Math 7 Unit 1

Patterns and Relations

Lesson 1.1 Patterns in Division

What does it mean when I say,A number is divisible by 2?A number is divisible by 5?A number is divisible by 10?

A number is divisible by 2 when • 2 divides even into the number with no

remainder.

Ex. 8 is divisible by 2 because 2 divides into 8, 4 times with no remainder.

A number is divisible by 5 when • 5 divides even into the number with no

remainder.

Ex. 15 is divisible by 5 because 5 divides into 15, 3 times with no remainder.

A number is divisible by 10 when • 10 divides even into the number with no

remainder.

Ex. 40 is divisible by 10 because 10 divides into 40, 4 times with no remainder.

We can use counters to show divisibility?

Is 12 divisible by 2? 5? 10?

(Use counters here!)

Divisibility Rules

Even numbers, numbers that end 0, 2, 4, 6, 8.

• What numbers are divisible by 5?Numbers ending with 0 or 5.

• What numbers are divisible by 10?Numbers ending with 0.

• What numbers are divisible by 2?

Divisibility Rules

Check the last two digits to see if it is divisible by 4.

• How do you know if a number is divisible by 8?

Check the last three digits to see if it is divisible by 8.

• How do you know if a number is divisible by 4?

Is 412 divisible by 4?

Is 2168 divisible by 8?

Hidden number exercise.

Venn Diagrams.

Create a Venn Diagram for “Divisible by 4” and Divisible by 5”, using the number

16, 95, 20, 132, 248, 341

Exercises:

Page 8-9 # 1, 2, 3, 4, 5, 6, 7

Finish for homework if not finished.

Pass in exercise book before start of classes tomorrow.

Lesson 1.2 More Patterns in Division

Are there any numbers that are divisible by 0?Can you divide a number by zero?

Example: Is 12 divisible by 0?Try taking 12 counters and putting them into 0 groups. Can you do it?

Try taking 12 counters and putting them into groups of zero?Can you do it?

So is 12 divisible by 0? No!

Is any number divisible by 0? No!

Explore Activity: Divisible by 3 and 9.(Handout: lesson1-2-explore.doc)

Divisible by 6:

Lets make a rule for divisible by 6.

We know that 2 x 3 = 6.

So any number that is divisible by 6 is also divisible by 2 and 3.

Rule: A number is divisible by 6 if it is divisible by 2 and 3.

Divisible by 6:Rule: A number is divisible by 6 if it is divisible by 2 and 3.

Is 432 divisible by 6?

Is 128 divisible by 6?

Carroll Diagram (Page 12)

Create a Carroll diagram for “Divisible by 3” and “Divisible by 4” using the data below:

128, 420, 531, 122, 816, 702, 315, 636

Exercises:

Page 12-13:

1, 2 (explain), 3, 5, 6, 7 (explain), 8, 9

(Omit #4 and 10)

Go over homework (look at difficult questions)

Worksheet – Practice all divisibility rules.

Using Divisibility Rules to Factor

Find the factors of each number using divisibility rules.

A) 116 B) 135

Exercises: Page 12, #4

Journal Entry #1Worksheet 2 – Extra Divisible RulesWorksheet 3 – Factoring with Div. Rules

Quiz 1.1 to 1.2

Algebra – Algebraic Expressions

The basis of algebra is the variable. It is a letter used to represent some quantity that can change.

Example: Suppose you work at McDonald’s and you get paid by the hour. The number of hours you work in a week could be represented by the variable h. If you get paid $10 an hour, then 10h would represent the amount of pay you would get when you work h hours. The 10h is an algebraic expression. Complete the table to show how much you would make if you worked each number of hours.

Hours, h Pay, 10h

0

1

2

3

4

10h = 10 x h

The algebraic expressions we will be working with will contain 3 parts: the variable, the numerical coefficient and the constant.

The variable is the letter being used, the numerical coefficient is the number in front of the variable (use a 1 if there is none) and the constant is the number which has no variable with it (use 0 if there is none).

Complete the table.

Algebraic Expression

Numerical Coefficient

Variable Constant

2x+3

6n

0.7y – 0.4

h+5

Writing algebraic expressions for phrases.

Add Subtract Multiply Divide

Identify some words that indicate each operation.

Writing algebraic expressions for phrases.

Write an algebraic expression for each phrase.

3 more than a number

4 times a number

a number decrease by 5

double a number

a number divided by 6

a number subtracted from 11

twice a number increased by 8

the sum of 3 times a number and 12

Exercises: Page 18, #1 to 6

Evaluating Algebraic Expressions

Evaluating an expression means to find the value of the expression for a certain value of the variable.

To evaluate an algebraic expression you substitute a value in for the variable and simplify.

Example: Evaluate each expression when n = 6

A. 2x – 5 B. C. 20 – 3n42

n

Evaluating Algebraic Expressions

Exercises: Page 19 #7, 8, 9

Input/Output Tables

We can create an input/output table for any algebraic expression.

Ex.Input

xOutput2x+3

1

2

3

4

5

Writing Linear Relations for Input/Output Tables

A linear relation is a relation in which the output values increase or decrease by the same amount each time.

Ex: Does this input/output show a linear relation. Write a linear relation for the input/output table.

Input Output

1 4

2 7

3 10

4 13

5 16

Exercises Page 27-28#1, 2, 3, 4

Writing algebraic expressions for word problems.

Exercises Page 23 & 24#2, 3, 4, 5, 6, 7, 8

Mid-Unit Review Page 29 #1, 2, 3, 4, 5, 6, 7, 8