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) x  6  9
b) n  9  6
c) w  6  9
d) y  9  6
e) x  9  7
f) a  7  3
g) 7 x  56
h) 12n  168
c
9
7
k) 4x  5  37
j)
i)
x
9
5
l) 7q  11  102
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’s sister has?
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 4x  12
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  3x  21
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
n
3
5
Exercise 2: Solve
t
 4
2
Method 1: By inspection.
Method 1: By inspection.
Ask yourself, “What number divided by 5
equals 3?”
Ask yourself, “What number divided by ___
equals ____?”
Method 2: By modeling with Algebra tiles.
Method 2: By modeling with Algebra tiles.
Ask yourself, “What value must one WHOLE
POSITIVE VARIABLE tile have?”
Ask yourself, “What value must one WHOLE
POSITIVE VARIABLE tile have?”
Method 3: Opposite Operation.
Method 3: Opposite Operation.
Ask yourself, “What is the opposite of dividing
by 5?”
Ask yourself, “What is the opposite of dividing
by _____?”
Example 3: Solve
n
n
 4 Note:

3
3
Exercise 3: Solve
w
 2
6
Method 1: By inspection.
Method 1: By inspection.
Method 2: By modeling with Algebra tiles.
Method 2: By modeling with Algebra tiles.
Ask yourself, “What value must one WHOLE
POSITIVE VARIABLE tile have?”
Ask yourself, “What value must one WHOLE
POSITIVE VARIABLE tile have?”
Method 3: Opposite Operation.
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
6w  18
 3c  15
y
 8
3
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.
Assignment page 376: 1, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19ac, 20ac, 21, 22, 23, 24, 27, 28*, 29*