Write and Expand Multiplication Expressions

Videos and solutions to help Grade 6 students learn how to identify parts of an expression and expand multiplication expressions.

New York State Common Core Math Grade 6, Module 4, Lesson 10

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Lesson 10 Student Outcomes

Students identify parts of an expression using mathematical terms for multiplication. They view one or more parts of an expression as a single entity.

Discussion
When we want to show multiplication of two numbers, like 5 and 7, we typically write 5 × 7, using the “×” to show the operations. When we start to use variables with multiplication, we can use other forms.

1. a × b
2. a • b
3. ab
4. (a)(b)

When writing expressions using the fewest number of symbols, we will have to refrain from using the symbols ×, •, or ().
We will also be using math terms to describe expressions and the parts of an expression. We will be using words like factor, product, quotient, coefficient, and term.
A term is a part of an expression that can be added to or subtracted from the rest of the expression. In the expression 7g + 8h + 3, 7g, 8h and 3 are all terms
A coefficient is a constant factor in a variable term. For example, in the term 4m, 4 is the coefficient and it is multiplied with m.

Example 1
Write each expression using the fewest number of symbols and characters. Use math terms to describe the expressions and parts of the expressions.
a. 6 × b
b. 4 • 3 • h
c. 2 × 2 × 2 × a × b
d. 5 × m × 3 × p
e. 1 × g × w

Example 2
To expand multiplication expressions we will rewrite the expressions by including the “ • ” back into the expressions.
a. 3g
b. 7abc
c. 12g
d. 3h • 8
e. 7g • 9h

Example 3
a. Find the product of 4f • 7g
b 3de • 9yz
c. Double the product of 6y and 3bc.

Lesson Summary
An Expression in Expanded Form: An expression that is written as sums (and/or differences) of products whose factors are numbers, variables, or variables raised to whole number powers is said to be in expanded form. A single number, variable, or a single product of numbers and/or variables is also considered to be in expanded form.

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Part 1: Writing Multiplication Expressions
Part 2: Expanding Multiplication Expressions
Part 3: Finding Products.

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Lesson 10 Exit Ticket

1. Rewrite the expression using the fewest number of symbols and characters possible.
   a. 5g • 7h
   b. 3 • 4 • 5 • m • n
2. Name the parts of the expression. Then expand.
   a. 14b
   b. 30jk

Lesson 10 Problem Set 1.Rewrite the expression in standard form (use the fewest number of symbols and characters possible).
a. 5 · y
b. 7 · d · e
c. 5 · 2 · 2 · y · z
d. 3 · 3 · 2 · 5 · d 2. Write the following expressions in expanded form.
a. 3g
b. 11mp
c. 20yz
d. 15abc 3. Find the product.
a. 5d · 7g
b. 12ab · 3cd

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