Laura Chambless

RESA Consultant

www.protopage.com/lchambless

5th GradeFractions &

Word Problems

CCSS and Gaps

What are your gaps in curriculum?1. Review CCSS for Fractions2. Think about your resources3. Think about your teaching– Highlight anything your resources

covers well in YELLOW.– Highlight any part of the standard you

would like more clarification on in BLUE.

Learning Target

Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.1, 5.NF.2

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3, 5.NF.4, 5.NF.5, 5.NF.6, 5.NF.7

Fraction Word Problem

40 students joined the soccer club.5/8 of the students were boys.How many girls joined the soccer club?

Draw a picture and solve it.1. 2 min. working problem on own2. 5 min. sharing with group3. Class discussion

Found at: http://www.mathplayground.com/wpdatabase/Fractions1_3.htm

Problem Solving withBar Diagrams

1. Understand: Identify what is known and what is unknown. Draw the bar diagram to promote comprehension and demonstrates understanding. (Situation vs. Solution Equation)

2. Plan: Decide how you will solve the problem (find the unknown). Analyze the bar diagram to find a solution plan.

3. Solve: Execute the plan. Use the bar diagram to solve.

4. Evaluate: Assess reasonableness using estimation or substitution. Substitute the solution for the unknown in the bar diagram.

Bar Diagrams

Watch Introduction Videohttp://www.mhschool.com/math/common/pd_video/mathconnects_bardiagram_p1/index.html http://www.mhschool.com/math/common/pd_video/mathconnects_bardiagram_p2/index.html

Practice Bar DiagramsTo: Rani earned $128 mowing lawns and $73

babysitting. How much money did Rani earn?

With: Jin had $67 in his pocket after he bought a radio controlled car. He went to the store with $142. How Much did Jin spend on the car?

By: There are 9 puffy stickers. There are 3 times as many plain stickers as puffy stickers. How many plain stickers are there?

You pick 2 more to do by yourself. Share with partnerDraw Your Way to Problem Solving Success Handout, Robyn Silbey

Thinking Blocks

http://www.mathplayground.com/thinkingblocks.html

Explore the site

When done exploring go to my Protopage and look at your grade level math tab.

Fractions

Stand and ShareMake a list of what you know and any

connections you have about the fraction ¼.

Representations

(Part 2 video, 5:16)Set Purpose of video: List why representations are important in

the classroom.

From: Dev-TE@M session 2

•Representations are mathematics content representing mathematical ideas is a practice that students need to learn.

•Representations provide tools for working on mathematics and contribute to the development of new mathematical knowledge.

•Representations support communication about mathematics.

•Using multiple representations can help develop understanding and support the diverse needs of students.

Benefit of Representations

(Part 4 video, 2:17)Set Purpose of video: Did you benefit from our

discussions, and how will your students benefit from class discussions?

1. As you listen , list benefits for students

2. Compare list with partner

From: Dev-TE@M session 3

Build Connections to Whole Numbers

0 1 2 3 4 5

0 11/21/4 3/4

¼ + ¼ + ¼ + ¼ = 1

1 + 1 + 1 + 1 + 1 = 5

FractionsFraction Activity

Paper Strips Fraction Kit: 1, ½, 1/4 , 1/8, 1/16

Add to Fraction Kit: 1/3, 1/6, 1/12

Add to Fraction Kit: 1/5, 1/10

Compare/Add/Subtract/Multi./Divide with StripsREAD and DO: 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.5,

5.NF.6, 5.NF.7

Smaller Answer Wins (need dice)• Prove with Fraction Strips

Lunch

Definition of Fractions

1. Make a list of what you would like to have in a definition of a fraction

2. Partner up and compare lists

3. Group discussion

Definition of a Fraction

(Part 5 and 6 videos, 11:48/4:27)Set Purpose of video: What are some key parts in

creating a definition of a fraction that you will use in your room?

–Give handout of working definition

Article: Definitions and Defining in Mathematics and Mathematics Teaching by: Bass and Ball

From: Dev-TE@M session 3

Definition Of Fractions• Identify the whole• Make d equal parts• Write 1/d to show one of the equal

parts• If you have d of 1/d, then you have the

whole• If you have n of 1/d, then you have n/d• n and d are whole numbers• d does not equal 0Dev-TE@M • School of Education • University of Michigan • (734) 408-4461 • dev-team@umich.edu For review only - Please do not circulate or cite without permission

Ordering Fractions

Order Fractions 8/6, 2/5, 8/10, 1/12

How did you figure out what order they went in?

