep; 38, 39, 40, beep. Continue with similar sequences, changing the sequential placement of the beep. 1. Count Coins Warm-up (On a rug) Note: We are not teaching how to count coins. This provides practice with recognizing pennies and dimes and counting with abstract representations of tens and ones. Coins (dimes and pennies) are used as a unit. This prepares for later lesson discussion. If you are not comfortable using coins, you are welcome to use other things that occur in tens (such as bowling pins, longs and cubes, hands and toes, and etc.).

a. Place dime to show students. Tell them this is same as 10 (10 pennies). b. Place penny next to dime one by one as you count, “11, 12, 13, 14, 15...20” c. When it becomes 20, take 10 pennies off and add one more dime next to the first dime. d. Repeat the steps b & c until you reach up to 40.

2. Concept Development (Move to their desk or stay on the rug) T: (Display a ten-stick to students) How many ones, or individual cubes, are in a ten-stick? (10 ones) T: Lay down 10 cubes into 5-groups (see picture) next to the ten-stick and ask, “Are these same or different?” (Answers may vary- They are the same amount, The ten stick is made up of 10 cubes, They are different because one of them is a ten and the other is 10 ones…) T: They are worth the same amount; they have same value. They are both made of 10 cubes. T: (Place dime) Now, how many pennies have the same value as one dime? Who remembers from last warm-up? (10 pennies). T: Lay down 10 pennies into 5-groups (like cubes) next to the dime, directly below the 10 cubes. “What is the same or different about these two groups of coins?” (Answers may vary - 10 pennies are worth 10 cents, The pennies group is made up to 10 coins, The coins are different….) T: Great observations! So 1 ten-stick has the same value as 10 individual cubes. And 1 dime has the same value as……..? (10 pennies!) T: I can take a ten-stick and break it apart into 10 individual cubes. Can I do the same with a dime? (No, dime is just 1 coin.) T: That’s another difference between the ten-sticks and dimes. The ten-stick has a value of 10 ones and we can

Modified from engageny.org Lesson Module 4 (From page 68 ~) http://www.engageny.org/sites/default/files/resource/attachments/g1-m4-full_module.pdf Comparison Cards (double sided) Classwork: Place Value Charts (3 pages) Day 2 HW: Place Value Charts (2 pages)

Materials: pennies and dimes.

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see why. It’s actually made up of 10 ones, and we can see them. The dime has the same value as 10 pennies but it’s just 1 coin. There are no pennies hiding inside. But it still has the same value as 10 pennies. T: (Display a ten-stick and 3 cubes.) How many tens and cubes are there? (1 ten 3 ones) T: How can I use my coins to show the same number as the cubes? Show 1 ten 3 ones with your coins, the share with your partner. T: Circulate and address any misconceptions while you circulate. Some students may want to put down 13 pennies but won’t be able to since each student is only given 10 pennies. T: “I noticed that some students wanted to lay down 13 pennies, but found that they didn’t have enough. Do you have any suggestion to help with this problem?” (Use dime for ten, then use 3 pennies for 3 ones.) -- Repeat the process using the suggested sequence: 15, 18, 28, 31, 40, 39 3. Independent Practice: Day 2 Classwork (2 pages). - Model 1-2 problem (one with object and another with coins) before you send students off to do Individual Practice. - Some students may need more support on the task where students require to draw or cross off tens or ones to figure out the answer. 4. Closure in Group Discussion Possible Guiding Question at the closing of this activity: - If you show that amount with dimes and pennies, how many each coin would you use? - If you show that amount with tens and cubes, how many each tens and cubes would you use? - How is problem #__ different from problem #__? Exit Slip: 3rd page of Classwork Notes: In this Lesson, we are not teaching how to count coins. This provides practice with recognizing pennies and dimes and counting with abstract representations of tens and ones. Coins (dimes and pennies) are used as a unit. This prepares for later lesson discussion. If you are not comfortable using coins, you are welcome to use other things that come in tens (such as bowling pins, longs and cubes, hands and toes, and etc.). Sentence Frames: ___ is 1 less than ___. ___ is 1 more than ___. ___ is 10 less than ___. ___ is 10 more than ___. Ones changed from _____ to _____ because we added/subtracted _____. Tens changed from _____ to _____ because we added/subtracted _____. ____ is ____ tens and ____ones.

