FOCUS

A curriculum with focus for deeper understanding!

Implementing the Common Core… Common Core Standards The standards call for greater focus in mathematics. Rather than “touching” on many pieces of content in a “mile-wide, inch-deep” curriculum, Common Core narrows the amount of content at a grade. This increases the time for a “deeper dive” and genuine emphasis, or focus, on the content. In Common Core, standards with a common focus are grouped into clusters. Major clusters get the most emphasis. Supporting clusters support the major work. Additional clusters complete the grade-level content.

Focus Within a Grade • Focus on Common Core Clusters One or more topics focus on each Common Core cluster. For example, the cluster wheel below shows that Topics 2, 3, 4, and 5 focus on Major Cluster 4.NBT.B, which is about multi-digit arithmetic. (Also see p. 62.)

MAJOR CLUSTER

SUPPORTING CLUSTER

enVisionmath2.0

LESSONS

The program is organized to help students focus on clusters of Common Core standards within a grade. Each Common Core cluster is the focus of one or more topics to promote in-depth development.

TOPICS

1

16

2

CLUSTERS

15

Within a topic, the Topic Essential Question identifies a focus for the whole topic, and Essential Understandings are often the focus for groups of related lessons. Highly effective teachers focus students’ attention on, and make explicit, the important ideas students need to understand in a lesson. Many elements of the lessons are resources that teachers can use to achieve this focus.

ADDITIONAL CLUSTER

4.NBT.A

4.G.A 4.MD.C

14

3

4.OA.C

13 4.MD.A 4.NBT.B

12

11

4

FOCUS ON COMMON CORE CLUSTERS

4.NF.C

4.MD.B

5

10 4.NF.B

4.OA.A 4.OA.B

9

4.NF.A

8

28

7

6

FOCUS

COHERENCE

MATH PRACTICES

RIGOR

ASSESSMENT

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EFFICACY

Digital

Focus Within a Topic

Focus Within a Lesson

• The Focus of a Topic At the start of a topic, one or more Essential Questions help students focus on key ideas in the topic. Essential Questions are revisited at the end of the topic.

• The Focus of a Lesson Some of the elements of a lesson that help teachers focus students’ attention on important lesson ideas include the Lesson Essential Question, the Visual Learning Bridge and its digital counterpart, the Visual Learning Animation Plus, as well as Do You Understand? Show Me! (Grades K–2) or Convince Me! (Grades 3–6).

Digital Resources

Understand Addition and Subtraction of Fractions

TOPIC

9

Solve

Essential Questions: How do you add and subtract fractions and mixed numbers with like denominators? How can fractions be added and subtracted on a number line?

Learn

Glossary Learn

Tools Assessment Help

Games

2 Mary rides her bike 10 mile to pick up her friend Marcy for soccer practice. Together, they ride 5 10 mile to the soccer field. What is the distance from Mary’s house to the soccer field?

Morse code uses a special machine to transfer information using a series of tones. A combination of dots and dashes stands for each letter, each number, and even some whole words.

How Do You Add and Subtract Fractions on a Number Line?

Glossary

A

Mary’s house

How do you write, “I love math?” using Morse code? Here is a project about fractions and information.

Marcy’s house

2 mile 10 B

You can use jumps on the number line to add or subtract fractions. Soccer

5 mile 10

2 + 5. Use a number line to show 10 10

C

2 Draw a number line for tenths. Locate 10 on the number line.

Write the addition equation. Add the numerators. Write the sum over the like denominator. 5 2+5 2 7 10 + 10 = 10 = 10

5 to the right. To add, move 10 5 10

0

?

2 10

1

When you add, you move to the right on the number line.

• The Focus of a Group of Lessons An Essential Understanding is stated in the Teacher’s Edition for each lesson. Often the same Essential Understanding is given for a group of consecutive lessons. As students focus on an Essential Understanding over multiple days, they develop deeper conceptual understanding.

The distance from Mary’s house to the 7 mile. soccer field is 10

Convince Me!

MP.5 Use Appropriate Tools Use the number line below to find 58 + 28. Can you also use the number line to find 58 - 28? Explain.

