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Unit 1- Place Value UNDERSTANDING PLACE VALUE (10 DAYS)

WHOLE NUMBER PLACE VALUE- COMPARING WHOLE NUMBERS-ROUNDING WHOLE NUMBERS

1. Overview

Students will extend their understanding of place value related to multiplying and dividing by multiples of 10, read and write numbers using a variety of

number forms, compare, and round two multi-digit numbers less than or equal to 1,000,000.

Manipulatives/Materials: place value chart, base ten blocks, number line template (vertical/horizontal)

FOCUS

STANDARDS 4.NBT.A.1 Recognize that in a multi-digit whole number less than or equal to 1,000,000, a digit in one place

represents ten times what it represents in the place to its right. Examples: (1) recognize that 700 ÷ 70 = 10; (2) in the number 7,246, the 2 represents 200, but in the number 7,426 the 2 represents 20, recognizing that 200 is ten times as large as 20, by applying concepts of place value and division.

4.NBT.A.2 Read and write multi-digit whole numbers less than or equal to 1,000,000 using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

4.NBT.A.3 Use place value understanding to round multi-digit whole numbers, less than or equal to 1,000,000 to

any place.

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STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

FOUNDATIONAL

STANDARDS

2.NBT.A.1 3.OA.B.5 3.OA.C.7 3.NBT.A.2 3.NBT.A.3

WHOLE NUMBER PLACE VALUE- COMPARING WHOLE NUMBERS-ROUNDING WHOLE NUMBERS

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 3: Lessons 3-1, 3-2 Topic 3: Lessons 3-3, 3-4 Topic 3: Lessons 3-5

*4-2 (Topic 4)

Module 1: Topic A

Lesson 2, Lesson 3, Lesson 4

Module 1: Topic B

Lesson 5, Lesson 6

Module 1: Topic C

Lesson 7, Lesson 8, Lesson 9, Lesson 10

Unit 1, Lessons 1 and 2 Unit 3, Lessons 11 and 12

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

Guidebook: Lessons:

Card Game: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-instructional-tasks.pdf?sfvrsn=5

LearnZillion: Lessons:

Round numbers to a specified place on a number line: https://learnzillion.com/lesson_plans/6255 Understand the value of a digit in a multi-digit number: https://learnzillion.com/lesson_plans/4635 Understand place value: multiplying by a power of 10: https://learnzillion.com/lesson_plans/6646 Understand that place value increases ten times with each shift to the left in a multi-digit number: https://learnzillion.com/lesson_plans/4630 Understand relationships between digits and their place value: https://learnzillion.com/lesson_plans/7426 Compare numbers using the symbols <, >, and =: https://learnzillion.com/lesson_plans/8016

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Read and write numbers in expanded form: https://learnzillion.com/lesson_plans/8840 Read and write numbers in word form: https://learnzillion.com/lesson_plans/8827 Round numbers to the leading digit using a number line: https://learnzillion.com/lesson_plans/5984

Illustrative Mathematics: Tasks:

What’s My Number: https://www.illustrativemathematics.org/content-standards/4/NBT/A/tasks/301 To regroup or not to regroup: https://www.illustrativemathematics.org/content-standards/4/NBT/B/tasks/1189

Discovery Education: Videos:

Whole Numbers and Place Value: https://app.discoveryeducation.com/learn/videos/7A5D0798-2839-4220-886F-D27236C6B30C?hasLocalHost=false

Math Mansion: Show 22: Hundredths and Thousands: https://app.discoveryeducation.com/learn/videos/CF73976C-09FD-4530-AC69-0966F425D75F?hasLocalHost=false

WHOLE NUMBER PLACE VALUE- COMPARING WHOLE NUMBERS-ROUNDING WHOLE NUMBERS

3. Activities for Understanding

SUGGESTIONS

Place Value Relationships:

Students will use the following chart to understand place value as it relates to multiplying and dividing by multiples of 10.

Hundred Thousands

Ten Thousands Thousands Hundreds Tens Ones

4 4 4 4 4 4

The value of this 4

is __________.

The value of this 4

is __________.

The value of this 4

is __________.

The value of this 4

is __________.

The value of this 4

is __________.

The value of this 4

is __________.

Display the chart above. Pose example questions to students:

o What is the value of the 4 in the thousands place? (4,000) o What is the relationship between the 4 in the hundred thousands place and the 4 in the ten thousands place?

(The value of the 4 in the hundred thousands place is 10 times greater than the value of the 4 in the ten thousands place.)

Repeat procedure with different numbers. (888,888 - 707,322 - 655,294)

SUGGESTIONS

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Have students write number sentences to match their relationships. (For example, 40,000 ÷ 4,000 = 10) Anchor Chart:

Students will demonstrate equality using place value blocks. Teacher will create an anchor chart for display similar to chart: Teacher’s Edition, Topic 3, pg 67. Have students represent various forms of a number. ADD to the chart examples of the following forms of a number: 364 = 36 tens and 4 ones; 364 = 2 hundreds, 16 tens, and 4 ones, etc.

Use horizontal/vertical number lines to round:

Students will round numbers using a vertical or horizontal number line. This strategy can also help students identify the mid-point of 2 numbers.

Round 6,345 to the nearest thousand. Vertical Number Line Horizontal Number Line

In this example, students should determine and record the midpoint of 6,000 and 7,000 (6,500) and draw a point to estimate where 6,345 will fall on the number line (between 6,000 and 6,500 or between 6,500 and 7,000). STUDENT WORK: 6,345 is between 6,000 and 7,000. 6,345 is closer to 6,000 (less than 6,500). Therefore, 6,345 rounded to the nearest thousand is 6,000.

7,000

6,000

6,500

6,345

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Comparing Digits: Students will work with a partner to solve place value problems and share solutions. Students needs to understand that

the value of a digit in one place represents ten times the value in the place to its right. http://www.k-5mathteachingresources.com/support-files/comparing-digits.pdf

Place Value Triangle:

Students will play a place value game with a partner comparing two multi-digit numbers. The activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/place-value-triangle.pdf

Numeral Word Expanded Form:

Students will practice representing multi-digit whole numbers in word and expanded form. The activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/numeral-word-expanded-form.pdf

Appalachian Steps: (pg. 18)

Students will practice reading multi-digit whole numbers. This activity can be downloaded at: http://maccss.ncdpi.wikispaces.net/file/view/4thgrade_GAMES_8.22.14.pdf?519547634/4thgrade_GAMES_8.22.14.pdf

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Unit 2- ADDITION AND SUBTRACTION WHOLE NUMBER OPERATIONS (10 DAYS)

ADDING WHOLE NUMBERS- SUBTRACTING WHOLE NUMBERS-WORD PROBLEMS USING WHOLE NUMBERS OPERATIONS

1. Overview

Students will build on their understanding of addition and subtraction using place value and multiple strategies to describe and justify the process used

to add and subtract with whole number sums and differences less than or equal to 1,000,000, and estimate (round) to determine reasonableness of sum

or difference. Students will understand decomposing into smaller units multiple times using the standard subtraction algorithm. Students will be able to

complete multi-step word problems using the standard algorithm and models (tape diagrams) to find solutions.