Materials: (T) 10 pennies and 4 dimes, 4 tens and 10 cubes, or linker cubes 40 (10x4) and 10 individuals Coin Chart to show value for dime and pennies. Visual provided in the binder. However it may be better to have a colored chart. (S) 4 dimes and 10 pennies and personal whiteboard for each.

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Description of Lesson: Compare quantities and numerals from left to right. Students will practice the term “greater than” and “less than” with 1 and 10 (+/- 1 & +/- 10). Math Talk: Anton Picked 25 strawberries. He picked some more strawberries. He had 35 strawberries. How many strawberries Anton picked? (Turn & Talk) Put place value chart out and encourage them to use them in their discussion. Activity: Beep Counting by Ones and Tens Say a series of four numbers but replace one of the numbers with the word beep (e.g., 1, 2, 3, beep). When signaled, students say the number that was replaced by the word beep in the sequence. Scaffold number sequences, beginning with easy sequences and moving to more complex ones. Choose sequences that count forward and backward by ones and tens within 40. (Suggested sequence type: 10, 11, 12, beep; 20, 21, 22, beep; 20, 19, 18, beep; 30, 29, 28 beep; 0, 10, 20, beep; 1, 11, 21, beep; 40, 30, 20, beep; 39, 29, 19, beep. Continue with similar sequences, changing the sequential placement of the beep.) (Sample Guiding Questions and Responses) 1. Write (or Display the Visual page 1) two sequences from the Beep Counting (if you have done as Math Talk). Example: 10, 11, 12, 13 and 40, 30, 20, 10 Teacher (T): You said these numbers at Math Talk. What is different about them? (One set goes up and one set goes down. One we count up by ones and one set we count down by tens.) T: “What do you mean it goes up?” (The numbers get bigger.) T: “Let’s use our math language to explain that. Who remembers the words we have been using this week that compare two numbers?” (Greater than, Less than, Equal to) T: “Are you saying this number (pointing 10) is less than or greater than 11 (pointing 11)?” (Less than) T: “What about the next numbers? 11is…” (less than 12) T: “Let’s say the whole sequence use the comparison words as we compare each number in the set.” S/T: (Continue pointing to each number.) “10 is less than 11. 11 is less than 12. 12 is less than 13.” T: “When we compare numbers using words, we read from left to right, just like when we are reading a sentence in a book or when we are reading an equation.” T: “40, 30, 20, 10 is in a different order. Turn to your partner and discuss which word we will use when comparing them. Remember we start from 40 (left).” (Greater than) T: Let’s read the whole sequence, using greater than to compare the number pairs as we go. S/T: 40 is greater than 30. 30 is greater than 20. 20 is greater than 10.

Modified from engageny.org Lesson Module 4 (From page 94) http://www.engageny.org/sites/default/files/resource/attachments/g1-m4-full_module.pdf

Classwork: Quick Tens (2 pages) HW: Numbers in Order (2 pages)

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T: Display Comparison Cards (Visual page 2 or you can write on post-its), greater than, less than, and equal to. Write two sets of numbers on a board for class. Ask which words goes between the numbers. Suggested Sequence:

● 14 and 17 ● 3 tens and 2 tens ● 24 and 38 ● 2 tens 9 ones and 3 tens ● 55 and 59

T: “Does anyone noticed anything interesting about which card we have been using when we are comparing the these numbers from left to right?” (Used only “less than” card) “Why is it?” (The numbers on the left is smaller than the number on the right.) T: Display 34 and 28. “Which digit in each number did you look at first to compare them? (Tens place - for being the bigger digit) 2. Independent Practice: Day 3 In class worksheet Read directions for the work. Three of the tasks (Items 3-5) are to order the numbers from least to the greatest and the greatest to the least. Item 5 is a challenge question. It is important to discuss about the findings at the closure discussions. Intervention: Do one item together before you send the students to do independent work. 3. Closure in Group Discussion on the Individual Work Possible Guiding Question at the closing of this activity: - Which number was the least number of all at question 3? - Which number was the greatest number of all at question 4? - What are the numbers that you come up for question 5? Anyone would like to share? Notes: - Make a laminated set of comparison cards as they will last longer. They can keep the cards for other lessons. Sentence Frames: ___ is 1/10 less than ___. ___ is 1/10 more than ___. ___ is less than ___. ___ is more than ___. ___ is greater than ___. Ones changed from _____ to _____ because we added/subtracted ____. Tens changed from _____ to _____ because we added/subtracted ____. ____ is ____ tens and ____ones.

