# Find the Number Rule

In this worksheet, students will identify a rule which is used to make a number and apply this rule to find a missing number.

Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Number Logic

Difficulty level:

### QUESTION 1 of 10

Hi number detective! We’ve got a challenge that we need your help with. Are you ready?

In these questions, we will have to use a third top secret number as well as our main four operations: addition, subtraction, multiplication and division.

How do the numbers on the outside of the brackets create the numbers on the inside of the brackets?

5 (33) 7        6 (22) 4

The first thing to do is find a way to make 33 using 5 and 7 together with an invisible secret number.

We know that 5 x 7 = 35 which is close to our target of 33.

We can guess that the secret number is 2 and that we need to take this away from our total to reach 33.

So our rule could be: multiply the two outside numbers together and then take away 2.

Let’s see if this rule works for our next set of numbers!

If we apply it, we get 6 x 4 = 24. Then if we take away the secret 2, we get 22.

This is the number we are aiming for so we’ve cracked the code! Well done!

For the next question we need to crack the code and then use the rule to work out a missing number:

3 (11) 5        4 (16) 9        2 (_) 7

First, we need to find a way to make 11 using 3 and 5 together with an invisible secret number.

We could try 3 x 5 = 15 and then take away the secret number of 4 to get 11.

So our rule could be: multiply the two outside numbers and then take away 4.

Let’s see if this rule works for the next set of numbers: 4 x 9 = 36 and 36 - 4 = 32.

Oh dear! We didn’t find the right rule this time which means we need to look for another.

We could try 3 + 5 = 8 and then add a secret number of 3.

So our rule could be: add the two outside numbers and then add an extra 3.

Let’s try that for the next set of numbers: 4 + 9 = 13 and then add the extra 3 is 16.

Jackpot! We’ve found the right rule!

Now let’s use this rule to work out the missing number in the final set of numbers.

2 + 7 = 9 and then add the extra 3 gives us 12.

So the correct answer is 12.

 Pssstt!! Here's a handy hint to help you reach superstar status: Look out for the secret number and don't worry if the first rule you find doesn't work, just stay calm and try another one!

It’s now your turn to put your skills to the test and be a number detective, hunting down those missing numbers!

Welcome, number detective - you're just in time!

Look at the number sets below:

5 (11) 5        6 (10) 3

How do the numbers on the outside of the brackets create the numbers on the inside of the brackets? They have used one of the main number operations (+, -, x and ÷) and then used a third top secret number.

Which of the rules below helps us make the inside numbers? It has to work for both sets of numbers.

Left number x right number + 1

Left number + right number + 1

Left number - right number - 1

Left number + right number + 4

Have a go at this one!

Look at the number sets below:

6 (21) 3        8 (35) 4

How do the numbers on the outside of the brackets create the numbers on the inside of the brackets?

Click on the rule below that helps us make the inside numbers. Remember that the rule has to work for both sets of numbers.

Left number x right number + 3

Left number x right number - 4

Left number + right number - 9

Left number x right number + 1

Look at the sets of numbers below:

36 (8) 6        40 (10) 5        24 (?) 8

The rule here is 'left number ÷ right number + 2'.

Use this rule to work out the mystery number in the final set.

5

38

194

1

Look at the number sets below:

9 (94) 10        8 (28) 3        3 (?) 9

The rule here is 'left number x right number + 4'.

Use this rule to work out the mystery number in the final set.

23

7

35

31

Now it's time for your next mission...

Look at the number sets below:

6 (49) 8        9 (28) 3        4 (?) 12

Your mission is to work out the rule that uses the outside numbers, as well as a top secret number, to create the middle numbers (the numbers in the brackets).

Then, use this rule to work out the mystery number in the final set.

47

49

4

2

Look at the number sets below:

90 (11) 9        44 (12) 4        21 (?) 3

Your mission is to work out the rule that uses the outside numbers and top secret number to create the middle numbers (the ones in the brackets).

Then, use this rule to work out the mystery number in the final set.

