1. Fourth Grade Fractions

2. Equivalent Fractions 4.NF 1
Explain why a fraction is equivalent to a fraction
ex: 1/2 = 2/4 = 6/12
Use visual models to represent changes in fractional pieces.
* Students can multiply the numerator and denominator by same factor or by dividing a shaded region into equal parts.
* area models
* number lines

3. Problems for Fraction lovers
Draw an area model to show the decomposition represented by the number sentence below.
4/5 = 8/10
Decompose the shaded fractions into smaller units using area models. Express the equivalent fractions in a number sentence using multiplication.
a b c d.

4. Web sites * Greg Tang * Gynzy * Illuminations * Illustrative Math
Resources
Web sites * Greg Tang * Gynzy * Illuminations * Illustrative Math
Resources
* Elementary and Middle School Mathematics
-Van de Walle
*About Teaching Mathematics A K-8 Resource
-Marilyn Burns
* Fraction Kit

5. CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
What’s this mean in student
friendly language please!? 
We can compare fractions w/ different denominators;
greater then, less than and equal to, by comparing them to equal parts of a whole number.
We can use symbols: < greater than, > less than
and equal to = Use fraction manipulatives & pictures to prove it!

6. Comparing fractions (here’s an easy way)
Plot fractions on a number line / & /8
0 ______l______l______1
0 __l__l__l__l__l__l__l__1
TIP! Remember the parts must be divided equally & if the denominator
is larger, then the equal parts between will be smaller > = = 16
Pizza & chocolate fractions comparisons are fun too!

7. 4.NF.B.3 Cluster Title
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
2 Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade..

8. a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3
Understand
a fraction a/b with a > 1
as a sum of fractions 1/b.
Translation:
Understand that fractions are the sum or difference of unit fractions.

9. There are four standards in this cluster:
4.NF.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.3.B Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = /8 = 8/8 + 8/8 + 1/8.
4.NF.3.C Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
4.NF.3.D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

10. Just what does that look like for students?
4.NF.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole
Just what does that look like for students?
Visual
Representations
Area Models
Number Lines

11. Just what does that look like for students?
4.NF.3.B Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.
Just what does that look like for students?

12. How would YOU add these fractions?
How would YOU subtract these fractions?

13. 4.NF.3.C Add and subtract mixed numbers with like denominators
(in different ways).
Just what does that look like for students?
Visual
Representations
Place Value
Understanding
Area Models

14. Just what does that look like for students?
4.NF.3.CD Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators
(in different ways).
Just what does that look like for students?
It might be creating a visual representation
like this:

15. Or maybe using a number line like this:
Or maybe using decomposition like this:

16. What strategy would YOU use to solve this problem?
What about this one?

17. One Last Thought………
Can you identify what might be misleading in this video clip?
These ARE all ½ but do they refer to the same whole?
We need to be careful that we don’t help create misconceptions!!

18. There are a lot of great Resources out there! Here are just a few:
Just remember to review them before sharing with students!!!

19. Examples of Assessment Tasks

20. 4.NF.B.4 NF.B.4a – Understand a fraction a/b as 1/b
NF.B.4b – Multiply a fraction by a whole number
NF.B.4c – Solve word problems involving multiplication of a fraction by a whole number

21. NF.B.4a ¼ ¼ ¼ ¼ ¼
5/4 = 5 x 1/4
NF.B.4b
2/ / /5
3 x 2/5 = 6 x 1/5
1/5 1/5 1/ / / /5
NF.B.4c Karla is unpacking boxes. If it takes her ¾ hour to unpack each box, how long will it take her to unpack 6 boxes?

22. LearnZillion on 4.NF.B.4

23. Numbers and Operations – Fractions: 4. NF. C. 5; 4. NF. C. 6; 4. NF. C
Numbers and Operations – Fractions: 4.NF.C.5; 4.NF.C.6; 4.NF.C.7 The BIG Idea : Understand decimal notation for fractions, and compare decimal fractions.
4.NF.C.5 – Express a fraction with a denominator 10 as an equivalent fraction with a denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
4.NF.C.6 – Use decimal notation for fractions with denominators 10 or 100.
4.NF.C.7 – Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions by using a visual model.