Lesson VIsual page 1

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Description of Lesson: Use the symbols >, =, and < to compare quantities and numerals. Math Talk: Use the digits 9, 6, 4, and 1 to make 4 different two- digit numbers less than 50. Write them in order from least to greatest. Turn and Talk and share what your partner came up. Activity: Digit Detective Note: This activity reviews the term digit and relates it to place value. Write a number on your personal white board, but do not show students. T: The digit in the tens place is 2. The digit in the ones place is 3. What’s my number? (23) T: What’s the value of the 2? ( 20 - tens) T: What’s the value of the 3? (3 - ones) T: The digit in the tens place is 1 more than 2. The digit in the ones place is 1 less than 2. What’s my number? (31) T: The digit in the ones place is equal to 8 – 4. The digit in the tens place is equal to 9 – 7. What’s my number? (24) As in the above example, begin with easy clues and gradually increase the complexity. Give students the option to write the digits on their place value chart as you say the clues. 1. introducing symbols >,=,< with alligator picture Post a group of 2 frogs and a group of 10 frogs with enough room in between the groups to place the alligator picture. (Sample Guiding Questions and Responses) T: “Here is an alligator. He is really hungry. Notice his open mouth. (Trace the shape of mouth with your finger.) Would this hungry alligator rather eat 2 frogs for dinner, or eat 10 frogs for dinner?” (10 frogs!) T: What would we say if we started comparing the numbers from the left starting with the number 2?” (2 is less than 10) -- Place alligator “less than” between the frogs facing the group of 10 frogs. T:(Post a group of 15 frogs and a group of 10 frogs in the same manner.) “Which group of frogs will the hungry alligator want to eat this time?” (15 frogs!) T: “ Can you explain how you know that?” (15 is 1 ten and 5 ones. 10 is just 1 ten./ I can show it with ten sticks.) -- Place alligator “greater than” to show the alligator facing the 15 frogs. 2. Practice with numbers (not with frog pictures) Repeat the process above with alligator pictures. Suggested Sequence of Numbers:

● 1 ten and 1 ten 6 ones ● 30 and 20 ● 4 tens and 3 tens 8 ones ● 39 and 32


Materials: (T/S) Personal whiteboards or use In class visual place value chart from Day 1 visual.

Alligator Picture

Materials: (T) Alligator pictures (double-sided), comparison cards. Group of frogs pictures. (S) Comparison cards, personal whiteboards Classwork: Comparisons (2 pages) HW: Comparisons (2 pages)

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● 14 and 40 ● 23 and 32 ● 50 and 93

3. Independent Practice: Day 4 In class worksheet. Read directions for the work. 4. Closure in Group Discussion on the Individual Work Possible Guiding Question at the closing of this activity: - What > signs? (greater than) What < signs? (less than) - Which number you start with when you compare the number? (left) - Say the equation for the item ____. Notes: Intervention & Support When comparing numbers, students tend to express the comparison by starting with the greater number, regardless of the order of the numbers on the page. For example, if the numbers 3 and 30 were displayed on the board, students may say 30 is greater than 3. The statement is true, even though the student was not comparing the number left to right. The best support we can give students is to affirm their true remark, and ask them to compare the numbers starting with the one on the left, pointing to the 3. Examples of this are embedded in the Sample Guiding Questions. Sentence Frames: ___ is 1/10 less than ___. ___ is 1/10 greater than ___. ___ is less than ___. ___ is greater than ___. __ is equal to __ __ is the same as __ Ones changed from _____ to _____ because we added/subtracted ____. Tens changed from _____ to _____ because we added/subtracted ____. ____ is ____ tens and ____ones.


Description of Lesson: Use the symbols >, =, and < to compare quantities and numerals. Math Talk: Carl has a collection of rocks. He collects 10 more rocks. Now he has 31 rocks. How many rocks did he have in the beginning?


