# Recognise and Apply the Correct 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 new challenge that we need your help with. Are you ready?

In the following 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!

Hello number detective - I'm glad you're here!

Look at the number sets below:

3 (14) 4         7 (23) 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 + right number + 2

Left number x right number + 2

Left number x right number + 4

Left number + right number - 3

Ready for another one, number detective?

Look at the number sets below:

5 (10) 4        10 (13) 2

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 + 4

Left number + right number + 4

Left number + right number + 1

Left number - right number - 2

Look at the number sets below:

10 (3) 4        17 (12) 2

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 + 4

Left number - right number - 3

Left number - right number - 7

Left number + right number + 3

Look at the number sets below:

30 (7) 5        16 (5) 4

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 + right number + 4

Left number - right number - 3

Left number ÷ right number + 1

Left number ÷ right number + 3

Halfway through this activity already, number detective!

Match the number sets below to the rules that make their middle number (the numbers in brackets).

## Column B

5 (13) 7
Left number x right number + 2
35 (9) 5
Left number - right number - 4
6 (26) 4
Left number + right number + 1
30 (25) 1
Left number ÷ right number + 2

Look at the sets of numbers below:

5 (22) 4        3 (20) 6        4 (?) 8

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

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

14

4

34

30

Look at the sets of numbers below:

28 (5) 4        30 (4) 5        27 (?) 3

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

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

83

11

28

7

Look at the sets of numbers below:

20 (13) 5        10 (1) 7        28 (?) 6

The rule here is 'left number - right number - 2'.

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

32

20

24

36

Look at the number sets below:

8 (18) 2        5 (27) 5        6 (?) 4

Your mission is to work out the rule that uses the outside numbers and a 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.

10

24

26

2

Your final mission is to work out the rule for the first two sets of numbers and then use this rule to work out the mystery number.

Type this number as digits below.

5 (14) 6        9 (22) 10        6 (?) 11

17

20

5

66

• Question 1

Hello number detective - I'm glad you're here!

Look at the number sets below:

3 (14) 4         7 (23) 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 + 2
EDDIE SAYS
Hi, there number detective! Did you manage to identify the rule? Let's look at the first set of numbers: 3 (14) 4 How can we make an answer of 14 with the numbers 3, 4 and an extra top secret number? 3 x 4 = 12 and if we add an extra 2 to this we get 14. Let's see if this works for the second set of numbers: 7 (23) 3 7 x 3 = 21 and if we add an extra 2 we get 23! This means that the rule is 'left number x right number + 2'.
• Question 2

Ready for another one, number detective?

Look at the number sets below:

5 (10) 4        10 (13) 2

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 + right number + 1
EDDIE SAYS
Did you try out all of the options here until you found one that worked? The rule here is 'left number + right number + 1'. Let's look at the first number set: 5 (10) 4 5 + 4 = 9 and then add an extra 1 is 10. Here's the second number set: 10 (13) 2 10 + 2 = 12 and then add an extra 1 is 13. Remember: left is this way <-- right is this way --> You may have found a different way to make one of the middle numbers but the rule has to work for both sets of numbers.
• Question 3

Look at the number sets below:

10 (3) 4        17 (12) 2

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 - right number - 3
EDDIE SAYS
Did you spot the rule here? So many options to consider! Let's look at the first set of numbers: 10 (3) 4 The middle number is smaller than one of the outside numbers, so it is quite likely that we are taking away or dividing. 10 - 4 = 6 How can we get to an answer of 3 from here? We take away a top secret number 3! 6 - 3 = 3 Let's see if this works for the second set of numbers: 17 (11) 2 17 - 2 = 15 and if we take away an extra 3 we get 12 (the middle number). This makes the rule 'left number - right number - 3' We've cracked the rule, detective! You have to try out all of the options until you find one that works for both number sets.
• Question 4

Look at the number sets below:

30 (7) 5        16 (5) 4

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 ÷ right number + 1
EDDIE SAYS
The middle numbers here are smaller than one of the outside numbers. This is a clue that we are probably taking away or dividing first. Let's look at the first number set: 30 (7) 5 30 ÷ 5 = 6 and to get from 6 to 7 we + 1. This means the rule could be 'left number ÷ right number + 1' We need to check if this works with the second set. 16 (5) 4 16 ÷ 4 = 4 + an extra 1 to get 5. Woohoo! We've found the rule. It's a good feeling, isn't it?
• Question 5

Halfway through this activity already, number detective!

Match the number sets below to the rules that make their middle number (the numbers in brackets).

## Column B

5 (13) 7
Left number + right number + 1
35 (9) 5
Left number ÷ right number + 2
6 (26) 4
Left number x right number + 2
30 (25) 1
Left number - right number - 4
EDDIE SAYS
Did you find some of the matches here, detective? The trick is to try each rule with each number set until you find one that works. Now your brain is nicely warmed up, it's time for your next challenge...
• Question 6

Look at the sets of numbers below:

5 (22) 4        3 (20) 6        4 (?) 8

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

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

34
EDDIE SAYS
Let's follow the rule 'left number x right number + 2' with the final set of numbers: 4 (?) 8 4 x 8 = 32 and then add the extra 2 = 34 Are you getting the hang of this now? It can be confusing, but are you getting used to the answer to a maths question being in the middle?
• Question 7

Look at the sets of numbers below:

28 (5) 4        30 (4) 5        27 (?) 3

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

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

7
EDDIE SAYS
Did you follow the rule for the final set of numbers? 27 (?) 3 27 ÷ 3 = 9 and if we subtract the secret number 2, we get 7. This makes 7 the correct answer. Did you get this one OK?
• Question 8

Look at the sets of numbers below:

20 (13) 5        10 (1) 7        28 (?) 6

The rule here is 'left number - right number - 2'.

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

20
EDDIE SAYS
Are you getting the hang of following these rules now? 28 (?) 6 28 - 6 = 22 and subtract the extra 2 = 20. It's time to make things a little more challenging...
• Question 9

Look at the number sets below:

8 (18) 2        5 (27) 5        6 (?) 4

Your mission is to work out the rule that uses the outside numbers and a 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.

26
EDDIE SAYS
Did you find the rule here? Let's look at the first set of numbers: 8 (18) 2 How can we make a number close to 18 with 8 and 2? 8 x 2 = 16. How can we get from 16 to 18? If we add the top secret number of 2, we can get from 16 to 18. The rule could be 'left number x right number + 2' We then need to check that this rule works for the next set of numbers: 5 (27) 5 5 x 5 = 25 and then add the extra 2 = 27 Yes! The rule works for both sets. Now we have to use the rule to work out the final number. 6 (?) 4 6 x 4 = 24 and then add an extra 2 to get 26. It's a long process but you can do it! You have all the skills you need.
• Question 10

Your final mission is to work out the rule for the first two sets of numbers and then use this rule to work out the mystery number.

Type this number as digits below.

5 (14) 6        9 (22) 10        6 (?) 11

20
EDDIE SAYS
Did you spot the rule here? Let's look at the first set of numbers: 5 (14) 6 5 + 6 = 11 How can we get from 11 to 14? We add an extra 3. The rule is 'left number + right number + an extra 3' This works for the second set of numbers too which means we are ready to work out the mystery number. 6 (?) 11 6 + 11 = 17 and then add the extra 3 to get 20. This makes 20 the mystery number. Well done for cracking these number puzzles today, detective!
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