Boost! Math Primary 3 Lesson 1: Recap Answer key 2 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 1 Qn Answer Solution 1 99 breads 65 + 34 = 99 2 34 passengers 42 – 8 = 34 3 26 badges 68 – 42 = 26 4 13 biscuits 25 – 12 = 13 5 $49 $33 + $16 = $49 6 9 packets $70 – $43 - $6 = $21 7 $21 8 $17 $52 - $10 - $25 = $17 Exercise 2 Qn Answer Solution 1 248 paper cranes N 130 – 12 = 118 Total 130 + 118 = 248 2 16 L B 20 L – 9 L = 11 L C 11 L + 5 L = 16 L
3 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Qn Answer Solution 3 119 books S 68 – 4 – 64 K 64 – 9 = 55 S + K = 64 + 55 = 119 4 8 stamps C 24 ÷ 3 = 8 5 9 apples 21 – 12 = 9 6 9 marbles The diff 216 – 198 = 18 18 ÷ 2 = 9 Exercise 3 Qn Answer Solution 1 7 bookmarks Total 16 + 12 = 28 Each bag 28 ÷ 4 = 7 2 6 bags Left 20 - 2 = 18 Each bag 18 ÷ 3 = 6 3 $8 4 cookies $3 Groups of 4 16 ÷ 4 = 4 Total 4 x $3 = $12 Change $20 - $12 = $8 4 $24 7 erasers and pencils $6 Groups of 7 28 ÷ 7 = 4 Cost 4 x $6 = $24 5 12 pens 28 notebooks 1 pack 3 pens 7 notebooks 4 packs 4 x 3 = 12 pens 4 x 7 = 28 notebooks 6 21 oranges Groups of 5 35 ÷ 5 = 7 Oranges 7 x 3 = 21
4 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 4 Qn Answer Solution 1 3 ice cream sticks 24 ÷ 8 = 3 2 9 more rulers 32 – 23 = 9 3 6 students 27 – 3 = 24 24 ÷ 4 = 6 4 35 magnets 4 x 8 = 32 32 + 3 = 35 5 22 coins 8 x 3 = 24 24 – 2 = 22 6 15 lollipops 2 x 6 = 12 27 – 12 = 15
Boost! Math Primary 3 Lesson 2: Whole Numbers 1 Answer key 5 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Number and Notation Thousands Hundreds Tens Ones 4 8 9 5 4000 800 90 5 Numbers can be written in different form in numeral 4895 in words Four thousand eight hundred and ninety-five 4895 = 4 thousands 8 hundreds 9 tens 5 ones = 4000 + 800 + 90 + 5 Example: In 4895, Para 1: the digit 4 stands for 4000. Para 2 : the digit 8 is in the hundreds place. Para 3: the value of the digit 9 is 90. Para 4: the digit 5 is in the ones place. the digit 5 stands for 5 the value of the digit 5 is 5. Compare and Order Example 1: Step 1:… Therefore, 895 is greater than 795. Example 2: Step 3: Therefore, 4849 is smaller than 4893. Descending From greatest to smallest Ascending From smallest to greatest Even and Odd Numbers that end with 1,3,5,7,9 are odd numbers. Numbers that end with 2,4,6,8,0 are even numbers.
6 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 1 : 1. 2. 3. 4. Greatest even number: 8754 Smallest odd number 2059 Ans: 7645, 8456, 8645, 8654 Match the correct values. 1749 • • 14 hundreds 2 tens 6 ones 4710 • • 7 thousands 13 tens 7130 • • 17 hundreds 3 tens 19 ones 1426 • • 4 thousands 6 hundreds 11 tens 5. 100 more than 3000 + 40 + 600 is 3740. 3640 + 100 = 3740 6. 1000 less than 4 ones, 30 hundreds and 80 tens is 2084. 3084 – 1000 = 2084 5685 – 75 = 561 tens 5685 - 75 = 5610 Ans: 231 tens, 21 hundreds, 12 hundreds, 1028 ones (Descending order) 7. 8. 231 tens 2310 1028 ones 21 hundreds 12 hundreds 1028 2100 1200 Exercise 2 : 1. 829 2. 9826 Hundreds 800 Ones 6 Thousands 100 + hundreds = 800 + 100 =900 Tens ones – 4 = 6 – 4 = 2 3. 8 + 10 = 70 + 29 = 99 99 – 10 = 89 Digit in the tens place 8 Th H T O 9 8 2 6
7 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 2 4. a) 19th day 2 Day 19 1 ÷ 2 = 1 (half) b) 18th day Day 18 1 ÷ 2 = 1 (one quarter) 2 4 Exercise 3 : 1. Rule: The next number is found by adding the 2 numbers before it. 3 + 7 = 10 7 + 10 = 17 10 + 17 = 27 27 + 44 = 71 2. a) 2989, 2995, 3001, 3007, 3013 b) 39, 36, 32, 27, 21, 14 c) 1, 2, 5, 10, 17, 26 Rule : +6 Rule: -3, -4, -5, -6, -7 Rule:+1, +3, +5, +7, +9 3. 8 20 – 3 – 5 – 4 = 8 (The sum of all the numbers in each circle is 20.) 4. Exercise 4 : 1. 11= 1 + 1 = 2 a) 2 + 5 = 7 b) 1 + 7 = 8 16 = 1 + 6 = 7 55 = 5 + 5 = 1 0= 1 + 0 = 1 c) 1 + 3 + 7 = 11 = 1 + 1 = 2 d) 5 + 8 + 0 + 2 = 15 = 1 + 5 = 6
8 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 4 2. Pattern rule + 6 12th number 11 groups of 6 + 3 (1st number) 11 x 6 = 66 66 + 3 = 69 3. 4. Difference at first 22 – 16 = 6 Difference in each addition 3 – 2 = 1 Number of weeks taken 6 ÷ 1 = 6 5. The difference does not change, as both of them increase by 33 steps. 10 – 3 = 7 Ans: 7 6. 10 – 1 = 9 9 + 3 = 12 12 – 1= 11 11 + 3 = 14 14 - 1 = 13 7 128 ÷ 2 = 64 82 – 64 = 18 64 - 14 = 50 50 ÷ 2 = 25 18 + 25 + 25 + 18 = 86 6. 4 ways 25 + 5 + 20 = 50 25 + 15 + 10 =50 30 + 15 + 5 = 50 35 + 10 + 5 = 50 -1 +3 -1 +3 -1 $128 $82 $14
Boost! Math Primary 3 Lesson 3: Whole Numbers 2 Answer key 9 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 1: Question No. Answer Process 1 121 Logical Reasoning: 1st 2nd 3rd Total 1,3,5 1st + 1 1,3,5 1st +2nd ,7,9 ,7,9 +3rd = 4 1 2 1 4 2 4 Systematic Listing : 259 529 925 295 3 A = 7063 Patterning : B = 7087 +2 +8 7057, 7059, _A_, 7069, 7077, _B_, 7099 +2 +4 +6 +8 +10 +12 4 287 Patterning : + 4 To find the 12th number, we need to add 4 to the previous number 11 times. 11 x 4 = 44 243 + 44 = 287 5 8 Condition : 1 to 9 , >5, - 4 > 3 , even number Result : 6, 8
10 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 2: Green Blue Pink B/C B/C A B C A Question No. Answer Process 1 21 From 1st to 14th13 students in front of Matt. From 1st to 8th 7 students from the back 13 + 7 = 20 20 + 1 = 21 2 Ann = Pink Besty = Green Cindy = Blue Elimination : 3 Green Ball 4 Step 1 : Fill the 5ℓ container and pour into the tub. Step 2 : Fill the 5 ℓ container, pour water from 5 ℓ into the 3 ℓ 5 ℓ container will be left with 2 litres of water. Step 3 : Pour the remaining 2 litres in the 5 ℓ into the tub 5 8 D1 Banana - 2 + 3 D2 - 2 + 3 D3 - 2 + 3 11 D1 D2 D3 11 - 3 = 8 10 - 3 = 7 9 - 3 = 6 8 + 2 = 10 7 + 2 = 9 6 + 2 = 8