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● Use place value charts to show how many rocks Carl had at the beginning. ● Write a statement in your journal comparing how many rocks Carl started and ended with, using one of

these phrases: greater than, less than, equal to. 1. Present Number Story: Elaine had 19 blueberries and ate 10. Mike had 13 and had picked 7 more blueberries. Compare Elaine and Mike’s blueberries after Elaine ate some and Mike picked some more.

● Use words and pictures to show how many blueberries each person has.. ● Use the term greater than, less than, equal to in your statement.

(Sample Guiding Questions and Responses) - What is a keyword/clue to understand if I have to add or subtract in the number story? (ate --- subtract, picked & more --- addition) - Who has more at the end? Say it in the sentence. (Elaine has less blueberries than Mike./Mike has more blueberries than Elaine.) - How many blueberries Elaine has? (9, 19-10=9) - How many blueberries Mike has? (20, 13+7=20) * If the question seems too much for the students, invite them to work in pairs and let one student be Mike, the other Elaine. (Or turn and talk to work on the problem with partner.) 2. Practice More with Symbols T: Write the numbers from the number story (9 and 20). T: Which number would be the hungry alligator want to eat? (20) T: (Place alligator “less than” symbol card) why? (9 is less than 20, Mike has 0 ten but Elaine has 2 tens.) T: Today, we will use math symbols to compare numbers. (Write numbers & symbol under the alligator symbols, “ 9 < 20” Display/refer the symbol with terms visual from Day 3). T: What do you notice is similar between the alligator equation and equation with symbol? Turn to your partner and talk about it. (Turn and Talk) S: The symbol looks like the alligator’s mouth. T: We call this symbol the less than sign. T: (Write number 38 and 15 on board.) Can you figure out which symbol we will use between these numbers? (Turn and Talk quickly --- the greater than sign.) T: We need to place the greater than sign, because 38 is greater than 15. It looks like this. I will draw on the board. Can you draw that in the air with me? (Students draw in the air). T: Let’s erase the teeth of your alligator symbols (if students drew them on their comparison cards). We are going to use real symbols! 3. Individual Work: Day 5 In class worksheet. Read directions for the work.

Math Talk: student response sample

1. Number Story

Classwork: Comparisons (2 pages) HW: Comparisons (2 pages)

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4. Closure in Group Discussion on the Individual Work Possible Guiding Question at the closing of this activity: - What do the > signs mean? (greater than) What do the < signs mean? (less than) - Which number do you start with when you compare the numbers? (left) - Say the equation for the item ____. Exit Slip: 3rd page of Worksheet Notes: Practicing with numbers, coins, tens and cubes may needed to further their understanding the concept. Sentence Frames: ___ is 1/10 less than ___. ___ is 1/10 greater than ___. ___ is less than ___. ___ is greater than ___. ___ is equal to __ ___ is the same as __ Ones changed from _____ to _____ because we added/subtracted ____. Tens changed from _____ to _____ because we added/subtracted ____. ____ is ____ tens and ____ones.

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Expert Task

Silly Symbols


Mathematics Objectives and Standards

Framing Student Experience

Math Objectives: ● Students will understand the order of

counting numbers and their relative magnitudes.

● Students will think of whole numbers between 10 and 100 in terms of tens and ones.

● Students will compare two numbers by examining the amount of tens and ones in each number using words, models and symbols greater than (>), less than (<), and equal to (=).

CCSS-M Standards Addressed: 1.NBT.1, 1.NBT.2a,b,c, 1.NBT.3 Potential Misconceptions Students should be familiar with representing and comparing numbers. The symbols will be a new concept for most students and there should be ample amount of time allotted for practice. It is important that students are connecting the language with the symbols and not a trick. Often when students learn to use an aid (Pac Man, bird, alligator, etc.) for knowing which comparison sign (<, >, = ) to use, the students don’t associate the real meaning and name with the sign. The use of the learning aids must be accompanied by the connection to the names: < Less Than, > Greater Than, and = Equal To.

