1.2 Written and mental calculations with whole numbers

Mathematics

Grade 4

Whole numbers and their relationships

Module 3

Written and mental calculations with whole numbers

Activities:

• Use a range of techniques to perform written and mental calculations with whole numbers [LO 1.10]
• Estimate and calculate by selecting and using operations appropriate to solving problems [LO 1.8]
• Solve problems that involve comparing two or more quantities of the same kind (ratio) [LO 1.7]
• Use a range of strategies to check solutions and judge their reasonableness [LO 1.11]

FINDING APPROXIMATE ANSWERS AND CHECKING ANSWERS

Now that you have studied “Place Value”, we are going to look at “Rounding Off” numbers so that we can use this to:

• calculate approximate answers quickly and also
• check our answers quickly.

1. APPROXIMATING, BY ROUNDING OFF

Consider the following:

1.1 You are riding your bike from your home to the home of a friend who lives 10km away. Your tyre bursts when you have gone 4km. Will you decide to walk home to fix it or go on to your friend?

Yes, you’ll walk home because it’s nearer. 4 is nearer to 0 than to 10

1.2 Now the tyre bursts when you have ridden 6km. Will you decide to walk to your friend’s home or back to your own home?

Yes, you’ll go on to your friend’s home because it is nearer.

6 is nearer to 10 than to 0.

1.3 Now the tyre bursts when you have ridden 5km exactly. Should you decide to walk to your friend’s home or back to your own home?

In Mathematics, always round off upwards if the last digit is 5.

• Now use the diagrams that we have just seen to help you to complete the table:

1.5 Now we are going to use “rounding off” to calculate, quickly, an approximate answer for the following sums, and then we shall calculate the exact answer , and compare the difference between the two answers. Fill in what is missing in each column:

1.6 Look at the sums that you have just completed. In which sums was the approximate answer and the exact answer not very close, and why?

ROUNDING OFF TO THE NEAREST 100 :

1.7 Complete the table below. .

ROUNDING OFF TO THE NEAREST 1 000:

1.8 Complete the table below.

1.9 Use rounding off to estimate the approximate answer of the following sums. Then calculate the exact answer:

2. WORD SUMS

• Now see how well you can solve word sums without a calculator. Check that your answers are reasonable by rounding off the numbers, but remember that your final answer must be the exact answer. The numbers are not very big and the sums are straightforward, but you will have to read carefully. Write down all you need to write down, and remember to write words with your answer. When you have finished the sums, compare your findings with those of a friend. Enjoy this task.