Overview and Implementation Guide84

Universal AccessUniversal Access

The writers of the Common Core State Standards for Mathematics recognized that it was beyond the scope of the Standards document to describe the range of support for students with special needs; nevertheless, they stressed that all students must have the opportunity to meet the same standards. Instructional resources must take into account the learning needs of all students and provide adaptation, accommodations, or differentiated instruction that can help all students be successful in achieving proficiency with both the Standards for Mathematical Content and for Mathematical Practice.

The Common Core Math ClassroomTeachers can expect that the language demands in the Common Core Math classroom will be greater during instruction as they engage students in the Standards for Mathematical Practice. Students will be expected to construct arguments and viable conclusions (MP.3), respond to and critique the reasoning of others (MP.3), communicate precise definitions of terms (MP.6), and explain correspondences between various representations (MP.1). These expectations place even higher demands on teachers to provide opportunities for all students to be successful.

These principles can guide teachers as they plan for the needs of all learners in their classrooms, including English learners, learners receiving specialized services, at-risk or below-level learners, and advanced learners.

Principle 1: Provide Multiple Means of Representations Because learners differ in how they input information, no one way of conveying information can be effective for all learners. When content is presented through different and multiple means, learners are better able to make connections among concepts, helping to make deeper and more lasting connections.

Principle 2: Provide Multiple Means of Action and Expression Just as learners differ in how they input information, they also differ in how they express their understanding of concepts. Some learners can express themselves more effectively using images rather than words, while others find oral expression a more productive means of expression. Allowing for multiple means of expression gives all students opportunities to show what they know and understand in ways that work best for them.

Principle 3: Provide Multiple Means of Engagement What learners find of interest in learning activities varies as much as does how they prefer to engage in these activities. Some learners find new learning situations interesting while others find the challenge of these situations unapproachable. Some have difficulty working with classmates while others thrive when working independently. Offering options for engagement—individual, pair, or small group work—gives students more ownership over their learning.

Instructional resources must take into account the learning needs of all students and provide adaptation, accommodations, or differentiated instruction that can help all students be successful in achieving proficiency with both the Standards for Mathematical Content and for Mathematical Practice.

Differentiating Instruction

ENV15_CA_TPO04_PG.indd Page 84 5/17/13 4:36 PM GG003 /131/PE01126_OIG/MATH/NA/TRM/MATH/G4/XXXXXXXXXX/Layout/Interior_Files

Advanced

Leveled Homework

Also available in print Also available in print Also available in print

Differentiated Instruction

Reteaching Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

Reteaching

12-1Modeling Addition of Fractions

Eight friends want to see a movie. Four of them want to see a comedy. Two want to see an action movie and two want to see a science-fiction movie. What fraction of the group wants to see either a comedy or a science-fiction movie?

You can use a model to add fractions.

Look at the circle. It is divided into eighths, because there are eight people in the group. Each person represents 1 _ 8 of the group. Four people want to see a comedy. Shade in four of the sections to represent 4 _ 8 . Two people want to see a science-fiction movie. Shade in two more sections to represent 2 _ 8 . Count the number of shaded sections. There are six. So, 6 _ 8 of the group wants to see either a comedy or a science fiction movie.

4 __ 8 + 2 __

8 = 6 __

8 Write the sum in simplest form. 6÷2 ____

8÷2 = 3 __

4

Find each sum. Simplify, if possible.

1. 2 __ 5 + 1 __ 5 2. 4 __ 6 + 1 __

6 3. 3 __

8 + 3 __

8

4. 1 __ 6 + 1 __

6 5. 2 __ 5 + 3 __ 5 6. 2 ___

10 + 3 ___

10

7. 5 __ 8 + 3 __

8 8. 3 ___

10 + 1 ___

10 9. 3 __

4 + 1 __

4

10. 5 ___ 10

+ 4 ___ 10

11. 1 __ 6 + 1 __

6 + 1 __

6 12. 1 ___

12 + 5 ___

12 + 2 ___

12

13. Number Sense We can express time as a fraction of an hour. For example, 15 minutes is 1 _ 4 hour. 30 minutes is 1 _ 2 hour. What fraction of an hour is 45 minutes?