11 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 3: Question No. Answer Process 1a 5 Pattern : +4, +4, … 1b 19 Pattern : +3, +2, +3, +2…. 2 D -2 lines each time it moves to the next box. 3 A the number of circles equal to the number of sides of each shape. 4 6 each arrow will pierce through 2 apples 5 15 C1, F1 C2, F1 C3, F1 C1, F2 C2, F2 C3, F2 C1, F3 C2, F3 C3, F3 C1, F4 C2. F4 C3, F4 C1, F5 C2, F5 C3, F5 6 a. 1 3 2 3 2 1 2 1 3 b. 3 2 2 1 1 3 2 1 4 3 4 3 2 1 1 3 2 3 2 1 4 c. 1 4 3 2
12 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 4: Question No. Answer Process 1a 3 princesses From Condition Number of Prince Number of Princesses Check Princess Twice as many Princes as Princesses 1 x 2 = 2 1 (+1 looking) X Prince Same number of both 2 (-1 looking) 2 Princess Twice as many Princes as Princesses 2 x 2 = 4 2 (+1 looking) √ Prince Same number of both 3 (-1 looking) 3 Question No. Answer Process 1b 5 princes and princesses From Condition Number of Prince Number of Princesses Check Thrice as Prince many Princesses 1 (+1 looking) 1 x 3 = 3 as Princes √ Princess Same number of both 2 2 (-1 looking)
Boost! Math Primary 3 Lesson 4: Addition Answer key 13 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Question Answer Process Addition Sum of More than Total Give Altogether Buy Plus Increase Add In all Step 1 Add the ones 10 ones = 1 tens 0 ones Step 2 Add the tens Step 3 Add the hundreds 13 hundreds = 1 thousands 3 hundreds 6390 Exercise 1 1 8040 40 + 8000 = 8040 2 5400 4000 + 1400 = 5400 3 3180 180 + 3000 = 3180 4 478 2459 – 1981 = 478 5 1117 1635 – 518 = 1117 6 5081 3492 + 941 = 4433 4433 + 648 = 5081 7 9688 Greatest 7,6,4,2,0 7642 Smallest 0,2,4,6,7 2046 7642 + 2046 = 9688
14 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. 8 7 6 8 4 a) 0 b) Ones 7 Tens 8 Hundreds 4 Thousands 7 4525 – 1219 = 3306 6 4 12 7 + 1 2 5 7 14 – 7 = 7 5 + 3 = 8 6 – 2 = 4 6 + 1 = 7 Exercise 2: 1 2223 1276 + 947 = 2223 2 $67 $(7 + 13 + 35 + 12) = $67 3 558 345 + 213 = 558 4 93 kg 27 + 27 + 39 = 93 5 322 127 + 195 = 322 6 9650 June 4576 + 498 = 5074 Total 4576 + 5074 = 9650 7 156 78 + 78 = 156 8 310 155 + 155 = 310 9 2590 485 + 1620 + 485 = 2590
15 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 3: 1 7 Pattern : Col 1 + Col 4 = Col 2,3 7 + 6 = 13 9 + 8 = 17 12 – 5 = 7 2 25 Pattern : Add 6 7 + 6 = 13 13 + 6 = 19 19 + 6 = 25 3 3.19 Pattern : Add 24 min 4 10 4 persons between 1 to 6 on each side. 8 + 2 = 10 5 1959 Number if intervals From the 1st to the 28th 28 – 1 = 27 Add 1 gap for 1963 Total of 28 gaps. Held every 2 years 28 x 2 yrs = 56 yrs 2015 – 56 = 1959 6 12 AEC, AEB, AFB, ADB, ADC, AED, AEF EBC, EBD, EFD FBD BDC
Boost! Math Primary 3 Lesson 5: Subtraction within 10 000 Answer key 16 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Question Answer Process Addition Difference Take away Left Used Less than Give Minus Remove Subtract Reduce Decrease fewer than Step 1 Subtract the ones Step 2 subtract the tens Regroup Rename from the 4 hundreds 4 hundreds 2 tens = 3 hundreds 12 tens Step 3 Subtract the hundreds 2163 Exercise 1 1 3800 4000 – 200 = 3800 2 9860 10 000 – 140 = 9860 3 3813 4000 – 187 = 3813 4 322 379 – 57 = 322 5 2896 2940 – 44 = 2896 6 807 893 – 86 = 807 7 1099 1492 + 341 = 1833 1833 – 734 = 1099 8 5585 Greatest 8,6,5,3,0 8650 Smallest 0,3,5,6,8 3065 8650 – 3065 = 5585 9 a) 3 a 3 7 3 9 - 1 2 1 6 2 5 2 3 2523 + 1216 =3739
17 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. b) 6, 1, 6 b 6 67 12 11 - 1 2 5 7 5 4 6 4 7 + 4 = 11 11 – 5 = 6 5 + 1 = 6 Exercise 2: 1 745 1508 – 763 = 745 2 798 9198 – 8400 = 798 3 755 3528 – 1739 – 1034 = 755 4 11 kg 64 – 53 = 11 5 1396 2385 – 989 = 1396 6 $912 2500 + 500 = 3000 3000 – 256 – 1832 = 912 7 69 105 – 27 – 9 = 69 8 54 ? 145 – 13 – 24 = 108 108 ÷ 2 = 54 9 18 If we compare 1 fruit to 1 fruit, there should still be 24 fruits. 30 – 24 = 6 The extra 6 fruits came from the fact that 1 orange became 2 apples. Thus there are 6 oranges in the beginning. Apples 24 – 6 = 18
18 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Exercise 3: 1 B = 5 A = 4 Check : 500 – 455 = 45 545 – 500 - 45 Logic : Step 1: Look at the ones in both cases 0 cannot minus 5, borrow from the tens, became 10 - 5 = 5 10 – 5 = b – 0 , thus b = 5 Step 2: Look at the tens Following step 1, the zero is case 1 is now 9. 9 – b = a – 0 Sub in b : 9 – 5 = a – 0 4 = a 2 3 Pattern : 7 – 2 – 4 = 1 9 – 1 – 2 = 6 5 – 2 – 0 = 3 8 – 2 – 3 = 3 3 3 or 45 Pattern : The difference between the 2 numbers in a triangle is equal to the number corresponding to the alphabet in the opposite triangle. Thus 4 – 3 = A = 1 Using the hint, U = 21 (21th alphabet) 24 - = 21 24 – 21 = 3 OR - 24 = 21 = 24 + 21 = 45 4 327 1st day49 2nd day 49 – 23 = 26 3rd day 49 x 2 = 98 / 49 + 49 = 98 4th day 56 + 98 = 154 Total 49 + 26 + 98 + 154 = 327 5 Step 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Find the common multiples of 1, 2 and 3. Match it against the foot each person will land with.