0

496

1

Topic 9

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Math and Science Project: Fractions and Information Transfer

Essential Understanding The

Do Research Morse Journal: Write a Report Include what you found. Also in your standard addition and subtraction code uses patterns to report: algorithms for multi-digit numbers transfer information. • Write one in Morse code. Write a fraction that tells what part Any wordbreak can be the calculation into simpler of the code for one is dashes. written using Morse calculations using place value • Write three in Morse code. Write a fraction that tells what code. Use the Internet starting with thepart ones, the of thethen code for three is dots. or other sources to find how to write fourth, tens, and so on. • Write and solve an equation to find how much greater grade, and school using the fraction for dots is than the fraction for dashes in Morse code. 2-3 Add Whole Numbers the word three.

2-4 Subtract Whole Numbers

Topic 9

461

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29

A coherent curriculum with new ideas connected to prior knowledge!

COHERENCE

Implementing the Common Core… Common Core Standards The standards identify coherence as the developmental progression of mathematics across grades and the links between related mathematics within a grade. One of these links is the way supporting clusters reinforce the content taught in major clusters. enVisionmath2.0

Coherence Across Grades • Look Back Connections to content taught in previous grades are highighted in the Coherence part of Cluster Overview pages in the Teacher’s Edition. Shown below is a Look Back from Topics 9–10. (Also see p. 63.)

Major Cluster 4.nf.b

tOPICS

9–10

The program achieves coherence across grades MatH through careful learning progressions. Coherence is also FOCUS supported by common elements across grades such as thinking habits questions for math practices and bar diagrams for representing quantities in a problem.

BaCkGROUNd: COHERENCE COHERENCE

Content Coherence in

Coherence across topics, clusters, and domains within a grade is the result of developing theStudents mathematics asideas are connected in a coherent learn best when curriculum. a body of interconnected concepts and skills.This coherence is achieved through various types of connections including connections within clusters, across clusters, across domains, and across grades.

Coherence across lessons and standards is achieved when new content is taught as an extension ofINprior BIG IdEaS GRadES k–6 learning—developmentally and mathematically. For Big Ideas are the conceptual underpinnings of example, Solve and Share at the startenVisionmath2.0 of lessons and provide conceptual cohesion of engages students in a problem-basedthe content. learningBig Ideas connect Essential Understandings throughout the program. Content Coherence in experience that connects prior knowledge to new ideas.

A Big Idea that connects most of the work in this cluster is that complex calculations involving fractions and mixed numbers ToPICs 9 AND can be broken into 10 simpler equivalent calculations involving unit fractions. For example, How is content connected within Topics 9–10? 3 2 + = 1+1+1 + 1+1 4 4 4 4 4 4 4 • Fractions and Mixed Numbers In Lessons 9-1 through 4=2× 4×1 2 × 9-6, students come to understand fraction addition and 4 4 subtraction. (4.NF.B.3a) In Lessons 9-8 through 9-10, they For a complete list of Big Ideas, see pages 90–91 in the extend these understandings to addition and subtraction of Teacher’s Edition Program Overview. mixed numbers. (4.NF.B.3c)

(

(

) ( )

RIGOR

)

LOOk BaCk How do Topics 9–10 connect to what students learned earlier? GRadE 3 • Meaning of Fractions In Topic 12, students strengthened their understanding of the meaning of fractions and used various models to represent them. (3.NF.A.1, 3.NF.A.2a, 3.NF.A.2b) (continued)

Look AhEAD

1

1 4

1 4

1 4

3 4

How will Topics 9–10 connect to what students will learn later? • Simple Equivalent Fractions In Topic 13, students LATER IN GRADE 4 learned how to recognize and generate simple equivalent fractions and to express numbers as In Topics 11 fractions. • Fractions in Data and whole Measurement (3.NF.A.3a, 3.NF.A.3b, 3.NF.A.3c) and 13, students will solve data and measurement problems involving adding and subtracting fractions with like denominators and multiplying a fraction by a whole number. (4.MD.A.2, 4.MD.B.4)