3 __ 5 5 __ 6 6 __ 8 or 3 __ 4

2 __ 6 or 1 __ 3 5 __ 5 or 1 5 ___ 10 or 1 __ 2

8 __ 8 or 1 4 ___ 10 or 2 __ 5 4 __ 4 or 1

9___10 3 __ 6 or 1 __ 2 8 ___ 12 5 2 __ 3

3 __ 4 hour

R 12•1

MTH15_ANC04_CA_T12_L01_RT.indd Page 47 4/26/13 5:26 PM user /116/PE01126_TRM/MATH_2013_TRM/CA/TRM/MATH_CC_TRM/G4/XXXXXXXXXX/Layout/Interior_F ...

Practice Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

Practice

12-1Modeling Addition of FractionsFind each sum. Simplify if possible. You may use fraction strips.

1. 1 __ 4 + 1 __

4 2. 2 __ 5 + 1 __ 5 3. 3 ___

12 + 1 ___

12

4. 2 __ 6 + 3 __

6 5. 1 __

2 + 2 __

2 6. 2 __

8 + 5 __

8

7. 3 __ 8 + 3 __

8 8. 3 ___

10 + 2 ___

10 9. 1 __

6 + 2 __

6

10. Draw a Picture A rectangular garden is divided into 10 equal parts. Draw a picture that shows 3 __ 10 + 3 __ 10 = 6 __ 10 , or 3 _ 5 .

11. Each day, Steven walked 1 __ 12 mile more than the previous day. The first day he walked 1 __ 12 , the second day he walked 2 __ 12 mile, the third day he walked 3 __ 12 mile. On which day did the sum of his walks total at least 1 complete mile?

12. Algebra Find the missing value in the equation.

3 ___ 12

+ 1 ___ 12

+ ? ___ 12

= 1 __ 2

A 1 B 2 C 3 D 4

13. There are five people sitting around the dinner table. Each person has 2 __ 10 of a pie on their plate. How much pie is left? Explain.

2 __ 4 5 1 __ 2 3 __ 5 4 ___ 12 5 1 __ 3

5 __ 6 3 __ 2 7 __ 8

6 __ 8 5 3 __ 4 5 ___ 10 5 1 __ 2 3 __ 6 5 1 __ 2

5th day

Sample answer: None; 2 ___ 10 1 2 ___ 10 1 2 ___ 10 1 2 ___ 10 1 2 ___ 10 5 1, so the entire pie has been served.

P 12•1

MTH15_ANC04_CA_T12_L01_PR.indd Page 48 4/26/13 5:30 PM user /116/PE01126_TRM/MATH_2013_TRM/CA/TRM/MATH_CC_TRM/G4/XXXXXXXXXX/Layout/Interior_F ...

Enrichment Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

Enrichment

12-1Figuring Fractions 1. JoeandSamsharedacheesecakecutinto

12pieces.Joeate3piecesandSamate5pieces.Whatfractionofthecheesecakedidtheyeatinall?Showhowyoufoundyouranswer.

2. Kimbiked1_5ofamiletoHazel’shouseandtheybothbiked3_5ofamiletothelibrary.HowfardidKimbike?Showhowyoufoundyouranswer.

3. Mrs.Greenadded1_8ofateaspoonofsalttohertomatosauce.Whileshewasansweringthedoor,Mr.Greenadded3_8ofateaspoonofsalttothetomatosauce.Howmuchsaltwasaddedtothetomatosauce?Showhowyoufoundyouranswer.

4. Apitcherholds10glassesofpunch.Juliadrank2glassesandBilldrank4glasses.Whatfractionofthepunchdidtheybothdrink?Showhowyoufoundyouranswer.