Boost! Math Primary 3 Lesson 8: Numbers to 10 000 Answer Key 1. 36320 + 39500 = 75820 Ans : $75820 2. geese = 389 + 128 = 517 geese + cows = 389 + 517 = 906 Ans: 906 3. a) female = 2200 – 486 = 1714 b) total = 2200 + 1714 = 3914 Ans a): 1714 Ans b): 3914 4. 2 units = 2200 – 1200 = 1000 1 unit = 1000 ÷ 2 =500 Ans: 500 5. Now a) Mother= 8 x 4 = 32 20 years’ time b) Mother = 32 + 20 = 52 Ans a): 32 Ans b): 52 Remind pupils to draw a margin to show their workings. Remind pupils to add the unit of measurement ($). ? (1) Geese Cows 389 128 ? (2) Find the number of geese first. 2200 Male Female ? (a) 486 ? (b) Malaysia Indonesia ? 1200 2200 Find 2 units first. + 75820 Working 36320 39500 6. 2 years’ time Jacky = 7 + 2 = 9 Sister = 9 x 4 = 36 Now Sister = 36 – 2 = 34 Ans: 34 19 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7. Now James + Father= 67 – 5 – 5 = 55 Father = 55 – 16 = 39 Ans: 39 8. Tuesday = 562 – 105 = 457 1670 – 562 = 1108 1108 – 457 = 651 Ans: 651 9. 1500 + 128 = 1628 1628 + 250 = 1878 Ans: 1878 10. a) females = 2660 + 3156 = 5816 b) children 9850 – 2660 = 7190 7190 – 5816 = 1374 OR 9850 – 3156 – 2660 – 2660 = 1374 Ans: (a) 5816 562 Monday Tuesday ? 105 562 457 1670 Mon Tue Wed ? ? - 250 – 128 = 1500 Use WorkingBackwards females males children 2660 3156 9850 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. 20
Boost! Math Primary 3 Lesson 9: Numbers to 10 000 Answer Key 1. Ans: 240 2. 1st day = 7 2nd day = 7 + 7 = 14 (or 7 x 2 = 14) 3rd day = 14 + 14 = 28 (or 14 x 2=28) 4th day = 28 + 28 = 56 (or 28 x 2 =56) 5th day = 56 + 56 = 112 (or 56 x 2 =112) 6th day = 112 + 112 = 224 (or 112 x 2 =224) 7th day = 224 + 224 = 448 (or 244 x 2 =448) Ans: 448 3. Extra = 110 + 110 + 59 = 279 3 units = 582 – 279 = 303 1 unit (2nd number)= 303 ÷ 3 = 101 Ans: 101 4. 987 + 1025 = 2012 Ans: 2012 Pupils have not learnt long division. Teach them to divide mentally. Jazz Linda ? 2 units = 600 – 120 = 480 1 unit = 480 ÷ 2 =240 120 600 480 400 ÷ 2 =200 80 ÷ 2 = 40 400 80 240 3rd 1st 2nd 582 110 59 110 59 110 ? 1st 2nd 3rd 1025 582 987 ? 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. 21
5. Th H T O 9 9 8 1 Step 1: Digit in hundreds place is the largestdigit = 9 Step 2: Digit in tens place 1 less than digit in hundredsplace = 8 Step 3: Digit in thousandsplace = digit in tens place + digit in ones place = 8 + 1 = 9 (largest possible 4-digit odd no.) Ans: 9981 6. Smallest 4-D odd number= 1001 Largest3-D even number = 998 Diff = 1001 – 998 = 3 Ans: 3 7. When there are 5 lamp posts, there will be 4 intervals. The stretchof road will be 24 m long. (6m x 4 = 24m) When there are 8 lamp posts, there will be 7 intervals. The stretchof road will be 42 m long. (6m x 7 = 42m) 9. 100 lamp posts = 99 intervals road = 99 x 3 m = 297m Ans: 297m 10. After giving 80 sardine puffs, she had 10 fewer sardine puffs than curry puffs = 100 – 10 = 90 sardine puffs Total sardine puffs= 90 + 80 = 170 Total puffs= 170 (sardine) + 100 (curry)= 270 Ans: 270 8. 10 trees = 9 intervals 9 x 50m = 450 m Ans: 450 m Remind pupils to write the unit of measurement. 22 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. Remind pupils to write the unit of measurement.