• Fraction Addition and Multiplication In Lessons 9-1, 9-2, 9-3, and 9-6, students add fractions with like • Look Ahead Connections to content in the next grade are denominators. (4.NF.B.3a) In Lessons 10-1 and 10-2, this also highlighted Heights of Orchid Plants in the Coherence part of Cluster Overview addition work is used to build a foundation for fraction 157 2 pages in the Teacher’s Edition. • • • = Shown4 below is 8a Look multiplication. (4.NF.B.4a, 4.NF.B.4b) 3 6 • •• • • • Ahead from Topics 9–10. •(Also see p.• 63.) - 1338 4=1+1+1+1 6 6 6 6 6

EaRLIER IN4GRadE 4 4 13 13 14 14 8 8

4=4×1=4×1 6 6 6

1 6

1 6

1 6

Content Coherence in

• Multiplication and Unit Fractions In Lesson 10-2,

ToPICs 9 AND 10 students come to understand that they can think of a fraction

as the product of a whole number and a unit fraction. How is content connected within Topics 9–10? (4.NF.B.4a) This helps them in Lessons 10-2 and 10-3 to view the product of a whole number and a fraction as a multiple of • Fractions and Mixed Numbers In Lessons 9-1 through a whole number and a unit fraction. (4.NF.B.4b) 9-6, students come to understand fraction addition and subtraction. (4.NF.B.3a) In Lessons 9-8 through 9-10, they • Word Problems Involving Fractions Throughout extend these understandings to addition and subtraction of Topics 9 and 10, students apply their knowledge of fraction mixed numbers. (4.NF.B.3c) addition, subtraction, and multiplication to solve problems. (4.NF.B.3d, 4.NF.B.4c) • Fraction Addition and Multiplication In Lessons 9-1, 9-2, 9-3, and 9-6, students add fractions with like • Time Problems Involving Fractions Topic 10 also 461C Topics 9–10 Cluster Overview denominators. (4.NF.B.3a) In Lessons 10-1 and 10-2, this develops content from Supporting Cluster 4.MD.A on solving addition work is used to build a foundation for fraction measurement problems involving simple fractions. See multiplication. (4.NF.B.4a, 4.NF.B.4b) Lesson 10-5. (4.MD.A.2) 4=1 1 +AM1sw-102 MTH16_TE04_CC2_T09_CM.indd Page 3 19/06/14 + 1 + 9:16 6 6 6 6 6 4=4×1=4×1 6 6 6

30

1 6

1 6

16

24 8

(continued)

• Decimal Fractions In Topic 12, students will add fractions with denominators of 10 and 100. (4.NF.C.5)

Look AhEAD7 = 7 × 2

14

= • Fractions and 8Angle 8 2Measure In Topic 15, students will 16 learn that an n-degree angle is an angle that turns n times How will Topics 9–10 connect to what students will learn later? n through 360 of a circle. (4.MD.C.5a, 4.MD.C.5b)

LATER IN GRADE 4 GRADE 5 • Fractions in Data and Measurement In Topics 11 and 13, students will solve data and measurement problems • Fraction Computation In Topic 7, students will add involving adding and subtracting fractions with like and subtract fractions and mixed numbers with unlike denominators and multiplying a fraction by a whole number. denominators. (5.NF.A.1) In Topic 8, they will multiply (4.MD.A.2, 4.MD.B.4) fractions. (5.NF.B.4a) In Topic 9, they will divide fractions and whole numbers. (5.NF.B.4a, 5.NF.B.7a, 5 NF.B.7b)

Heights of Orchid Plants

• • • •• 13

4

13 8

• • • 14

• •

•

157 8

- 133 8

4 /151/PE01513_TE_1of1/ENVISION_MATH_ENGLISH/NA/TE/2013/G4/XXXXXXXXXX/Layout/Interi ... 4 4

14 8

15

15 8

16

28

Inches

1 1 6

4

15 8

InchesIn Topic 8, students recognized and • Equivalent Fractions generated equivalent fractions that have a greater variety of denominators. (4.NF.A.1) inches taller than the shortest plant. The tallest plant is 24 8