5. Scottswam1_4ofamileacrossthelaketovisitafriend.Onthewayback,heswamalongtheshore3_4ofamile.HowfardidScottswim?Showhowyoufoundyouranswer.

6. Tencamperssetuptheirtentsalongsideastream.Ofthe10tents,3tentsareyellowand2tentsaregreen.Whatfractionofthetentsareeitheryelloworgreen?Showhowyoufoundyouranswer.

3 ___ 12 1 5 ___ 12 5 8 ___ 12 5 2 __ 3

1 __ 5 1 3 __ 5 5 4 __ 5 mi

1 __ 8 1 3 __ 8 5 4 __ 8 5 1 __ 2 tsp

2 ___ 10 1 4 ___ 10 5 6 ___ 10 5 3 __ 5

1 __ 4 1 3 __ 4 5 4 __ 4 5 1 mile

3 ___ 10 1 2 ___ 10 5 5 ___ 10 5 1 __ 2 E 12•1

MTH15_ANC04_CA_T12_L01_EN.indd Page 49 4/26/13 5:38 PM user /116/PE01126_TRM/MATH_2013_TRM/CA/TRM/MATH_CC_TRM/G4/XXXXXXXXXX/Layout/Interior_F ...

Share your thinking while you work.

PartnerTalk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

5616

+

320820

+

1757

+

3515

+

510310

+

712312

+

720420

+

2838

+

2525

+

3626

+

818518

+

4818

+

4939

+

412612

+

916616

+

415615

+

1012

1015

79

1318

45

1

If you have more time  Play again! Talk about your strategies as you play.

Get Started or

Get 10 squares in one color and 10 in another color, one paper clip, one number cube, and fraction strips. Take turns.

At Your Turn

Toss one cube to find your ovals. EXAMPLE: Choose the 3rd oval on the left, or choose the 3rd oval on the right. Mark your oval with a paper clip.

How to Play

The number you chose is a sum. Find two numbers that you can add to get that sum. Find and cover the answer. Lose your turn if the answer is taken.

How to Win The first player or team to get any three connected rectangles in a row or column wins.

56

67

58

810

1516

1120

12-1Center Activity ★★

MTH15_ANC04_CA_T12_L01_CG.indd Page 2 4/26/13 4:49 PM user /116/PE01126_TRM/MATH_2013_TRM/CA/TRM/MATH_CC_TRM/G4/XXXXXXXXXX/Layout/Interior_F ...

On-Level

Share your thinking while you work.

PartnerTalk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

1112

612

1312

1012

912

812

912

312

1412

1212

512

1112

612

1112

812

812

If you have more time  Play again! Talk about how you know that your answer is reasonable.

Get Started or

Get 10 squares in one color and 10 in another color, two paper clips, two number cubes, and fraction strips. Take turns.

At Your Turn

Toss two cubes to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paper clips.

How to Play

Explain how to add the two numbers you chose. Use fraction strips to model each problem. Find and cover the sum. Lose your turn if the answer is taken.

How to Win The first player or team to get any three connected rectangles in a row or column wins.

312

612

112

412

312

112

512

212

712

512

812

212

12-1Center Activity ★

MTH15_ANC04_CA_T12_L01_CG.indd Page 1 4/26/13 4:49 PM user /116/PE01126_TRM/MATH_2013_TRM/CA/TRM/MATH_CC_TRM/G4/XXXXXXXXXX/Layout/Interior_F ...

Modeling Addition of Fractions

15 min

Materials Fraction models: strips or circles (Teaching Tool 15 or Teaching Tool 16)

Ask students to use fraction models to show the simplified answers to the following fraction addition problems:

• 1 __ 6 1 2 __

6 [ 1 __

2 ]

• 2 ___ 10

1 4 ___ 10

[ 3 __ 5 ]

• 3 __ 8 1 3 __

8 [ 3 __

4 ]

• 1 __ 3 1 1 __

3 [ 2 __

3 ]

• 1 __ 4 1 1 __

4 [ 1 __

2 ]

• 5 ___ 12

1 4 ___ 12

[ 3 __ 4 ]

• 1 __ 8 1 2 __

8 [ 3 __

8 ]

Intervention

Partner Talk Listen for evidence that a student is using correct vocabulary. For example, a student might say: “To find 3 __ 12 1 7 __ 12 , you add 3 1 7 to get 10 for the numerator and keep twelfths for the denominator.”

