Method 1: Total distance → 4 groups of intervals + the width of the 5 trees = 4 × 4 m + 5 × 0.5m = 16 m + 2.5m = 18.5 m Method 2: Total Distance → 5 groups of intervals – last interval of the 5th tree = 5 × 4.5 m – 0.5m = 22.5 m - 4m = 18.5 m 2) 3) 51 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 21: Heuristics (Patterns) Answer Key 1. (a) 7 x 8 + 5 = 61 9 x 6 + 4 = 58 8 x 6 + 9 = 57 The missing number is 6. (b) 5 x 9 – 3 = 42 7 x 3 – 9 = 12 4 x 9 – 6 = 30 The missing number is 30. 2. (a) (72 ÷ 8) x 5 = 45 (144 ÷ 12) x 8 = 96 (52 ÷ 4) x 10 = 130 The missing number is 10. (b) The sum of the 3 numbers on top is equal to the sum of the 3 numbers at the bottom. (5 + 10 + 20) = (15 + 5 + 10) = 35 6 + 14 + 30 = 50 50 – 25 – 15 = 10 The missing number is 10. 3. a) (1 x 7) + 3 = 10 (2 x 8) + 3 = 19 (4 x 10) + 3 = 43 (3 x 9) + 3 = 30 The missing number is 30. (b) (2 x 3) + 10 = 16 (4 x 5) + 10 = 30 (6 x 7) + 10 = 52 (8 x 8) + 10 = 74The missing number is 8. 52 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
4. Working from top to bottom, column by column: Step 1: 1strow + 2nd row =Sum Step 2: Sum ÷ 2 4 + 4 = 8 8 ÷ 2 = 4 3 + 7 = 10 10 ÷ 2 = 5 8 + 6 = 14 14 ÷ 2 = 7 12 + 6 = 18 18 ÷ 2 = 9 Work backwards: 8 x 2 = 16 16 – 3 = 13 The missing number is 13. 5. (2 x 2) + 8 = 12 (3 x 3) + 9 = 18 (5 x 5) + 3 = 28 ( x ) + 4 = 40 ( x ) = 40 – 4 = 36 36 = 6 x 6 (or √36 = 6) (7 x 7) + 1 = = 50 The represents 6. The represents 50. 53 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
6. There are 3 numbers with a total of 30. To find the middle number, we take 30 ÷ 3, which gives us 10. (a) For the sum of 60, the middle number is 60 ÷ 3 = 20 (see answer below) (b) For the sum of 96, the middle number is 96 ÷ 3 = 32 (see answer marked by oval) 7. Get pupils to draw the next figure in the pattern to visualise the pattern rule. Pattern rule : Circles = No of rectangles x 4 + 2 (at the end) (a) Pattern 7 circle → 7 x 4 + 2 = 30 (b)Pattern 15 circle → 17 x 4 + 2 = 70 (c) 50 – 2 = 48 48 ÷ 4 =12 Ans: Pattern 12 8. Figure 1: 1 + 3 = 4 squares (2 x 2) Figure 2: 1 + 3 + 5 = 9 squares (3 x 3) Figure 3: 1 + 3 + 5 + 7 = 16 squares (4 x 4) Figure 4: 5 x 5 = 25 squares Figure 5: 6 x 6 = 36 squares Perimeter: Figure 1: 10 cm Figure 2: 16 cm Figure 3: 22 cm +6 +6 +6 10, 16, 22, 28, 34, 40, 46, 52, 58, Fig.5 Fig.9 (b) The perimeter is 34 cm. 54 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
(c) Number of squares in Figure 9 → 10 x 10 = 100 Ans (a) 25 squares and 28 cm (b) 34 cm (c) 100 9. Simplify the question. Divide the pattern into 3 equal rows. 186 – 3 – 3 = 180 Number of houses in each row → 180 ÷ 3 = 60 Now we can label the figure as follows: X → 64 + 60 – 1 = 123 X is 123. 10. (a) Each set in the pattern consists of 4 shapes. 42 ÷ 4 = 4 R2 Remainder 2 → 2nd item in the set Ans: 10 (b) Each set in the pattern consists of 5 letters. 98 ÷ 5 = 19 R3 Remainder 3 → 3rd item in the set Ans: T 10 (c) Each set in the pattern consists of 6 arrows. 155 ÷ 6 = 25R5 Remainder 5 → 5th item in the set Ans: 1 2 3 58 59 60 61 62 63 64 55 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
11. Draw one more grid. We do this to establish a pattern. (Explain that a pattern cannot be established by using information from only 2 tables/figures etc.) This forms a series of odd numbers. 3, 5, 7 , 9, 11, 13, 15, 17, 19 From this, we learnthat: 2 x 2 grid → 3 squares 3 x 3 grid → 5 squares 4 x 4 grid → 7 squares (10 x 10 grid) It crosses 19 squares in a 10 x 10 grid paper. 56 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 22: Guess and Check / Supposition Answer Key 1. Method 1: Guess and Check (Draw aTable) No of Horses No of Horses’ Legs (4 each) No of Ducks No of Ducks’ Legs (2 each) Total Numberof Legs Check 12 48 12 24 48 + 24 = 72 X 15 60 9 18 60 + 18 = 78 ✓ For second guess: 78 – 72 = 6 (difference of the total number of legs) 4 – 2 = 2 (difference of legs between a horse and a duck) 6 ÷ 2 = 3 (3 more horses to first guess) 12 + 3 = 15 15 x 4 = 60 12 – 3 = 9 9 x 2 = 18 60 + 18 = 78 Method 2: Supposition Assume all are horses. 24 x 4 = 96 legs 96 – 78 = 18 legs (too many) Difference= 4 – 2 = 2 legs 18 ÷ 2 = 9 ducks 24 – 9 = 15 horses OR Assume all are ducks. 24 x 2 = 48 legs 78 – 48 = 30 legs (too little) Difference= 30 ÷ 2 = 15 horses 24 – 15 = 9 ducks Ans (a): 15 horses Ans (b): 9 ducks 57 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
