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 &...
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Transcript of 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 &...
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.