24. 4.NF.5 – Express a fraction with a denominator 10 as an equivalent fraction with a denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. AND THEN
4.NF.6 – Use decimal notation for fractions with denominators 10 or 100
4.NF.5 Activate background knowledge … Earlier in the school year students were asked to explain and generate equivalent fractions (4.NF.A.1)
In this standard they can call on this background knowledge to perform the following task:
To express 3/10 as 30/100:
3/10 X 10/10 = 30/100
30/100+ 4/100= 34/100
equivalent_fractions.html
4.NF.6 requires students to use decimal notation for fractions with denominators 10 or 100, then locate on a number line.
Express .62 as 62/100
Represent decimal fractions using the base 10 model. Utilize tenths and hundredths squares to CONCRETELY model
then locate .62 on a number line

25. Activity using a money “bag”:
4.NF.C.7 – Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions by using a visual model.
Expand the knowledge acquired by modeling and sizing decimals through reminding the students about money!
Ask, “Which pieces of the base 10 model match with dimes? With pennies? With the dollar?”
If the “whole” is one dollar, a dime represents a tenth and a penny represents a hundredth!
Activity using a money “bag”:
Decimal fractions such as 36/100 can easily be modeled as 3 dimes and 6 pennies
Students can see that
30/10 +6/100 is the same as 3/10 +6/100
video/using-decimals-to understand-money-1863
When you tie decimals to money, kids listen!
Decimal
Decimal made with pennies (with expanded notation)
Decimal made with Pennies and Dimes (with expanded notation)
.36
30 pennies = 6 pennies
30/ /100
3 dimes + 6 pennies
3/10 + 6/100

26. Use decimal notation for fractions with denominators 10 or 100.
For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

27. What does that mean?

28. Source:

29. Example Task
Task
A dime is 1/10 of a dollar and a penny is 1/100 of a dollar.
What fraction of a dollar is 6 dimes and 3 pennies? Write your answer in both fraction and decimal form.
IM Commentary
Students may think of this task in different ways. Some may think of the equivalence between dimes and pennies, stating that 6 dimes is equivalent to 60 pennies, thus giving a total of 63 pennies which can be represented as 63/100 or 0.63 of a dollar. Others may think of 6/10 as being equivalent to 60/100 and then add 60/100 plus 3/100 to total 63/100 or 0.63 of a dollar.
Solution
6 dimes is 60 pennies, so 6 dimes and 3 pennies is 63 pennies, which is 63/100=0.63 of a dollar.
Source:

30. 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. Kid Friendly Language: You will compare two decimals to the 100ths place based on their size. But when you compare decimals they need to be decimals of the same size whole. You must use a model to justify your conclusions and using >, =, or <.

31. Examples of Comparing

32. Possible Student Questions and Work

33. Assessment Rubric (Checklist)
Extend understanding of fraction equivalence and ordering
A.1. Explain why a faction is equivalent to another fraction by using visual fraction models.
Recognize and create equivalent fractions
A.2. Compare two fractions with different numerators and different denominators
Create common denominators and numerators
Compare fractions to a benchmark fraction
Recognize that comparisons are only valid when the two fractions refer to the same whole
Record the results of comparisons with symbols >, =, <, and justify their conclusions

34. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
B.3. Understand a fraction a/b with a>1 as a sum of fraction 1/b (ex.: ¾ with 3>1 as a sum of fractions ¼)
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way.
Record each decomposition by an equation
Justify decompositions
c. Add and subtract mixed numbers with like denominators
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators
Use visual fraction models and equations to represent a problem

35. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
B.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number
a. Understand a fraction a/b as a multiple of 1/b, (ex.: ¾ is a multiple of ¼)
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiple a fraction by a whole number (ex.: 3x(2/5) as 6x(1/5))
c. Solve word problems involving multiplication of a fraction by a whole number.
Use visual fraction models and equations to represent a problem

36. Understand decimal notation for fractions, and compare decimal fractions.
C.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with denominators 10 and 100
C.6. Use decimal notation for fractions with denominators 10 or 100.
C.7. Compare two decimals to the hundredths place by reasoning about their size.
Recognize that comparisons are valid only when the two decimals refer to the same whole
Record the results of comparisons with the symbols >, =, or <, and justify conclusions.