Materials needed: ● bags of 90 - 100 objects (colored counters, buttons, ribbons,1-inch tiles, beans, noodles: same object in

each bag, 1 bag for each partnership ● Silly Symbols recording sheet ● number line to at least 100 (classroom number line)

Launch: ● Pass out one bag to each set of partners that were prepared before the lesson. ● Provide a student number line or remind students of a number line in the classroom for reference. ● Instruct students to empty the contents of their bag on their desk and separate the objects into 4 piles

(the piles do not have to be equal). ● Students will count the number of objects in the first pile and record that number on the “Silly Symbols”

recording sheet. ● Ask the students: How are you counting your manipulatives? Is there another way? How do you keep

track of what has been counted? ● As you observe students counting, look for efficient counting strategies. For example, you may observe

some students counting by 2’s, 3’s, 5’s, 10’s etc. Allow students to choose their own counting strategy and picture representation.

During: ● Students will do the same for the objects in the 2nd, 3rd and 4th pile. ● Remind students that they need to show that number using the number and a picture representation.

The students will then identify where the numbers live on the number line. The visual location of these numbers on a number line will help students understand the size of each number when comparing.

● Students will complete the sentences at the bottom using the symbols. There should be practice with completing these at the beginning of the lesson. Students can reference the numbers on the number line when reading the sentences aloud to check their work.

Closure Come back to whole group. Have 2 or 3 partners share some information from their sheets. Ask partnerships share any counting strategies they may have used. How did they determine >, < = in their comparisons. Extension Play the game “Silly Symbols”. Students will play the game with a partner. Each pair will need a recording sheet, brown bag with 90-100 objects game board and the 3 symbols cut out. A student number line may also

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More importantly, students need to begin to develop the understanding of what it means for one number to be greater than another. In Grade 1, it means that this number has more tens, or the same number of tens, but with more ones, making it greater. Additionally, the symbols are shortcuts for writing down this relationship. Finally, students need to begin to understand that both inequality symbols (<, >) can create true statements about any two numbers where one is greater/smaller than the other, (15 < 28 and 28 >15).

be provided to aid in comparing numbers. Player 1 will reach their hand in the bag, pull out a handful and count the number of objects. Place the objects under player one of the Silly Symbols game board. Player 2 will repeat this same process. The players will decide together which symbol to place in the middle section to make the number sentence true. The students will then identify where the numbers live on the number line. The visual location of these numbers on a number line will help students understand the size of each number when comparing. Both players will then record the information on their own game sheet. In the last column, the students will create an addition sentence combining the two sets for the total sum of pieces. Place the manipulatives back in the bag and repeat for round 2-10. After the students have completed this game, gather in a common area. Allow the students to read some of their number sentences aloud and share their experiences with this game. Several practice opportunities are needed with reading the symbols aloud for the students to build a deep understanding. The teacher can gather assessments through informal observations, conversations with individual students, and the recording sheet responses.

Silly Symbols


Focus Standards for Mathematical Practice: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. Structures for Student Learning: Academic Language Support:

Vocabulary: greater than / less than / equal to / names of the manipulatives used Sentence frames:

● __ is greater than __ ● __ is less than __ ● __ is equal to __ ● __ is the same as __

Differentiation Strategies: Extension

● Students can write a mathematical story with at least two different comparisons. Students will need to identify the idea of the story, the numbers to be used and the comparisons with words and representations. The students may illustrate the story when complete.

Intervention ● Students can work with numbers smaller than 30, then progress to larger numbers once they have developed some experience with smaller quantities. ● Students can use the 10s and 1s manipulatives (base 10 blocks) to assist in visually seeing the difference in the quantities of each number.

Participation Structures (group, partners, individual, other): ● whole group ● partners ● you may want to strategically pair your students (an above basic student with a basic or below basic student) or form a small group for intervention work

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Lesson Series #3 Lesson Series Overview: In this lesson series, students will continue with their understanding of place values. Students will use strategies to locate, add and subtract numbers ten more, ten less, one more and one less. Students will further strengthen their adding skills by adding a pair of two digit numbers with the ones digit sum less than ten. CCSS-M Standards Addressed: 1.NBT.1, 1.NBT.4, 1.NBT.5, 1.NBT.6 Time: 5 Days