1 1 6

15

1 6

inches taller than the shortest plant. The tallest plant is 24 8

FOCUS

COHERENCE

RIGOR

DEVELOP: VISUAL LEARNING

MATH PRACTICES

ASSESSMENT

All materials available at PearsonRealize.com

EFFICACY

PearsonRealize.com

The Visual Learning Bridge connects students’ thinking in the Solve & Share to important math ideas in the lesson. Use the Visual Learning Bridge to make these ideas explicit. Also available as a Visual Learning Animation Plus at PearsonRealize.com

Visual Learning

Coherence Across Topics, Clusters,

Learn

Digital

Glossary

Coherence Across Lessons

Make Sense and How Do You Add and Subtract Fractions on a and Domains and Standards vere Number Line? A information are• Supporting you Clusters Topics that focus on supporting • Connections to Prior Knowledge in Problemin this problem? clusters provide 2 topics that focus on major support for Based Learning The Solve and Share in every lesson Mary rides her bike 10 mile to pick up her friend y rides her bike clusters. The Teacher’s Marcy for soccer practice. Together, they ride Edition identifies that support in supports coherence. It engages learners by connecting 5 You can use jumps 10 mile to the soccer field. What is the distance e to Marcy’s house; the Coherencefrom part of the Cluster Overview pages. prior knowledge to new ideas through a problem-solving on the number line Mary’s house to the soccer field? to add or subtract experience. he rides her bike fractions. Mary’s Marcy’s e to the soccer field.] house house Soccer must you find? [The distance Mary rides ke to get to soccer 2 5 mile mile ce] What operation 10 10 MP.3 Construct Arguments ou use to find the How can using a number DEVELOP: PROBLEM-BASED LEARNING B C 2 + 5. Write the addition equation. Use a number line to show 10 1 ce? [Addition] 10 line help you write an Learn

Glossary

Visual Learning Bridge

STEP

PearsonRealize.com

2 on the Draw a number line for tenths. Locate 10

number line.

5 to the right. To add, move 10

COHERENCE: Engage learners by connecting prior knowledge to new ideas. Students extend their understanding of adding and subtracting fractions with like denominators by showing these operations on a number line.

Add the numerators. Write the sum over the like denominator. 5 2+5 2 7 10 + 10 = 10 = 10

LESSON 9-6

Whole Class

BEFORE

equation and solve the problem? [Sample answer: It helps me find the total distance to the soccer field, the distance Mary rides to Marcy’s house, and the distance Mary and Marcy ride their bikes to the soccer field.]

1. Pose the Solve-and-Share Problem MP.5 Use Appropriate Tools Strategically In this problem, look for students who use a number line to find the fraction of the charge left on a phone and explain their work.

