#### Math - 2017-18

# 6.4 and *6.5a - Multiply and Divide Fractions

**6.4 **The student will **demonstrate**
multiple representations of multiplication and division of fractions.

6.5The student willa)

multiplyanddividefractions and mixed numbers;* (with NO CALCULATOR)

**Bloom's Level:** Apply

*Adopted: 2009*

### BIG IDEAS

- If I have 3/4 of a pizza I will be able to evenly share it with 4 friends, I am able to increase a recipe to produce 12 dozen cookies, and if I have 16 yards of ribbon I can determine how many bows I can make if each requires 3/4 yd.
- I will better understand the concept of
multiplication and division of fractions as I move into more abstract
applications.

### UNDERSTANDING THE STANDARD

- Using manipulatives to build conceptual
understanding and using pictures and sketches to link concrete examples to the
symbolic enhance students’ understanding of operations with fractions and help
students connect the meaning of whole number computation to fraction
computation.
- Multiplication and division of fractions can be
represented with arrays, paper folding, repeated addition, repeated
subtraction, fraction strips, pattern blocks and area models.
- When multiplying a whole by a fraction such as 3 x 1/2, the meaning is the
same as with multiplication of whole numbers: 3 groups the size of 1/2 of the whole.
- When multiplying a fraction by a fraction such
as 2/3 ⋅ 3/4, we are asking for part of a part.
- When multiplying a fraction by a whole number
such as 1/2 x 6, we are trying to
find a part of the whole.
- For measurement division, the divisor is the
number of groups. You want to know how
many are in each of those groups. Division of fractions can be explained as how
many of a given divisor are needed to equal the given dividend. In other words, for 1/4 ÷ 2/3, the question is, “How many 2/3 make 1/4?”
- For partition division the divisor is the size
of the group, so the quotient answers the question, “How much is the whole?” or
“How much for one?”

2016 VDOE Curriculum Framework - 6.5 Understanding

· The symbol can be used in grade six in place of “x” to indicate multiplication.

· In exponential notation, the base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In , 8 is the base and 3 is the exponent (e.g., ).

· Any real number other than zero raised to the zero power is 1. Zero to the zero power () is undefined.

· A perfect square is a whole number whose square root is an integer (e.g., ). Zero (a whole number) is a perfect square.

· Perfect squares may be represented geometrically as the areas of squares the length of whose sides are whole numbers (e.g., , etc.). This can be modeled with grid paper, tiles, geoboards and virtual manipulatives.

· The examination of patterns in place value of the powers of 10 in grade six leads to the development of scientific notation in grade seven.

### ESSENTIALS

- When multiplying fractions, what is the meaning
of the operation?

When multiplying a whole by a fraction such as 3 x 1/2, the meaning is the same as with multiplication of whole numbers: 3 groups the size of 1/2 of the whole.

When multiplying a fraction by a fraction such as 2/3 ⋅ 3/4, we are asking for part of a part.

When multiplying a fraction by a whole number such as 1/2 x 6, we are trying to find a part of the whole. - What does it mean to divide with fractions?

For measurement division, the divisor is the number of groups and the quotient will be the number of groups in the dividend. Division of fractions can be explained as how many of a given divisor are needed to equal the given dividend. In other words, for the question is, “How many for 1/4 ÷ 2/3, the question is, “How many 2/3 make 1/4?”

For partition division the divisor is the size of the group, so the quotient answers the question, “How much is the whole?” or “How much for one?”

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

6.4_{1} **Demonstrate**
multiplication and division of fractions using multiple representations.

6.4_{2} **Model**
algorithms for multiplying and dividing with fractions using appropriate
representations.

·
6.5a_{1} **Demonstrate**/**model** multiplication and division of
fractions (proper or improper) and mixed numbers using multiple
representations.

### KEY VOCABULARY

multiplication, division, product, quotient, dividend, divisor,
remainder, simplest form, fraction, mixed numbers, numerator, denominator,
reciprocal, inverse operations

*Updated: Oct 27, 2017*