Manipulatives/Materials: place value blocks or place value disks, numeral cards (0-9)

FOCUS

STANDARDS 4.OA.A.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using

the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers with sums less than or equal to 1,000,000, using the standard algorithm.

STANDARDS FOR MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

FOUNDATIONAL

STANDARDS 3.NBT.A.1 3.NBT.A.2

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ADDING WHOLE NUMBERS- SUBTRACTING WHOLE NUMBERS- WORD PROBLEMS USING WHOLE NUMBER OPERATIONS

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 4: Lesson 4-3 Topic 4: Lesson 4-4, 4-5

Module 1: Topic D

Lesson 11, Lesson 12

Module 1: Topic E Lesson 13, Lesson 14, Lesson 15, Lesson 16

Module 1: Topic F Lesson 18

*Lesson 17 can be embedded as extension in Module 2 or Module 3 **Lesson 19 may be omitted

Unit 1, Lessons 3 – 4

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

Guidebook: Lesson:

Distance Traveled: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-extended-contructed-response-tasks.pdf?sfvrsn=7

LearnZillion:

Lessons: Add using the standard addition algorithm: https://learnzillion.com/lesson_plans/6181 Subtract using the standard subtraction algorithm: https://learnzillion.com/lesson_plans/6901

Illustrative Mathematics:

Tasks: Rounding on the Number Line: https://www.illustrativemathematics.org/content-standards/4/NBT/A/3/tasks/1683 Rounding to the Nearest 100 and 1000: https://www.illustrativemathematics.org/content-standards/4/NBT/A/3/tasks/1806

Discovery Education:

Videos: Rounding Whole Numbers: https://app.discoveryeducation.com/learn/videos/62E8860E-C444-4297-8082-C2C3849C014F?hasLocalHost=false

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ADDING WHOLE NUMBERS- SUBTRACTING WHOLE NUMBERS- WORD PROBLEMS USING WHOLE NUMBER OPERATIONS

3. Activities for Understanding

Make the Largest Sum: Students will work with a partner rearranging numeral cards to create two 5-digit numbers to add with the goal of

creating the largest possible sum. The activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/make-the-largest-sum.pdf

Roll and Round to the Nearest Hundred:

Students will practice rounding a 4-digit number to the nearest hundred playing a rounding game with a partner. The activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/roll-and-round-nearest-hundred.pdf

What’s the Nearest Hundred:

Students will practice rounding a 4-digit number to the nearest hundred by locating the mid-point on a horizontal number line. The activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/whats-the-nearest-hundred-4-digit.pdf

Climbing Chimney Rock: (pg.23)

Students will add multi-digit numbers. The activity can be downloaded at: http://maccss.ncdpi.wikispaces.net/file/view/4thgrade_GAMES_8.22.14.pdf/519547634/4thgrade_GAMES_8.22.14.pdf

Valuable Digits!!: (pg.24)

Students will add multi-digit numbers using place value. The activity can be downloaded at: http://maccss.ncdpi.wikispaces.net/file/view/4thgrade_GAMES_8.22.14.pdf/519547634/4thgrade_GAMES_8.22.14.pdf

SUGGESTIONS

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Unit 3- Metric Units METRIC UNITS (5 DAYS)

LENGTH- VOLIME- CAPACITY

1. Overview

Students will solve problems involving measurement and conversion of measurements (customary and metric length, capacity, weight/mass). Students’

prior experiences were limited to measuring length, mass, and liquid volume. Students did not convert measurements. Students need ample opportunities

to become familiar with these new units of measure. Relating units within the metric system is another opportunity to think about place value. Relating

units within the traditional system provides an opportunity to engage in mathematical practices, especially “look for and make use of structure” and “look

for and express regularity in repeated reasoning.”

When students solve multi-step word problems, involving addition and subtraction involving metric length, mass, and capacity.

NOTE: Students in Grade 4 will be assessed on multiplying a fraction and a whole number as indicated in the NF domain. Some students may be able to

multiply a fraction by a fraction as a result of generating equivalent fractions; however, mastery of multiplying two fractions occurs in Grade 5.

Manipulatives/Materials: inch/centimeter ruler, capacity containers, balance scale, ounce weights, gram/kilogram weights

FOCUS

STANDARDS 4.MD.A.1 Know relative sizes of measurement units within one system of units including: ft, in; km, m, cm; kg,

g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. (Conversions are limited to one-step conversions.) Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving whole numbers and/or simple fractions (addition and subtraction of fractions with like denominators and multiplying a fraction times a fraction or a whole number), and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

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STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them. MP.7 Look for and make use of structure. MP.8 Look for and express regulatory in repeated reasoning.

FOUNDATIONAL

STANDARDS 3.OA.C.7 3.MD.A.2

LENGTH- VOLUME- CAPACITY

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 14: Lessons 14-6, 14-7,

14-8

Topic 15: Lesson 15-2

Module 2: Topic A Lesson 1, Lesson 2, Lesson 3

Module 2: Topic B Lesson 4, Lesson 5

Unit 5, Lesson 23 – 24

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

LearnZillion:

Lessons:

Compare and convert customary units of length: https://learnzillion.com/lesson_plans/5003 Compare and convert customary units of weight: https://learnzillion.com/lesson_plans/5615 Compare and convert metric units of length: https://learnzillion.com/lesson_plans/7014

Illustrative Mathematics:

Tasks:

4.MD – Who is the tallest? https://www.illustrativemathematics.org/content-standards/4/MD/A/1/tasks/1508

4.MD – Margie Buys Apples: https://www.illustrativemathematics.org/content-standards/4/MD/A/2/tasks/873

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MEASUREMENT UNITS AND CONVERSIONS (13 DAYS)

3. Activities for Understanding

Measure and Estimate: Students will use customary units to estimate and measure the lengths of classroom objects (TE pg. 366B)

Toss and Talk:

Students will determine the best customary unit. (TE pg. 367B) Making a Kilogram:

Students will predict weights in kilograms. http://www.k-5mathteachingresources.com/support-files/making-a-kilogram.pdf

Measurement Concentration:

Students will convert measurements within the customary and metric systems. http://www.k-5mathteachingresources.com/support-files/measurement-concentration-ver.1.pdf

SUGGESTIONS

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Unit 4- Multiplication and Division UNDERSTANDING MULTI-DIGIT MULTIPLICATION BY A SINGLE DIGIT (32 DAYS)

MULTIPLICATIVE COMPARISON- MULTIPLYING MULTI-DIGIT BY SINGLE DIGITS- MULTIPLICATION WORD PROBLEMS

DIVISION WITH REMAINDERS- DIVISIBILITY- DIVISION WITH PLACE VALUE

1. Overview

Students will review multiplication and division and the ways the two operations are related. Multiplication is the extension of repeated addition or joining

equal groups and connects the concepts and simplifies the process when adding larger equal groups. Division can be thought of as separation of equal

groups and repeated subtraction. In order to understand multiplication and division, basic facts must be mastered as multi-digit multiplication is

dependent on the automaticity of fact recall.

