Problems like … + 29 = 81

I am learning to reverse problems like □ + 29 = 81 to 29 + □ = 81 and then use an appropriate mental method to solve the problem.

This means working it out in your head.

By now you know a number of different methods. Let’s try to choose the best method for each type of question.

First let’s check that the order (e.g. ? + 3 = 8 or 3 + ? = 8) doesn’t matter.

? + 3 = 8 3 + ? = 8

Below are the total amount of counters we should end up with.

Below are the total amount of counters we should end up with.

Now let’s record the three counters he starts with.

Zane has some counters, he gets 3 more and now has 8 counters. How many counters did he start with?

Zane has 3 counters, he gets some more and now has 8 counters. How many counters did he get?

We don’t know how many counters Zane starts with but we know the second amount of counters he got was 3.

You can see from the diagram above Zane must have stated with 5 counters. 5 + 3 = 8

You can see from the diagram above Zane must have been given 5 counters. 3 +5 = 8

Notice how the answer (5) is the same using both methods.

Kirsty has some money and earns $18 more. She now has $46. How much money did she start with? ? + 18 = 46

Step 1: Change the question around. 18 + ? = 46

Step 2: Choose an appropriate method. A good choice here would be ‘Jumping the Number Line”.

Try to do each step in your head before clickingStep 3: Place the starting and end numbers on the number line.

18 46

Step 4: Choose a tidy number to jump to.

20

+2

Step 5: Jump from the tidy number (20) up to the target number (46).

+26

Step 6: Add the jumps together. This is your answer.

2 + 26 = 28 so 18 + 28 = 46

A farmer has some sheep. He buys 13 more. He now has 87. How many sheep did he start with? ? + 13 = 87

Step 1: Change the question around. 13 + ? = 87

Step 2: Choose an appropriate method. A good choice here would be adding the ones and tens separately (see “Problems like 37 + … = 79).

Try to do each step in your head before clicking

Step 3: We have 3 ones and need 7 ones. How many more ones do we need?

Step 4: We have 1 ten but need 8 tens. How many more tens do we need?

Step 5: Add these amounts together. This is how many sheep the farmer must have started with.

so 13 + 74 = 87

4

7 tens (70)

70 + 4 = 74

Now try these questions on your own.

Remember to first change the question then answer.

Need some more practise? Try Pg49 of Teacher Tools Addition and Subtraction Book Numeracy resources

1) … + 67 = 84

2) … + 19 = 56

3) … + 13 = 75

4) …. + 67 = 79

5) … + 21 = 82

Click again when you have completed each question and the answer will be displayed.

67 + 17 = 84

19 + 37 = 56

13 + 62 = 75

67 + 12 = 79

21 + 61 = 82