Fractions

Prove with Fraction Strips

Number Line: (Benchmarks) 0, ½, 1

Equivalent Fractions: Same Name Frame

Compare (>/<): same numerator or same denominator

Strategies for Comparing Fractions

• Dev-TE@M session 9

Fraction On A Number Line

Writing about Fractions: Draw a number line.Place 3/6 and 7/12 on the number line.Compare the two fractions- why did put

them where you did?

Key Ideas About the Number Line

What were some intentional talk moves others used to explain their number line?

(Part 5 video, 5:26)Set purpose of video: Listen to the detail that is given in

explaining how to construct a number line.

From: Dev-TE@M session 4

Conventions Of A Number Line

Dev-TE@M • School of Education • University of Michigan • (734) 408-4461 • dev-team@umich.edu For review only - Please do not circulate or cite without permission

Talking Through A Number Line

1. Understand the problem.

2. Think about which representation you are going to use.

3. Describe your thinking process while constructing the number line.

4. Sum up the solution that proved your answer.

Model Example: 3/10 & 6/8

Fraction On A Number Line

Using a number line, compare 5/6 and 3/8 and tell which one is greater . Have a partner listen to you as you construct the fractions and find the answer.

Fractions

What conceptual understanding do students need?

1. Begin with simple contextual tasks.2. Connect the meaning of fraction computation with

whole number computation.3. Let estimation and informal methods play a big role in

the development of strategies.4. Explore each of the operations using models.

Van De Walle Book: Number Sense and Fraction Algorithms Pg. 310

Equivalence with Fraction Strips

• Fraction Strips½ + ¼ = ¾ + 1/3 =

Methods for Generating and Explaining Equivalent Fractions

• Dev-TE@M session 9

Add/Subtract Fractions with Unlike Denominators

Developing Equivalent Fractions• Slicing Squares

Van de Walle book: pg. 304-305

34

=x

34

=x34

=x

34

=x

Add/Subtract Fractions with Unlike Denominators

Developing Equivalent Fractions• Missing-Number Equivalencies

Van de Walle book: pg. 304-305

53

=6

23

=6

Fraction Multiplication Strategies

TOOLKIT for Multiplication of Fractions1. Skim over TOOLKIT2. Read assigned page (2 min)3. 30 second report: What are the

important part of your page?4. Questions from audience

Fractions

Multiply a fraction by a whole number• Work as a group• Use Fraction strips to show answers

4 x 1/3¼ x 12

• What connection can you make to multiplication? What other representations can you use? Can you use a number line?

Multiple a Fraction by a Whole Number

4 x 1/3 (4 groups of 1/3) = 4/3 = 1 1/3I want 4 ribbons each at 1/3 of a yard. How much

ribbon will I need to purchase?

¼ x 12 (1/4 of 12) = 3I have 12 cookies and want each of my friends

to have ¼ of them. How many cookies will each friend get?

1/3 2/3 3/3 4/3

Scaling (resizing)

• 5.NF.5– Read learning targets and discuss– Prove greater/less than given number

statements with last slide.– Making equivalent fractions

Multiply Fraction by Fraction

AIMS• Fair Squares and Cross Products

MMPI• Worksheet 1: Show different

representations2/3 of ¾ ¾ of 2/3

Multiply Fractions and Mixed Numbers

MMPI• Area Model Rectangular Multiplication PPT http://www.michiganmathematics.org/

Fraction as Division(a/b = a ÷ b)

• I can explain that fractions (a/b) can be represented as a division of the numerator by the denominator (a ÷ b) can be represented by the fraction a/b.

• I can solve word problems involving the division of whole numbers and interpret the quotient- which could be a whole number, mixed number, or fraction – in the context of the problem.

• I can explain or illustrate my solution strategy using visual fraction models or equations that represent the problem.

Divide Fraction by Whole Number

½ ÷ 6 =6 ÷ ¼ =

4 ÷ 2 = (how to connect division of whole numbers with fractions)

Divide Fraction by Whole Number

½ ÷ 6 = If I have ½ cup of sugar and divide it among 6 people, how much sugar does each person have? 1/12

6 ÷ ¼ = If I have 6 candy bars and divide each one into fourths, how many pieces will I have? 24

1 2 3 4 5 6 7 8 9 10 11 12

MOPLS

http://mi.learnport.orgSearch: MOPLS Math

(navigate by using top tabs)

Look at Concepts Tab– Introduction– Math Behind the Math– Misconceptions– Tasks & Strategies

Fractions Online

Check out some sites on my 5th grade math Protopage

Learning Target

Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.1, 5.NF.2

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3, 5.NF.4, 5.NF.5, 5.NF.6, 5.NF.7

Closer Activity

List something you learn about story problems and fractions today.

Thanks for a great day

Please contact me if you have any questions or

would like more information.