2. Method 1: Guess and Check (Draw aTable) No of 2- propeller Helicopters No of Propellers (2 each) No of 3- propeller Helicopters No of Propellers (3 each) Total Numberof Propellers Check 17 34 17 51 34 + 51 = 54 X 16 32 18 54 32 + 54 = 86 ✓ For second guess: 86 – 54 = 32 (difference of the total number of propellers) 3 – 2 = 1 (difference of propellers between a 3-propeller helicopter and a 2-propeller helicopter) We reduce the number of 2-propeller helicopters by 1 and increase the number of 3- propeller helicopters by 1.) 32 ÷ 2 = 16 16 x 2 = 32 34 – 16 = 18 18 x 3 = 54 32 + 54 = 86 Method 2: Supposition Assume all are 3-propeller helicopters. 34 x 3 = 102 propellers 102 – 86 = 16 propellers Difference= 3 – 2 = 1 propeller OR Assume all are 2-propeller helicopters. 34 x 2 = 68 propellers 86 – 68 = 18 propellers Difference= 3 – 2 = 1 propeller Ans (a): 16 2-propeller helicopters Ans (b): 18 3-propeller helicopters 3. Method 1: Guess and Check (Draw aTable) No of 50¢ coins Value No of 20¢ coins Value Total Value Check 20 1000¢ 20 400¢ 1400¢ X 10 500¢ 30 600¢ 1100¢ ✓ For the second guess: 1400¢ - 1100 = 300 50¢ - 20¢ = 30¢ 58 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
300¢ ÷ 30¢ = 30 (twenty-cent coins) Method 2: Supposition Assume all are 50¢ coins. 40¢ x 50¢ = 2000¢ = $20 $20 - $11 = $9 (or 900¢ short) 50¢ - 20¢ = 30¢ 900¢ ÷ 30¢ = 30 twenty-cent coins 40 – 30 = 10 fifty-cent coins Ans (a): 30 twenty-cent coins Ans (b): 10 fifty-cent coins 4. Method 1: Guess and Check (Draw a Table) No of $1 coins Value No of 50¢ coins Value Total Value Check 25 $25 25 $12.50 $37.50 X 20 $20 30 $15 $35 ✓ For the second guess: $37.50 - $35 = $2.50 (250¢) 100¢ - 50¢ = 50¢ 250¢ ÷ 50¢ = 5 (more fifty-cent coins added to first guess) Method 2: Supposition Assume all are one-dollar coins. 50 x $1 = $50 (total) Difference= $50 - $35 = $15 (1500¢) 100¢ - 50¢ = 50¢ 1500¢ ÷ 50¢ = 30 (fifty-cent coins) 50 – 30 = 20 (one-dollar coins) Ans (a): 20 one-dollar coins Ans (b): 30 fifty-cent coins 5. Method 1: Guess and Check (Draw aTable) No of Basketballs Cost No of Rugby Balls Cost Total Cost Check 5 $225 6 $210 $435 X 6 $270 5 $175 $445 ✓ 59 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
For the second guess: $445 - $435 = $10 $45 - $35 = $10 10 ÷ 10 = 1 5 + 1 = 6 basketballs Method 2: Supposition Assume all are basketballs. 11 x $45 = $495 $495 - $445 = $50 (short of $50) $45 - $35 = $10 $50 ÷ $10 = 5 rugbyballs 11 – 5 = 6 basketballs Ans (a): 6 basketballs Ans (b): 5 rugby balls 6. Method 1: Guess and Check (Draw aTable) No of Adult Movie Tickets Cost ($7per ticket) No of Child Movie Tickets Cost ($4 per ticket) Total Cost Check 6 $42 6 $24 $66 X 5 $35 7 $28 $63 ✓ For the second guess: $66 - $63 = $3 $7 - $4 = $3 3 ÷ 3 = 1 6 + 1 = 7 child movie tickets 12 – 7 = 5 adult movie tickets Method 2: Supposition Assume all are adult movie tickets. 12 x $7 = $84 (total) $84 - $63 = $21 $7 - $4 = $3 21 ÷ 3 = 7 12 – 7 = 5 Ans (a): 5 adult movie tickets Ans (b): 7 child movie tickets 60 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7. Using the Supposition Method: Assume all are girls. 29 x 5 = 145 pencils 145 – 113 = 32 pencils Difference= 5 – 3 = 2 pencils 32 ÷ 2 = 16 boys Ans: 16 boys 8. Using the Supposition Method: Assume all are boys. 34 x 3 = 102 party poppers 156 – 102 = 54 party poppers Difference= 6 – 3 = 3 party poppers 54 ÷ 3 = 18 girls Ans: 18 girls 9. Using the Supposition Method: Assume all answers were answered correctly. 40 x 4 = 160 marks (total) Marks Marcus lost = 160 – 124 = 36 marks Marks taken away for every wrong answer = 4 + 2 = 6 marks 36 ÷ 6 = 6 wrong answers 40 – 6 = 34 correct answers Ans: 34 correct answers No of correctans Marks No of wrong ans Marks Total marks Check 40 40 x4 = 160 0 0 x 2 = 0 160 – 0 = 160 X 39 39 x 4 = 156 1 1 x 2 = 2 156 – 2 = 154 X 34 34 x 4 = 136 6 6 x 2 =,12 136 – 12 = 124 √ 61 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
