Understand a fraction a/b with a > 1 as 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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

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.

Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Quarter 1

Quarter 2

Quarter 3

Quarter 4

Understand a fraction a/b with a > 1 as 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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

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.

Understand a fraction a/b with a > 1 as 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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

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.

Revisit to make connections with other fraction concepts in this quarter.

Understand a fraction a/b with a > 1 as 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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

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.

Revisit to make connections with other fraction concepts in this quarter.

Understand a fraction a/b with a > 1 as 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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

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.

Will 6/10 + 6/10 be greater than one whole? Explain how you know.

How can you figure out what ¼ + ½ is without finding a common denominator? Explain how you did found the answer.

Decompose 11/12 in 3 different ways.

Esther ate ¾ of a small pizza on Monday and she ate ¼ of a large pizza on Tuesday. She says that she has eaten a whole pizza. Is she correct? Why or why not? Explain your answer.

Think of a time in your life where you might you need to add or subtract fractions.

How many ways can you decompose 7/8? Show your representations.

What set of numerators can you find to make this equation true? Is there a different answer?

5/10 + 1/10 + 4/10 = /10 + /10 + _/10

Lily is having a sleepover with 2 friends. They order one party size submarine sandwich and it is cut into 12 equal parts. They eat the entire sandwich, but each person has a different number of parts. What is one way the sandwich was shared? Write an equation to represent your answer equal to 12/12. Is there a different way the friends could have shared the sandwich?

Play “Can You Get There In ? Jumps”. Using a number line, give students a fraction such as 10/12. Ask students to get there in 3 jumps on the number line. One answer might be 2/12, to 5/12, to 10/12 and can be represented by 2/12 + 3/12 + 5/12. Then ask if they can get there in 4 jumps?

At noon, the bakery had 1 whole pumpkin pie and 5/12 of a pumpkin pie available to sell. At the end of the day, 3/12 of a pie was left. How much pumpkin pie did the bakery sell during the afternoon?

Shelly needs 1 ⅜ cups of oats for a cookie recipe. How many cups of oats does Shelly need if she is tripling the recipe? (This question is not exclusive to multiplication of fractions, repeated addition can be used)

The answer is 5 ⅙, write a story problem involving addition and/or subtraction to result in this answer.

Jashae has 3 ¾ foot of yarn. She uses 1 ¼ foot of the yarn to make a bracelet. Then she gave her sister 1 ¼ foot of yard for her bracelet. How much yarn does she have left? Represent this problem visually.

Don came home and found a fraction of a large pizza on the counter. He eats 3/8 of the pizza and now there is 2/8 of a pizza left. What fraction of the pizza was on the counter when he got home?

About the Math

Illustrative Mathematics Project (click picture)

Addition and subtraction of fractions with like denominators can easily be solved using an algorithm of adding or subtracting the numerators and keeping the same denominator. However, prior to this, students need instruction on the conceptual understanding of adding and subtracting fractions and what a reasonable answer looks like. Questions such as will the answer when you add 7/8 + 3/8 be more or less than a whole and why? should be part of instruction. Concrete materials should be used to introduce addition and subtraction prior to moving to the algorithm.

Students need to see that a fraction can be decomposed just like whole numbers. There are many different ways to decompose a fraction. Understanding this helps students see the value of fractions and enhances their fraction sense.7/10 = 1/10 + 1/10 +1/10 + 1/10 +1/10 + 1/10 + 1/10 or 3/10 + 3/10 + 1/10 or 5/10 + 2/10 or 4/10 + 2/10 + 1/10.

A mixed number is a whole number and a fraction. Students need to see that 3 ¼ is the same as 3 + ¼. This can be connected to the previous standard of decomposing fractions.

Drawing a picture and writing an equation are two effective strategies when solving word problems with fractions. Writing an equation helps students translate word phrases into numbers. Encourage students to use these two strategies instead of looking for key words. Looking for key words should be avoided because key words can indicate different operations depending on the context in the problem.

Before teaching students how to add with like denominators, have students initially use manipulatives After they are comfortable with the concrete model, have them move onto the semi-concrete and draw pictures to show the addition and subtraction of fractions.

Use fraction strips or fraction pieces to model addition of fractions with like denominators. Help students estimate a reasonable sum.

Good Questions / Problems about Fractions
Be sure to have students work with partners or small groups to write their answers to the questions below. It is critical that students have an opportunity to share their thoughts with the whole class after completing the problem.

How do you know that 5/8 + 5/8 is more than one whole? Explain your thinking.