11. Ming Li (count on by hundreds from 2000) Wei Shan (counted backwards by thousands) Ans: 6400 2000 2100 2200 2300 2400 1st count 2nd count 3rd count 4th count 1. After 4 counts, Ming Li and Wei Shan reached the same number. 2. For Wei Shan, we work backwards from2400. +1000 +1000 +1000 +1000 6400 5400 4400 3400 2400 23 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 10: Multiplication and Division [1] Answer Key 1. 92 - 32 = 60 60 ÷ 3 = 20 Ans: $20 2. 126 x 2 = 252 252 – 73 = 179 Ans: 179 3. No of $3 → 18 ÷ 3 = 6 No of mangoes → 6 x 4 = 24 Ans: 24 4. 5 blouses → 18 x 5 = 90 3 skirts→ 25 x 3 = 75 total → 90 + 75 = 165 Ans: $165 5. Mon to Fri → 8 x 5 = 40 1 week → 40 + 6 = 46 4 weeks → 46 x 4 = 184 Ans: 184 hours 6. Total no pack → 95 – 11 = 84 No of boxes → 84 ÷ 7 = 12 Ans: 12 7. Save from 1 bottle → 12.50 – 9.90 = 2.60 Saved from 3 bottles → 2.60 x 3 = 7.80 Ans: $7.80 8. 6 bracelets → 6 x 38 = 228 2 hairclips → 2 x 4 = 8 Total → 228 + 8 + 23 = 259 Ans: 259 9. 10 masks → 6 5 masks → 6 ÷ 2 = 3 15 masks → 3 x 3 = $9 2 bottles → $8 6 bottles → 8 x 3 = 24 Total → 9 + 24 = 33 Ans: $33 10. 10 children → 10 + 2 free = 12 tickets For the 12 tickets, she pays → 10 x 6 = 60 For 24 tickets → 60 + 60 = $120 Ans: $120 11. a) $1 = 5 20-cent coins So for $1, John can buy → 5 rulers For $5→ 5 x 5 = 25 rulers (b) $1 = 2 50-cent coins So for $1, Peter can buy → 2 erasers For $5→ 2 x 5 = 10 erasers 12. No of fruit tarts for $48 → 48 ÷ 4 = 12 Every 4 fruit tarts → 1 free For 12 fruit tarts → 12 ÷ 4 = 3 free Total fruit tarts → 12 + 3 = 15 Ans: 15 24 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 11: Multiplication and Division (2) Answer Key 1. a) Tues=8 x 12 = 96 b) Both= 12 + 96 = 108 Ans: (a) 96 (b) 108 2. a) Bakery A = 216 x 3 = 648 b) A + B = 216 + 648 = 864 Ans: (a) 648 (b) 864 3. a) Fiction = 7 x 425 = 2975 b) Total = 2975 + 425 = 3400 Ans: (a) 2975 (b) 3400 4. Total = 320 x 7 = 2240 Ans: 2240ml 5. a) Chiku = 29 x 8 = 232 b) More (6 units) = 29 x 6 = 174 Ans: (a) 232 (b) 174 6. Hall B = 316 - 32 = 284 Hall C = 248 x 2 = 568 Total = 316 + 284 + 568 = 1168 Ans: 1168 (b) ? A B 216 (a) ? 29 (a) ? Guava Chiku (b) ? 320 ? A B (b)? Mon Tue 12 (a) ? (b) ? Non - Fiction Fiction (a) ? 425 ? A B C 32 316 25 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7. 9 units = 126 1 unit = 126 ÷ 9 = 14 (Benny) More = 6u – 2u = 4u 4 units = 4 x 14 = 56 Ans: (a)14 (b) 56 8. a) Peter (1 min) = 45 + 12 = 57 b) Total (1 min) = 45 + 57 = 102 Total (9min) = 102 x 9 = 918 Ans: 918 9. Tues = 26 x 3 = 78 Wed= 78 – 18 = 60 Total = 26 + 78 + 60 = 164 Ans: 164 10. Kumar to Mingfa = 2735 x 2 = 5470 Total (1 way) = 2735 + 5470 = 8205 Total (2 ways) = 8205 x 2 = 16 410 Ans: 16 410m 11. Last year = 89 x 2 = 178 This year = 178 + 109 = 287 Altogether= 89 + 178 + 287 = 554 Ans: (a) 178 (b) 287 (c) 554 12. a) Jia Li = 72 ÷ 3 =24 Kala = 72 ÷ 2 =36 All= 72 + 24 + 36 = 132 b) More (1 min)= 36 – 24 = 12 More (10 min) = 12 x 10 = 120 OR Using Models a) 6 units = 72 1 unit = 72 ÷ 6 = 12 11 units = 12 x 11= 132 b) more in 10 min = 10 x 12 = 120 Ans: (a) 132 words (b) 120 words Peter Jane (a)? 45 12 Mon Tue Wed 18 ? 26 Jafal Kumar 2735 m 2735 m x 2 Ming Fa J to K K to MP Aisha Jiali 72 Kala More ? (a) (1 min) Andy Benny Caden (b)? (a)? 126 ? (c) 2 yrs ago 89 This Yr 109 ? (b) LastYr ? (a) 26 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 12: Multiplication and Division [3] Answer Key 1. 2 units = 50 1 unit = 50 ÷ 2 =25 (Jonah) 3 units = 3 x 25 = 75 Ans: $75 2. 353 + 7 = 360 360 ÷ 9 =40 Ans: 40 3. 8 lamp posts → 7 intervals No. of trees → 7 x 7 = 49 Ans: 49 4. Total apricots → 7 x 42 = 294 AfterKept, left → 294 – 21 = 273 No. of bags → 273 ÷ 3 = 91 Ans: 91 5. 2 units = 143 – 11 = 132 1 unit = 132 ÷ 2 =66 Mimi → 66 + 11 = 7 Ans: 77cm Teach pupils → 36 ÷ 9 = 4, then add the 0 Remind pupils to write the unit of measurement → cm J D ? 50 9 9 360 muffins ? boxes Use this question to teach multiplication of a 2-digit number by a 1 -digit number. 25 3 75 x Use this question to teach Long division as some pupils have not learnt yet. 3 91 273 - 27 - 3 3 0 Peter Mimi 143 11 ? 2 66 - 132 12 12 - 12 0 7rt 7rt 7rt 7rt 7rt 7rt 7rt road 27 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
6. 9 units = 783 1 unit = 783 ÷ 9 = 87 (Andy) 6 units = 6 x 87 = 522 Ans: 522 7. 15 – 11 = 4 4 lollipops → 320 1 lollipop → 320 ÷ 4 = 80 15 lollipops → 80 x 15 = 1200 cents = $12.00 Ans: $12 8. 5 units = 345 1 unit = 345 ÷ 5 =69 (Isa) 4 units = 4 x 69 = 276 Ans: 276 9. 9 units = 162 1 unit = 162 ÷ 9 =18 (Yuli) 2 units = 2 x 18 = 36 (More) 5 units = 5 x 18 = 90 Ans a): 36 b): 90 10. 2 units = 238 – 36 -36 = 166 1 unit = 166 ÷ 2 = 83 Mickey at first → 83 + 36 + 36 = 155 Ans: $155 Cut the bars into equal partsfirst Cut the bars into equalpartsfirst Remind pupils to write the unit of measurement → $ 783 ? 15 lollipops Colin Benson Andy 11 lollipops 3.20 80 x 15, teachpupils to break it into 80 x 10 = 800 and 80x 5 =400 800+ 400 = 1200 5 69 345 - 30 45 - 45 0 69 4 276 x 18 9 - 162 9 72 - 72 0 Yuli 162 Siti ? (b) Zara ? (a) 9 83 - 166 16 - 6 6 0 87 9 783 - 72 - 63 63 0 87 6 522 x Mickey Joe 36 238 36 ? Isa Mikki 345 28 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
11. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 4, 8, 12, 16, 20, 24, 28, 32, 36 The answer is the second common multiple→ 24 Ans: 24 12. 48 ÷ 6 = 8 (teams) 8 – 3 = 5 (teams) 5 x 6 = 30 (pupils) Ans a): 8 b): 30 Find the highest common multiple of 3 and 4 which is less than30. Since Miss Tan had enough money to buy 30 sweets, → the first common multiple 12 is too small. → the third common multiple 36 is too big. 29 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 13: Review1 Answer Key 1. 1089 + 437 = 1526 Ans: 1526 2. Girls → 6475 – 2491 = 3984 More girls → 3984 – 2491 = 1493 Ans: 1493 3. More Motorcycles → 258- 37 – 37 = 184 Ans: 184 4. (Draw After Model: the total of A and B is the same) total books → 116 + 79 = 195 shelf B (in the end) → 195 ÷ 3 = 65 transferred → 79 – 65 = 14 Ans: 14 5. 3 chickens → 3 x 2 = 6 legs 1 goat → 4 legs Total legs in 1 group → 6 + 4 = 10 No. of groups → 220 ÷ 10 = 22 No. of chickens → 22 x 3 = 66 Ans: 66 6. 2 units = 342 – 54 = 288 1 unit = 288 ÷ 2 = 144 Buttons → 144 + 54 = 198 Ans: 198 7. Half → 248 ÷ 2 = 124 The rest → 246 – 124 = 124 Sean → 124 ÷ 4 = 31 Ans: 31 Green Red Blue 1089 437 ? 2491 Boys Girls 6475 ? B A 37 37 37 238 B A 79 116 Goats Chickens Beads Buttons 342 54 ? 30 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
8. 6 units = 156 1 unit = 156 ÷ 6 = 26 Pants → 26 x 3 = 78 Ans: $78 9. 1 group (1 boy + 1 girl) → 4 + 3 = 7 (buns) No. of groups → 98 ÷ 7 = 14 Ans: 14 10. Small bags No. of sweets → 7 x 12 = 84 Big bags No. of sweets → 9 x 26 = 234 Total → 84 + 234 = 318 Ans: 318 11. Tues→ 973 – 218 = 755 Mon + Tues → 973 + 755 = 1728 Wed→ 1728 (same as Mon + Tues) 3 days → 1728 + 1728 = 3456 Ans: 3456 12. ( ? + 13) ÷ 6 = quotient Quotient– 7 = Result Result x 20 = 100 Working backwards 100 ÷ 20 = 5 5 + 7 = 12 12 x 6 = 72 72 – 13 = 59 Ans: 59 13. Ans: 14 Translate questioninto number equations shirts pants 156 ? 4 4 3 3 Boys Girls Tues Mon ? 218 973 31 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 14: Models (Before and After) Answer Key 1. 2. 3. 4. 1 unit 1 unit M. Siti M. Yong 5 20 1 unit 1 unit = 20 – 5 = 15 Mdm Yong had 15 cupcakes. Notes: 1. Draw the after model first.Draw 2 units for Mdm Siti and 1 unit for Mdm Yong. 2. Then add in the small box which represents 5 cupcakes for Mdm Siti. 1 unit 1 unit 2 units goldfish angelfish 11 11 1 unit 11 1. Draw 2 boxes for goldfish and 1 box for angelfish . 2. Cut every box into 1 unit + 11. 2 units cars motorcycles 1 unit = 11 + 11 = 22 goldfish → 3 x 22 = 66 angelfish → 22 + 11 = 33 total → 66 + 33 = 99 Daniel had 99 fishes. 1 unit 45 1. Draw 2 boxes for cars and 1 box for Motorcycles. 2. Since motorcycles remain unchanged, cut the box for motorcycles into 2 parts representing 2 units (after). 3. Proceed to cut every box into 2 parts. 3 units = 45 1 unit = 45 ÷ 3 = 15 6 units = 6 x 15 = 90 (total) There were 72 vehicles in the carpark at first. chairs tables 1 unit 1 unit 88 200 4 units = 88 + 200 = 288 1 unit = 288 ÷ 4 = 72 6 units = 5 x 72 = 360 (total) There were 360 chairs in the exhibition hall. 32 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
5. 6. 7. 8. croissants baguettes 2 units 40 1 unit 1. Draw 2 boxes for croissants and 1 box for baguettes. 2. Since croissants remain unchanged, cut the box for baguettes into 2 parts with 1 box representing the 40 baguettes being sold. 3. Take note that after removing the box for the 40 baguettes, croissants will be 4 times the baguettes.So cut the box for croissants into 4 parts and the remaining box for baguettes will be 1 part. 1 unit = 40 (croissants)4 units = 4 x 40 = 160 There were 160 croissants in the café. Eng Chinese 3 units 1 unit 656 8 units = 656 1 unit = 656 ÷ 8 = 82 (Eng at first) 9 units = 9 x 82 = 738 Jenny has 738 English storybooksat first. 1 unit 4 units Geraldine Josephine 16 1 unit 16 1 unit 16 1 unit 1 unit 16 1. Draw 3 boxes for Geraldine and 1 box for Josephine. 2. Cut every box into 1 unit + 16. 1 unit 2 units = 16 + 16 + 16 = 48 1 unit = 48 ÷ 2 =24 Geraldine → 5 x 24 = 120 Geraldine had 120 stickers. 5 units C. Suffi C. Luna 1 unit 36 2 units = 36 1 unit = 36 ÷ 2 =18 (C. Suffi at first) 5 units = 5 x 18 = 90 Cikgu Suffi had 90 pupils at first. 33 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