Description of Lesson: In this lesson, students will be able to build numbers with an understanding of place value in tens and ones and locate the numbers on a number grid. Students will use strategies to locate numbers ten more, ten less, one more, and one less on a number grid. Whole Group: Show students the 99 chart on an overhead projector or ELMO. Cover the number 17. How can we identify a number that is one more than 17? Model for students where you place the middle square on the 5 square reader, 17. Explain how you can use this reader to help with locating 10 more, 10 less, 1 more and 1 less. Show the students the connection from number to equation. Provide the addition equation and ask the students if they see a connection with one more. 17+1=18. How can we identify a number that is one less than 84? Connect counting back one to subtraction and show how the equation represents this idea 84-1=83. Repeat the process to locate 10 more and ten less. Pass out one 5 square reader, copied on clear transparency paper, to each student and a 99 chart. (there are 6 on a page, copy on transparency paper and cut to give one to each student) Allow students to explore with these readers using several different numbers. Ask the students what happens when your reader is on the edge. Model and explore this concept with your students. Individual: Give each student a 0-9 spinner or dice, 99 chart, one 5 square reader and a copy of the 10 More/Less 1 More/Less recording sheet. Students will work independently for this activity. The student will need to spin the spinner twice to create a 2-digit number. Write this number in the middle of the 5 square reader on the recording sheet.

https://www.georgiastandards.org Materials:

● number grid ● More/Less transparency sheet (each student

will need one 5 square reader) ● More/Less recording sheet ● Clear counters ● 0-9 spinner or 0-9 dice

HW: Number Grids (2 pages)

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Students will then use the 5 square reader on transparency paper to find the numbers that are 10 more, 10 less, 1 more and 1 less on the 99 chart. Complete all ten problems on the recording sheet. Although students are working independently, it is beneficial to allow students to have conversations while completing this activity. The conversations surrounding the concept of more and less can be very helpful in building a deeper understanding. While students are working, walk around and ask students to give the related addition or subtraction sentence to a number on their recording sheet. Note: This is Part III of Task 9 in Common Core Georgia Performance Standards Framework.


Description of Lesson: In this lesson students will count forward and backward by 1s and 10s, identify and extend patterns using a number grid. They will use these skills to solve number grid puzzles. Getting Started: Math Message Give each student a quarter of the sheet Number Grid Pieces (Math Masters page 258). Have them fill in the missing numbers. When done, gather to the rug, project or draw piece on the board. Have students fill in the missing numbers. Discuss the patterns in the problem:

● Which digit repeats in the 1s place? ● What is happening to the digits in the 10s place? ● (Point to the digit in the 10s place.) What number does this digit represent?

Tell the students they will use patterns on the number grid to solve number grid puzzles. Whole group (continued) Repeat the process using different shaped pieces covering portions of the number grid. Ask children to close their eyes. Use a T-shaped piece to cover a portion of the number grid poster. Fill in one cell with the number that corresponds to the number under it on the grid. (Begin by using only horizontal- or vertical-shaped pieces. Add diagonal-shaped pieces.) Discuss how to fill in the remaining numbers on the T-piece. Write the missing numbers. Partners Have students cut out the number grid pieces from Activity Sheet 16 (tagboard sheets at the end of Math Journals). Have students work in pairs. While partner A closes his/her eyes, Partner B places a number grid piece on the number grid on Activity Sheet 16 so that it covers whole cells. Partner A fills in the covered numbers and ten lifts the piece to check answers. Partners trade roles and repeat the process. They will continue until all the pieces have been used.

Everyday Mathematics Unit 9.3

Number Grid Poster EM Master p. 258 Number Grid Puzzle EM Journal Activity Sheet 16 Number Grid Shapes EM Journal Activity p. 180 Number Grid Puzzles EM Journal Activity Sheet 15 Number Grid HW: EM Homelink 9.3 Number Grid Puzzles Enrichment: Math Masters, page 261, Solving Number Codes