154 – 124 = 30 30 ÷ 6 = 5 10. Using the SuppositionMethod: 20 x 5 = 100 marks (total) Marks Denise lost = 100 – 79 = 21 marks Marks taken away for every wrong answer = 5 + 2 = 7 marks 21 ÷ 7 = 3 wrong answers 20 – 3 = 17 correct answers Ans: 17 correct answers 11.Using the Supposition Method: Assume all questions were answered correctly. 20 x 5 = 100 (total) Marks Kyeran lost = 100 – 72 = 28 marks Marks taken away for every wrong answer = 5 + 2 = 7 marks 28 ÷ 7 = 4 wrong answers Ans: 4 wrong answers 12.Using the Supposition Method: Assume all questions were answered correctly. 50 x 3 = 150 (total) Marks Brian lost = 150 – 125 = 25 marks Marks taken away for every wrong answer = 3 + 2 = 5 marks 25 ÷ 5 = 5 wrong answers Ans: 5 wrong answers 62 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 23: Working Backwards Answer Key 1. Amount of money Mr Chai had left = $3827 - $1435 = $2392 Amount of money Mr Chai had at first = $2392 + $1999 + $760 = $5151 Ans: $5151 2. Amount of money Judith had left = $2 860 - $995 = $1 865 Amount of money Judith had at first = $1 865 + $1 755 + $1 359 - $100 = 4 879 Ans: $4879 3. Amount of money Stacey had left = $7 880 + $1 015 = $8 895 8895 – 250 =8645 Amount of money Stacey had at first = $8645 + $899 +530 + $350 = $10 824 Ans $10 424 4. Total number of erasers in the 3 containers= 3 x 20 = 60 Number of erasers Zen after 1stround = (60 ÷ 2) = 30 Number of erasers Zen had at first= 30 + 12 = 42 Ans: 42 erasers 5. Number of seashells Priscilla picked = 2 x 12 = 24 Number of seashells Ann picked = 24 + 22 = 46 Number of seashells Lydia picked= 46 – 19 = 27 Number of seashells Joan picked = 27 ÷ 3 = 9 Ans: 9 seashells 6. Number of game cards in 7 pages= 7 x 22 = 154 Number of game cards Nigel had at first= 154 – 18 + 10 = 146 Ans: 146 game cards 63 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7. Tyrion $75 Ralph $65 Deon $80 + $5 + $7 + $4 $80 $72 $84 $85 $79 $88 $90 $86 $92 $95 $93 $96 $100 $100 $100 Ans: $100 8. Mandy $31 Nora $22 Lisa $25 + $4 + $7 + $6 $35 $29 $31 $39 $36 $37 $43 $43 $43 Ans: $42 9. Adria $122 Brenda $110 Cindy $118 + $7 + $10 + $8 $129 $120 $126 $136 $130 $134 $143 $140 $142 $150 $150 $150 Ans: $150 64 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
10. Total volume of water in the 5 glasses= 5 x 190 = 950 ml Volume of water in total = 950 ml + 350 ml = 1 ℓ 300 ml Volume of water in tank at first = 1ℓ 300 ml - 1ℓ 50 ml = 1300 ml – 1050 ml = 250 ml Ans: 250 ml 11a) Volume of water in Pot C = 5 ℓ - 1 ℓ 350 ml = 3 ℓ 650 ml Volume of water in Pot B = 3 ℓ 650 ml + 2 ℓ 30 ml = 5 ℓ 680 ml Volume of water in Pot A = 5 ℓ 680 ml + 5 ℓ 680 ml = 11 ℓ 360 ml (a) Ans: 11 ℓ 360 ml 11b) Difference in volume = 11 ℓ 360 ml - 3 ℓ 650 ml = 7 ℓ 710 ml (b) Ans: 7 ℓ 710 ml 12. Surf ShopE 80 Surf Shop D 2 units = 80 – 20 = 60 surfboards 1 unit = 60 ÷ 2 = 30 surf boards Number of surfboardsSurf Shop E has = 30 Number of surfboardsSurf Shop D has = 30 + 20 = 50 Number of surfboardsSurf Shop C has = 50 – 35 = 15 Number of surfboardsSurf Shop B has = 2 x 15 = 30 Number of surfboardsSurf Board A has = 3 x 30 = 90 Ans: Surf Shop A: 90 Surf Shop B: 30 Surf Shop C: 15 Surf Shop D: 50 Surf Shop E: 30 20 1 unit 65 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 24: Heuristics Review [2] Answer Key 1. 