# Year 9 Equations Developing algebraic thinking from number properties used in mental calculations.

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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?

Moanas 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 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 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 about97×42 + 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 about3×4 + 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?

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