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8.01 Introduction to variables

Worksheet
Pictures representing variables
1

The key shows how many apples are in each sized box:

Using algebra, state how many apples are in each of the following boxes:

a
b
2

The following key shows how many oranges are in each sized box:

Using algebra, state how many oranges are in each of the following boxes:

a
b
Adding variables
3

The given key shows how many oranges are in each size of box:

If Vincent has one box of each size, write an algebraic expression for the amount of oranges he has altogether.

4

Tom is selling some apples in boxes and some apples individually. To the right is the key showing how many apples are in each box:

a

State the number of apples that each symbol represents:

i
ii
b

Hence, determine the number of apples that the following images represent:

i
ii
c

If there were three times as many apples in each of the images in part (b):

i

Describe how the images would change.

ii

What would the new algebraic expressions be for both diagrams?

Multiplying variables
5

For each of the following situations, complete the pattern in the table:

a

A single box contains x apples.

Number of boxes12345
Number of applesx2 x
b

A single box contains 2y+1 oranges.

Number of boxes123510
Number of oranges2y+14 y+2
c

A single box contains z+2 bananas.

Number of boxes123510
Number of bananasz+22z+4
6

Write an algebraic expression for the number of pieces of fruit in each of the following situations:

a

A single box contains x apples.

b

A single box contains q apples.

7

Using the given key, state how many apples are represented in the following diagrams using algebra:

a
b
c
d
8

Using the given key, state how many oranges are represented in the following diagrams using algebra:

a
b
c
d
9

Xanthe is selling some oranges in boxes and some oranges individually. The key is provided to show how many oranges each box represents:

Use the key to state the number of oranges that the following image represents:

10

For each of the following situations:

i

Use the given key to draw a diagram to represent the number of pieces of fruit each person has.

ii

Write an algebraic expression for the number of apples that they have altogether.

a

Georgia has three boxes containing x apples each, and is then given four more apples.

b

Jimmy has two boxes of oranges containing x oranges each and is then given two more oranges.

11

For each situation, use the given key to draw a diagram that represents the expression:

a

2 y + 3 apples

b

2 a + 2 oranges

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Outcomes

MA4-8NA

generalises number properties to operate with algebraic expressions

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