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

3981

• Solution

= ?

• Phil sells 37 cows. Now he has 49 cows. How many did he have to begin with?

• Problem

- 37 = 49

• Solution

= ?

• Box Diagram

3749

• 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

718

• 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 718

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 calculating2×3 + 15×4 + 8×3 - 5×4 ?

What about 3×4 + 13×7 + 7×4 - 3×7 ?

And 72×3 + 23×4 + 28×3 - 13×4 ?

• What patterns do you see?• Can you make up some similar problems yourself?