64

62

8

6

Here's another puzzle for you to solve.

Look at the sets of numbers below:

10 (28) 3        4 (30) 8        6 (?) 6

Your mission is to work out the rule that uses the outside numbers to make the inside numbers.

This will also use a top secret number. Then use this rule to work out the mystery number and type it in as digits below.

38

34

35

37

Look at the numbers below:

Work out the rule to make the middle numbers (the ones in brackets) and use this rule to work out the mystery number.

40 (12) 4        88 (10) 11        48 (?) 4

14

10

12

8

Look at the sets of numbers below.

Your mission is to work out the rule that uses the outside numbers to create the inside numbers. Then, use this rule to work out the mystery number in the final set.

12 (18) 4        20 (29) 7        15 (?) 5

18

1

22

4

It's time for your final mission, number detective!

Use all of your improved number puzzle skills to work out the rule for the number sets below. Then use this rule to work out the mystery number.

27 (21) 3        17 (7) 7        30 (?) 8

25

19

35

42

• Question 1

Welcome, number detective - you're just in time!

Look at the number sets below:

5 (11) 5        6 (10) 3

How do the numbers on the outside of the brackets create the numbers on the inside of the brackets? They have used one of the main number operations (+, -, x and ÷) and then used a third top secret number.

Which of the rules below helps us make the inside numbers? It has to work for both sets of numbers.

CORRECT ANSWER
Left number + right number + 1
EDDIE SAYS
Hi number detective! Did you find the rule here? Let's look at the first set of numbers: 5 (11) 5. How can we make an answer of 11 with the numbers 5, 5 and an extra top secret number? 5 + 5 = 10 and if we add an extra 1 to this we get 11. Let's see if this works for the second set of numbers: 6 (10) 3. 6 + 3 = 9 and then add the extra 1 to get 10! This means that the rule is 'left number + right number + 1'.
• Question 2

Have a go at this one!

Look at the number sets below:

6 (21) 3        8 (35) 4

How do the numbers on the outside of the brackets create the numbers on the inside of the brackets?

Click on the rule below that helps us make the inside numbers. Remember that the rule has to work for both sets of numbers.

CORRECT ANSWER
Left number x right number + 3
EDDIE SAYS
Did you try out all of the options here until you found one that worked? The rule here is 'left number x right number + 3' Let's look at the first number set: 6 (21) 3. 6 x 3 = 18 and then we add the extra top secret number of 3 to get 21. This also works for the second set of numbers. Make sure that you know your lefts and rights, as this will be very helpful for this activity.
• Question 3

Look at the sets of numbers below:

36 (8) 6        40 (10) 5        24 (?) 8

The rule here is 'left number ÷ right number + 2'.

Use this rule to work out the mystery number in the final set.

CORRECT ANSWER
5
EDDIE SAYS
Let's follow the rule 'left number ÷ right number + 2' with the final set of numbers. 24 (?) 8. 24 ÷ 8 = 3 and then add the extra 2 = 5. Are you getting the hang of this now? I know we normally see the answer at the end of a question (rather than in the middle!) so it is confusing at first.
• Question 4

Look at the number sets below:

9 (94) 10        8 (28) 3        3 (?) 9

The rule here is 'left number x right number + 4'.

Use this rule to work out the mystery number in the final set.

CORRECT ANSWER
31
EDDIE SAYS
Did you follow the rule for the final set of numbers? 3 (?) 9 3 x 9 = 27 and if we add the secret number 3 we get 31. This makes 31 the correct answer.
• Question 5

Now it's time for your next mission...

Look at the number sets below:

6 (49) 8        9 (28) 3        4 (?) 12

Your mission is to work out the rule that uses the outside numbers, as well as a top secret number, to create the middle numbers (the numbers in the brackets).

Then, use this rule to work out the mystery number in the final set.