Solve

10–15 min

Name

Lesson 9-6

Use Appropriate Tools gically 0 ? 2 1 10 does each segment The distance from When you add, you move to the right on the Mary’s house to the e number line number line. 7 mile. soccer field is 10 1 sent? [10 ] Why is umber line divided 0 equal segments? Convince Me! MP.5 Use Appropriate Tools Use the number line below to number line should Prevent find 58 + 28. Can you also use the number line to find 58 - 28? Explain. vided into 10 equal DIGITAL RESOURCES PearsonRealize.com misconceptions ents because 10 is Some students may still be Listen and 0 1 enominator of all• Connections the Across Clusters, and • Connectionsadding Across in a Topic The Focus 5 7 3Topics, Student and Today’s Solve and theLessons denominators. Look For 8 8 8 ers in this problem.] Domains The Teacher’s Edition notes for lessons point out and Coherence part of Math Background in the Teacher’s Teacher eTexts Challenge Share Ask them how many equal 5 + 28 = 78; Yes,connections I used the number line to subtract by moving to the left: 58Lesson − 28 = 38Edition .Video for each lesson describes connections between opportunities to8 highlight across PD Solve Think eText topics, clusters, segments the number line and domains. lessons in the is topic and some connections to other topics. divided into and if that Online Another Look 496 Topic 9 Lesson 9-6 changes they add. Math Tools Quickafter Check Personalized Homework Point out that the number Practice Video Tools Practice Assessment of equal segments on Help Convince Me! mP.5 use Appropriate tools Strategically Both Buddy the number line stays the addition and subtraction can be shown on a number line. For both, same when parts of the the number line is divided into equal segments as determined by the LESSON OVERVIEW same whole are combined like denominator. or separated. Common Core Standards math background Coherence Students have added and subtracted fractions with like Focus and Coherence In previous lessons, 4.nFwhole, Number Operations— denominators, that are partsDomain of the same withand fraction strips, with students added and subtracted fractions with Fractions number lines, and symbolically without any tools. Next, they will use like denominators by joining segments or what they have learned to add and4.nF.b subtractBuild mixedfractions numbers. (4.NF.B.3c) Cluster from unit by separating segments on the number line. fractions by applying and extending In this lesson, the meanings of adding and previous understandings of operations on subtracting fractions is extended to counting Point out that positive fractions can be added or subtracted by whole numbers. forward on the number line for addition locating a fraction on the number line and then moving to the 5 2 Standard 4.nF.b.3a Understand 5 2 Content and counting backward on the number line right to add (as for 8 + 8) or to the left to subtract (as for 8 - 8). addition and subtraction of fractions as for subtraction. joining and separating parts referring to Rigor This lesson blends conceptual the same whole. understanding with procedural skill. It Mathematical Practices mP.2, mP.4, mP.5 is conceptual in that it extends students’ understanding of addition and subtraction objective Use number lines to add and from joining and separating parts to the subtract fractions with like denominators, idea of counting forward and backward. It referring to the same whole. 5 10

2. Build Understanding What information are you given? [Sebastian has 68 of the full charge left on his phone and uses 28 of the full charge playing a game.] What are you asked to do? [Find what fraction of the full charge Sebastian has left.]

Solve

Sebastian has 68 of the full charge left on his phone. He uses 28 of the full charge playing a game. What fraction of the full charge does Sebastian have left? Solve this problem any way you choose.

Add and Subtract Fractions with Like Denominators

I can …

use a number line to add and subtract fractions when the fractions refer to the same whole.

You can use appropriate tools such as a number line to show this problem.

ADD AnD SubtRACt FRACtionS with Like DenominAtoRS Pairs

DURING

Content Standard 4.NF.B.3a Mathematical Practices MP.2, MP.4, MP.5

3. Ask Guiding Questions As Needed What operation will you use to find the amount of charge Sebastian’s phone has left? [Subtraction] How can you draw a number line for this problem? [Draw a number line from 0 to 1 that is divided into 8 equal parts. Label each tick mark as 1 2 3 , , , and so on.] 8 8 8

Whole Class

AFTER

4. Share and Discuss Solutions Start with students’ solutions. If needed, project Grace’s work to discuss how to subtract fractions using a number line. Solve 5. Transition to the Visual Learning Bridge A number line can be used to add and subtract fractions with like denominators.

1

See margin for sample student work.

Look Back!

MP.2 Reasoning Write a fraction that is equivalent to the amount of a full charge that Sebastian used when playing the game. Sample answer: 1 4

Visual Anima

6. Extension for Early Finishers

On the board, write (56 - 26) - 16. Use a number line to simplify

Digital Resources at PearsonRealize.com

this expression. [26 or 13]

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Topic 9

Lesson 9-6

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Analyze Student Work Grace’s Work

495

Learn

Gabrielle’s Work

Math

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Grace uses a number line and writes an equation to help explain her work.

MTH16_TE04_CC2_T09_L06.indd Page 495 26/06/14 1:44 PM sw-102

Games

Gabrielle draws a number line but does not show her work.

495

MATH AN

Daily Co

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1. Shira ha Of those are abou Shira’s b

𝖠 𝖡 𝖢 𝖣

5 10 4 10 3 10 2 10

4.NF.A.2

2. The tabl four peo

Nam Bill

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Em

Which p amount

31

𝖠 𝖡

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A rigorous curriculum with a balance of concepts, skills, and applications!