  289B

MTH15_TE04_CA_T12_L01.indd Page 2 5/9/13 12:44 AM epg /144/PE01126_TE/MATH_2013/CA/TE/CA_CC_MATH/G4/XXXXXXXXXX/Layout/Interior_Files/To ...

Universal accessAdding and Subtracting Fractions and Mixed Numbers with Like Denominators

Considerations for ELL StudentsDiscuss with students the meaning of the terms common, same and like. Discuss the general meanings as well as the meanings within the specific context of fractions.• Emerging When explaining how to add and subtract

fractions, emphasize the fractional parts. For example, say, “To add 1 fifth and 3 fifths, add the numerators. 1 fifth 1 3 fifths equals 4 fifths.”

• Expanding Have volunteers explain how to change a fraction into simplest form. Encourage students to use proper vocabulary words such as greatest common factor.

• Bridging Write two fractions with like denominators on the board. Ask pairs of students to write addition or subtraction word problems involving the fractions shown.

Considerations for Special-Needs Students• Although models are used in only 3 of the lessons in

this topic, allow special-needs students to use models for as long as necessary.

• To help students express fractions in simplest form, allow them to use fraction strips or a fraction equivalency chart.

• If students have a hard time marking divisions on a number line, allow them to fold and mark fraction strips.

Considerations for Below-Level Students• To help below-level students, make a list of steps

for adding and subtracting fractions with like denominators: 1. Add or subtract numerators, 2. Rewrite common denominator, 3. Use the greatest common factor to change to simplest form.

• If students have difficulty solving word problems, encourage them to draw models to represent the problem.

Considerations for Advanced/Gifted Students• If students seem proficient adding fractions with like

denominators, challenge them to add fractions with like denominators whose sum is greater than 1 or to add mixed numbers with like denominators.

• Discuss with students how you might go about adding and subtracting fractions with unlike denominators.

Ongoing Intervention

• Lessons with guiding questions to assess understanding

• Support to prevent misconceptions and to reteach

Strategic Intervention

• Targeted to small groups who need more support

• Easy to implement

Intensive Intervention

• Instruction to accelerate progress• Instruction focused on

foundational skills

Response to Intervention

Topic

12

285C Topic 12

MTH15_TE04_CA_T12_FM.indd Page 3 5/8/13 1:45 PM epg /144/PE01126_TE/MATH_2013/CA/TE/CA_CC_MATH/G4/XXXXXXXXXX/Layout/Interior_Files/To ...

Program Guide 85

enVisionMATH California Common Core provides comprehensive support to differentiate instruction for all learning needs. enVisionMATH California Common Core provides support for English Language Learners (ELL), students receiving specialized services, struggling students, and advanced learners.

In the front matter of each topic are topic-specific considerations and strategies for ELL, Special Needs, Below Level, and Advanced/Gifted students. Teachers will find instructional activities that can help the targeted group of students be more successful with the content of the topic. Often, these activities can be beneficial for all learners.

In Part 4 of each lesson, Close/Assess and Differentiate, teachers will find data-driven differentiation. It includes an Intervention Activity and a Reteaching Master for Below-Level students, an On-Level Center Activity and a Practice Master for students who are working at grade level, and an Advanced Center Activity and an Enrichment Master for advanced learners.

Teachers will also find an ELL strategy that they can implement with the two Center Activities.

ENV15_CA_TPO04_PG.indd Page 85 5/24/13 7:10 PM s-w-018 /131/PE01126_OIG/MATH/NA/TRM/MATH/G4/XXXXXXXXXX/Layout/Interior_Files