ACTIVITY 8

Attempt 1: Guess an answer that will make the number sentence TRUE. Guess that a 6 in the block will make the number sentence true.

3 156 – 6 = 3 149

Attempt 2: To choose 6 as the answer will make the number sentence FALSE. Guess another answer. Since 6 is not enough to subtract from 3 156 to get 3 149, you must choose a greater number. Use the number 7. 3 156 – 7 = 3 149  Using this method, it may take a few tries to solve the number sentence. It is time-consuming and not always the best choice.

1. Solve the number sentences using trial and improvement.

Question

1.1 1 458 –  = 1 443 1.2 239 +  = 343 1.3 985 +  = 999

1.4 1 326 –  = 1 316 1.5 515 +  = 1 415

Answer 15 104

14 10

900

Checking the solution by substitution is very similar to trial and improvement. You must study the number sentence and then decide on an answer. You then replace the answer in the number sentence and do the calculation. The number sentence must be TRUE.

Number sentences are also a way of showing equivalence. What does equivalence mean?

Equivalence is when one side of the number sentence is equal to the other side of the number sentence. In other words, showing that the number sentence is true.

The left side of the number sentence is equivalent (equal to) the right side of the number sentence. It means the number sentence is true. Equivalence

Number sentences may also be used in flow charts and tables. Look at a few examples.

In the flow chart below, the number sentence is on the left-hand side and the equivalent value is on the right-hand side. Complete the flow chart so all the number sentences have equivalent values.

44 + 256

156 – 57

19 + 199

186 + 359

999 – 190

Addition and subtraction in number sentences

You already know that addition and subtraction are opposites. If you add 14 sweets to the 6 you already have, you will have 20 sweets. To return to what you originally had, you are going to do the opposite. Instead of adding 14 sweets, you are going to subtract them. The 20 sweets minus the 6 sweets give you the original 14 sweets you had at the beginning. If you write this in a number sentence, it will look like this: 300

99

218

545

809

Description in words

I have 14 sweets and add 6. I have 20 sweets and subtract 6.

Number sentence

14 + 6 = 20 20 – 6 = 14

Can you think of more examples where addition and subtraction can be used as opposite calculations in number sentences?

Learners must give their own examples. Let them go through this thought process on their own. Try not to help them but guide them if they really need help and let them think of more examples on their own.

You know addition and subtraction are opposites and they can be used to check the answers of number sentences. Multiplication and division are also opposites and used as inverse operations to test answers in number sentences. Study the examples: • 164 – 73 = 91 so 91 + 73 = 164 • 1 034 + 496 = 1 530 so 1 530 – 496 = 1 034 and 1 530 – 1 034 = 496 • 78 × 3 = 234 so 234 ÷ 3 = 78 and 234 ÷ 78 = 3 • 165 ÷ 3 = 55 so 55 × 3 = 165