RIGOR

Implementing the Common Core… Common Core Standards The standards identify three aspects of a rigorous program that should be balanced with equal intensity: conceptual understanding, procedural skills and fluency, and applications. enVisionmath2.0 The program has a core instructional model that facilitates conceptual understanding. To begin, concepts emerge as students solve a problem in which new concepts are embedded (problem-based learning). Then, those concepts are made explicit through direct instruction (visual learning) that is supported by highlevel, question-driven classroom conversations. Procedural skills are taught with understanding using concrete and pictorial representations, place-value concepts, and properties. Resources are provided to help all students achieve fluency. Applications include rich, cognitively demanding tasks and a variety of problem situations, as well as infused instruction and reinforcement of the Standards for Mathematical Practice.

Conceptual Understanding • Problem-Based Learning In Step 1 of the instructional model (problem-based learning), the Solve and Share problem at the start of a lesson helps students connect what they know to new ideas embedded in the problem. When students make these connections, conceptual understanding emerges. (Also see pp. 44–45.)

7.

7.

MP.2 Reasoning Mike says that he 1 , even can find a fraction equivalent to 10 1 is in simplest form. Is Mike though 10 correct? Explain.

Yes; Sample answer: He can divide

MP.21 Reasoning Mike says that he interval on a number1line in eachfind 10a fraction equivalent to 10 , even can 2 1 . half to find though 20simplest form. Is Mike 10 is in correct? Explain. 2 A-Z Vocabulary Point X is at can a 9. Yes; Sample answer: He 3 on divide number1 line. On the same number line, each 10 interval on a number line in point Y is the same distance from 0 as 2 . half findhas pointto X, but 20a numerator of 8. What is the denominator of the fraction at point Y? A-Z Vocabulary Point X is at 2 on a 9. 12 3 number line. On the same number line, point Y is the same distance from 0 as point X, but has a numerator of 8. What is the denominator of the fraction at point Y? You can draw a picture

12to show this problem.

Common Core Assessment

MP.4 Model with Math There are 267 students and 21 adults going on a school trip. An equal number of people will ride on each bus. If there are 9 buses, how many people will ride on each bus? Model with Math There are 267 8. 32MP.4 people students and 21 adults going on a school trip. An equal number of people will ride on each bus. If there are 9 buses, how 10. many Higher Orderwill Thinking recipe calls people ride on A each bus? cup of flour. Carter only has a for 14people 32 measuring cup that holds an eighth of a cup. How can Carter measure the flour he needs for his recipe? 10. Sample Higher Order Thinking recipeuse callsa answer: CarterAcould for 14 cup of flour. Carter only has a 1 -cup measuring cup and fill it 8 measuring cup that holds an eighthtwo of a 2 , which is the same timesHow to make cup. can Carter 8 measure the flour he 1 needs as . for his recipe? 8.

4

Sample answer: Carter could use a 1 -cup measuring cup and fill it two 8 times to make 28, which is the same as 14. instructional model

• Visual Learning In Step 2 of thePart A 11. Monty is using number line to find You can draw aa picture to showthat this are problem. fractions equivalent to 46 . use the Visual (visual learning), teachers Learning Write to explain how MontyBridge can use the He says he can find an equivalent fraction number line to find his first equivalent and/orCommon Visual Learning Animation Plus to make important Core Assessment with a denominator greater than 6 and fraction. one with a denominator less than lesson concepts explicit by 6.connecting them to students’ Part A answer: Monty can divide 11. Monty is using a number line to find Sample are equivalent to 46 . Step 1.Write 1 explain thinkingfractions and that solutions from (Also seehow 46–47.) to Monty can use section ofpp. the number linethe each 6 2 3 5 1fraction He0 says61 he can find an 64equivalent 6 6 6 with a denominator greater than 6 and one with a denominator less than 6.

number to find his firsttwelfths. equivalent into twoline parts to show fraction. 8 4

This will show that 6 = 12 . Sample answer: Monty can divide each 6 section of the number line Write to explain Monty can use the into two parts how to show twelfths. number line to find his4 second equivalent 8 . This will show that 6 = 12 fraction. Part B1

