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3rd Grade Word Problems and
Fractions
Laura ChamblessRESA Consultant
www.protopage.com/lchambess
Learning Target
Develop understanding of fractions as numbers
1.Understand what a fraction is2.Understand a fraction is a number on
the number line3.Explain equivalence of fractions in
special cases, and compare fractions by reasoning about their size
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.
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
(Session 2: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 • [email protected] 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
Benchmarking
AIMS: Between Zero and One
iPod: Estimate Fractions
Strategies for Comparing Fractions
Key points• The following practices are helpful when analyzing
students’ work on tasks:• Anticipate the strategies and representations students
may use.• Identify the strategies students did use. If the student
used a different strategy than predicted, consider if is it a fitting choice.
• If the strategy is unfamiliar, explore whether or not the strategy is mathematically valid.
• Identify questions to ask the student about her/his strategy or new problems to pose that would further reveal her/his understanding.
From: Dev-TE@M session 9
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 • [email protected] 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?
From: Dev-TE@M session 4
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 2 video, 1:21)Set purpose of video: listen to directions and practice
narrating on the number line.
Partner WorkCompare ¾ and 4/3
From: Dev-TE@M session 5
Number Lines
(Part 3 video, A 3:32/C 1:29/ E :28)Set purpose for video: Where are the problems when
narrating the number line?
(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 Strips1/8 + 5/8 = 1/3 + 1/3 =
• Number line1/8 + 5/8 = 1/3 + 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
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 3rd grade math Protopage
Learning Target
Develop understanding of fractions as numbers
1.Understand what a fraction is2.Understand a fraction is a number on
the number line3.Explain equivalence of fractions in
special cases, and compare fractions by reasoning about their size
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.
