In this unit, students extend their understanding of multiplication and division to include all rational numbers. They first represent multiplication and division of rational numbers with number lines, building on their understanding from addition and subtraction. They then verify the operational rules by using the properties of numbers. By the end of this unit, students should be comfortable applying all four operations to all rational numbers in arithmetic and problemsolving situations.
Key Concepts:
 The properties of operations hold for all rational numbers (commutative, associative, and distributive) and can be used to verify the operational rules for multiplying and dividing with rational numbers.
 We can use equivalent forms of rational numbers and the relationship between multiplication and division to verify products and quotients.
 Simplifying expressions, solving equations, and solving inequalities (Grade 7, Units 67)
Prior Knowledge Needed:
 Numbers have distance and direction; (Grade 6, Unit 6; 6.NS.6).
 Addition and subtraction of rational numbers can be represented on the number line; (Grade 7, Unit 4; 7.NS.1).
 Multiplication and division are inverse operations; (Grade 4, Unit 14; 4.NBT.B).
 The properties of operations can be used to generate equivalent expressions; (Grade 6, Unit 8; 6.EE.3).
Units on the Horizon:
 Simplifying expressions, solving equations, and solving inequalities; (Grade 7, Units 6, Unit 7)
 Rational and irrational numbers; (Grade 8, Unit 4)
Lessons

Lesson objective: Multiply negative and positive numbers by representing problems on the number line. From 6.NS.6, students bring prior knowledge of representing opposites on the number line, and from 7.NS.1, students bring prior knowledge of representi...

Lesson objective: Fluently multiply with negative numbers. This lesson helps to build fluency with multiplication of rational numbers. Number lines are used here so students can build on their prior knowledge of representing opposites, addition, and sub...

Lesson objective: Divide negative and positive numbers by representing problems on the number line. From 7.NS.A.2a, students bring prior knowledge of representing multiplication with negative numbers on the number line. This prior knowledge is extended ...

Lesson objective: Fluently divide with negative numbers. This lesson helps to build fluency with division of rational numbers. Number lines are used here so students can build on their prior knowledge of representing multiplication on the number line. B...

Lesson objective: Apply multiplication and division of rational numbers to solve problems about investment. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplication and division of rational numbers to...

Lesson objective: Understand that the properties of numbers can be used to prove the rules for multiplying with negative numbers. From 6.EE.3, students bring prior knowledge of the distributive property, and from 7.NS.1, students bring prior knowledge o...

Lesson objective: Fluently multiply with negative numbers. This lesson helps to build fluency with rational number multiplication. Students use their prior knowledge of properties and definitions to develop proofs of the rules for multiplying with negat...

Lesson objective: Understand that realworld situations can be represented by quotients with negative numbers. From 6.RP.3, students bring prior knowledge of unit rates. From 6.NS.5, students bring prior knowledge that positive and negative numbers can ...

Lesson objective: Fluently divide negative numbers. Fluently translate between reallife situations and quotients with negative numbers. This lesson helps to build fluency with dividing negative numbers. An extended example of hiking is used to develop ...

Lesson objective: Apply multiplication and division of rational numbers to solve problems about rates of temperature change. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplication and division of ra...

Lesson objective: Solve multistep problems involving rational numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of addition and subtraction with fractional numbers to a reallife situation. Students ar...

Lesson objective: Apply properties of operations to expressions with negative rational numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of properties of operations to a mathematical situation. Students...