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Individuals/Partners Give directions to complete Math Journal 2, page 180. Students will write the missing numbers on their number grid puzzles. Have them check their work using the number grid on Activity Sheet 15. Closure Re-group to rug. Ask what patterns they noticed on the number grid that helped them solve the puzzles, did they have any challenges or insights. Differentiation Enrichment: Math Masters, page 261, Solving Number Codes To apply their understanding of patterns on the number grid, have students solve arrow-path problems. Children use the key to decipher number codes. The arrows direct their jumps on the number grid from a starting point to the final answer. Students fill in missing arrows and write their own codes for a partner to solve. Intervention: Pin the Number on the Number Grid (exploration of patterns on the number grid) Have children look closely at the number grid poster and describe the patterns they see in the numbers. Ask : Where are numbers with 5 in the ones place? With 5 in the tens place? If no one mentions the following, be sure to include some version of each:

● The numbers get larger as you move down. ● The numbers get larger as you move to the right. ● The tens digit increases as you move down. ● The ones digit stays the same down a column. ● The tens digit stays the same across a row.

Next, blindfold one student. Tell the children a number between 1 and 100. The blindfolded child tries to place a sticky note on the poster as close to the selected number as possible. The child may ask for “hints” from other students. The hints have to be in terms of the patterns that were described: e.g., “You have to add tens.”


Description of Lesson: In this lesson students will practice adding and subtracting 10 on a number line. Whole Group Review addition and subtraction on the number line with the following story: Sammy had 8 pencils. He

Materials: Base-10 blocks Adapted from: K-5MathTeachingResources.com

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got 3 more from his mom. How many pencils does he have now? Model and demonstrate how to use the number line to find the answer: Say: Sammy had 8 pencils, so I’ll start at 8. He got 3 more, so I count up. I’ve landed on 11. That’s how many pencils Sammy has now.

Then write the equation for the problem: 8 + 3 = 11. Model a few more problems with this number line. Next, introduce the blank the number lines and model the process:

Tell students they will need to roll a die. Record the number they roll on the first space on the left on the number line. Add 10 to their starting number and record the new total. Continue adding 10 until they have ten numbers in the sequence.

Tell the students to record a 2-digit number with a 9 in the tens place on the last space on the number line. Subtract 10 from the starting number and record the new number. Continue subtracting 10 until you have ten numbers in the sequence. Individually: Students will practice adding and subtracting using the provided worksheet. Note: Please provide Base-10 blocks as manipulatives if needed. Closure: Regroup and ask students share a couple of problems on the overhead projector.

TLS Books http://www.tlsbooks.com/pdf/addandsubtracttens.pdf Everyday Mathematics Classwork: Adding on a Number Line (2 pages) Adding and Subtracting Tens (2 pages)

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Description of Lesson: This lesson continues to provide opportunities for students to develop proficiency in adding and subtracting 10s. Introduce the Number Grid Game Project the number grid (Math Masters, page 249) to explain the rules of the game. The objective of the game is to land on 110 with an exact roll. Directions: 1. Players place their markers at 0 on the number grid. 2. Take turns. When it is your turn: * Roll the die. * Use the table to see how many spaces to move your marker. * Move your marker that many spaces. Model the game with a student as your partner: Variations: � A player lands on 110 or past to win. � To practice subtracting 10s, start at 110 and move back to 0. � Modify the Roll/Spaces table. For example, allow the same choice for 3 through 6 that the current table offers for 1 and 2. � Play the game with 2 dice.For rolls of 7 to 12, move 7 to 12 spaces, respectively. This version provides practice with the addition facts and with adding 11 and 12. Closure: Regroup - Ask students how times they played the game with the partner. Ask them what strategies they used to play the game without having to count the spaces one by one. Notes: Everyday Mathematics

EM Student Reference Book p.142: Number Grid Game Math Masters, p. 249 - number grid (1 per 2 students) Homework: Home Link 9.1 Materials: dice, counters


Description of Lesson: In this lesson students again extend their learning from Day 4, students add pairs of two-digit numbers in which the ones digits sometimes have a sum greater than 10, recording their work using various methods based on place value. Concept Development (whole group): T: (Write 40 + 30 = ? on chart paper.) On your personal board, write the number sentence and replace

the question mark with the missing number. (Wait as students complete the task.)