4 units = 106 + 30 = 136 1 unit = 136 ÷ 4 = 34 5 units = 5 x 34 = 170 Ans: 170 chickensatays No. of cupcakes Cost of cupcakes No. of egg tarts Cost of egg tarts Total Cost Check 12 12 x 4 = 48 11 11 x 2 = 22 48 + 22 = 60 X 13 13 x 4 = 52 10 10 x 2 = 20 52 + 20 = 62 X 14 14 x 4 = 56 9 9 x 2 = 18 56 + 18 = 64 √ Method 2: Make a Supposition Suppose/If all are egg tarts= 23 x 2 = 46 Excess ($) = 64 – 46 = 18 (difference between actual total and supposed total) Difference bet 1 cupcake& 1 egg tart = 4 – 2 = 2 Total number of cupcakes= 18 ÷ 2 = 9 (Divide Excess by Difference) Total numberof egg tarts = 23 – 9 = 14 Ans: (a) 14 strawberry cupcakes (b) 9 egg tarts 3. Lead pupils to see that the total number of students before and afteris the same. 1u 106 30 1u 106 chicken mutton 5 units? 1unit 2. Guess and Check using a Table Using the results in the 1st two lines, lead pupils to see that the total cost increases by $2 with every increase in the number of cupcakes and every decrease on the number of egg tarts. Chess Art 4 units = 29 + 43 = 72 1 unit = 72 ÷ 4 = 18 3 units = 3 x 18 = 54 (Chess club in the end) Ans: 54 pupils ? 29 + 43 After Term 1 66 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
4. Extra = 15 x 3 = 45 7 units = 213 – 45 = 168 1 unit = 168 ÷ 7 = 24 1 dress = 24 + 15 = 39 Ans: $39 5 6 units = 123 + 3 = 126 1 unit = 126 ÷ 6 = 21 4 units = 21 x 4 = 84 1 dress = 24 + 15 = 39 Ans: $39 6. 8 units = 124 + 76 = 200 1 unit = 200 ÷ 8 = 25 (Susan at the end) No of beads given = 76 – 25 = 51 Ans: 51 beads 7. WorkBackwards 230 x 2 = 460 460 – 100 = 360 360 + 35 = 395 Ans: 395 stamps 8. Extra = 5 x 5 = 25 9 units = 124 – 25 = 99 1 unit = 99 ÷ 9 = 11 1 big box = 11 + 5 = 16 3 big boxes = 16 x 3 = 48 Ans: 48 $213 Dress Dress Dress Shirt Shirt Shirt Shirt 15 15 15 ? 1 unit Diane Cindy Ellen 3 123 + 3 Louisha Susan 124 + 76 After 124 Big Big Big Big Big Small Small Small Small 5 5 5 5 5 ? 67 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
9. 1 interval= 16 ÷ 4 = 4 (a) Between 1st and 16th tree = 16 – 1 = 15 intervals Distance = 15 x 4 = 60 m (b) No of intervals= 30 – 1 = 29 Length of road = 29 x 4 = 116 m Ans: (a) 60m (b) 116 m 10. 5 units = 80 1 unit = 80 ÷ 5 = 16 More = 3 units = 3 x 16 = 48 Give = 48 ÷ 2 = 24 Ans: 24 11a) 2 units = 107 – 7 = 100 1 unit = 100 ÷ 2 = 50 Father (now) = 50 + 7 = 57 Father (3 years’ time) = 57 + 3 = 60 11b) Simon (3 years’ time) = 60 ÷ 3 = 20 Simon now = 20 - 3 = 17 Ans: (a) 60 years old (b) 17 years old Justin Simon give 80 more Father Mother 107 ? 7 Father Simon 3 years’ time 60 ? 68 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
12. Guess and Check using a Table Using the results in the 1st two lines, lead pupils to see that the total cost decreasesby 6 with every decrease in the number of correct answer and every increasee on the number of wrong answer. 80 – 56 = 24 24 ÷ 6 = 4 (4 wrong answers) Ans: 16 correct answers Method 2: Using the Supposition Method: Assume all answers were answered correctly. 20 x 4 = 80 marks (total) Total Marks lost = 80 – 56 = 24= 24 marks Marks lost for every wrong answer = 4 + 2 = 6 marks No of wrong answers = 24 ÷ 6 = 4 wronganswers No. of correct answers = 20 – 4 = 16 correct answers Ans: 16 correct answers No of correctans Marks No of wrong ans Marks Total marks Check 20 20 x 4 = 80 0 0 x 2 = 0 80 – 0 = 80 X 19 19 x 4 = 76 1 1 x 2 = 2 76 – 2 = 74 X 16 16 x 4 = 64 4 4 x 2 = 8 64 – 8 = 56 √ -6 -4 69 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 25: Review2 Answer Key Section A (2 marks each) 1) 4 2) 4 3) 4 4) 3 5) 1 6) 3 7) 1 8) 4 9) 4 10) 3 Section B (2 marks each) 11.The pattern is -100, +200, -100, +200… Ans: 1 500, 1 700 (1m each) 12. 8 x 9 = 72 72 - 4 = 74 (M1, A1) Ans: 74 13. Number of coin pouches Blythe collected = 8 x 9 = 72 Total number of coin pouches collected= 72 + 9 (M1) = 81 (A1) Ans: 81 coin pouches 14. 5 x 8 – 3 = 37 8 x 3 – 9 = 15 7 x 9 – 6 = 57(M1,A1) Ans: 57 15. $100 5 units = $100 1 unit = $100 ÷ 5 (M1) = $20 (A1) Ans: $20 OR 3 books = 2 pens 6 books = 4 pens (Sub 6 books with 4 pens) 4 pens + 1 pen = $100 5 pens = 100 1 pen = 100 ÷ 5 = 20 70 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
