Laura Chambless

RESA Consultant

www.protopage.com/lchambless

4th GradeWord Problems and

Fractions

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

Extend understanding of fraction equivalence and ordering.

4.NF.1, 4.NF.2

Build fractions from unit fractions by

applying and extending previous understandings of operations on whole numbers.

4.NF.3, 4.NF.4

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

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.

Examining Representations

(Part 3 & 4 Video 1:48/2:15)Set Purpose of videos: listen to the set up of your task and

example.

1. Examining Representations of ¾ with a partner (10 min)

2. Whole group discussion3. Review math notes

From: Dev-TE@M session 2

Making Connections

(Part 6 video, 2:22)Set Purpose of video: think about our discussion of ¾,

what connection types did we use?

Have you ever used connections for the different math representations in your classroom?

From: Dev-TE@M session 2

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

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

From: Dev-TE@M session 3

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

Lunch

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/with StripsREAD and DO:4.NF.3a, 4.NF.3b, 4.NF.3c

Play Greater Than, Less Than, Equal• Prove with Fraction Strips

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

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

Equivalent Fractions: Same Name Frame

Strategies for Comparing Fractions

Math Notes: Strategies for Comparing Fractions

Which strategies do you use in your classroom?

From: 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 From: Dev-TE@M session 4

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.

Student Errors

What value should be written where the arrow is pointing? What would kids write?

Session 4-6: Analyzing students’ errors when labeling marked points on the number line- see slides

From: Dev-TE@M session 4

Student Errors

Key pointsWhen determining how to respond to a student, it can be helpful to consider:

• What question(s) could be asked to learn more about the student’s thinking?

• What key mathematical idea(s) might be raised with the student?

Narrating a Representation

• Make clear the mathematical problem or context.

• Describe how a particular representation is useful for this problem.

• Construct the representation and use it to solve the task while describing and giving meaning to each step.

• Summarize what the representation has helped to do.

From: Dev-TE@M session 5

Number Lines

(Part 5 video, 4:24)Set purpose for video: review narration

(Part 6 video, 1:53)Set purpose for video: What fractions do you use for

examples

From: Dev-TE@M session 5

Equivalence with Fraction Strips

• Fraction Strips½ + ¼ = ¾ + 1/3 =

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

Developing Equivalent Fractions

Missing-Number EquivalenciesVan de Walle book: pg. 304-305

53

=6

23

=6

Methods for Generating and Explaining Equivalent Fractions

Math Notes: Methods for Generating and Explaining Equivalent Fractions

Pair Share1. Partner 1: Reads - Reasoning about

equivalent fractions using an area model2. Partner 2: Reads - Reasoning about

equivalent fractions using a number line3. One minute report4. Report on how your model was different

than your partners.

From: Dev-TE@M session 9

Fractions

Multiply a fraction by a whole numberREAD and DO: 4.NF.4a, 4.NF.4b

• 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

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 4th grade math Protopage

Learning Target

Extend understanding of fraction equivalence and ordering.

4.NF.1, 4.NF.2

Build fractions from unit fractions by

applying and extending previous understandings of operations on whole numbers.

4.NF.3, 4.NF.4

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.