0

1 6

2 6

3 6

4 6

5 6

1

Part B answer: Monty can label Sample

everytosecond theuse the Write explaintick howmark Montyofcan number his second numberline linetotofind show thirds. equivalent This fraction. 4 2

378

MTH16_SE04_CC2_T08_L02.indd 378

378

MTH16_SE04_CC2_T08_L02.indd 378

32

will show that 6 = 3 . Sample answer: Monty can label © Pearson Education, Inc. 4 Topic 8 Lesson 8-2 every second tick mark of the number line to show thirds. This will show that 46 = 23 . 1/8/14 © Pearson Education, Inc. 4

Topic 8

2:05 PM

Lesson 8-2

1/8/14 2:05 PM

FOCUS

COHERENCE

MATH PRACTICES

RIGOR

ASSESSMENT

All materials available at PearsonRealize.com

EFFICACY

Digital

Procedural Skills and Fluency

Applications

• Teaching Procedural Skills with Understanding Do Youon Addprocedural and Subtract Fractions a Students perform How better skillson when the procedures make Number senseLine? to them. So procedural skills are developed with2 mile conceptual understanding through careful Mary rides her bike 10 to pick up her friend Marcy for soccer practice. Together, they ride learning progressions. 5 You can use jumps 10 mile to the soccer field. What is the distance

• Math Practices and Problem Solving Rich, real-world problems are provided throughout the lessons, including the Math Practices and Problem Solving lessons which focus on developing the kind of thinking needed to be a good problem solver. (Also see pp. 56–57.)

Learn

Glossary

A

on the number line to add or subtract fractions.

from Mary’s house to the soccer field? Mary’s house

Marcy’s house

Soccer

2 mile 10 B

5 mile 10

2 + 5. Use a number line to show 10 10

C

Learn

Write the addition equation. Add the numerators. Write the sum over the like denominator.

2 on the Draw a number line for tenths. Locate 10 number line.

5 2+5 2 7 10 + 10 = 10 = 10

5 to the right. To add, move 10

7.

5 10

0

?

2 10

1

When you add, you move to the right on the number line.

How Can You Use Math to Model Problems?

Glossary

A

Gadsen Trail 9 110 mile

Brad and his father hiked the Gadsen Trail and the Rosebriar Trail on Saturday. They hiked the Eureka Trail on Sunday. How much farther did they hike on Saturday than on Sunday?

MP.2 Reasoning Mike says that he 1 , even can find a fraction equivalent to 10 What do1you need to find? though 10 is in simplest form. Is Mike I need toExplain. find how far Brad and his father correct?

MP.4 Model with Math There are 267 students and 21 adults going on a school trip. An equal number of people will ride on each bus. If there are 9 buses, how Rosebriar Trail hiked on Saturday and much farther they Yes; Sample answer: can divide 105 mile many people will ride on each bus? hiked on Saturday than on He Sunday. 8.

32 people

1 4 interval on a number line in each 2 10 miles 10 on Saturday 2 . half to1find 9 20 5

The distance from Mary’s house to the 7 mile. soccer field is 10

10

9.

Eureka Trail 6 10 mile

10

A-Z Vocabulary Point X is at 2 on a How can I model with math? 3 number line. On the same number line, I canY is the same distance from 0 as point point but has alearned numerator of 8. What • useX,previously concepts and skills.is the denominator of the fraction at point Y?

C

B

Convince Me!

MP.5 Use Appropriate Tools Use the number line below to find 58 + 28. Can you also use the number line to find 58 - 28? Explain.

• use bar diagrams and equations to

10. Higher Order Thinking A recipe calls Here’s my thinking. for 14 cup of flour. Carter only has a 6 4measuring cup that holds an eighth of a Find 210 - 10 . cup. How can Carter measure the flour he Use a bar diagram and write needs his recipe? an equation tofor solve.

Sample 4 answer: Carter could use a 2 10 miles 1 6 -cup measuring cup and fill it two d 8 10 times to make 28, which is the same 8 4 - 6 =d 2 d = 110 1 include 10a variety of problem 10 as 4.