9. 10. 11. 7 units = 154 1 unit = 154 ÷ 7 = 22 No of necklaces → 22 + 154 = 176 176 necklaces were put up for sale. 12. 4 units Samuel Leonard 1 unit 36 45 3 units = 36 + 15 = 90 1 unit = 90 ÷ 3 =30 (C. Suffi at first) 5 units = 5 x 18 = 90 Samuel had 90 magic cards at first. 1 unit 3 units 3-bedroom 2-bedroom 24 1 unit 24 1 unit 24 1 unit 1 unit 24 1. Draw 3 boxes for 3-bedroom and 1 box for 2-bedroom. 2. Cut every box into 1 unit + 24. 1 unit 1 unit = 24 + 24 + 24 = 72 3-bedroom → 4 x 72 = 288 There were 288 3-bedroomapartments. 1. Draw 2 boxes for necklacesand 1 for bracelets. 2. Cut every box into 4 units. 1. Since grey remains the same, cut the box for grey into 2 units. 1 unit 2 units 1 unit = 64 – 44 = 20 P i n k → 20 + 64 =84 Sue had 84 pink-coloured post-it notes at first. 64 Pink Grey 1 unit 44 1 unit 1 unit 154 necklaces bracelets 1 unit 34 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 15: Models (Comparison & Stacking) Answer Key 1. 2 units = 240 1 unit = 240 ÷ 2 = 120 1 armchair = 120 ÷ 5 = 24 1 wooden shelf = 120 ÷ 3 = 40 1 armchair+ 1 wooden shelf = 24 + 40 = 64 Ans: 64 kg 2. Extra = 3 x 23 = 69 5 units = 144 – 69 = 75 1 unit = 75 ÷ 5 = 15 1 Bluetooth speaker = 15 + 23 = 38 2Bluetooth speakers= 2 x 38 = 76 Ans: $76 3. Extra = 3 x 14 = 42 5 units = 232 – 42 = 190 1 unit = 190 ÷ 5 = 38 1 lipstick = 38 + 14 = 52 Ans: $52 4. Extra = 4 x 8.50 = 34 6 units = 112 – 34 = 78 1 unit = 78 ÷ 6 = 13 (1 chicken chop) 1 fish & chip = 13 + 8.50 = $21.50 1 chicken chop + 1 fish & chip = 21.50 + 13 = 34.50 Ans: $34.50 5. 5 units = 90 + 5 = 95 1 unit = 95 ÷ 5 = 19 2 units = 2 x 19 = 38 More = 38 + 5 = 43 Ans: 43 6. 10 units = 90 1 unit = 90 ÷ 10 = 9 1 big box = 2 x 9 = 18 2 big boxes = 2 x 18 = 36 Ans: 36 240 144 23 23 23 Bs Bs Bs Wm Wm 232 14 14 14 L L L Sb Sb 112 8.50 FC FC FC FC FC CC CC 5 90 + 5 G K S 5 ? 90 AC AC AC AC AC WS WS WS BF BF RV RV RV RV Note: Use makingwhole by additionmethod to solve the sum. It is easier to 5 to Mdm Sannu so that the 5 boxes become the same compared to subtracting5 from the other 4 boxes to make the boxes the same. 35 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7. 11 units = 44 1 unit = 44 ÷ 11 = 4 Lucy = 3 x 4 = 12 Ans: 12 8. Hope Society= 3 groups of children Care Association= twice the number of groupsof children = 2 x 3 groups = 6 groups Extra = 6 x 10 = 60 9 units = 204 – 60 = 144 1 unit = 144 ÷ 9 = 16 (no. childrenin 1 group from Hope Society) Hope (3 groups)= 3 x 16 = 48 Care (1 group)= 16 + 10 = 26 Care (6 groups)= 6 x 26 = 156 Ans: a) 48 b) 156 9. 10 units = 520 1 unit = 520 ÷ 10 = 52 More (3 units) = 3 x 52 = 156 Ans: 156 10. Extra = 3 x 782 = 2346 7 units = 11362 – 2346 = 9016 1 unit = 9016 ÷ 7 = 1288 (1 handbag) 1 gown = 1288 + 782 = 2070 1 gown + 1 handbag= 1288 + 2070 = 3358 Ans: $3358 11. 4 units = 345 + 35 = 380 1 unit = 380 ÷ 4 = 95 Difference= 95 + 35 = 130 Ans: 130 cm 12. 36 units = 144 1 unit = 144 ÷ 36 = 4 (36 + 36 + 36 + 36 = 144) 4 boxes of macaroonsand 2 almond croissants = 23 units + 2 units = 26 units Total = 26 x 4 = 104 Ans: $104 204 10 10 10 10 10 10 H H H C C C C C C K A N 520 (?) 11362 782 G G G Hb Hb Hb Hb 345 1st 2nd 3rd 35 ( ? ) M M M M 144 12 almond croissants Z C L 44 ? Note: Use makingwhole by additionmethod to solve the sum.Similarto how we solved question5. 36 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 16: Models (Internal Transfer) Answer Key 1. 1 unit = 5 + 20 + 5 = 30 3 units = 3 x 30 = 90 Ans: 90 2. 2 units = 23 + 84 + 23 = 130 (altogether) 4 units = 2 x 130 = 260 Ans: 260 3. 3 units = 67 + 130 + 67 = 264 1 unit = 264 ÷ 3 =88 (altogether)4 units = 4 x 88 = 352 Ans: 352 4. 3 units = 210 1 unit = 210 ÷ 3 = 70 Darika → 70 ÷ 2 = 35 Ans: 35 5. 5 units = 610 1 unit = 610 ÷ 5 = 122 (more) 3 units = 3 x 122 = 366 No. staff from North to South → 366 ÷ 2 = 183 Ans: 183 6. 6 units = 1260 1 unit = 1260 ÷ 6 = 210 (A more than B by) 4 units = 4 x 210 = 840 A poured into B → 840 ÷ 2 = 420 Ans: 420ml 7. (a) extra → 2 x 68 = 136 2 units = 236 – 136 = 100 1 unit = 100 ÷ 2 =50 (b) physically at first → 50 + 68 + 68 = 186 Ans: (a) 50 (b) 186 5 5 5 A B A B 20 Start with after model→ twice in A than B Then add infofrom before transfer 23 23 23 84 Lucky Fortune 67 67 67 130 Learners Star D A 210 610 North Zone South Zone A B 1260 68 68 68 Physical Online ? (a) ? (b) 236 37 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
8. 9. (a) extra → 2 x 60 = 120 2 units = 582 – 120 = 462 (Robert at first) 1 unit = 462 ÷ 2 = 231 (b) Darren at first → 231 + 60 + 60 = 351 Ans: (a) 231 (b) 351 10. (a) 1 unit = 109 (morning) 3 units = 3 x 109 = 327 (b) morning + afternoon = 327 + 109 = 436 Or → 4 x 109 = 436 Ans: (a) 327 (b) 436 11. (a) 3 units = 2 x 318 = 636 1 unit = 636 ÷ 3 = 212 (savings accountat first) 4 units = 4 x 212 = 848 (b) two accounts → 848 + 212 = 1060 Or → 5 x 212 = 1060 Ans: (a) $848 (b) $1060 12. (a) 1 unit = 15 + 15 = 30 (Huskies)2 units = 2 x 30 = 60 (b) (Dogs Total) 3 units = 3 x 30 = 90 Ans: (a) 60 (b) 90 22 22 (a) extra → 2 x 22 = 44 2 units = 104 – 44 = 60 ? (b) 1 unit = 60 ÷ 2 = 30 Soon (Mdm Tang at first) 104 Tang 22 (b) Mdm soon at first → 30 + 22 + 22 = 74 Ans: (a) 30 (b) 74 ? (a) 60 60 60 D R ? (a) ? (b) 582 morning afternoon 109 109 Savings Current ? (a) 318 318 H GR ? (a) 15 15 ? (b) 38 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 17: Heuristics Review 1 Answer Key 1. 