Students will use base ten blocks, mental math strategies, compensation strategy, distributive property and/or other strategies to multiply a whole

number (up to 4 digits) by 1 digit number and use these strategies to explain their thinking. Students will also use estimation when determining the

reasonableness of a product. The use of the standard algorithm for multiplication is an expectation in 5th grade.

Students will develop number sense as it connects to dividing (up to) four-digit dividends and one-digit divisors. In this topic, students will learn to divide

using mental math strategies, compatible numbers, relationship between multiplication/division, and estimation. Manipulatives (i.e. counters) are

encouraged when teaching students the difference between partitive and measurement division word problems. Students will also practice using words

and models to represent multiplication and division problems accurately. Students will need opportunities to develop their understandings by using

problems in and out of context. The use of the standard algorithm for division is an expectation in 5th grade.

Students will continue their work with division using strategies based on place value, the properties of operations, and/or the relationship between

multiplication and division to demonstrate their understanding of dividing (up to) four-digit dividends and one-digit divisors. Since the use of the

standard algorithm for division is an expectation in 5th grade, 4th grade students will need to practice illustrating and explaining their division

calculations using equations, rectangular arrays, and/or area models. Students will also need opportunities to develop their understandings by using

problems in and out of context.

Manipulatives/Materials: centimeter grid paper, place-value blocks, crayons, colored pencils or markers, hundred chart, index cards, colored chalk,

counters

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FOCUS

STANDARDS 4.OA.A.1 Interpret a multiplication equation as a comparison and represent verbal statements of multiplicative

comparisons as multiplication equations, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5.

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and/or equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison (Example: 6 times as many vs. 6 more than).

4.OA.A.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using

the four operations, including problems in which remainders must be interpreted. Represent these problems

using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using

mental computation and estimation strategies including rounding.

4.OA.B.4 Using whole numbers in the range 1–100,

o (4.OA.B.4a) Find all factor pairs for a given whole number.

o (4.OA.B.4b) Recognize that a given whole number is a multiple of each of its factors.

o (4.OA.B.4c) Determine whether a given whole number is a multiple of a given one-digit number.

o (4.OA.B.4d) Determine whether a given whole number is prime or composite.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit

numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

STANDARDS FOR

MATHEMATICAL PRACTICE

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

MP.6 Attend to precision. MP.8 Look for and express regulatory in repeated reasoning.

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FOUNDATIONAL

STANDARDS

3.OA.A.1 3.OA.A.3 3.OA.B.5

3.OA.C.7

3.OA.D.8

3.NBT.A.2

3.NBT.A.3

MULTIPLICATIVE COMPARISON- MULTIPLYING MULTI-DIGIT BY SINGLE DIGITS- MULTIPLICATION WORD PROBLEMS

DIVISION WITH REMAINDERS- DIVISIBILITY- DIVISION WITH PLACE VALUE

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Multiplication:

Topic 15: Lessons 15-1

Topic 5: Lessons 5-1, 5-2

Topic 5: Lessons 5-3, 5-4

Topic 6: 6-1, 6-2, 6-3, 6-4, 6-5

Division: Topic 9: Lesson 9-1, 9-4 Topic 10: Lesson 10-3, 10-5, 10-6,

10-7

Topic 11: Lessons 1-3

Multipllication:

Module 3: Topic A Lesson 1, Lesson 2, Lesson 3

Module 3: Topic B Lesson 5, Lesson 5, Lesson 6

Module 3: Topic C Lessons 7-9, Lesson 11

Module 3: Topic D Lesson 12, Lesson 13

Division: Module 3: Topic E

Lessons 14-18, Lesson 19-20

Module 3: Topic F: Lessons 22-25

Module 3: Topic G Lessons 26-29, Lessons 30 and 33, Lesson 32

Unit 2, Lessons 5 – 6 Unit 3, Lesson 11

Unit 3, Lesson 12

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A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

Guidebook: Lesson:

Big Ben’s Bakery: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-extended-contructed-response-tasks.pdf?sfvrsn=7

LearnZillion: Lessons: See multiplication as a comparison using number sentences: https://learnzillion.com/lesson_plans/7986 Solve multiplicative comparison word problems by using bar models: https://learnzillion.com/lesson_plans/4896 Solve multiplicative comparison word problems by using a multiplication sentence: https://learnzillion.com/lesson_plans/5223

Solve multiplicative comparison word problems using multiplication or division: https://learnzillion.com/lesson_plans/6944 Math Video Lessons:

4th Grade Operations and Algebraic Thinking (4.OA): https://LearnZillion.com/resources/74906-4th-grade-operations-and-algebraic-thinking-4-oa

LearnZillion:

Multiplication Lessons:

VIDEO: Solve 1 by 1 digit multiplication problems: using area model: https://learnzillion.com/lesson_plans/6772-solve-1-by-1-digit-

multiplication-problems-using-area-model

Use an array to multiple a two- digit number by a one -digit number: https://learnzillion.com/lesson_plans/6737-use-an-array-to-multiply-a-two-

digit-number-by-a-one-digit-number

Use place value understanding to multiply three and four digit numbers: https://learnzillion.com/lesson_plans/6751

Use an array to multiply a two digit number by a one digit number: https://learnzillion.com/lesson_plans/6737

Illustrative Mathematics:

Tasks:

Thousands and Millions of Fourth Graders: https://www.illustrativemathematics.org/content-standards/4/NBT/B/5/tasks/1808 Discovery Education:

Multiplication Basics: https://app.discoveryeducation.com/learn/videos/40D1679D-7CBE-49C1-8CBA-62BA678DF1A7?hasLocalHost=false

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Guidebook (Division): Lessons:

School Store: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-extended-contructed-response-

tasks.pdf?sfvrsn=7

Alien Contest: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-extended-contructed-response-

tasks.pdf?sfvrsn=7

Class Picnic: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-instructional-tasks.pdf?sfvrsn=5

LearnZillion:

Division Lessons: Interpret the remainder of a division problem: https://learnzillion.com/lesson_plans/7861

Divide two-digit dividends using friendly multiples: https://learnzillion.com/lesson_plans/8961

Divide four-digit dividends: https://learnzillion.com/lesson_plans/8945

Illustrative Mathematics: Tasks:

4.NBT – Mental Division Strategy: https://www.illustrativemathematics.org/content-standards/4/NBT/B/6/tasks/1774

Discovery Education:

Lesson 1: Place Value and Division Number Families (Video and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/4666a01b-

ebec-491e-a355-c0d1cab65e09

Lesson 2: Short Division (Video and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/861a757f-5529-422d-8078-

ec6d11946b93

Lesson 3: Solving Division Problems (Video and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/79929190-65a7-469f-9ab7-

97a483bbf0a2

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MULTIPLICATIVE COMPARISON- MULTIPLYING MULTI-DIGIT BY SINGLE DIGITS- MULTIPLICATION WORD PROBLEMS

DIVISION WITH REMAINDERS- DIVISIBILITY- DIVISION WITH PLACE VALUE

3. Activities for Understanding

SUGGESTIONS Multiplication: Meanings of Multiplication:

Students work in pairs with counters to practice repeated addition up to five addends. For example, students will add 1 + 1, then 1 + 1 + 1 … to 1 + 1 + 1 + 1 + 1. One student will arrange the counters in groups and the other student will add the numbers of counters. After each repeated addition, have students write a number sentence using the multiplication and equal signs to show the total number of counters.

