Division

Terminology b ÷ n=a iff a∙n=b b is the dividend n is the divisor a is the quotient a and n are the factors of b and b is a multiple of a and n.

The number line! We use the number line with multiplication when we thought about continuous models, or multiplication as repeated addition. We can use the number line here to show division as repeated subtraction.

What Properties Hold for Division?

Dividing by Zero

Exploration Do by yourself, then discuss with your group. 2. –a.

–b. –c.

Division with Remainder What does it mean to have a remainder?:

Mathematical language

Exploration 3.19 Read the description of the scaffolding algorithm Part 1a. Compute the following-try it yourself, then check your work with a partner.

Exploration 3.19 The Scaffolding Algorithm

Mental Division Some are easier to do in our heads than others: 6000/30 How about 152 divided by 8?

Division with remainders Meaning ContextExploration 3.18 Calculators

Simplify

Rules for order of operations Pleaseparentheses from inside out excuseexponents mymultiplication and Deardivision from left to right Auntaddition and Sallysubtraction from left to right

Rules for order of operations Why do we have the rules? Where did the rules come from?

Order of operations

Exploration 3.20 “gazinta”

Exploration 3.20 Work together in your group. Use the base 10 blocks to work the problem Write an explanation of how and why for each step. Describe what you do with the manipulatives and in mathematical terms.

Connections Addition and Multiplication Subtraction and Division

Connections Addition and Subtraction

Inverse Operations Addition and subtraction Number line representations

Inverse Operations Multiplication and Division number line representation