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

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. 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! Big idea is that equivalent fractions represent the same portion of the whole.

Numbers & Operations – Fractions .NF.1 3rd Grade Develop understanding of fractions as numbers Parts of a set Parts of a whole Partitioning Fractions as numbers 5th Grade Use equivalent fractions as a strategy to add & subtract fractions Concrete models Grid models Meaning +/- +/- fractions & mixed numbers 3rd Graders learn that fractions are parts of a set, & parts of a whole. They learn that they can split the sets & wholes, & then give numerical meaning to the models. 5th Graders learn the meaning of addition and subtraction as it relates to fractions and mixed numbers. They add and subtract fractions and mixed numbers with unlike denominators using concrete models, grid models and eventually using numbers.

4.NF.1 Equivalent Fractions: Recognize & Generate Equivalent Fractions 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 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 <, >, = 4.NF.2 Fourth graders will compare fractions using common denominators, common numerators, or benchmark fractions. They will use less than, greater than, and equal symbols to compare the fractions using fraction models. The big idea is renaming fractions so they can compare them & understanding that the larger the denominator the smaller the pieces & the smaller the denominator the bigger the pieces.

Numbers & Operations – Fractions .NF.2 3rd Grade Understand a fraction as a number on the number line; represent fractions on a number line diagram. 5th Grade Solve word problems involving addition and subtraction of fractions referring to the same whole including cases of unlike denominators. 4th grade is compare two fractions with different numerators and different denominators.

4.NF.2 Benchmark Fractions 4/4 ¼ ¾ 1/3 2/3 ½ 4/4 Is not really a benchmark fraction, but I make my kids think about what the whole is and looks like before we start comparing to a benchmark fraction.

4.NF.2 Common Denominators Compare 4/5 & 5/6 4/5 < 5/6 24/30 < 25/30 Common denominators show that both models have the same amount of pieces that are the same size, but I get one more piece in 25/30.

4.NF.2 Common Numerators Compare 4/5 & 5/6 4/5 < 5/6 4/5 < 5/6 20/25 < 20/24 Common numerators show that you get the same amount of pieces, but the pieces are a little bit bigger in the fraction 20/24 because there is one less piece than there is in the smaller fraction 20/25.

4.NF.2 Number lines Compare 4/5 & 5/6 5/5 0 1/5 2/5 3/5 4/5 1 0 1/5 2/5 3/5 4/5 1 0 1/6 2/6 3/6 4/6 5/6 1 6/6 Using a number line shows that the comparison of 4/5 & 5/6 that 5/6 is greater than 4/5.

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.

Understand a fraction a/b with a >1as a sum of fractions 1/b. 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. The big idea is that we don’t add or subtract denominators because the whole doesn’t change. We add or subtract the numerators only. says when we add fractions we join them and when we subtract fractions we are taking them apart. Says I can take ¾ and add 3-1/4 fractions to get ¾ or I can take 2/4 and add ¼ to get ¾. Says we can add & subtract mixed numbers by creating improper fractions (equivalent fractions) with like denominators. Says we can solve word problems involving fractions using models and equations.

Numbers & Operations – Fractions .NF.3 3rd Grade Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 5th Grade Interpret a fraction as division of the numerator by the denominator.

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 + 3/8 5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 5/8 = 2/8 + 3/8 Or 5/8 - 4/8 = 1/8 5/8 – 1/8 -1/8 -1/8 -1/8 = 1/8 To me a) and b) are the same thing!

Numbers and Operations - Fractions 4.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. I am unable to add and subtract fractions and mixed numbers with like denominators. 6

4.NF.3 C.) 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

Operations with Fractions 4.NF.3.a.b.c.d Operations with Fractions Task #3 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? 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?

Operations with Fractions 4.NF.3.a.b.c.d Operations with Fractions Task #3 Answers Vaughn used 1 1/3 more cups of cereal than marshmallows. cereal marshmallows 1 2 3 4 5 The big idea is that the wholes are broken into the same amount of pieces as the fractions.

Operations with Fractions 4.NF.3.a.b.c.d Operations 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

Example: 5/4 is the product of 5 x 1/4. 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. Standard 4 is multiplication of a fraction and a whole number. The kids need to understand that 5 over 1 is 5 wholes and 5 over 5 in one whole. The big idea is that multiplication is repeated addition and that strategy can be used for multiplying fractions as well.

Numbers & Operations- Fractions .NF.4 3rd Grade 5th Grade Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

4/1 ‘vs’ 4/4 ‘VS’ 4.NF.4 Multiplying fractions by whole numbers. The denominator represent how many pieces the whole is broken into and the numerator represents how many pieces are selected. In 4 over 1 there are for things broken into 1. In 4 over 4 the one thing is broken into 4 pieces and all 4 pieces are selected.

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 Answer Claire did not run 2 miles her first week. She ran 1 2/5 miles that week.