Unit 5 Building Understanding of Addition, Subtraction and Multiplication of Fractions

In Unit 5 students will:

  • Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 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 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.
  •  Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 3
    • a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (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. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
    • c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

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

By the end of Unit 5 your child should be able to answer the following questions:

 

  •       How do we add and subtract fractions and mixed numbers?
  •         How is multiplying fractions different than adding mixed numbers?
  •       How can I recognize the whole in an improper fraction?
  •       How can I multiply a whole number by a fraction?

The following videos explain some of the topics covered in Unit 6.

  • Unit Fractions

  • Placing Improper Fractions on a Number Line

  • Visual Models of Improper Fractions

  • Fractions and Mixed Numbers on a Number Line

  • Fractions and Mixed Numbers on a Number Line

  • Convert Mixed Numbers into Improper Fractions

  • Review of Improper Fractions

  • Adding and Subtracting Mixed Numbers with Models

  • Converting Improper Fractions to Mixed Numbers

  • Multiply a Fraction By a Whole Number Using a Algorithm

 

To view the following LearnZillion Videos you will need to become a member. It is FREE to join and being a member allows you access to a large collection of LearnZillion videos.

 

  • To learn about Decomposing Fractions at LearnZillion
  • To learn how to Add Fractions with Like Denominators on a Number Line at LearnZillion
  • To learn how to Subtract Fractions with Like Denominators on a Number Line at LearnZillion
  • To learn how to Plot Improper Fractions on a Number Line
  • To learn how to Multiply a Fraction by a Whole Number using a Number Line
  • To learn how to Multiply a Fraction by a Whole Number using Repeated Addition
  • To learn how to Multiply a Fraction by a Whole Number using a Fraction Model