Multiplication Strategy: Doubling and Halving: Students will simplify multiplication problems by doubling one factor and halving the other factor.

Example: 5 x 16 = 10 x 8 = 80 or 10 x 8 = 20 x 4 = 80. This activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/multiplication-strategy-doubling-and-halving.pdf

Double and Halve:

Students will multiply a 2-digit number by a one-digit number using the strategy Doubling and Halving. This

activity can be downloaded at:

http://www.k-5mathteachingresources.com/support-files/double-and-halve-ver.1.pdf 3, 4, 6, 7, and 8 as Factors:

Students will build arrays. Have students build an array with cubes to show 4 x 5. Guide students to display 4 rows of 5 columns of cubes. Have the students split the cubes into 2 rows each of 5 columns of cubes. Students will then count the number of cubes in each column and the number of cubes in each row. Have students count the number of cubes in each section. Students will then solve using both operations - multiplication and addition.

Additional activities for differentiated instruction and learning centers are available in the Topic 1 enVisionMATH Teacher’s Edition. Multiplication as Comparison:

Students will interpret a multiplication equation as a comparison. The activity can be downloaded at: http://www.k-5mathteachingresources.com/support-files/multiplication-as-comparison.pdf

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Word Problems in Multiplicative Comparison: Students will use multiplicative comparison cards. Students will work with a partner. They will choose five word

problems to solve. Solve the word problems independently. For each problem: Write an equation with a symbol for the unknown number. Use a drawing to represent the problem. Answer the question in a complete sentence. After completing five problems, they will share their work with a partner. Students should explain how they solved each problem using accurate mathematical vocabulary. Repeat with another five problems form the set. The activity can be downloaded at:

http://www.k-5mathteachingresources.com/support-files/word-problems-multiplicative-comparison.pdf Multiplication Race:

Students will multiply a whole number of up to four digits by a one-digit whole number using a calculator to check

products.

http://www.k-5mathteachingresources.com/support-files/multiplication-race-1x3-digit.pdf

Make the Largest Product:

Students will multiply a whole number of up to four digits by a one-digit whole number to create the largest product possible. Students will check their products using a calculator. http://www.k-5mathteachingresources.com/support-files/make-the-largest-product-ver.1.pdf

Division: Estimate the Quotient:

Students will estimate quotients using the compatible numbers strategy with division of a three-digit number by a one-

digit number. Challenge: Have the students try estimating quotients for problems with 4-digit dividends and 1-digit

divisors. http://www.k-5mathteachingresources.com/support-files/estimate-the-quotient-ver.1.pdf

The Great Raleigh Road Race: (pg.32)

Students will divide 2 and 3-digits by 1-digit, with and without remainders.

http://maccss.ncdpi.wikispaces.net/file/view/4thgrade_GAMES_8.22.14.pdf/519547634/4thgrade_GAMES_8.22.14.pdf

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Division Strategy for Partial Quotients: Students will divide a 3-digit number by a 1- digit number using the partial quotient strategy. http://www.k-

5mathteachingresources.com/support-files/division-strategy-partial-quotients-ver.1.pdf

Division Strategy with Partitioning the Dividend:

Students will divide a two-/three-digit number by one-digit number using the strategy, Partition the Dividend.

http://www.k-5mathteachingresources.com/support-files/division-strategy-partition-the-dividend-ver.1.pdf Brain Only: (pg. 86) Students will analyze multiplication and division expressions to find patterns and make connections among division and multiplication problems. https://www.georgiastandards.org/Georgia-Standards/Frameworks/4th-Math-Unit-2.pdf

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Unit 5- Two-Digit By Two-Digit Multiplication UNDERSTANDING MULTI-DIGIT MULTIPLICATION BY A TWO-DIGIT NUMBER (5 DAYS)

MULTIPLYING TWO-DIGITS BY TWO-DIGITS

1. Overview

Students will multiply two 2-digit numbers using base ten blocks, area models, partitioning, and/or other place value strategies. These tools can help

students explain their thinking as they write in math. In addition, students will also use estimating (rounding) to determine reasonableness when

determining products. The use of the standard algorithm for multiplication is an expectation in 5th grade.

Students take strategies introduced in Topic 6 and 7 as they continue their study of multiplication. These place value strategies can help students explain

their thinking as they write in math as they multiply two two-digit numbers. The use of the standard algorithm for multiplication is an

expectation in 5th grade.

Manipulatives/Materials: base ten block, grid paper, calculators

FOCUS

STANDARDS 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers, less than or equal to 1,000,000 to

any place.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply 2 two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.4 Model with mathematics. MP.8 Look for and express regulatory in repeated reasoning.

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FOUNDATIONAL STANDARDS

3.OA.B.5 3.OA.C.7 3.NBT.A.1 3.NBT.A.2 3.NBT.A.3

MULTIPLYING TWO-DIGITS BY TWO-DIGITS

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 7: Lessons 7-1, 7-2 Topic 8: Lessons 8-1-, 8-2, 8-3,

8-4

Module 3: Topic H Lessons 34-38

No lessons support this topic.

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

LearnZillion:

Lessons: Practice rounding to different place values depending on the quantities: https://learnzillion.com/lesson_plans/3840-5-practice-rounding-to-

different-place-values-depending-on-the-quantities-fp

Apply rounding to different place values depending on the context: https://learnzillion.com/lesson_plans/3841-6-apply-rounding-to-different-place-values-depending-on-the-context-a

Multiply multi-digit numbers using an area model: https://learnzillion.com/lesson_plans/4881

Use area models for multiplication: https://learnzillion.com/lesson_plans/8122

Use partial products for multiplication: https://learnzillion.com/lesson_plans/8117

Illustrative Mathematics:

Tasks: 4.NBT – Rounding on the Number Line: https://www.illustrativemathematics.org/content-standards/4/NBT/A/3/tasks/1683 4.NBT – Rounding to the Nearest 1000: https://www.illustrativemathematics.org/content-standards/4/NBT/A/3/tasks/1807 4.NBT – Thousands and Millions of Fourth Graders: https://www.illustrativemathematics.org/content-standards/4/NBT/B/5/tasks/1808 4.NBT – Mental Division Strategy: https://www.illustrativemathematics.org/content-standards/4/NBT/B/6/tasks/1774