2 units = 78 1 unit = 78 ÷ 2 = 39 Ans: 39 2. 3 units = 63 + 15 = 78 1 unit = 78 ÷ 3 = 26 (Rachel at first) 4 units = 4 x 26 = 104 Ans: 104 3. 3 units = 96 1 unit = 96 ÷ 3 = 32 (pineapple tarts) 10 units = 10 x 32 = 320 Ans: 320 4. 11 units = 132 1 unit = 132 ÷ 11 = 12 (GreenTea at first) 12 units = 12 x 12 = 144 Ans: 144 5. 216 ÷ 2 =108 1 ribbon = 108 ÷ 4 = 27 1 rope = 108 ÷ 3 = 36 1 ribbon + 1 rope = 27 + 36 = 63 Ans: 63cm 6. Extra = 3 x 18 = 54 5 units = 199 – 54 = 145 1 unit = 145 ÷ 5 = 29 1 dictionary= 29 + 18 = 47 2 dictionaries= 2 x 47 = 94 (or 47 + 47 = 94) Ans: $94 Care Future (?) 78 Rachel June 63 15 (?) gave friends Pine Choco Green Peach 132 96 (?) Ri Ri Ri Ri Ro Ro Ro 216 199 18 D D D SB SB 1. Draw AfterModel first pineapple (5 boxes) & chocolate (1 box) 2. Then cut the 5 boxes for pineapple into half and add boxes to chocolate to show pineapple was twice as many as chocolate at first. 3. Finally, cut every box into 2 parts. (?) 39 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
7. 5 units = 342 + 48 = 390 1 unit = 390 ÷ 5 = 78 Mrs J = 3 x 78 = 234 Mrs G = 78 – 48 = 30 more = 234 – 30 = 204 Ans: 204 8. 7 units = 392 1 unit = 392 ÷ 7 = 56 (more) 2 units = 2 x 56 = 112 Ans: 112 9. 10 units = 170 1 unit = 170 ÷ 10 = 17 (give) 3 units = 3 x 17 = 51 Ans: 51 10. 1 unit = 57 + 57 = 114 (Suzy at first) 2 units = 2 x 114 = 228 Ans: $228 11. (a) 3 units = 120 1 unit = 120 ÷ 3 = 40 (Enzo at first) 8 units = 8 x 40 = 320 (b) (altogether) 10 units = 10 x 40 = 400 Ans: a) 320 b) 400 12. 3 units = 28 + 76 + 28 = 132 1 unit = 132 ÷ 3 = 44 (total students) 5 units = 5 x 44 = 220 Ans: 220 48 Mrs G Mrs J Mrs T 342 + 48 48 Use the addition to make whole method to solve the problem. 392 S C A (?) Jacob Max 170 Suzy Rose 342 57 Kenneth 120 Enzo Baking Cooking 76 3 units (?) 28 28 28 40 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 18: Four Operations[1] Answer Key 1. Males → 3375 – 1493 = 1882 fewer females→ 1882 – 1493 = 389 Ans: 389 2. Nadul → 145 + 20 = 165 Jun Xiang → 165 + 15 = 180 3 boys → 145 + 165 + 180 = 490 Ans: 490 cm 3. Curry puffs for 5 coffee shops → 5 x 37 = 185 left → 280 – 185 – 60 = 35 Ans: 35 4. Total sausages→ 89 + 129 = 218 sausages for guests → 218 – 2 = 216 no. people → 216 ÷ 4 = 54 Ans: 54 5. 1 day sold → 273 ÷ 3 = 91 a week = 7 days 7 days sold → 7 x 91 = 637 Ans: 637 6. Pattern rule : Participants = No of tables x 2 + 2 (at the end) No. Participants → 8(table) x 2 + 2 = 16 + 2 = 18 Some pupils need to draw the squares and circles to visualise the pattern rule. Ans: 18 7(a) 7(b) Stella → 5 x 49 = 245 Ling Qi → 352 – 49 – 245 = 58 or Jeevika + Stella → 49 + 245 = 294 Ling Qi → 352 – 294 = 58 Ans: 58 8. No. of bicycles No. of wheels No. of tricycles No. of wheels Total(wheels) Check 8 8 x 2 = 16 7 7 x 3 = 21 16 + 21 =37 X 7 7 x 2 = 14 8 8 x 3 = 24 14 + 24 =38 X 9 9 x 2 = 18 6 6 x 3 = 18 18 + 18 =36 √ OR Using Supposition Suppose/If all are bicycles → 15 x 2 = 30 wheels Differencebetween actual and total → 36 – 30 = 6 Differencebetween the no. of wheels of 1 bicycle and 1 tricycle→ 3 – 2 = 1 Total number of bicycles → 6 ÷ 1 = 6 Total number of tricycles → 15 – 6 = 9 Ans: (a) 6 (b) 9 9. extra → 2 x 2.50 = 5 3 units = 29 – 5 = 24 1 unit = 24 ÷ 3 = 8 1 duck → 8 + 2.50 = 10.50 duck duck chicken 2.50 2.50 29 Ans : $10.50 41 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
42 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed. 4 12 28 10. No. of 20Ȼ Amount No. of 50ȼ Amount Total Amount Check (3 times) (880) 3 3 x 20 = 60 1 1 x 50 = 50 60 + 50 = 110 X 7 x 3 = 21 21 x 20 = 420 7 7 x 50 = 350 420 + 350 = 770 X 8 x 3 = 24 24 x 20 = 480 8 8 x 50 = 400 480 + 400 = 880 Ans: 24 11. Work backwards to get the total at first. ? Total in the end 22 x 2 = 44 Total at first 44 + 4 = 48 Aiman 4 units (at first) = 48 44+4 1 unit = 48 ÷ 4 = 12 Syed (Aiman at first) 3 units = 3 x 12 = 36 Ans: 36 12. 2 units = 12 + 28 = 40 1 unit 1 unit = 40 ÷ 2 = 20 JH 1 boy at first 20 + 12 = 32 2 boys at first 32 x 2 = 64 A 3 units Ans: 64 13. pink 360 ÷ 5 = 72 strips blue 360 ÷ 6 = 60 strips more 72 – 60 = 12 strips Ans: 12 14. Total macarons 123 + 234 = 357 1 tin 357 ÷ 3 = 119 Taken from A 123 – 119 = 4 Taken from B 234 – 119 = 115 A + B 4 + 115 = 119 Ans: 119 15. 140 ÷ 5 = 28 (number must be less than 28) 100 ÷ 4 = 25 (number must be more than 25) The only 2-digit odd number between 25 and 28 is 27. Sum of digits 2 + 7 = 9 (check ) Ans: 27 OR 2-digit odd numbers totalling 9 27, 45, 63, 81 Try out with 27 27 x 5 = 135 (less than 140) 27 x 4 = 108 (more than 100) Ans: 27
