Name: ______Blk: ______

Mathematics 8 – Chapter 10

Lesson 1 – 10.1 Modelling and Solving One-Step Equations

REVIEW OF SOLVING ALGEBRAIC EQUATIONS FROM GRADE 7.

1) Solve each equation using whatever method you wish.

a) / b) / c)
d) / e) / f)
g) / h) / i)
j) / k) / l)

2) Write an equation you can use to solve each problem. Then solve the equation using algebra.

a)  Sara collects 56 leaves for a science project. She collects the same number of each of 7 different types. How many of each type did Sara collect?

b)  The Grade 8 classes at Burnaby South sold “giant cookies” to raise money for charity. They raised $642. Each “giant cookie” sold for $3. How many cookies did they sell?

c)  Johnson has 25 hockey cards. He has one more than 3 times the number of cards his sister has. How many cards does Johnson have?

Some definitions:

An EQUATION: a math statement with ______expressions that have the ______value, separated by an ______sign. Example:

A LINEAR EQUATION: when ordered pairs are graphed, they lie along a ______line.

Let’s look at Simone’s experiment data to determine if the relationship between DISTANCE STRETCHED and FORCE is a linear equation!

Distance stretched “D” (cm) / Force “F” (Newtons)
5 / 10
10 / 20
15 / 30
20 / 40
25 / 50

Plot the data on the grid above.

Questions:

1)  What is the relationship between FORCE and DISTANCE STRETCHED?

2)  Write a linear equation to represent the data.

3)  If you use a force of 600 N, what is the distance the spring would stretch?

You will learn how to solve an equation using

INSPECTION, MODELLING and using the OPPOSITE OPERATION.

For modeling, you will need to use algebra tiles:

______represents a POSITIVE variable. ______represents +1.

______represents a NEGATIVE variable. ______represents -1.

Example 1: Solve

Method 1: By inspection.

Ask yourself, “What number multiplied by 4 equals 12?”

Method 2: By modeling with Algebra tiles. Show your picture below.

Ask yourself, “What value must one POSITIVE VARIABLE tile have? Try grouping.”

Method 3: Opposite Operation.

Ask yourself, “What is the opposite of multiplying by 4?”

Exercise 1: Solve

Method 1: By inspection.

Ask yourself, “What number multiplied by ____ equals _____?”

Method 2: By modeling with Algebra tiles. Show your picture below.

Ask yourself, “What value must one POSITIVE VARIABLE tile have? Try grouping.”

Method 3: Opposite Operation.

Ask yourself, “What is the opposite of ______by _____?”

Example 2: Solve
Method 1: By inspection.
Ask yourself, “What number divided by 5 equals 3?”
Method 2: By modeling with Algebra tiles.
Ask yourself, “What value must one WHOLE POSITIVE VARIABLE tile have?”
Method 3: Opposite Operation.
Ask yourself, “What is the opposite of dividing by 5?”
/ Exercise 2: Solve
Method 1: By inspection.
Ask yourself, “What number divided by ___ equals ____?”
Method 2: By modeling with Algebra tiles.
Ask yourself, “What value must one WHOLE POSITIVE VARIABLE tile have?”
Method 3: Opposite Operation.
Ask yourself, “What is the opposite of dividing by _____?”
Example 3: Solve Note:
Method 1: By inspection.
Method 2: By modeling with Algebra tiles.
Ask yourself, “What value must one WHOLE POSITIVE VARIABLE tile have?”
Method 3: Opposite Operation.
/ Exercise 3: Solve
Method 1: By inspection.
Method 2: By modeling with Algebra tiles.
Ask yourself, “What value must one WHOLE POSITIVE VARIABLE tile have?”
Method 3: Opposite Operation.

Exercises for you to TRY! Solve each equation using a MODEL and by OPPOSITE OPERATION.

EQUATION / SOLVING BY MODELLING / SOLVING WITH OPPOSITE OPERATION

Example 3: The cost of one-quarter of a super juicy sweet Hawaiian pineapple is $1.29.

a)  Write an equation to represent this problem, then solve it using any method you wish.

b)  Check to make sure your answer is correct.