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Discovery Education:

Lesson 5: Multiplying by Two Digit Numbers (Video and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/1e0de8d7-b3d5-

4a62-8cb4-bb7a4a5a7f55

MULTIPLYING TWO-DIGITS BY TWO-DIGITS

3. Activities for Understanding

SUGGESTIONS

Arrays:

Students will use arrays to multiply 2-digit numbers by 10. (TE page 166B) Clip and Cover:

Students will use mental math to multiply multiples of 10. (TE page 171B) Arrays to Multiply:

Students will use arrays and an expanded algorithm to multiply 2-digit numbers. (TE pg. 190B)

Clip and Cover:

Students will multiply two 2-digit numbers using mental math, paper, or pencil. (TE pg. 193B)

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Unit 6- GEOMETRY LINES, ANGLES, AND SHAPES (12 DAYS)

LINES AND ANGLES- ANGLE MEASUREMENT- PROBLEM SOLVING WITH AREA- TWO-DIMENSIONAL SHAPES

1. Overview

Students will identify, classify, and describe points, lines, line segments, rays, angles, parallel and perpendicular lines, and 2-dimensional figures. They will

use unit angles and fractions of a circle to find angle measures, measure angles using a protractor, add to find the measure of an unknown angle using

the additive property, and identify a line of symmetry. This is the first time that students are exposed to rays, angles, and perpendicular and parallel

lines. Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen daily. Students may not easily identify lines and rays

because they are more abstract.

Manipulatives/Materials: polygons, pattern blocks, protractors, popsicle sticks, block letter, pipe cleaners

4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

o (4.MD.C.5a) An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle.

o (4.MD.C.5b) An angle that turns through 1

360 of a circle is called a "one-degree angle," and can be used to

measure angles.

FOCUS

STANDARDS

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o (4.MD.C.5c) An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a letter for the unknown angle measure.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regulatory in repeated reasoning.

FOUNDATIONAL

STANDARDS

1.OA.D.8 3.G.A.1 1.G.A.2

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LINES, ANGLES, AND SHAPES (12 DAYS)

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 16: Lessons 16-1, 16-2, 16-3, 16-4, 16-5, 16-6, 16-7, 16-8, 16-9, 16-10

Module 4: Topic A Lessons 1-4 Moduel 4: Topic B Lessons 5-8 Module 4: Topic C Lessons 9-11 Module 4: Topic D Lessons 12-15

Unit 5, Lessons 28 – 30 Unit 6, Lessons 31 – 33

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

LearnZillion:

Lessons:

Identify angles using angle characteristics: https://learnzillion.com/lesson_plans/7574 Measure an angle using fractions of a circle: https://learnzillion.com/lesson_plans/8576 Classify two-dimensional figures by examining their properties: https://learnzillion.com/lesson_plans/5735 Identify points, lines, line segments, and rays: https://learnzillion.com/lesson_plans/4667 Identify line symmetry in regular polygons: https://learnzillion.com/lesson_plans/7275 Classify and draw various types of angles: https://learnzillion.com/lesson_plans/4648 Identify parallel, intersecting, and perpendicular lines: https://learnzillion.com/lesson_plans/8511

Illustrative Mathematics:

Tasks: 4.MD, G – Measuring Angles: https://www.illustrativemathematics.org/content-standards/4/G/A/1/tasks/909 4.G – The Geometry of Letters: https://www.illustrativemathematics.org/content-standards/4/G/A/1/tasks/1263 4.MD, G – Finding the unknown angle: https://www.illustrativemathematics.org/content-standards/4/G/A/2/tasks/1168 4.G – Defining Attributes of Rectangles and Parallelograms: https://www.illustrativemathematics.org/content-standards/4/G/A/2/tasks/1275

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LINES, ANGLES, AND SHAPES (12 DAYS)

3. Activities for Understanding

SUGGESTIONS

Angles and Lines: Students will use popsicle sticks and an angle checker to identify parallel and perpendicular lines and acute, obtuse,

and right angles. Students will make an angle checker using a pipe cleaner and 2 coffee stirrers. Students will use the angle checker to identify the types of angles in polygons. Each student can use a set of power polygons in a bag or a worksheet with a set of polygons. Students will use the popsicle sticks to test if the polygon has parallel and/or perpendicular lines. Students can share results with the class.

Lines of Symmetry:

Students will identify the lines of symmetry in block letters. Each student can use a set of block letters in a bag or a worksheet with a set of block letters. Students draw all lines of symmetry for each letter (worksheet) or trace the block letters on paper and draw all lines of symmetry for each letter. Students can share results with the class.

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Unit 7- Fractions UNDERSTANDING FRACTIONS (28 DAYS)

UNDERSTANDING EQUIVALENT FRACTIONS- COMPARING FRACTIONS- ADDING AND SUBTRACTING FRACTIONS- MULTIPLYING FRACTIONS-

FRACTION PATTERNS

3. Overview

Students will cover a variety of skills: factors, prime and composite numbers, multiples, number lines and equivalent fractions, and comparing and

ordering fractions in Topic 11. Students should understand the process of finding factor pairs so they can do this for any number 1 – 100. When

determining whether a number is prime or composite, students need time building rectangles (arrays) with the given area and finding which numbers

have more than two rectangles (e.g., 7 is a prime number because it can be made into 2 rectangles, 1 × 7 and 7 × 1; therefore, a prime number can

be shown 2 different ways). Students in 4th grade extend their study of fractions from 3rd grade by using additional denominators (5, 10, 12, and

100). Students’ experiences should focus on visual fraction models rather than algorithms when generating equivalent fractions and

comparing/ordering fractions. See examples below:

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Students will add and subtract fractions and mixed numbers with like denominators using visual models. Remember, a fraction with a numerator of one

is called a unit fraction. When students investigate fractions other than unit fractions, such as 2

3, they should be able to decompose the non-unit fraction

into a combination of several unit fractions: 2

3 =

1

3 +

1

3. Being able to visualize this decomposition into unit fractions helps students when adding or

subtracting fractions. Fraction strips and region models are often used to model the addition and subtraction of fractions with like denominators. Using a

number line to add and subtract fractions with like denominators builds on students’ experiences of adding and subtracting whole numbers on a number

line. A separate algorithm for mixed numbers in addition and subtraction is not necessary. Students will tend to add or subtract the whole numbers first

and then work with the fractions using the same strategies they have applied to problems that contained only fractions. Note: There is no

mathematical reason to simplify fractions. Therefore, students are not required to do so.

Students extend their studies with fraction concepts in Topic 13 and learn how to multiply a fraction by a whole number.

In a relay race, each runner runs 1

2 of a lap. If there are 4 team members, how long is this race?

Students will investigate different patterns to find rules in a number sequence, geometric sequence, repeating pattern, growing pattern or by extending a

table. Students will also identify features in the patterns and justify the reason for those features.