12 represent and solve this problem. 0

• decide if my results make sense.

1

• Steps to Fluency Success A wealth of resources is provided to ensure all students achieve fluency on the Common Core fluency standards at each of Grades K–6. 496 Topic 9 Lesson 9-6 (Also see pp. 70–71.) © Pearson Education, Inc. 4

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• Bar Diagrams Lessons 8 can draw a picture Brad and his father hiked 110 miles situationsYou operations. Bar diagrams are included toinvolving show this problem. farther on Saturday than on Sunday. How Can You Use Math to Model Problems? to help students understand and represent the relationship Common Core Assessment Bradquantities and his father hiked the Gadsen Trail and between inModel a problem, as well ashelpdecide what Convince Me! MP.4 with Math How do the bar diagrams you Rosebriar Trail on Saturday. They hiked the Part A 11. the Monty is ifusing a number line to find decide your answer makes sense? Eureka Trail on Sunday. How much farther 4 didproblem. (Also see pp. 58–61.) operation to use solvetothe . fractions that areto equivalent 6 Learn

Glossary

A

Gadsen Trail 9 110 mile

Write to explain how Monty can use the number line to find his first equivalent fraction.

they hike on Saturday than on Sunday?

He says he can find an equivalent fraction with a denominator greater than 6 and What do you need to find? one with a denominator less than 6. I need to find how far Brad and his father hiked on Saturday and much farther they hiked than on4 Sunday. 2 3 5 1 0 on1Saturday 6

6

6

6

4 526 9 Lesson 9-11 2 10 miles on Topic Saturday 9

Sample answer: Monty can divide each 16 section of the number line into two parts to show twelfths. © Pearson Education, Inc. 84 4 = 12 This will show that Eureka Trail. 6

Rosebriar Trail 5 10 mile

6

6 10

5 10

1 10

Part B

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StepS to fluency SucceSS

TOPIC

2

B

FLUENTLY ADD AND SUBTRACT MULTI-DIGIT WHOLE NUMBERS

How can I model with math?

4 - 6. Findfraction. 210 10

• use previously learned concepts and skills.

Use a bar diagram and write Sample answer: Monty an equation to solve.

• decide if my results make sense.

OK

STEP 1

STEP 2

Fluency Development with Understanding

Ongoing Assessment of Fluency Subskills

Not OK

STEP 3

STEP 4

STEP 5

STEP 6

Fluency Intervention

Practice on Fluency Subskills

Fluency Maintenance

Summative Fluency Assessment

Here’sto myexplain thinking. how Monty can use the Write number line to find his second equivalent

I can

• use bar diagrams and equations to represent and solve this problem.

In Grade 4, students are expected to fluently add and subtract multi-digit whole numbers using the standard algorithm. (4.NBT.B.4) To help all students achieve fluency by the end of the year, follow the 6 steps outlined below and use the support materials described on pages 43L, 43M, 43N.

C

mile

/DATA%20DISK/ROSHAN/%20July2014/08:07:2014/G4_TE_T1

can label every second tick mark of the 4 2 10 miles number line to show thirds. This 6 d 10 will show that 46 = 23 .

4 - 6 =d 210 10

8 d = 110 Topic 8 8 Brad and his father hiked 110 miles farther on Saturday than on Sunday.

378

© Pearson Education, Inc. 4

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Resources Student’s Edition Resources

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Lesson 8-2

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Convince Me!

MP.4 Model with Math How do the bar diagrams help you decide if your answer makes sense?

Topic 2 Lessons Fluency Practice Activities

Fluency Practice/Assessment Worksheets Teacher’s Resource Masters ExamView® CD-ROM

Math Diagnosis and Intervention System 2.0 Diagnostic Tests Intervention Lessons Practice Buddy

526

Topic 9

Lesson 9-11

© Pearson Education, Inc. 4

Online Practice/Assessment

Auto-Scored Items On-Screen Help

Games

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Game Center Online

Games

“My Fluency Progress” Form Teaching Tool 30 43K Topic 2

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