Grade 4 Decimals (4.NF.7 a, b, and c)

Full Standard

4.C.5 Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole.

Math Framework Resources

4.C.6 Add and subtract mixed numbers with common 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).

Math Framework Resources

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Learning Targets

I can add and subtract fractions with common denominators. (4.C.5)
I can break apart a fraction into a sum of smaller fractions with common denominators. (4.C.5)
I can add and subtract mixed numbers with common denominators using a variety of strategies. (4.C.6)

About Math
Preferred Resources
Additional Resources
Independent Work
Assessment

About Math

About the Math

Addition and subtraction of fractions with like denominators can 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 illustrative_math_4.nf.3b.png 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.

Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).

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.

Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.

When adding or subtracting fractions, the values must refer to the same-size whole with the same number of partitions. This is also thought of as common denominators. In fourth grade, students only work with addition and subtraction of fractions with like denominators.

Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).

Addition and subtraction of fractions can be represented by a variety of models. Students should also represent addition and subtraction of fractions on a number line. Students should justify their sums and differences with models and connect that work to their equations. In time, students can work solely with the symbols/equations.

Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add and subtract fractions and mixed numbers with varied strategies.

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. This understanding can be reinforced through the representations students use to add and subtract mixed numbers. Like other understandings, students should work with varied models including pattern blocks, Cuisenaire rods, and fraction tiles.

Solve word problems with adding and subtracting fractions and mixed numbers.

Students should represent problems with diagrams or drawings before attempting to solve. Bar diagrams or part-to-whole models are good for reinforcing this understanding. Students can then use tools to represent the computation with fractions as needed. Students should not rely on key words for finding the solution to these problems.

Essential vocabulary for this standard includes unit fraction, fraction, numerator, and denominator.

Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Quarter 1

Quarter 2

Quarter 3

Quarter 4

Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).
Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.

Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).
Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.
Add fractions and mixed numbers with varied strategies.
Subtract fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence MapLinks to an external site.. Information is not the complete standard.

Grade 3	Grade 5
Understand unit fractions (3.NF.1) Understand fractions as a number and respresent fractions on a number line (3.NF.2)	Add/subtract fractions with unlike denominators (5.NF.1)

Preferred Resources

Preferred Tasks

These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.

Comparing two different pizzas Links to an external site.(Illustrative Math)
Comparing Sums of Unit FractionsLinks to an external site. (4.NF.3a) (Illustrative Math)
Making 22 Seventeenths in Different WaysLinks to an external site. (4.NF.3b) (Illustrative Math)
Writing a Mixed Number as an Equivalent FractionLinks to an external site. (4.NF.3c) (Illustrative Math)
PeachesLinks to an external site. (4.NF.3c) (Illustrative Math)
Plastic Building BlocksLinks to an external site. (4.NF.3c) (Illustrative Math)
Cynthia's Perfect PunchLinks to an external site. (4.NF.3c) (Illustrative Math)
Adding and Subtracting Fractions (HCPSS-adapted print resource)
Fractions Decomposed (HCPSS-adapted print resource)
Pattern Block Fractions (HCPSS-adapted print resource)
Sharing Brownies (HCPSS-adapted print resource)
Sharing Cherry Pie (HCPSS-adapted print resource)
Target Differences (HCPSS-adapted print resource)
The Sum is 6 (HCPSS-adapted print resource)
Write and Solve Fraction Problems (HCPSS-adapted print resource)
PretzelsLinks to an external site. (HCPSS-created task)+++
Coconut CakeLinks to an external site. (HCPSS-created task)+++
Intervention Materials for Fractions

BrainPop Resources:

4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole.

	BrainPOP Adding and Subtracting Fractions
	BrainPOP Mixed Numbers
	BrainPOP Fractions
	GameUp Satisfraction
	GameUp Drop Zone

4.C.6: Add and subtract mixed numbers with common 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).

	BrainPOP Mixed Numbers
	BrainPOP Adding and Subtracting Fractions
	GameUp Satisfraction

Lesson Seeds (Prompts for Rigor)

Rigorous mathematics instruction balances the teaching and learning of conceptual understanding, procedural understanding, and the application of mathematics standards. Below are prompts for applying rigor in your classroom. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning. See the Increasing Rigor page for more information.