Boost! Math Primary 3 Lesson 19: Four Operations[2] Answer Key 1. Oct → 678 – 222 = 456 Oct + Nov + Dec → 456 + 541 + 678 = 1675 Unsold → 2000 – 1675 = 325 Ans: 325 2. Makayla → 2150 + 359 = 2509 Fiona → 2509 + 1785 = 4294 Ans: $4294 3. Green Tea → 1140 + 317= 1457 Ice lemon tea → 1457 + 564 = 2021 Ans: 2021 4. 4 times → 996 1 time → 996 ÷ 4 = 249 7 times → 7 x 249 = 1743 Ans: 1743 m 5. 3 weeks = 21 days 21 days painted → 21 x 9 = 189 unpainted → 250 – 189 = 61 Ans: 61 m 6. Tank B →60 – 19 = 41 Tank C → 75 – 19 = 56 3 Tanks → 19 + 41 + 56 = 116 (A) (B) (C) Ans: 116 litres 7. Using Substitution + = 200 into equation 1. + 200 Step 2: rewriteequation = 540 Step 1: substitute 200 200 + 200 + =540 = 540 – 200 –200 = 140 = 140 ÷ 2 = 70 Ans: 70 19 19 A B A C 75 60 Li Ting Makayla Fiona 1785 359 2150 ? 1140 317 564 Peachtea GreenTea Ice LemonTea ? 43 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
8. Note: Men → 894 – 237 = 1131 Find total number of women and girls. women + girls → 3000 – 1131(men) – 894(boys) = 975 Now we can draw comparison model for women & girls 3 units = 975 1 unit = 975 ÷ 3 =325 Ans: 325 9. 2 units = 8 1 unit = 8 ÷ 2 = 4 amount of money at first → 6 x 4 = 24 Ans: $24 12. 1 calculator → 9 + 14 = 23 6 calculators → 6 x 23 = 138 Jonathan has → 138 + 9 = 147 Ans: $147 13. Ans: 12 No.of birds legs (birds) No.of cats legs (cats) Total legs Check (44 legs) 8 8 x 2 = 16 9 9 x 4 = 36 16 + 36 = 52 X 9 9 x 2 = 18 8 8 x 4 = 32 18 + 32 = 50 X 12 12 x 2 = 24 5 5 x 4 = 20 24 + 20 = 44 ✓ As we know that the exact no. of boys→ 894, we work on finding no. of men first. 975 Women Girls ? $14 $9 short left 6 calculators 10. 1 day difference between April and Tessa → $1 Total difference between April and Tessa → $27 - $18 = $9 No. of days taken → $9 ÷ $1 = 9 Tessa saves in 1 day → $27 ÷ 9 = $3 Ans: $3 11. $28 ÷ $4 = 7 (Jennifer takes 7 days to put $28 into her piggy bank) $28 + $2 = $30 (after father put in another $2) 150 ÷ 30 = 5 (groups) No. of days → 5 x 7 (days) = 35 Ans: 35 7 calculators Men Boys 894 ? 237 6 coinpouches 4 coinpouches $8 left 44 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
14. Draw a diagram a) 8 – 6 =2 b) First → Diana Last → Elise Ans: (a) 2m (b) First:Diana Last:Elise 15. First Number to try → between 20 & 60 → multiples of 7 Groups of 7 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42 Groups of 4 (remainder 2) 21 ÷ 4 = 5 r 1 (x) 28 ÷ 4 = 7(x) 35 ÷ 4 = 8 r3(x) 42 ÷ 4 = 10 r2(✓) Ans: 42 Front Diana 8m 6m Betty 3m Cindy Anita Elise 7 7 x 3 = 21 45 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Boost! Math Primary 3 Lesson 20: Heuristics [Interval & Age] Answer Key Interval 3) No. of intervals→ 150 m ÷ 3 m = 50 No. of trees planted → 50 + 1 = 51 Ans: 51 4a) 4b) No. of intervalsbetween 3rd and 10th lanterns→ 10 – 3 = 7 Each interval → 21 m ÷ 7 = 3 m No. of intervals between 1st and 10th lanterns→ 10 – 1 = 9 Distance between 1st and 10th lanterns → 9 x 3 m = 27 m No of intervals with 30 lanterns → 30 – 1 = 29 Ans: 27m Length of walkway with 30 lanterns → 29 x 3 m = 87m Ans: 87 m 1a) 18 m 1b) 6 m 1c) Start and End of theroad 1d) 3 1e) 4 Interval: m 6 2 Interval: 6 m 1 6 Interval: m 3 Lamp posts placed at the two ends of the road The stretch of road is 18 m long. Based on this pattern, 2a) When there are 5 lamp posts, there will be 4 intervals. 2b) 4 x 6 m = 24 m The stretchof road will be 24 m long. 2c) When there are 8 lamp posts, there will be 7 intervals. 2d) 7 x 6 m = 42 m The stretch of road will be 42 m long. 46 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
5) 18 m = 1 800 cm 12 m = 1 200 cm 1 800 ÷ 40 = 180 ÷4 = 45 Length→ 45 + 1 = 46 1 200 ÷ 40 = 120 ÷4 = 30 Breadth→ 30 – 1 = 29 Total flags needed → 46 + 46 + 29 + 29 = 150 Ans: 150 6) 1 st 2nd 3rd 4th 5th 6th – 12th ….. 33rd ..... 18 m ….. ? 33 – 1 = 32 (intervals) 12 – 6 = 6 (intervals) 18 m ÷ 6 = 3 m 1st to 33rd trees→ 32 x 3 m = 96 m Ans: 96 m 7) 10 – 3 = 7 (intervals) 35 m ÷ 7 = 5 m 1st to 420th lamp posts → 419 x 5 m = 2 095 m 420 – 1 = 419 (intervals) Ans: 2 095m ? 47 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
Age Difference 9) Method 1: 3 515 cm – 15 cm = 3 500 3 500 cm ÷ 35 cm =100 100 + 1 = 101 Method 2: 3 515 cm + 20 cm = 3 535cm 3 535 cm ÷ 35 cm =101 Ans: 101 8) Method 1: Total distance→ 29 groups of intervals+ the width of the 30 trees = 29 × 4 m + 30 × 0.5 m = 116 m + 15 m = 131 m Method 2: Total Distance → 30 groups of intervals – last interval of the 30th tree = 30 × 4.5 m – 0.5 m = 135 m - 4 m = 131 m Ans: 131 m 48 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
3) 4) 49 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.
5) 6) Extension 1 ) tree 1 tree2 tree3 tree4 tree5 When there are 5 trees, there are 4 intervals. Observe the pattern, Based on the same exampleabove: When there are 6 trees, there are 5 intervals. When there are 38 trees, there are 37 intervals. 3rd 4 A th B 0.5m 4 m 4.5 m 1 st interval 4.5 m 2nd 0.5m 50 2021 Copyright of PAL Solutions. No furtherreproductionanddistribution is allowed.