Materials: Personal whiteboards counting manipulatives Classwork: Solve Using Quick Tens

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T: 40+30 is...? S: 70. T: Explain how you know that 40 + 30 equals 70. You can draw or write on the chart paper to explain

your thinking. S: first, you draw 4 tens and then 3 tens, and that’s 7 tens or 70. Four tens plus 3 tens is 7 tens. That’s

70. In the Place Value Chart, you add 3 tens to the 4 tens you have. T: (Draw a line to start a new section of the chart paper. Write 45 + 30 = ?) On your personal board,

write this number sentence and replace the question mark with the solution. S: 45 + 30 is 75 T: Share with you partner how you got the answer. (give them a minute to share their strategies.)

Regroup and ask for student volunteers to show how they got their answer. S: I started at 45 and counted on ten 3 times. 45, 55, 65, 75. T: Does anyone have a question or comment about the counting on solution? S: I broke 45 into 40 and 5 with the number bond, and then I added 40 and 30 first, 70, and added on 5

to make 75. T: Did anyone solve 45 + 30 a different way? S: I thought of the place value chart, and just added 3 tens to 4 tens and left the 5 ones alone. That

gave me 75 T: It is important to really listen to your friends’ solution strategies so you can comment and ask

questions. Provide time for students to solve the following suggested sequence of problems. Students who would benefit from more concrete or pictorial support may use linking cubes in ten-sticks and ones, or quick ten drawings. 51+40 24+60 50+38 Individual: Pass out the following worksheet for further practice of the concept. Notes: Adapted from EngageNY Module 6 - http://www.engageny.org/sites/default/files/resource/attachments/math-g1-m6-full-module.pdf

HW: Solve Using Pictures (2 pages)

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Milestone Task

What Do You Know?



Math Objectives: ● Students will understand the order of the counting numbers and their

relative magnitudes. ● Students will unitize a group of ten ones as a whole unit: a ten. ● Students will compose and decompose numbers from 11 to 19 into

ten ones and some further ones. ● Students will think of whole numbers between 10 and 100 in terms of

tens and ones. ● Students will compare two numbers by examining the amount of tens

and ones in each number using words, models and symbols greater than (>), less than (<) and equal to (=).

● Students will create concrete models, drawings and place value strategies to add and subtract within 100. (Students should not be exposed to the standard algorithm of carrying or borrowing in first grade).

● Students will use place value understanding and properties of operations to add and subtract.

● Students will use concrete models, drawings and place value strategies to subtract multiples of 10 from decade numbers (e.g., 30, 40, 50).

CCSS-M Standards Addressed: 1.NBT.1, 1.NBT.2, a,b,c, 1.NBT.3, 1.NBT.4, 1.NBT.5, 1.NBT.6 Potential Misconceptions

● Students may confuse <,>,=. ● When thinking about numbers on a number grid, students may

confuse -1/+1 (left/right) and -10/+10 (up/down).

This task is designed to take 2 days: parts 1 and 2 on day 1, parts 3 and 4 on day 2. It was felt that trying to get all parts done in one sitting could be too much for first graders, even at the end of the year. This is up to teacher choice. Launch:

● Bring whole group to the rug. ● Show assessment to students on elmo ● Read the directions for the parts they will be working on during this

session. ● Have students echo read the directions. ● Review vocabulary as needed. ● Send students off to work independently ● Students will not have access to number grids for this task.

During: Teacher will circulate, answering questions concerning directions (not questions about how to get answers). Teacher can pull students needing interventions. Closure/Extension: At the end of math time, bring students together on the rug. Debrief task, what was easy, what was challenging. Repeat process with parts 3 and 4 on day 2.

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What Do You Know?


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure. Structures for Student Learning: Academic Language Support:

Vocabulary:

● sequence ● greater than, less than, equal to ● tens, ones

Sentence frames:

Differentiation Strategies: Extention:

● Have finished students work (in pairs or individually) to find the solution to Challenge Problem. Intervention

● Struggling students may need to be pulled into a small group, to work with the teacher guidance. Supply a number grid for support. Make note of interventions used.

Participation Structures (group, partners, individual, other):

● Whole group for directions and closure. ● Individual for written tasks.

Note: This is the last formal math activity for the school year. Everyday Math Unit 10.7 offers activities for place value practice and extensions using three digit numbers greater than 120 and into 4 digit numbers (this especially applies to number scrolls).

sfusd mathematics core curriculum development project · one grain of rice: a mathematical folktale...

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