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 3.18

• 1. Do by yourself, then discuss with your group.

• 2.– a.

– b.

– c.

Division with Remainder

• What does it mean to have a remainder?:

57527

Mathematical language

brrqbaWrqbWba 0,,)0(,,

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.

2356

Exploration 3.19The Scaffolding Algorithm

6145123

2658658

Mental Division

• Some are easier to do in our heads than others:

6000/30

• How about 152 divided by 8?

Division with remainders

• Meaning

• Context Exploration 3.18

• Calculators

Simplify

1264

Rules for order of operations

• Please parentheses from inside out

• excuse exponents

• my multiplication and

• Dear division from left to right

• Aunt addition and

• Sally subtraction from left to right

Rules for order of operations

• Why do we have the rules?

• Where did the rules come from?

Order of operations

3224

3610

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