16. Pattern: Black Beads: 1, 2, 3, 4, 5 WhiteBeads: 1, 2, 3, 4 MissingBlack Beads = 4 – 1 = 3 MissingWhite Beads = 4 – 2 (M1, A1) = 2 Ans: Black Beads: 3 White Beads: 2 17. Number of bookmarks Krystal has now = 20 Number of bookmarksKrystal had before she gave away 12 to Tim and 4 to Rob = 20 + 12 + 4 (M1) = 36 Number of bookmarks Krystal had at first = 36 – 5 = 31 (A1) Ans: 31 bookmarks 18. 3 = 375 1 = 375 ÷ 3 = 125 + = 175 = 175 – 125 = 50 + + = 50 + 125 + 125 (M1,A1) = 300 Ans: 300 19. Number of chocolates Leslie gave to his classmates = 35 x 6 = 210 Number of chocolates Leslie had at first = 210 + 19 (M1) = 229 (A1) Ans: 229 chocolates 71 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
20. The multiplication of the outer number by the middle number 12 will equate to the opposite outer number. A = 96 ÷ 12 = 8 B = 10 x 12 = 120 Ans: A: 8 and B: 120 Section C (3 marks each) 21. Adria Carla 425 Devi 5 units = 425 – 5 = 420 1 unit = 420 ÷ 5 (M1) = 84 Adria = 84 + 5 (M1) = 89 (A1) Ans: 89 paperflowers 22. 76 – 8 – 8 = 60 (M1) Now: 60 6 units = 60 1 unit = 60 ÷ 6 (M1) = 10 5 units = 5 x 10 = 50 (A1) Ans: 50 years old 5 72 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
23. Pattern 1: 1 = 1 x 1 Pattern 2: 4 = 2 x 2 Pattern 3: 9 = 3 x 3 Therefore, Pattern 9: 9 x 9 = 81 (M1, A½) (a) Ans: 81 squares Pattern 13: 13 x 13 = 169 (M1, A½) (b) Ans: Pattern 13 24. (Method 1) Guess and Check: No of Basketballs Cost ($45 each) No of Rugby Balls Cost ($35 each) Total Cost Check 5 $225 6 $210 $435 X 6 $270 5 $175 $445 ✓ For the second guess: $445 - $435 = $10 $45 - $35 = $10 $10 ÷ $10 = 1 5 + 1 = 6 basketballs *If pupil shows the guess and check solution clearly, award him/her M2, (a) A½ and (b) A½.) (Method 2) Supposition If all were basketballs, 11 x $45 = $495 $405 - $445 = $50 (There would be a shortage of $50.) $45 - $35 = $10 (Difference between 1 basketball and 1 rugby ball) $50 ÷ $10 = 5 rugby balls (M½, A½) 11 – 5 = 6 basketballs (M½, A½) (a) Ans: 6 basketballs (b) Ans: 5 rugby balls 25. Number of clue cards Patty picked= 2 x 12 = 24 Number of clue cardsAvery picked= 24 + 20 = 44 Number of clue cards Lisa picked = 44 – 19 = 25 Number of clue cards Jasmine picked= 25 ÷ 5 = 5 Ans: 5 clue cards 19 20 J L A P 73 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 26: Review3 Answer Key Section A (2 marks each) 1) 3 2) 3 3) 4 4) 4 5) 1 6) 1 7) 4 8) 4 9) 2 10) 2 Section B (2 marks each) 11. The pattern is +10, +20, +10, +20… Ans: 765 12. 628 + 15 = 643 (M1,A1) Ans: 643 13. Ans: 1083 14. Pattern: (12 + 34) – 10 = 36 (26 + 14) – 15 = 25 (18 + 32) – 26 = 24 (M1, A1) Ans: 24 15. Price of 2nd pair of shoes = $70 ÷ 2 = $35 Total cost of shoes = $70 + $35 = $105 Amount of money left = $1 000 - $105 (M1) = $895 (A1) Ans: $895 16. (a) False (b) False 74 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
17. (a) No(A1) (b) Change = $100 - $59.90 (M½) = $40.10 (A½) 18. = 260 - 155 = 105 = 155 - 105 = 50 + + = 50 + 50 + 105 (M1) = 205 (A1) Ans: 205 19. Mangoes at first = 344 - 172 + 1352 + 56 (M1) = 1580 (A1) Ans: 1 580 mangoes 20. 77 ÷ 8 = 9 R 5 (M1) 5 adults = 1 van 9 + 1 = 10 vans (A1) Ans: 10 vans 75 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Section C 21.Number of boxes bought = 72 ÷ 8 (M1) = 9 Total number of crepes = 9 x 2 (M1) = 18 (A1) Ans: 18 crepes 22. Ken’s age now = 11 – 2 (M1) = 9 years Phillip’s age now = 9 + 4 (M1) = 13 years (A1) Ans: 13 years old 23.Austin 35 Brendon 385 Charlie 6 units = 385 + 15 (M1) = 420 1 unit = 420 ÷ 6 = 70 Austin = 70 – 35 (M1) = 35 (A1) Ans: 35 trading cards 76 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
