Year 9 Equations
Developing algebraic thinking from
number properties used in mental
calculations.
Word Problems
• Bill has $6. His mum gives him some more
money. Now he has $13. How much did his
mum give him?
6+
= 13
=
?
More problems
• Jenny has 28 marbles. She wins some. Now
she has 32 marbles. How many did she win?
• Carol has 33 sheep. She buys some more. Now
she has 80 sheep. How many did she buy?
• Garry has $339.96 and he needs money to buy
a TV costing $880.78. How much more does
he need?
• Phil sells 47 cows. Now he has 46 cows. How
many did he have to begin with?
- 47 = 46
= ?
• Nara spends $157.30. Now she has $380.63 left.
How much did she have to begin with?
- 157.3 = 380.63
= ?
Similar problems
• Ben spends $36. Now he has $5. How much
did he have to begin with?
• Renee has 801.08 metres of material. She
makes some shirts. Now she has 298.89
metres of material. How much material has
she used?
• Moana’s father gave her $25. She now has
$43. How much did she have to begin with?
+ 25 = 43
=
?
• Jerry has some sheep. He buys 38 more. He
now has 92. How many did he have at the
start?
+ 38 = 92
= ?
• In 5 bags of apples there are 45 apples. How
many apples are in each bag?
5×
= 45
= ?
• Craig buys 1.5 kg of fish. He pays $27.75. How
much does the fish cost per kg?
× 1.5 = 27.75
= ?
Box Diagrams
• Jim has some money. He does some work and
earns $39. Now he has $81. How much did he
have to begin with?
• Problem
+ 39 = 81
• Box Diagram
39
81
• Solution
= ?
• Phil sells 37 cows. Now he has 49 cows. How
many did he have to begin with?
• Problem
- 37 = 49
• Box Diagram
49
37
• Solution
= ?
• Laura thinks of a number. When she multiplies
it by 2 and adds 7, she gets 18.
What was her number?
• Problem
×2 +7 = 18
• Box Diagram
7
18
• Solution
= ?
Problem
• The three shapes contain three different
numbers.
+
+ 7 =
+ 18
• Fill in the shapes with numbers that make the
statement true.
Problem 2
• Find one number that can be put in all 3 boxes
to make the statement true.
+
+ 7 =
+ 18
• Box diagram
7
18
Algebraic symbolism
• The previous problem
can be represented using
algebraic symbolism as:X + X + 7 = X + 18
X+7 =
18
X
=
11
+ 7 = +18
Can you solve these?
•
•
•
•
•
•
•
7x = 2x + 20
9x = 5x + 24
6x = 3x + 6
13x = 9x + 28
7x = 6x + 18
13x = 3x + 40
14x = 36 + 11x
• 7x = 2x + 20
=
+
20
Adding like terms
An open ended approach
Exploring for patterns
• What is a quick way of calculating:97×53 + 3×53 ?
What about
97×42 + 3×42 ?
And how about 6×37 + 4×37 ?
What patterns did you see?
Can you make up some similar problems yourself?
Combining terms
• What is a quick way of calculating
2×3 + 15×4 + 8×3 - 5×4 ?
What about
And
3×4 + 13×7 + 7×4 - 3×7 ?
72×3 + 23×4 + 28×3 - 13×4
?
• What patterns do you see?
• Can you make up some similar problems
yourself?