2.1 In a General Knowledge Competition the Girls’ Team scored 642 points by tea-time. The Boys’ Team scored 493 points. By how many points was the Boys’ Team behind the Girls’ Team?
2.2 By lunch-time the Girls’ Team had 734 points and the Boys’ Team had 655 points.
- Was the Boys’ Team catching up?
- Why do you say this? Answer carefully.
- By how many points was the Boys’ Team behind the Girls’ Team at lunch-time?
2.3 After lunch, the boys made a determined effort. During the afternoon they scored another 619 points. The girls scored 519 points in the afternoon. When all the points were added up, which team eventually won the competition, and by how much?
3. CALCULATOR GAME: two players, one calculator
- Continue in this manner. If one of the players makes a mistake, correct it and then the other player gets an extra turn to ask a question. Keep the numbers not more than 4-digit numbers at the most. It’s valuable to become very good at 2-digit numbers first.
- Complete:
a. 100 – 7 =
b. 1 000 – 7 =
c. 500 – 7 =
d. 500 – 17 =
e. 500 – 27 =
f. 700 – 70 =
g. 1 000 – 70 =
h. 2 100 – 70 =
4. SOME TECHNIQUES to perform written and mental calculations.
- How can one add 8 + 7 easily?
4.2 Discuss: which learner was right? What method must you use?
- You must use the method that you understand best, the one that you feel comfortable with, and you must also try to listen to others when they explain their methods. But be sure to use the method that you really understand well enough to explain to others what you did.4.3 Try to see a link between these sums as you write down the answers
a. 8 + 7 =
b. 18 + 7 =
c. 8 + 17 =
d. 18 + 17 =
e. 8 – 7 =
f. 18 – 7 =
g. 28 – 7 =
h. 28 – 17 =
5. Now use your method and try some written sums. Write down all the steps you needed to reach the answer. You may not use a calculator.
- 87 － 54
- 84 － 57
- Now discuss these two sums and their answers with a friend.
- Explain what you noticed.
6. Now calculate, without a calculator and using the method that you feel you understand most. Write down all the steps of your calculation:
- 1 345 + 278
- 978 – 245
- 1 278 + 1 133
- 845 – 672
- 684 – 659
- 4 092 + 3 214
- Check the last sum by rounding off the numbers to the nearest 10 or nearest 100 and then calculating an approximate answer. Then discuss how you reached your answers with a friend. If necessary, check your answers on a calculator.
7. MORE WORD SUMS
Sales at a Craft Market for the first 5 months of the year:
| Months | Cooldrinks | Hot dogs | Ice-creams | Mugs of Soup |
| January | 3 064 | 1 754 | 2 356 | 225 |
| February | 3 215 | 1 036 | 2978 | 54 |
| March | 1 964 | 2 375 | 2 035 | 987 |
| April | 874 | 3 752 | 1 096 | 1 952 |
| May | 756 | 3 904 | 788 | 2 659 |
7.1 How many cooldrinks were sold altogether during the five months?
7.2 Were cooldrinks or ice-creams more popular during the five months? Explain why you give this answer.
7.3 Cooldrinks cost R5,00 each. How much money was collected for cooldrinks in May? Try to find an easy way of calculating this and write it down.
7.4 At the beginning of January the ice-cream stall holder buys 24 boxes of ice-creams. Each box contains 100 ice-creams. How many ice-creams are over at the end of the January Market?
7.5 Which month was the coldest? Why do you say so? (Look back at the table showing the sales.)
7.6 Round off the numbers of cups of soup to the nearest 100 and say approximately how many cups of soup were sold altogether.
Assessment
| Learning outcomes(LOs) |
| LO 1 |
| Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. |
| Assessment standards(ASs) |
| We know this when the learner: |
1.7 solves problems that involve:
|
1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve:
|
1.9 performs mental calculations involving: addition and subtraction:
|
1.10 uses a range of techniques to perform written and mental calculations with whole numbers including:
|
| 1.11 uses a range of strategies to check solutions and judge the reasonableness of solutions. |
Memorandum
ACTIVITY
1.1 home
1.2 friend’s home
1.3 either / friend’s home
1.4 50; 1 350; 280; 980; 250; 1 130; 680
1.5
| Sum | Numbers rounded off to nearest 10 | Approximate answer | Exact answer | Difference |
| 24 + 36 | 20 + 40 | 60 | 60 | 0 |
| 52 + 48 | 50 + 50 | 100 | 100 | 0 |
| 33 + 52 | 30 + 50 | 80 | 85 | 5 |
| 79+ 23 | 80 + 20 | 100 | 102 | 2 |
| 17 + 47 | 20 + 50 | 70 | 64 | 6 |
| 125 + 46 | 130 + 50 | 180 | 171 | 9 |
| 411 + 732 | 410 + 730 | 1 140 | 1 143 | 3 |
1.6 They are close when one number is rounded off upwards and the other, downwards. When both numbers are rounded off upwards, or both are rounded off downwards the totals are not very close, e.g. the third sum; the fifth sum and the last two sums. The rounding off increases the gap.
1.7 300; 300; 500; 1 200; 1 400
1.8 1 000; 2 000; 4 000; 1 000; 1 000; 0
- 873 + 46 = 919;
870 + 50 = 920
934 – 87 = 847;
930 – 90 = 840
2 WORD SUMS
2.1 642 – 493 =149; 640 – 490 = 150
The boys were behind by 149 points.
2.2 (a) Yes
(b) 734 – 655 =79; 730 – 660 = 70
At tea-time the difference between the Girls’ points and the boys’ was 149 points; at lunch-time the difference was only 79 points, so the boys were catching up.
(c) 79 points, see above
(d) Girls
734 + 519 = 1 253
Boys
655 + 619 = 1 274
The boys won by 21 points.
3.1 Calculator Game
3.2 (a) 93
(b) 993
(c) 493
(d) 483
(e) 473
(f) 630
(g) 930
(h) 2 030
4.1 and 4.2 Discussion: Techniques
4.3 (a) 15
(b) 25
(c) 25
(d) 35
(e) 1
(f) 11
(g) 21
(h) 11
5. WRITTEN SUMS
5.1 33
5.2 27
5.3 and 5.4 discussion and explanation
6.1 1623
6.2 733
6.3 2 411
6.4 173
6.5 25
6.6 7 306
6.7 Checking by rounding off and discussion
- 9 873 cool drinks
- Cool drinks; 620 more cool drinks were sold than ice-creams
- 44 ice-creams were over
- Hot dogs
- May; many hot-dogs and mugs of soup were sold; few cool drinks and ice creams were sold.
- 6 000 cups of soup