Manipulatives/Materials: fraction strips, base ten blocks, pattern blocks, polygons, t-chart template, attribute shapes, snap cubes or blocks, hundreds

chart, color tiles

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FOCUS

STANDARDS 4.OA.B.4 Using whole numbers in the range 1–100,

o (4.OA.B.4a) Find all factor pairs for a given whole number. o (4.OA.B.4b) Recognize that a given whole number is a multiple of each of its factors. o (4.OA.B.4c) Determine whether a given whole number is a multiple of a given one-digit number. o (4.OA.B.4d) Determine whether a given whole number is prime or composite.

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating

common denominators or numerators, or by comparing to a benchmark fraction such as 1

2. Recognize that

comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Denominators are limited to 2, 3, 4, 5,

6, 8, 10, 12, and 100.)

o (4.NF.B.3a) Understand addition and subtraction of fractions as joining and separating parts referring to

the same whole. Example: 3

4=

1

4+

1

4+

1

4.

o (4.NF.B.3b) Decompose a fraction into a sum of fractions with the same denominator in more than one

way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual

fraction model. Examples: 3

8=

1

8+

1

8+

1

8 ;

3

8=

1

8+

2

8 ; 2

1

8= 1 + 1 +

1

8 =

8

8+

8

8+

1

8.

o (4.NF.B.3c) Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed

number with an equivalent fraction, and/or by using properties of operations and the relationship

between addition and subtraction.

o (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same

whole and having like denominators, e.g., by using visual fraction models and equations to represent the

problem.

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STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

1.OA.B.3

1.OA.B.4

1.OA.D.8

2.OA.A.1

3.OA.C.7

3.NF.A.1

3.NF.A.2

3.NF.A.3

FOUNDATIONAL

STANDARDS

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UNDERSTANDING FRACTIONS (28 DAYS)

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 11: Lessons 11-1, 11-2, 11-3,

11-4, 11-5, 11-6, 11-7

Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 12-8, 12-9, 12-10, 12-11

Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5

Topic 1- Lesson 5 (Problem Solving Look for A Pattern), may be taught with Topic 2: Generate and Analyze Patterns.

Module 5: Topic A Lessons 1/2- 6 Module 5: Topic B Lessons 7/8-11 Module 5: Topic C

Lessons 12/13-14/15 Module 5: Topic D Lessons 16-19 Module 5: Topic D Enrichment Lessons Lessons 20-21 Module 5: Topic E Lessons 22-28 Module 5: Topic F Lessons 29-34 Module 5: Topic G Lessons 35-41 Module 5: Topic H Lesson 41

Unit 2, Lesson 7 Unit 4, Lesson 13 – 14 Unit 4, Lessons 15 – 17 Unit 2, Lessons 7 and 8

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

Guidebook:

Lesson:

Birthday Party Food: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-extended-contructed-response-

tasks.pdf?sfvrsn=7

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LearnZillion: Lessons: Topic 11

Find all the factor pairs of a number using area models: https://learnzillion.com/lesson_plans/8409

Find all factor pairs of a number using a t-chart: https://learnzillion.com/lesson_plans/6637

Determine if a number is prime or composite using area models: https://learnzillion.com/lesson_plans/8345

Generate equivalent fractions using area models: https://learnzillion.com/lesson_plans/4809

Make equivalent fractions: using an equation: https://learnzillion.com/lesson_plans/8279

Recognize equivalent fractions using area models: https://learnzillion.com/lesson_plans/9049

Recognize equivalent fractions using number lines: https://learnzillion.com/lesson_plans/4739

Compare fractions to a benchmark of one half using number lines: https://learnzillion.com/lesson_plans/5115

Compare fractions to a benchmark of one using number lines: https://learnzillion.com/lesson_plans/5110

Lessons: Topic 12

Decompose fractions into unit fractions: https://learnzillion.com/lesson_plans/8474

Add mixed numbers using an area model: https://learnzillion.com/lesson_plans/9065

Add and subtract fractions with like denominators: https://learnzillion.com/lesson_plans/8191

Add fractions by joining parts: https://learnzillion.com/lesson_plans/8168

Lesson:

Understand repeating patterns: https://learnzillion.com/lesson_plans/8894

Multiple lesson plan link for 4.OA.C.5:

https://LearnZillion.com/search?utf8=%E2%9C%93&query=4.oa.c.5&page=1&sort=Relevance&models%5B%5D=LessonPlan

Performance Task:

4th Grade OA task: https://LearnZillion.com/resources/16024

Illustrative Mathematics: Tasks: Topic 11

4.NF – Using Benchmarks to Compare Fractions: https://www.illustrativemathematics.org/content-standards/4/NF/A/2/tasks/812

4.NF - Comparing Fractions using Benchmarks Game: https://www.illustrativemathematics.org/content-standards/4/NF/A/2/tasks/2109

4.NF – Listing fractions in increasing size: https://www.illustrativemathematics.org/content-standards/4/NF/A/2/tasks/811

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Tasks: Topic 12

4.NF – Cynthia’s Perfect Punch: https://www.illustrativemathematics.org/content-standards/4/NF/B/3/tasks/874

4.NF – Plastic Building Blocks: https://www.illustrativemathematics.org/content-standards/4/NF/B/3/tasks/856

4.NF – Writing a Mixed Number as an Equivalent Fraction: https://www.illustrativemathematics.org/content-standards/4/NF/B/3/tasks/835

4.NF – Peaches: https://www.illustrativemathematics.org/content-standards/4/NF/B/3/tasks/968

Tasks: Topic 2

Identifying Multiples 4.OA: https://www.illustrativemathematics.org/content-standards/4/OA/B/tasks/959

Multiples of 3, 6, and 7: https://www.illustrativemathematics.org/content-standards/4/OA/B/tasks/1484

Numbers in a Multiplication Table: https://www.illustrativemathematics.org/content-standards/4/OA/B/tasks/1493

Discovery Education:

Lesson 6: Adding and Subtracting Fractions with Like Denominators (Video and Teacher’s Guide):

https://app.discoveryeducation.com/learn/videos/BDFB91C4-79E8-4CFD-B8D5-D32369FCA081?hasLocalHost=false

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UNDERSTANDING FRACTIONS (28 DAYS)

3. Activities for Understanding

Exploring Multiples:

The student will color multiples of 2, 3, and 4 on a hundred chart and describe the patterns created. http://www.k-5mathteachingresources.com/support-files/exploring-multiples.pdf

Prime or Composite:

The student will find and record in a chart the factor pairs for given numbers, recording the factors to determine if the number is prime or composite. http://www.k-5mathteachingresources.com/support-files/prime-or-composite.pdf

Fraction Card Games: (pg. 28)

Students will compare two fractions and identify equivalent fractions playing a “Gold Fish” game. http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade4-2014new.pdf/521000852/CCSSMathTasks-Grade4-2014new.pdf

Place the Fraction: (pg.34)

Students will use benchmark fractions to compose fractions and find fractions equivalent to 1/2. Students will place fraction cards on a number line (0, ½, and 1) closer to 0, ½, or 1 and have them identify their strategy for their placement. http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade4-2014new.pdf/521000852/CCSSMathTasks-Grade4-2014new.pdf

