Properties of numbers can be used to prove rules for multiplying integers. The distributive property allows multiplication to be extended from fractions to rational numbers, including products like (-1)(-1)=1. Properties like the distributive property can be applied as strategies to multiply and divide rational numbers. For example, using properties one can prove that 2(-1)=-2 by writing expressions like 0=2+2(-1) and applying the distributive property to show 2(-1) must equal -2.

1. HOW can properties be
used to prove rules for
multiplying integers?
The Number System
Course 2, Inquiry Lab after Lesson 3-4

2. • 7.NS.2
Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
• 7.NS.2a
Understand that multiplication is extended from fractions to rational
numbers by requiring that operations continue to satisfy the
properties of operations, particularly the distributive property, leading
to products such as (–1)(–1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers by describing real-
world contexts.
• 7.NS.2c
Apply properties of operations as strategies to multiply and divide
rational numbers.
The Number System
Course 2, Inquiry Lab after Lesson 3-4 Common Core State Standards © Copyright 2010. National Governors Association Center
for Best Practices and Council of Chief State School Officers. All rights reserved.

3. Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
The Number System
Course 2, Inquiry Lab after Lesson 3-4 Common Core State Standards © Copyright 2010. National Governors Association Center
for Best Practices and Council of Chief State School Officers. All rights reserved.

4. Course 2, Inquiry Lab after Lesson 3-4
Activity
Continued

The Number System
Properties are used by scientists to classify elements into categories,
such as metals. One property of a metal is that it is shiny.
You have studied the mathematical properties listed in the table
below. In mathematics, properties can be used to justify statements
you make while verifying or proving another statement.
For example, you have used models to show that 2(–1) = –2
You can prove 2(–1) = –2 by using properties.

5. Course 2, Inquiry Lab after Lesson 3-4
The Number System
Properties are used by scientists to classify elements into categories,
such as metals. One property of a metal is that it is shiny.
Statements Properties
0 = 2(0) __________________________
0 = 2[1 + (–1)] __________________________
0 = 2(1) + 2(–1) __________________________
0 = 2 + 2(–1) __________________________
Write the correct property from the table above to provide the missing
justifications. Use each property name once.
Conclusion In the last statement, 0 = 2 + 2(–1). In order for this to be true,
2(–1) must equal –2. therefore, 2(–1) =

6. Course 2, Inquiry Lab after Lesson 3-4
HOW can properties be
used to prove rules for
multiplying integers?
The Number System