24. Use Guess andCheck Lizard lizard legs praying mantis praying mantis legs Total Legs (92) check 10 10 x 4 = 40 10 10 x 6 = 60 40 + 60 = 100 x 11 11 x 4 = 44 9 9 x 6 = 54 44 + 54 = 98 x 98 – 92 = 6 11 + 3 = 14 14 x 4 = 56 9 – 3 = 6 6 x 6 = 36 56 + 36 = 92 6 ÷ 2 = 3 25. Total possible marks = 40 x 4 = 160 marks Number of marks Paula lost = 160 – 24 (M1) = 36 marks Every wrong answer = 4 + 2 = 6 marks 36 ÷ 6 = 6 wrong answers (M1) 40 – 6 = 34 correct answers (M1, A1) Ans: 34 correct answers 26. Pattern:+2 6 + 2 = 8 Ans (a): 8 (A1) Pattern: +3 12 + 3 = 15 Ans (b): 15 (A1) Ans (c): 24 tiles (M1, A1) Pattern Total Number of Tiles 4 15 5 18 6 21 7 24 77 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 27: Review 4 Answer Key Section A (2 marks each) 1) 4 2) 3 3) 3 4) 2 5) 4 6) 4 7) 3 8) 3 9) 1 10) 4 Section B (2 marks each) 11. Six thousand seven hundred andforty-one 12. The pattern is +300, -200, +300, -200 … Ans: 1490 13. 7 203 – 2 370 = 4 833 (M1,A1) Ans: 4 833 14. 2 x 750 = 1 500 (M1,A1) Ans: 1kg 500 g or 1 500g 15.Ans A: 5 Ans B: 6 16. Max number of boxes = 247 ÷ 6 = 41 r 1 Ans: 41 boxes 17.Ans: 48 78 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
18. Length of longer pencil = 2 x 7 = 14 cm Ans: 14 cm 19. Number of seashells each person gets = 360 ÷ 4 = 90 Ans: 90 seashells 20.Age of Polly’s cousin now = 2 x 12 = 24 Age of Polly’s cousin in 9 years’ time = 24 + 9 = 33 Ans: 33 years Section C 21.Total number of students = 4 x 35 (M1) = 140 Number of adults needed = 140 ÷ 10 (M1) = 14 (A1) Ans: 14 adults 22. Remaining number of pages = 235 – 37 = 198 Number of days needed to complete reading the book = 198 ÷ 9 = 22 Ans: 22 days 79 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
23. Tulips Carnation 50 590 Sunflower 5 units = 590 – 50 (M1) = 540 1 unit = 540 ÷ 5 (M1) = 108 (A1) Ans: 108 carnations 24. 3 units = 72 –27 = 45 (M1) 1 unit = 45 ÷ 3 = 15 (M1) Ray = 15 + 72 = 87 (A1) Ans: $87 25. Method 1: Guess and Check (Draw a Table)(M2) For the second guess: $66 - $63 = $3 $7 - $4 = $3 3 ÷ 3 = 1 6 + 1 = 7 child carnival tickets (A1) 12 – 7 = 5 adult carnival tickets (A1) No of Adult Carnival Tickets Cost ($7per ticket) No of Child Carnival Tickets Cost ($4per ticket) Total Cost Check 6 $42 6 $24 $66 X 5 $35 7 $28 $63 ✓ $27 $72 Ray Tom ? 80 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Method 2: Supposition Assume all are adult carnival tickets. 12 x $7 = $84 (total) (M1) $84 - $63 = $21 (M1) $7 - $4 = $3 21 ÷ 3 = 7 (A1) 12 – 7 = 5 (A1) Ans (a): 5 adult carnival tickets Ans (b): 7 child carnival tickets 26. (a) Pattern 2: 1 white triangle Pattern 3: 3 white triangles Pattern 4: 6 white triangles +2 +3 +4 +5 +6 +7 1, 3, 6, 10, 15, 21, 28 (M1) Pattern 8 (b) Pattern 1: 1 triangle Pattern 2: 4 triangles Pattern 3: 9 triangles The pattern is that it is a series of square numbers: 1, 4, 9, 16, 25, …, 100 10 x 10 = 100 (M1) Ans (a): 28 white triangles (A1) Ans (b): Pattern 10 (A1) 81 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 28: Review5 Answer Key Section A (2 marks each) 1) 2 2) 2 3) 4 4) 3 5) 3 6) 1 7) 1 8) 2 9) 3 10) 2 Section B (2 marks each) 11. 2 268 12. 370 x 6 = 2220 2 220 + 4 = 2 224 (M1,A1) Ans: 2 224 January February March April 200 200 +120 = 320 320 + 120 = 440 440 + 120 = 560 13. (M1,A1) Ans: 560 14. 7 x 7 x 7 = 343(M½) = 7 = (37 – 7) ÷ 2 (M½) = 15 - = 15 – 7 = 8 (A1) Ans: 8 82 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
+ 50 180 + 50 = 230 (M1, A1) Ans: 230 16. Workingbackwards: 490 – 61 + 28 + 137 = 594 Ans: 594 stamps 17. 46 ÷ 4 = 11 r2 Ans: 11 sticker sheets 18. Length of crayon at first = 13 – 1 = 12 cm Length of crayon left = 12 ÷ 2 (M1) = 6 cm (A1) Ans: 6 cm 19. = 310 – 140 = 170 g = 320 – 170 = 150 g Ans: 150 g 20. ? A 50 15. Pattern: ÷ 2 180 B 83 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. 50 145
50 + 50 = 100 145 + 100 = 245 Ans: 245 chickens Section C 21. Mass of PeanutButter = 350 – 200(M1) = 150 g (A½) Mass of Cheese = 230 – 150 (M1) = 80 g (A½) Ans (a): 150 g Ans (b): 80 g 22. Red Green 227 Yellow 227 – 27 = 200 4 units = 200 1 unit = 200 ÷ 4 (M1) = 50 (A½) No of red ice lollies = 2 x 50 = 100 No of yellow ice lollies = 50 + 27 = 77 Difference between red and yellow ice lollies = 100 – 77 (M1) = 23 (A½) 27 84 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Ans (a): 50 green ice lollies Ans (b): 23 more red ice lollies 23. Bag A 42 Bag B 6 units = 42 I unit = 42 ÷ 6 (M1) = 7 No of candy canes each bag should have = 42 ÷ 2 = 21 No of candy canes Bag B needs = 21 – 7 (M1) = 14 (A1) Ans: 