4.NF.3a	4.NF.3b	4.NF.3c	4.NF.3d
Why is ¼ + ¼ not equal to 2/8? 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?	If the sum of two mixed numbers is 6, what could the two addends be? Is the sum of 4 ⅖ + 2 ⅘ over or under 7? Explain why or why not. Is the difference of 5 ⅔ - 3 ⅓ over or under 2? Explain why or why not. How can you demonstrate how 4 ½ is equal to 9/2? Use models, drawings and/or equations to explain your thinking. Write two problems that have a difference of 3 4/10?	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?

Additional Resources

Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	3-5	First Estimates, Activity 5.13, Page 150
$hands_on_standards_cc_fractions_4.jpg$	Hands-On Standards, Common Core	4	48-66 (Add/Subtract Fractions Lessons 1-5)
	Beyond Pizzas and Pies		32-36
	Hands-On Standards	3-4	54
	Ten Minute Math		110-113
	Math Intervention: Building Number Power	3-5	159-161
	NumberSense	4-6	7
	Brain-Compatible Activities for Mathematics	4-5	73-76
	Roads to Reasoning	4	37

Additional Tasks and Lesson Seeds

These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.

Write About Fractions (pdf)
Pizza Parlor (pdf)
Making Granola (MSDE lesson seed)
Fraction JigsawLinks to an external site. (Nrich lesson seed)
Pizza PartyLinks to an external site. (Georgia Department of Education, pg.15-20 )
EggsactlyLinks to an external site. (Georgia Department of Education, pg.21-29)
Tile TaskLinks to an external site. (Georgia Department of Education, pg.30-36)
Sweet Fraction BarsLinks to an external site. (Georgia Department of Education, pg. 37-42)
Fraction Cookies BakeryLinks to an external site. (Georgia Department of Education, pg. 43-51)
Fraction Field EventLinks to an external site. (Georgia Department of Education, pg. 75-82)
Give 'em Chocolate! (NC Dept. of Public Instruction)
Flag Fractions (Utah Core Academy Lesson)
Pizza Party (Utah Core Academy Lesson)
Fun Run Relay (Utah Core Academy Lesson)
Sidewalk Chalk Dilemma (Utah Core Academy Lesson)

Connecting to Children's Literature

Children's literature provides an opportunity to put mathematics in context. This title connects well with this standard.

Picture Pie

By Ed Emberley

Independent Practice

Student-Facing Centers

These links provide online and print resources to engage students during independent or center time. These resources could also be used as lesson seeds.

Adding FractionsLinks to an external site. (virtual manipulative)
Adding and Subtracting Fractions (HCPSS-adapted print resource)
Fractions Decomposed (HCPSS-adapted print resource)
Pattern Block Fractions (HCPSS-adapted print resource)
Sharing Brownies (HCPSS-adapted print resource)
Sharing Cherry Pie (HCPSS-adapted print resource)
Target Differences (HCPSS-adapted print resource)
The Sum is 6 (HCPSS-adapted print resource)
Write and Solve Fraction Problems (HCPSS-adapted print resource)
Modeling Fractions with Cuisenaire RodsLinks to an external site. (PBS Kids, student-facing resource, pictured)
Splat Fraction AdditionLinks to an external site. (student-facing resource)
Splat Fraction SubtractionLinks to an external site. (student-facing resource)

Independent Practice

These resource sheets can be used for independent practice or homework. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Assessment

Learning Targets

Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).
Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add and subtract fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. The recording sheet can be used to collect data. The rubric can be applied to any task. Select the preview icon to preview the task before downloading.

Recording Sheet (docx)

Rubric (docx)

Assessment Tasks

These tasks align with the learning targets for the standard. They can be combined with other tasks for extended assessment opportunities. Teachers/students are not expected to complete all these tasks.

PARCC Released Items

These items are PARCC released items. They can be used for assessment or instruction. See notes at the bottom of each slide for more information.

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