Number Riddles: (pg. 104)

Students will use deductive reasoning to solve number riddles involving identifying multiples, factors, place value, and numeric expressions. https://www.georgiastandards.org/Georgia-Standards/Frameworks/4th-Math-Unit-2.pdf

The Sieve of Eratosthenes:

Students will find all factor pairs for a whole number in the range 1-100 and create a list of prime numbers between 1 and 100. https://www.georgiastandards.org/Georgia-Standards/Frameworks/4th-Math-Unit-2.pdf

Birthday Fractions:

Students will solve a problem with fractions using the strategy Draw a Model, and use a benchmark fraction to

compare two fractions to determine equivalency. http://www.k-5mathteachingresources.com/support-files/birthday-

fractions.pdf

SUGGESTIONS

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Who Ate More:

Students will draw fraction models to compare two fractions using the symbols >,<, or = and explain their thinking

using mathematical reasoning. http://www.k-5mathteachingresources.com/support-files/who-ate-more.pdf

Decompose a Fraction:

Students will find how many different ways to decompose each fraction into a sum of fractions with the same

denominator. The students will record each decomposition using a fraction model and equation. http://www.k-

5mathteachingresources.com/support-files/decompose-a-fraction.pdf

Give ‘Em Chocolate! (Fraction Bars): (pg. 43)

Students will decompose a fraction into a sum of fractions with the same denominator and record each decomposition

using an equation. http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade4-

2014new.pdf/521000852/CCSSMathTasks-Grade4-2014new.pdf

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Patterns and Rules are Related

Students will follow a stated rule to create a pattern. Have the students follow a rule and record the pattern. For

example:

RULE: Start with 1, and then add 3.

STUDENT WORK: 1, 4, 7, 10, 13, 16.

Next, have students identify a feature from a chart that matches the pattern created. Call on students to share their

matches and justify their choices to the class.

STUDENT WORK: The numbers alternate between even and odd numbers. 4 is even, 7 is odd, 10 is even, 13

is odd, 16 is even. I know 4, 10 & 16 are even because they are divisible by 2.

Example Rules:

Start with 1, and then add 4. Start with 1, and then add 5. Start with 5, and then add 5. Start with 3, and then add 5. Start with 2, and then multiply by 2.

Example Features:

The numbers are all even. The numbers are all odd. The numbers alternate between even and odd numbers. The numbers alternate between odd and even numbers. The numbers alternately end with a 3 or 8. The numbers are multiples of 5 and end with either a 0 or 5.

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UNIT 8- DECIMAL FRACTIONS

DECIMAL FRACTIONS (30 DAYS)

1. Overview

Students extend their studies with fraction concepts in Topic 13 and learn how to multiply a fraction by a whole number, discover the relationship

between fractions and decimals, write equivalent fractions and decimals, compare/order decimals, and use money to understand decimals. When

multiplying a fraction by a whole number, students need many opportunities to work with problems in context to understand the connections between

models and corresponding equations. Contexts involving a whole number times a fraction lend themselves to modeling and examining patterns:

In a relay race, each runner runs 1

2 of a lap. If there are 4 team members, how long is this race?

In order to prepare students for working with decimals (4.NF.6 and 4.NF.7), experiences that allow students to shade decimal grids (10 × 10 grids) can

support this work. Student experiences should focus on working with grids rather than algorithms. Students can also use base-ten blocks and other place

value models to explore the relationship between fractions with denominators of 10 and denominators of 100. Decimals are introduced for the first time

in fourth grade. Students should have ample opportunities to explore and reason about the idea that a number can be represented as both a fraction and

a decimal.

Manipulatives/Materials: fraction strips, base ten blocks

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FOCUS

STANDARDS 4.NF.B.4 Multiply a fraction by a whole number. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

o (4.NF.B.4a) Understand a fraction 𝑎

𝑏 as a multiple of

1

𝑏.

o (4.NF.B.4b) Understand a multiple of 𝑎

𝑏 as a multiple of

1

𝑏, and use this understanding to multiply a

fraction by a whole number. o (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using

visual fraction models and equations to represent the problem.

4.NF.C.5 Express a fraction with a denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general, but addition and subtraction with unlike denominators in general is not a requirement at this grade.)

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100.

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving whole numbers and/or simple fractions (addition and subtraction of fractions with like denominators and multiplying a fraction times a fraction or a whole number), and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regulatory in repeated reasoning.

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DECIMAL FRACTIONS (30 DAYS)

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 13: Lessons 13-4, 13-5, 13-6, 13-7,

13-8, 13-9, 13-10

For Lesson 4, only focus on having students generate fractions equivalent to tenths and hundredths.

For Lesson 6, only focus on having students express fractions with denominator 10 as an equivalent fraction with denominator 100.

Module 6: Topic A Lessons 1-4 Module 6: Topic B Lessons 5-8 Module 6: Topic C

Lessons 9-11 Module 6: Topic D Lessons 12-14 Module 6: Topic E Lessons 15-16

Unit 4, Lessons 18 – 22 Unit 5, Lessons 24 – 25

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

Guidebook: Lessons:

Event Signs: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-instructional-tasks.pdf?sfvrsn=5 Teachers Appreciation Week: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-instructional-

tasks.pdf?sfvrsn=5

Dollars and Cents: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/4th-grade-instructional-tasks.pdf?sfvrsn=5 LearnZillion:

Lessons:

Multiply fractions by whole numbers: using models: https://learnzillion.com/lesson_plans/4654 Use a fraction model for multiplication of fractions and whole numbers: https://learnzillion.com/lesson_plans/6656

Illustrative Mathematics:

Tasks:

4.NF – Adding Tenths and Hundredths: https://www.illustrativemathematics.org/content-standards/4/NF/C/5/tasks/153 4.NF – Dimes and Pennies: https://www.illustrativemathematics.org/content-standards/4/NF/C/5/tasks/152 4.NF – Expanded Fractions and Decimals: https://www.illustrativemathematics.org/content-standards/4/NF/C/5/tasks/152 4.NF – Fraction Equivalence: https://www.illustrativemathematics.org/content-standards/4/NF/C/5/tasks/154

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DECIMAL FRACTIONS (30 DAYS)

3. Activities for Understanding

SUGGESTIONS

Multiply a Unit Fraction by a Whole Number: Students will multiply fractions by a whole number using decomposition and number lines. http://www.k-

5mathteachingresources.com/support-files/multiply-a-unit-fraction-by-a-whole-number.pdf Multiply a Fraction by a Whole Number:

Students will use fraction models to multiply a fraction by a whole number and asking themselves: When you multiply a number by a fraction less than 1, is the product less than the number, greater than the number, or equal to the number? http://www.k-5mathteachingresources.com/support-files/multiply-a-fraction-by-a-whole-number.pdf

Sums of One:

