Fourth Grade Fractions

4.NF.1 4.NF.2 4.NF.3 4.NF.4 4.NF.5 4.NF.6 4.NF.7

Extend understanding of fraction equivalence & ordering

Build fractions from unit fractions by applying & extending previous understandings of operations on whole numbers

Multiplying the numerator & denominator by the same number changes the size of the pieces, & how many pieces, but not the total amount given.

You still get the same amount!

4.NF.1Explain why a fraction a/b is equivalent to a fraction (nxa)/(nxb) by using visual fraction models, with attention to how the number & size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize & generate equivalent fractions.

3rd GradeDevelop understanding of fractions as numbers

Parts of a set Parts of a whole Partitioning Fractions as numbers

5th GradeUse equivalent fractions as a strategy to add & subtract fractions

Concrete models Grid models Meaning +/- +/- fractions & mixed

numbers

Numbers & Operations – Fractions.NF.1

Task #1

Jan needs ¾ of a cup of brown sugar. She only has a 1/3 measuring cup & an ⅛ measuring cup. Which

should she use, and why?

4.NF.1 Equivalent Fractions: Recognize & Generate

Equivalent Fractions

4.NF.1 Equivalent Fractions: Recognize & Generate

Equivalent Fractions

Task #1 Answer Jan should use the ⅛ cup because she can

make an equivalent fraction that has a denominator of 8 by multiplying both the

numerator & denominator of ¾ by 2.

4.NF.2 Compare two fractions with different numerators & different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, <, =, and justify the conclusions, by using a visual fraction model.

Common denominators Common numerators Benchmark fraction Number lines Use <, >, =

3rd GradeUnderstand a fraction as a number on the number line; represent fractions on a number line diagram.

5th GradeSolve word problems involving addition and subtraction of fractions referring to the same whole including cases of unlike denominators.

Numbers & Operations – Fractions.NF.2

4.NF.2 Benchmark Fractions 4/4 ¼ ¾

1/3 2/3 ½

4.NF.2 Common DenominatorsCompare 4/5 & 5/6

4/5 < 5/6

24/30 < 25/30

4.NF.2 Common NumeratorsCompare 4/5 & 5/6

4/5 < 5/6

20/25 < 20/24

4.NF.2 Number lines

Compare 4/5 & 5/6 5/50 1/5 2/5 3/5 4/5 1

0 1/6 2/6 3/6 4/6 5/6 1 6/6

4.NF.2 Comparing Fractions

Task #2

Savannah & Mia are selling boxes of fruit as a fundraiser. Savannah has sold 9/10

of her boxes of fruit & Mia has sold 5/8 of her boxes. Which girl has sold a greater

fraction of her boxes of fruit?

4.NF.2 Comparing Fractions

Task #2 Answer 9/10

5/8

Savannah sold more boxes of fruit than Mia because 9/10 > 5/8. Nine tenths

has a larger shaded portion of the whole than 5/8.

4.NF.3 Understand a fraction a/b with a >1as a sum of

fractions 1/b. 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, recording each decomposition by an equation. Justify decomposition, by using a visual fraction model.c.) Add & subtract mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, & by using properties of operations and the relationship between addition and subtraction.d.) Solve word problems involving +/- of fraction referring to the same whole & having like denominators, by using visual fraction models & equations to represent the problem.

3rd GradeExplain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

5th GradeInterpret a fraction as division of the numerator by the denominator.

Numbers & Operations – Fractions.NF.3

4.NF.3 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 in more than one way and writing an equation for them.

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

5/8 = 1/8 + 1/8 + 3/85/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/85/8 = 2/8 + 3/8

Or 5/8 - 4/8 = 1/85/8 – 1/8 -1/8 -1/8 -1/8 = 1/8

Numbers and Operations - Fractions4.NF.3 Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction. Add and subtract mixed numbers. Solve word problems involving addition and subtraction of fractions.

4 I can add and subtract fractions and mixed numbers with like denominators and unlike denominators.

3 I can easily add and subtract fractions and mixed numbers with like denominators.

2 Most of the time, I can add and subtract fractions and mixed numbers with like denominators.

1 I am beginning to add and subtract fractions and mixed numbers with like denominators.

0 I am unable to add and subtract fractions and mixed numbers with like denominators.

6

4.NF.3C.) Add & subtract mixed numbers with like denominators, renaming the mixed number.

2 ¼ = 4/4 + 4/4 + ¼ = 9/4

0 1 2 3 4 5 6 7 8 9 10 11 12

0 ¼ 2/4 ¾ 4/4 5/4 6/4 7/4 8/4 9/4 10/4 11/4 12/4

4.NF.3.a.b.c.dOperations with Fractions

Task #31. Vaughn used 4 2/3 cups of cereal & 3 1/3

cups of marshmallows to make cereal bars. How many more cups of cereal did Vaughn use than marshmallows?

2. Madison ran the first part of a relay in 4 4/6 minutes. Noah ran the next part in 3 5/6 minutes. How long did they take to run both parts of the relay?

4.NF.3.a.b.c.dOperations with Fractions

Task #3 Answers1. Vaughn used 1 1/3 more cups of cereal than

marshmallows.

cereal marshmallows 1 2 3 4 5

4.NF.3.a.b.c.dOperations with Fractions

Task #3 Answers

2. It took Madison & Noah 8 3/6 or 8 ½ minutes to run both parts of the relay.

Madison Noah

4NF.4 Apply & 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. Use fraction models to represent the product, record the conclusion as an equation. Example: 5/4 is the product of 5 x 1/4.

b.) Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Use fraction models to show the equation and the product.

c.) Solve word problems involving multiplication of a fraction by a whole number. Use visual fraction models and equations to represent the problem.

3rd Grade 5th GradeApply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Numbers & Operations- Fractions.NF.4

4.NF.4 Multiplying fractions by whole numbers.

4/1 ‘vs’ 4/4

‘VS’

4.NF.4 Multiplying fractions by whole numbers.

5 x ¼

Multiplication is repeated addition. 1/4 +1/4 + 1/4 + 1/4 +1/4 = 5/4

Using a number line: 1 2 0 ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

0 ¼ 2/4 ¾ 4/4 5/4 6/4 7/4 8/4

Using Models:

One fourth two fourths three fourths four fourths five fourths

4.NF.4 Multiplying fractions by whole numbers.

Task #4

Claire is starting to run a little each day. She ran 1/5 of a mile on all 7 days last week. Tessa and Claire each wanted to run at least 2 miles during the week. Did they?

4.NF.4 Multiplying fractions by whole numbers.

Task #4 AnswerClaire did not run 2 miles her first week. She ran 1 2/5 miles that week.