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.

Enduring Understanding
illustrative_math_4.nf.3b.png
Illustrative Mathematics Project (click picture)

Fractions of the same whole can be added and subtracted.
illustrative_math_4.nf.3.png
Illustrative Mathematics Project (click picture)

Essential Questions

  • What is a unit fraction?
  • What does it mean to add and subtract fractions?

Vocabulary (online dictionary, multilingual dictionary)

unit fraction, fraction, numerator, denominator

About the Math

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.

Illustrative Math Project: Seventeenths in Different Ways, Peaches, Writing a Mixed Number to an Equivalent Fraction


Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

VDW3-5.png

Teaching Student-Centered Mathematics (Grades 3-5)

pg. 150 * First Estimates Activity 5.13


Representations for Concepts Before Procedure
  • 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.

Learnzillion Video Resources

(4.NF.3a and 4.NF.3b - 3 Lessons)


4nf3_lz.png
Select image for lessons.


Learnzillion Video Resources

(4.NF.3c - 4 Lessons)

4nf3-2_lz.png
Select image for lessons.


Learnzillion Video Resources

(4.NF.3d - 5 Lessons)

4nf3-3_lz.png
Select image for lessons.


Print Resources:
nimble_with_numbers_4-5.png
building_number_power3-5.png
numbersense.png
braincompatible4-5.png
Nimble with Numbers 4-5 (110-111)
Math Intervention: Building Number Power
3-5 (159-161)
Number Sense 4-6 (7)
Brain-Compatible Activities
for Mathematics Grades 4-5 pg 73-76
hands-on_standards.png
ten_minute_math.jpg
roadstoreasoninggrade1.png
hands_on_standards_cc_fractions_4.jpg
Hands-On Standards
(54, Add and Subtract Fractions)
Ten Minute Math (110-113)
Roads to Reasoning Gr. 4 pg 37
Hands-On Standards, Common Core Fractions Gr 4
Add/Subtract Fractions Lessons 1-5, pgs 48-66

Web Resources:

games_centers.jpg
lessons.jpg
student_resources.jpg
video_segments.jpg
Games and Centers
Lessons
Student Resources
Video Segments
Fraction Word Problems
Same Denominator
The Fraction Bar Problem
lesson seed
Printable Fraction Circles
Adding Like Fractions 1:59
Adding Mixed Numbers
Write About Fractions

Learnzillion Video Resources(3 Lessons)
Subtracting Mixed Numbers
Pizza Parlor

Learnzillion Video Resources
(4 Lessons)
Adding Fractions eTool
Making Granola
MSDE Lesson Seed

Learnzillion Vidoe Resources
(6 Lessons)
Fruit Shoot Fraction Addition
Fraction Jigsaw
lesson seed



Decomposing Fractions
lesson seed/center
Plastic Building Blocks
Illustrative Mathematics Project,
U of Arizona


Adding Fractions with Pattern Blocks
lesson seed/center
Pizza Party
Georgia Dept. of Education


Adding and Subtracting Like Fractions
lesson seed/center
Eggsactly
Georgia Dept. of Education




Tile Task
Georgia Dept. of Education



Sweet Fraction Bars
Georgia Dept. of Education




Fraction Cookies Bakery
Georgia Dept. of Education



Fraction Field Event



Give 'em Chocolate!
NC Dept. of Public Instruction















Connecting to Children's Literature:

picture_pie.png
Picture Pie


Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.


Creative_Commons.pngUse and Sharing of HCPSS Website and Resources
Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.