Numeric patterns  (Page 3/5)

Examples of methods:

• 7 × 18

Estimation: 7 × 20 = 140; the answer is about 140

7 × 10 + 7 × 8 i.e. 7 times all of 18

Other ways of finding the exact answer:

or: 18 + 18 + 18 + 18 + 18 +18 + 18

or: 7 × 20 － 14

There are other methods. Try to think of them.

• 64 × 35

i.e. all of 64 × all of 35

Estimation: 60 × 40 =2 400

60 × 30 = 1 800

60 × 5 = 300 i.e. add all answers

4 × 30 = 120

4 × 5 = 20

2 240

When you are really comfortable with this method, you can proceed to the old traditional vertical method. Don’t try to get there too quickly; more haste, less speed.

2. Word sums.

2.1 Share 54 Smarties equally amongst 9 friends. What does each one receive?

2.2 54 learners have to be transported to an Athletics Meeting. The coach wants to hire vehicles that may take 8 passengers. How many vehicles will be needed?

2.3 A shopkeeper has 106 apples. He puts them on little trays to sell them in his shop. There are 6 apples on each tray. How many trays can he fill?

Some methods:

• 9 + 9 + 9 + 9 + 9 + 9 (How many 9’s in 54?)

or: 54  9

9 × ? = 54

There are other methods

• 54  8

6 × 8 = 48; 6 rem. 6, but they are people who have to get to the athletics meeting.

7 × 8 = 56

7 vehicles will be needed and there will be 2 empty seats on one of them.

• 106  6

10 × 6 = 60

5 × 6 = 30

2 × 6 = 12

102

17 trays rem. 4 apples (The key word here is “fill”.)

There are other ways. Discuss them with your friends and find the way that you understand best.

3. Calculate the answer. Write down the steps of your calculations, explaining (in numbers) how you reached your solution. Then write down the steps which you used to check that your answer is reasonable.

3.1 The mass of a van after it has been loaded is 2 500 kg. If the mass of the load is 500 kg, what is the mass of the van when it is empty?

3.2 The mass of one bag of cement is 25 kg. How many bags of cement will there be if the mass of the whole load is 500 kg?

3.3 The petrol tank of the van can hold 55 litres of petrol when it is full. The van needs one litre of petrol to travel 13 km. The driver fills his tank with petrol. How far can he travel before he needs to fill his tank again?

3.4 When the van is used for short trips around the town, it only travels 11 km per litre of petrol. The driver fills his petrol tank, which holds 55 litres of petrol. How many kilometres can it travel in the town?

3.5 Your school soccer team has to travel from Cape Town to Grahamstown to take part in a soccer tournament. Your team can go by bus along the coast, a distance of 899 km, or you can go by train via De Aar. The distance between Cape Town and De Aar is 762 km. From De Aar to Grahamstown is 444 km.

How much further will you travel if you go by train?

3.6 A special tour to the Kruger National Park is arranged for 134 tourists from overseas. At the rest camp 8 people can sleep in a rondavel. How many rondavels are needed for the tourists?

3.7 There is a tourist shop at the rest camp in the Kruger Park. In this shop special torches called Bush Baby Lanterns are sold. Seven tourists buy a torch each and together they pay R273 for them. How much does one Bush Baby Lantern cost?