# Numeric patterns  (Page 2/5)

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If you are aware of the pattern in which 8; ..6; ..4; ..2; ..0; is repeated, and concentrate, you should be able to count in 8’s forever, without mistakes.

• Now, work with a friend. Count in 8’s from 0 to 104 while your friend checks you on a calculator. Then swap over.

3.5 Now count backwards in 8’s from 104 to 0 while your friend checks you on a calculator.

Then swap over.

4. Multiples of 9

4.1 Do what Sue suggested. Write down the missing multiples of 9 in the flow diagram and look at the last digit of each one. Spot the pattern.

4.2 Counting in 9’s is the easiest of all! Now complete the table below.

 1 2 3 4 5 6 7 8 9 10 11 12 × 9 9 18 27 90 99

4.3 Now count backwards in 9’s while a friend checks you on the calculator. Begin with 108.

Now you should feel comfortable when you count in 6’s; 7’s; 8’s and 9’s and you already know how to count in tens. Practise this with a friend, forwards and backwards.

1. Complete the following by doing one column each day or all four columns in one day, or two columns per day, as your educator chooses:

 (a) 7 × 4 =………… 6 × 8 =…………….. 8 × 9 =…………….. 2 × 8 =……………. (b) 9 × 8 = 3 × 7 = 1 × 7 = 6 × 9 = (c) 7 × 6 = 8 × 7 = 6 × 5 = 8 × 7 = (d) 2 × 5 = 3 × 9 = 7 × 9 = 5 × 5 = (e) 10 × 10 = 2 × 8 = 9 × 9 = 4 × 6 = (f) 3 × 6 = 8 × 5 = 9 × 0 = 9 × 8 = (g) 4 × 2 = 5 × 8 = 7 × 3 = 7 × 10 = (h) 5 × 6 = 6 × 6 = 8 × 8 = 3 × 8 = (j) 4 × 4 = 0 × 10 = 4 × 9 = 5 × 7 = (k) 5 × 9 = 4 × 8 = 5 × 7 = 4 × 7 = TOTAL: TOTAL: TOTAL: TOTAL:

2. Now write all those that you got wrong and write down a way of finding the correct answer for each of them.

Activity 2:

To do mental calculations involving multiplication of whole numbers [LO 1.9]

1. Now complete this flow diagram:

2. Ways of solving 7 x 8.

Example of solving 7 x 8.

• 7 x 4 + 7 x 4 OR double (7 x 4)
• 8 + 8 + 8 + 8 + 8 + 8 + 8
• Counting in 8’s till you reach 7 x 8
• 7 x 5 + 7 x 3 i.e. breaking up the 8 as we did previously
• 2 x 8 + 5 x 8 i.e. breaking up the 7 to make it easier; I know 2 x 8 and 5 x 8
• Double 3 x 8 + 8
• 7 x 10 - 2 x 7Be sure that you know what you are doing!

3. Now take each one that bothers you, and find a way of reaching the answer without a calculator and write your solution in the table below.

My way of solving each problem:

 e.g. 8 × 8 Double 4 × 8 =32 + 32 = 64 3 × 6 6 × 3 (I know my 3 times table) = 18

• Complete each of the following:

1.

2.

3.

4.

5.

6. Explain the link between 4 and 5.

7. Use what you have learnt in 4 and 5 to complete the following:

 (a) 6 × 20 = (f) 40 × 20 = (b) 7 × 70 = (g) 60 × 60 = (c) 50 × 3 = (h) 50 × 80 = (d) 9 × 70 = (j) 60 × 7 = (e) 8 × 30 = (k) 90 × 50 =

Activity 3:

To estimate and calculate by selecting and using a range of techniques [LO 1.1, 1.8]

1. You have found ways of calculating answers of tables that you have not memorized. Now estimate the answer by rounding off. Estimations should be quick and easy, but they only give approximate answers. Then find ways of reaching the exact answer of the following sums and write down all your steps:

1.1 7 x 18

• 24 x 6

1.3 36 x 54

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