14 candy canes 24. Work Backwards Total at the end, 4 units = 552 1 unit = 552 ÷ 4 = 138 Mr Tan, 3 units = 3 x 138 = 414 Mr Tan, at first 414 – 92 = 322 25. Method 1: Make a Table (M2) 10 – 8 = 2 years go (M1,A1) Method 2: Use a Model Difference in age remains the same. Diff in age = 66 – 10 (M1) = 56 7 units Jane’s Age Grandmother’s Age 8 times? Yes/No 10 66 No 9 65 No 8 64 Yes 85 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7 units = 56 I unit = 56 ÷ 7 M1) = 8 10 – 8 = 2 years ago (M1,A1) Ans: 2 years ago 26. Max Tristen 400 160 4 units = 160 + 400 (M1) = 560 I unit = 560 ÷ 4 (M1) = 140 No of trading cards Tristen had at first = 140 + 160 (M1) = 300 (A1) Ans: 300 trading cards 86 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
16 8 2 1 9 3 4 5 6 7 10 15 14 13 12 11 8 2 1 9 3 4 5 6 7 10 15 16 14 13 12 11 (1a) Split the circle into two regions so that the sum of the numbers in each region is the same. (1b) Split the circle into four regions so that the sum of the numbers in each region is the same. Yippee! ! We are going on a campingtrip! Join us to complete every mission in this fun-filled adventure! Mission One: In the camp, everyone is seated in a circle holding a number as shown below. Mission 1 Circle of Numbers! Funwith Math (Lesson29) 87 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
18 12 14 15 17 13 11 16 19 A C 44 45 46 Columns B Totals = A B C Rows 44 45 46 =Totals 54 We need to prepare for the the campfire. Solve the following problem and you can exchange them for a bag of twigs. Mission Three: 3. Place the numbers 11 to 19 in the grid below. Use each number only once. Follow the following rules: • Row A has all evennumbers. • Row B has all odd numbers. • 12 and 16 are in the same column. • 16 is not in the same row as 14. • 11and 19 are in the same row. Mission 2 Light the Fire! 88 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Mission 3 Pick Me! Pick Me! Try this !! Move 3 toothpicks to mark 4 identical squares. Look at the figures below. Follow the instructions and use the toothpicks given to you to work out your answer. Then draw your answers in the boxes. Move 3 toothpicks to mark 4 identical squares. Move 3 toothpicks to make 3 identical squares. 89 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
How many ways can Johnny take to walk from his home to the park? He can only walk to the right or downwards. Mission 4 Johnny Walker! Example ways 6 90 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Joe had 4 different tops and 3 different pants. How many different ways can he match his tops and pants? Draw lines to match the tops and pants. Mission 5 What a Match! 12 ways 91 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Number equation to get the total number of ways: 4 x 3 = 12 (No of items in 1st grp i.e. shirts x No of items in 2nd grp ie. pants)
B. Find the total number of triangles in the figurebelow. Mission 6 Let’s Try-n-Guess the Tri-Angles! triangles A. Find the total number of triangles. (Hint: There are 4 sizes of triangles) or or or 12 There are 10 triangles in the figure. 6 2 20 92 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
North-west Hawker Centre North Aquarium North-east Swimming Pool West Library ME East School South-west My home South Playground South-east Car Park Activity 7 My 8-Point Compass 1. To my North is the Aquarium . Draw a fish to represent the aquarium. 2. To my South is the playground, Draw a swing to represent the playground. 3. To my East is my School. Write your school name here. 4. To my West is the Library. Draw a book. 5. To my North-east is the Splash Swimming Pool. Draw a pool. 6. To my South-east is a car park. Draw a car. 7. To my South-west is my home. Draw a house. 8. To my North-west is the Hawker Centre. Draw a bowl with chopsticks. Let’s learn how to read the 8-point compass. You are standing in the middle. Around you are different places. Read and follow the instructions. Name the places and draw the legend to represent the places in their corresponding boxes. 93 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