CORRECT ANSWER
49
EDDIE SAYS
Did you find the rule here? Let's look at the first set of numbers: 6 (49) 8 How can we make a number close to 49 with 6 and 8? 6 x 8 = 48 and if we add the top secret number 1 we get to 49. This means that our rule could be 'left number x right number + 1'. We need to check that this rule works for the second set of numbers: 9 (28) 3 9 x 3 = 27 and if we add the extra 1 we get 29. Now we have to use the rule for the final set of numbers. 4 (?) 12 4 x 12 = 48 and then add the extra 1 is 49. There's a lot to think about here but we can do it!
• Question 6

Look at the number sets below:

90 (11) 9        44 (12) 4        21 (?) 3

Your mission is to work out the rule that uses the outside numbers and top secret number to create the middle numbers (the ones in the brackets).

Then, use this rule to work out the mystery number in the final set.

CORRECT ANSWER
8
EDDIE SAYS
A clue here is that the middle number is smaller than one of the numbers outside the brackets. This is a clue that we are dividing or taking away. Let's look at the first set: 90 (11) 9 90 ÷ 9 = 10 and then we can get to 11 by adding 1. The rule could be 'left number ÷ right number + 1'. To confirm this, we need to check that this rule works for the second set of numbers: 44 (12) 4 44 ÷ 4 = 11 and if we add the extra 1 we get 12. Great! The rule works for both sets so we can now use it to work out the mystery number: 21 (?) 3 21 ÷ 3 = 7 and then add the extra 1 is 8. If the rule you come up with doesn't work for both sets of numbers, then you'll need to try another rule.
• Question 7

Here's another puzzle for you to solve.

Look at the sets of numbers below:

10 (28) 3        4 (30) 8        6 (?) 6

Your mission is to work out the rule that uses the outside numbers to make the inside numbers.

This will also use a top secret number. Then use this rule to work out the mystery number and type it in as digits below.

CORRECT ANSWER
34
EDDIE SAYS
Did you find the rule here? Let's look at the first set of numbers: 10 (28) 3. The number in the middle is a lot bigger so this is a clue that we are multiplying: 10 x 3 = 30. To get from 30 to 28 we take away 2. The rule could be 'left number x right number - 2'. This rule also works for the second set of numbers, which means that we are ready to work out the mystery number: 6 x 6 = 36 36 subtract the extra 2 is 34. This makes 34 the mystery number.
• Question 8

Look at the numbers below:

Work out the rule to make the middle numbers (the ones in brackets) and use this rule to work out the mystery number.

40 (12) 4        88 (10) 11        48 (?) 4

CORRECT ANSWER
14
EDDIE SAYS
Did you work out the rule here? The rule was 'left number ÷ right number + 2' 40 (12) 4 40 ÷ 4 = 10 and then add the extra 2 to get 12. 88 (10) 11 88 ÷ 11 = 8 and then add the extra 2 to get 10. Let's do this with the final set: 48 ÷ 4 = 12 12 + 2 = 14. The mystery number is 14.
• Question 9

Look at the sets of numbers below.

Your mission is to work out the rule that uses the outside numbers to create the inside numbers. Then, use this rule to work out the mystery number in the final set.

12 (18) 4        20 (29) 7        15 (?) 5

CORRECT ANSWER
22
EDDIE SAYS
Here, the rule is 'left number + right number + 2'. Let's use this rule for the final set of numbers: 15 (?) 5 15 + 5 = 20 and then add an extra 2 to get 22. One more challenge, detective and then your mission is complete!
• Question 10

It's time for your final mission, number detective!

Use all of your improved number puzzle skills to work out the rule for the number sets below. Then use this rule to work out the mystery number.

27 (21) 3        17 (7) 7        30 (?) 8

CORRECT ANSWER
19
EDDIE SAYS
Did you spot the rule here? The rule was 'left number - right number - 3'. Can you see how this makes the middle numbers for the first two sets? Let's use this rule to work out the mystery number: 30 - 8 = 22 22 - the secret number 3 = 19. Well done for your awesome number puzzle skills today, detective! You should now feel confident when asked to find a number rule using your knowledge of basic operations. Why not attempt a more challenging activity?
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