ALEX Resources

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

This learning activity introduces the concept of decomposing a whole into fractional parts. Using the book Whole-y Cow Fractions Are Fun by Taryn Souders, students will have fun exploring different fraction-based situations with a friendly little cow who helps guide readers through the story. Prompted by a poem and visual clue, students are encouraged to solve fraction-based problems on each page.

This activity results from the ALEX Resource Development Summit.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

In this learning activity, students will use Cuisenaire rods to decompose fractions. Students will explore fractional decompositions using these concrete materials. Students will show how a whole can be broken into parts and use an equation to represent the decomposed fraction. 

This activity results from the ALEX Resource Development Summit.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

This activity gives students an opportunity to explain how to decompose a fraction as a sum of fractions with the same denominator in more than one way using equations. This activity should be used at the end of a lesson or unit on fractional decomposition. 

This activity results from the ALEX Resource Development Summit.

   View Standards     Standard(s): [MA2019] (3) 13 :

13. Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

[MA2019] (3) 14 :

14. Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.

a. Represent a unit fraction (¹/_b) on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts as specified by the denominator.

b. Represent a fraction (^a/_b) on a number line by marking off a lengths of size (¹/_b) from zero.

[MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

[MA2019] (5) 11 :

11. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

a. Model and interpret a fraction as division of the numerator by the denominator (^a/_b= a ÷ b)

b. Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers

[MA2019] (5) 15 :

15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

In this lesson video you’ll learn multiple ways to divide a number by a fraction; plus you’ll get actual examples to make this concept real.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

This video helps students practice decomposing fractions to get ready for mixed numbers and performing operations with fractions.

   View Standards     Standard(s): [MA2019] (3) 13 :

13. Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

[MA2019] (3) 15 :

15. Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

a. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

b. Compare two fractions with the same numerator or with the same denominator by reasoning about their size (recognizing that fractions must refer to the same whole for the comparison to be valid). Record comparisons using < , >, or = and justify conclusions.

[MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

[MA2019] (5) 15 :

15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

In this lesson, students are asked to share certain numbers of objects among different numbers of people. They begin with unit fractions and move to divide multiple objects (a) among multiple people, (b) in which a < b, to produce fractions less than one. This CYBERCHASE activity is motivated by two video clips in which the CyberSquad has to share objects fairly in order to overcome obstacles and challenges assigned to them by Zeus as they try to recover Pandora's Box, which was stolen by their nemesis, Hacker.

   View Standards     Standard(s): [MA2019] (3) 13 :

13. Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

[MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

In this interactive lesson, students will build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. They will understand a fraction a/b with a > 1 as a sum of fractions 1/b and decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. 

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

[MA2019] (5) 10 :

10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

[MA2019] (5) 14 :

14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

While doubling a cupcake recipe, students practice three ways of doubling fractions using representations, addition, and multiplication. They also convert between improper fractions and mixed numbers.

   View Standards     Standard(s): [ARTS] VISA (2) 3 :

3) Extend skills by individually following sequential steps to create works of art on subjects that are real or imaginary.

Example: Use the book A House for Hermit Crab by Eric Carle.
Create a real or imagined home.

[ARTS] VISA (3) 1 :

1) Elaborate on an individual or prompted imaginative idea.

Examples: Create an imaginative mask showing his/her personality.
Look at masks from different cultures such as Chinese, African and Native American.

[ARTS] VISA (4) 3 :

3) Generate ideas and employ a variety of strategies and techniques to create a work of art/design.

[MA2019] (3) 13 :

13. Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

[MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Students will analyze the painting, Cakes, by Wayne Theibaud.  They will practice fractions and paint a decorated cake.  

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

In this interactive activity, students will be led through steps to add and subtract mixed numbers. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught in the interactive can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

In this interactive activity, students will be led through steps to add and subtract fractions with like denominators. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Use a visual model to subtract fractions with like and unlike denominators. This video focuses on using an equivalent fractions chart to compare fractions and find the missing piece.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Use a visual model to add fractions with like and unlike denominators. This video focuses on using an equivalent fractions chart to compare fractions and find the correct sum.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

In this video segment from Cyberchase, the CyberSquad has to help Shari Spotter make a batch of Cosmic Crumpets in order to give the masters at Frogsnorts their power. The recipe they have is for four crumpets, but they need to make eight crumpets. Everything in the recipe has to be doubled, including some tricky fractions which Shari and the CyberSquad find they must convert from improper fractions to mixed numbers.

   View Standards     Standard(s): [MA2019] (4) 15 :

15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

To decompose means to break apart. Students already decomposed whole numbers with number bonds, tape diagrams, and place value charts. In fourth grade, they will decompose fractions.