1. 4th
Grade
Word Problems and
Fractions
Laura Chambless
RESA Consultant
www.protopage.com/lchambless

2. CCSS and Gaps
What are your gaps in curriculum?
1. Review CCSS for Fractions
2. Think about your resources
3. 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.

3. 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

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

5. 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 own
2. 5 min. sharing with group
3. Class discussion
Found at: http://www.mathplayground.com/wpdatabase/Fractions1_3.htm

6. Problem Solving with
Bar 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.

7. Bar Diagrams
Watch Introduction Video
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p1/index.html
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p2/index.html

8. Practice Bar Diagrams
To: 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
partner
Draw Your Way to Problem Solving Success Handout, Robyn Silbey

9. Thinking Blocks
http://www.mathplayground.com/think
ingblocks.html
Explore the site 
When done exploring go to my
Protopage and look at your grade
level math tab.

10. Fractions
Stand and Share
Make a list of what you know and any
connections you have about the
fraction ¼.

11. Representations
(Part 2 video, 5:16)
Set Purpose of video: List why representations are
important in the classroom.
•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.
From: Dev-TE@M session 2

12. 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 discussion
3. Review math notes
From: Dev-TE@M session 2

13. 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

14. 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

15. 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

16. 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

17. 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 0
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

18. Lunch

19. Build Connections to Whole
Numbers
0 1 2 3 4 5
1+1+1+1+1=5
1/4 1/2 3/4
0 1
¼ +¼ +¼+¼ =1

20. Fractions
Fraction 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 Strips
READ and DO:4.NF.3a, 4.NF.3b, 4.NF.3c
Play Greater Than, Less Than, Equal
• Prove with Fraction Strips

21. Ordering Fractions
Order Fractions
8/6, 2/5, 8/10, 1/12
How did you figure out what order
they went in?

22. Fractions
Prove with Fraction Strips
Number Line: (Benchmarks) 0, ½, 1
Compare (>/<): same numerator or same
denominator
Equivalent Fractions: Same Name Frame

23. 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

24. Strategies for Comparing
Fractions
Math Notes: Strategies for Comparing
Fractions
Which strategies do you
use in your classroom?
From: Dev-TE@M session 9

25. 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?

26. 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

27. 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

28. 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

29. 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.

30. 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

31. Student Errors
Key points
When 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?

32. 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

33. Number Lines
(Part 2 video, 1:21)
Set purpose of video: listen to directions and practice
narrating on the number line.
Partner Work
Compare ¾ and 4/3
From: Dev-TE@M session 5

34. 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

35. Equivalence with Fraction
Strips
• Fraction Strips
½+¼= ¾ + 1/3 =

36. Add/Subtract Fractions with
Unlike Denominators
Developing Equivalent Fractions
• Slicing Squares
Van de Walle book: pg. 304-305
3 x = 3 x
4 =
4
3 x 3 x =
= 4
4

37. Developing Equivalent
Fractions
Missing-Number Equivalencies
Van de Walle book: pg. 304-305
5 2 6
= =
3 6 3

38. Methods for Generating and
Explaining Equivalent Fractions
Math Notes: Methods for Generating and
Explaining Equivalent Fractions
Pair Share
1. Partner 1: Reads - Reasoning about
equivalent fractions using an area model
2. Partner 2: Reads - Reasoning about
equivalent fractions using a number line
3. One minute report
4. Report on how your model was different
than your partners.
From: Dev-TE@M session 9

39. Fractions
Multiply a fraction by a whole number
READ and DO: 4.NF.4a, 4.NF.4b
• Work as a group
• Use Fraction strips to show answers
4 x 1/3
¼ x 12
• What connection can you make to
multiplication? What other
representations can you use? Can you
use a number line?

40. Multiple a Fraction by a Whole
Number
4 x 1/3 (4 groups of 1/3) = 4/3 = 1 1/3
I want 4 ribbons each at 1/3 of a yard. How much
ribbon will I need to purchase?
1/3 2/3 3/3 4/3
¼ x 12 (1/4 of 12) = 3
I have 12 cookies and want each of my friends
to have ¼ of them. How many cookies will
each friend get?

41. MOPLS
http://mi.learnport.org
Search: MOPLS Math
(navigate by using top tabs)
Look at Concepts Tab
– Introduction
– Math Behind the Math
– Misconceptions
– Tasks & Strategies

42. Fractions Online
Check out some sites on my 4th
grade math Protopage

43. 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

44. Closer Activity
List something you learn about story
problems and fractions today.

45. Thanks for a great day 
Please contact me if you have any questions or
would like more information.