Report

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?