START 2 squares E 2 squares SW 2 squares SW 2 squares South 1 square North 1 square SE 2 squares East 1 square SE 2 squares South 2 squares NE 2 squares NE 2 squares NE 1 square SW W S E Activity 8 Compass Fun! Follow the clues to reach the magic castle. Trace the path you take. N Follow the instructions and you will be amazed by the final answer. Memorize the steps. Try it on your friends and family.Amaze them! Magic (1) Write your age. Multiply it by 3. Add 18. Multiply it by 2. Subtract 36. Divide by 6. Magic (2) Write your favouritenumber. Double that number. Add 43. Subtract 18. Add 11. Divide by 2. Subtract 18. Activity 9 Magic Numbers! Pupils may use any numbers! 94 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Mission 10 Shape Up! The following shape has been given to you. Cut the figure along the lines . Then use all 4 pieces to make each shape below. Then draw the outlines of the pieces as shown in the example below. A B C D E F Example 95 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
A B C D E F G H I J K 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Draw a line from: F1 TO F2 F2 TO B5 B5 TO B8 B8 TO D10 D10 TO D12 D12 TO A12 A12 TO C14 C14 TO D13 D13 TO E13 E13 TO C14 C14 TO E14 E14 TO F12 F12 TO F10 F10 TO D8 D8 TO F8 F8 TO I6 I6 TO K6 K6 TO H2 H2 TO I1 *B13 TO D12 Mission 11 96 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Plot Your Graph! Draw the lines as directed from point to point on the graph to reveal a duck .
2. A farmer bought a goat and a cabbage from the market and had to cross the river to get home. He met a wolf at the river and agreed to ferry the wolf as well but he could only take one item at a time. He could not leave the goat alone with the cabbage because the goat would eat it. He could not leave the goat with the wolf as it would eat the goat. How did the farmer get everything on the other side of the river? Write down the trips that the farmertook to get everything across the river. There are seven trips in all. The first trip has been done for you. Mission 12 Let’s Cross the River! Goat Farmer Wolf Cabbage River Mission 2 (Pg 2) Other Side of River W C G W C G W C G W G C G W C G W C G W C 97 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 30: Revision Answer Key 98 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 1 For Q8: Get pupils to erase stacking model to solve the qn. Exercise 2 Exercise 3 1. mother□ 14 + 20 = 34 (years old) 100 – 14 – 34 = 52 52 ÷ 2 = 26 Ans: 26 2. 1) 4 2) 2 3) 3 4) 2 5) 3 6) 3 7) 3 8) 4 Qn Answers Working 1 (a)See > (b) 12 353 (a) one hundred twenty-five thousand and ninety-nine (b) 11 000 + 1200 + 150 + 3 = 12 353 2 10283 3 see > 3303 , 3033 , 3030 , 3003 4 69 300 70 000 – 700 = 69 300 5 8 47 groups of 50 47 groups of 58 47 groups of 8 6 180 10 units = 200 1 unit = 200 ÷ 10 = 20 (more girls) 9 units = 9 x 20 = 180 7 489 g 108 boxes □ 108 x 10 = 1080 fruit tarts not crushed □ 1080 – 49 = 1031 fruit tarts 8 154 2 units = 360 – 52 = 308 1 unit = 308 ÷ 2 = 154
99 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. 3. Extra □ 33 + 33 + 50 = 116 3 units = 386 – 116 = 270 1 unit = 270 ÷ 3 = 90 (Keith) Ans: 90 4. Ans: 13 cars, 17 motorcycles
Boost! Math Primary 3 Lesson 31:Money Answer Key 1. Value of 2 one-dollar coins = 2 x $1 = $2 Value of fifty-cent coins = $5 - $2 = $3 $3 ÷ 50¢ = 300¢ ÷50¢ = 6 Ans: 6 fifty-cent coins 2. Amount of money she gave to each sister = 8 x 50¢ = 400¢ = $4 Amount of money she gave to her two sisters = $4 + $4 = $8 Amount of money she had left = 7 x 20¢ = 140¢ = $1.40 $8 + $1.40 = $9.40 Ans: $9.40 3. Value of 3 fifty-dollarnotes = 3 x $50 = $150 Value of 5 ten-dollar notes = 5 x $10 = $50 Amount of money she went shoppingwith = $150 + $50 = $200 Amount of money spent = $59 + $28 = $87 Amount of money left = $200 - $87 = $113 Ans: $113 100 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.