Students will work with a partner to add two fractions: one with a denominator of 10 and one with a denominator of 100, to reach a sum of one. Students must rename tenths as hundredths before calculating the sum. http://www.k-5mathteachingresources.com/support-files/sums-of-one.pdf

Multiplying Fractions by a Whole Numbers (Pattern Blocks): (pg. 56) Students will identify unit fractions, decompose fractions in unit fractions, and multiply a whole number by a

fraction. http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade4-2014new.pdf/521000852/CCSSMathTasks-Grade4-2014new.pdf

Show What You Know: Multiple Representations of Decimals and Fractions (Decimal Grids): (pg.59)

Students will create multiple representations of a decimal, compare and order decimals to the hundredths and use decimal notation for fractions. http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade4-2014new.pdf/521000852/CCSSMathTasks-Grade4-2014new.pdf

Zach’s Zoo Adventure: (pg.49)

Students will practice multiplying a whole number by a fraction. http://maccss.ncdpi.wikispaces.net/file/view/4thgrade_GAMES_8.22.14.pdf/519547634/4thgrade_GAMES_8.22.14.pdf

Fraction Go Fish: (pg.60)

Students will practice expressing a fraction with denominator 10 as an equivalent fraction with denominator 100 to add two fractions with denominator 100. http://maccss.ncdpi.wikispaces.net/file/view/4thgrade_GAMES_8.22.14.pdf/519547634/4thgrade_GAMES_8.22.14.pdf

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UNIT 9- MEASUREMENT AND CONVERSIONS

MEASUREMENT AND CONVERSIONS (14 DAYS)

1. Overview

Students will solve problems involving measurement and conversion of measurements (customary and metric length, capacity, weight/mass) and units of

time within a system. The units of measure that have not been addressed in prior years are pounds, ounces, kilometers, milliliters, and seconds.

Students’ prior experiences were limited to measuring length, mass, liquid volume, and elapsed time. Students did not convert measurements. Students

need ample opportunities to become familiar with these new units of measure. Relating units within the metric system is another opportunity to think

about place value. Relating units within the traditional system provides an opportunity to engage in mathematical practices, especially “look for and make

use of structure” and “look for and express regularity in repeated reasoning.”

When students solve multi-step word problems, they should have ample opportunities to use number line diagrams to solve word problems. Number line

diagrams that feature a measurement scale can represent measurement quantities. Examples include a ruler, a diagram marking off distance along a road

with cities at various points, a timetable showing hours throughout the day, or a volume measure on the side of a container.

Students will use the formulas for the perimeter and area of rectangles and rectilinear figures to solve real-world problems. While students are expected

to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of

why the formulas work. “Apply the formula” does not mean write down a memorized formula and replace with known values because 4th grade

students do not evaluate expressions until grade 6. Students will also have the opportunity to create line plots to display a set of measurements in

fractions of a unit. Students will work with fractions by measuring objects to an eighth of an inch (1

2,

1

4,

1

8). Students make a line plot of this data and

then add and subtract fractions based on data in the line plot.

NOTE: enVisionMATH does not contain any lessons that support the standard 4.MD.D.8. Refer to Section 2 for supporting resources.

NOTE: Students in Grade 4 will be assessed on multiplying a fraction and a whole number as indicated in the NF domain. Some students may be able to

multiply a fraction by a fraction as a result of generating equivalent fractions; however, mastery of multiplying two fractions occurs in Grade 5.

Manipulatives/Materials: inch/centimeter ruler, capacity containers, balance scale, ounce weights, gram/kilogram weight, color tiles, grid paper

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FOCUS

STANDARDS 4.MD.A.1 Know relative sizes of measurement units within one system of units including: ft, in; km, m, cm; kg,

g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. (Conversions are limited to one-step conversions.) Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving whole numbers and/or simple fractions (addition and subtraction of fractions with like denominators and multiplying a fraction times a fraction or a whole number), and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

4.MD.A.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1

2,

1

4,

1

8). Solve problems

involving addition and subtraction of fractions by using information presented in line plots.

4.MD.D.8 Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems. This was formally 3.MD.C.7d.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regulatory in repeated reasoning.

FOUNDATIONAL

STANDARDS

3.OA.A.4 3.OA.C.7 3.MD.A.2 3.MD.B.4 3.MD.C.7 3.MD.D.8

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MEASUREMENT UNITS AND CONVERSIONS (14 DAYS)

2. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 14: Lessons 14-1, 14-2,

14-6, 14-7, 14-8, 14-9, 14-10

Enrichment Lessons- Topic 15: 15-1

Module 7: Topic A Lessons 1/2- 4 Module 7: Topic B Lessons 6-10/11 Module 7: Topic C

Lessons 12-14 Enrichment Lessons: Topic D Lessons 15/16-18

Unit 5, Lesson 23 – 24

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

LearnZillion: Lessons:

Compare and convert customary units of length: https://learnzillion.com/lesson_plans/5003 Compare and convert customary units of weight: https://learnzillion.com/lesson_plans/5615 Compare and convert metric units of length: https://learnzillion.com/lesson_plans/7014

Illustrative Mathematics:

Tasks:

4.MD – Who is the tallest? https://www.illustrativemathematics.org/content-standards/4/MD/A/1/tasks/1508

4.MD – Margie Buys Apples: https://www.illustrativemathematics.org/content-standards/4/MD/A/2/tasks/873

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STEP-UP TO 5TH GRADE TOPIC 17 – STEP-UP TO GRADE 5 (18 DAYS)

1. Overview

The Step-Up lessons will help prepare students for important content that is taught in 5th grade. These lessons are intended to be used at the end of the

school year.

FOCUS

STANDARDS 5.OA.A.1 Use parentheses or brackets in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2 Write simple expressions that record calculations with whole numbers, fractions, and decimals, and interpret numerical expressions without evaluating them.

5.NBT.A.3 Read, write, and compare decimals to thousandths. o (5.NBT.A.3a) Read and write decimals to thousandths using base-ten numerals, number names, and

expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1

10) + 9 x (

1

100) + 2 x (

1

1000).

o (5.NBT.A.3b) Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.A.4 Use place value understanding to round decimals to any place.

5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, subtracting multiples of the divisor, and/or the relationship between multiplication and division. Illustrate and/or explain the calculation by using equations, rectangular arrays, area models, or other strategies based on place value.

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation.

5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a

b = a ÷ b). Solve word problems

involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a

fraction.

o (5.NF.B.4a) Interpret the product (𝑚

𝑛) x q as m parts of a partition of q into n equal parts; equivalently, as

the result of a sequence of operations, m x q ÷ n. o (5.NF.B.4b) Construct a model to develop understanding of the concept of multiplying two fractions and

create a story context for the equation. o (5.NF.B.4c) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the

appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

o (5.NF.B.4d) Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regulatory in repeated reasoning.

TOPIC 17 – STEP-UP TO GRADE 5 (10 DAYS)

2. Resources

e n V i s i o n M A T H

Step-Up Lessons 1, 2, 3, 4, 5, 6, 7, 8, 9, 10