Is 1 1/8 a reasonable answer for 3/8 + 2/8? Explain your thinking.

If I subtract 3/8 from 7/8, is 4/16 a reasonable answer? Explain your thinking.

Pattern Block Fractions (addition)

Ask students to predict what the sum of 4 1/3 + 2 2/3 is.

Using think-pair-share, have students describe why their predictions are correct.

Using pattern blocks (yellow hexagons and blue rhombi) model the two. Have students draw pictures of the models and record the sum. Make connections between the models and the numbers.

Have students create other addition sentences with mixed numbers using pattern blocks. Yellow hexagons should represent 1 whole. Red trapezoids should represent 1/2. Green triangles should represent 1/6.

Have students share their equations with the class.

Pattern Block Fractions (subtraction)

Ask students to predict what the difference of 2 4/6 - 3/6 is.

Using think-pair-share have students describe why their predictions are correct.

Using pattern blocks (yellow hexagons and blue rhombi) model the two. Have students draw pictures of the models and record the sum. Make connections between the models and the numbers.

Have students create other subtraction sentences with mixed numbers using pattern blocks. Yellow hexagons should represent 1 whole. Red trapezoids should represent 1/2. Green triangles should represent 1/6.

Have students share their equations with the class.

That’s Messed Up

Have students write three addition/subtraction sentences using fractions on a piece of paper.

Two of their sentences should be correct. The third should be incorrect.

Have students trade papers with a partner.

Partners work through the number sentences to identify which one is “messed up.”

Partners correct the “messed up number sentence.”

Students come back together to share messed up number sentences with the class and how they found them.

## Understand a fraction a/b with a > 1 as 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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.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.

Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.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.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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

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.

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 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 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Increasing Rigor (4.NF.3a)Increasing Rigor (4.NF.3b)Increasing Rigor (4.NF.3c)Increasing Rigor (4.NF.3d)About the MathAddition and subtraction of fractions with like denominators can easily be solved using an algorithm of adding or subtracting the numerators and keeping the same denominator. However, prior to this, students need instruction on the conceptual understanding of adding and subtracting fractions and what a reasonable answer looks like. Questions such as will the answer when you add 7/8 + 3/8 be more or less than a whole and why? should be part of instruction. Concrete materials

should be used to introduce addition and subtraction prior to moving to the algorithm.

- Students need to see that a fraction can be decomposed just like whole numbers. There are many different ways to decompose a fraction. Understanding this helps students see the value of fractions and enhances their fraction sense.7/10 = 1/10 + 1/10 +1/10 + 1/10 +1/10 + 1/10 + 1/10 or 3/10 + 3/10 + 1/10 or 5/10 + 2/10 or 4/10 + 2/10 + 1/10.
- A mixed number is a whole number and a fraction. Students need to see that 3 ¼ is the same as 3 + ¼. This can be connected to the previous standard of decomposing fractions.
- Drawing a picture and writing an equation are two effective strategies when solving word problems with fractions. Writing an equation helps students translate word phrases into numbers. Encourage students to use these two strategies instead of looking for key words. Looking for key words should be avoided because key words can indicate different operations depending on the context in the problem.

Essential vocabulary for this standard includes:unitfraction,fraction,numerator, anddenominator(online dictionary, multilingual dictionary)The Illustrative Math Project tasks below demonstrate the expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)Teaching Student-Centered Mathematics(Grades 3-5)pg. 150 * First Estimates Activity 5.13Representations for Concepts Before ProcedureGood Questions / Problems about FractionsBe sure to have students work with partners or small groups to write their answers to the questions below. It is critical that students have an opportunity to share their thoughts with the whole class after completing the problem.

Pattern Block Fractions (addition)Pattern Block Fractions (subtraction)That’s Messed Up## Learnzillion Video Resources

Lesson Sets from Learnzillion:Print Resources:3-5 (159-161)

for Mathematics Grades 4-5 pg 73-76

(54, Add and Subtract Fractions)

Add/Subtract Fractions Lessons 1-5, pgs 48-66

Web Resources:(same denominator)

(eTool)

Teacher guide for virtual manipulatives 4.NF.3

(game, eTool)

(online game)

(lesson seed)

(Illustrative Mathematics Project,

U of Arizona)

(Georgia Dept. of Education)

(Georgia Dept. of Education)

(Georgia Dept. of Education)

(Georgia Dept. of Education)

(Georgia Dept. of Education)

Connecting to Children's Literature:Picture Pie

## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.Use and Sharing of HCPSS Website and ResourcesHoward County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.