Identify 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.

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 the 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 act as a number detective, hunting down those missing numbers!

Hey number detective, welcome to a new exciting activity!

I need your help with this puzzle.

Look at the two sets of numbers below.

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

5 (35) 7        6 (24) 4

Left number + right number = middle number

Left number x right number = middle number

Left number - right number = middle number

Left number ÷ right number = middle number

Here's another puzzle for you. Look at the two sets of numbers below.

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

7 (10) 3        8 (14) 6

Left number x right number

Right number - left number

Left number + right number

Right number ÷ left number

Look at the two sets of numbers below.

Which rule creates the inside number by using the outside numbers?

4 (5) 20        5 (6) 30

Right number + left number

Left number x right number

Right number ÷ left number

Right number - left number

Are you getting the hang of these yet, detective?

Which rule helps you create the middle numbers here using their outside numbers?

15 (4) 11        20 (11) 9

Left number - right number

Right number - left number

Left number + right number

Left number x right number

Match the sets of numbers below to their rules.

The rules tell us how to make the middle numbers.

Column B

5 (15) 3
Left number x right number
3 (13) 16
Left number + right number
4 (6) 24
Right number - left number
7 (13) 6
Right number ÷ left number

Now we have a mystery number for you to find!

Look at the number sets below:

5 (14) 9      6 (14) 8        7 (?) 10

The rule for the first two sets of numbers is 'left number + right number'.

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

Look at the sets of numbers below.

Work out the rule to make the middle number in the first two number sets.

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

5 (20) 4        7 (21) 3        8 (?) 2

Ready for another one, number detective?

Look at the number sets below.

21 (18) 3        20 (17) 3       34 (?) 2

Work out the rule for the first two sets of numbers and use this rule to work out the mystery number in the final set.

32

36

16

68

Here's another number puzzle for you to solve.

Work out the rule for the first two sets of numbers and use this rule to work out the missing number in the final set.

4 (7) 28        8 (4) 32        3 (?) 27

30

24

9

81

It's time for your final, and most challenging, number puzzle!

Work out the rule that makes the middle numbers using the outside numbers.

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

7 (21) 3        9 (36) 4        10 (?) 11

1.1

21

1

110

• Question 1

Hey number detective, welcome to a new exciting activity!

I need your help with this puzzle.

Look at the two sets of numbers below.

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

5 (35) 7        6 (24) 4

Left number x right number = middle number
EDDIE SAYS
Hey number detective, did you spot the pattern here? Let's look at the first set of numbers: 5 (35) 7 How do the outside numbers (5 and 7) make the inside number (35)? 5 x 7 = 35 so the rule is left number x right number = middle number. We then have to check if this rule works for the second set of numbers. 6 (left number) x 4 (right number) = 24 (middle number). It works! We've found the rule. Excellent detecting skills!
• Question 2

Here's another puzzle for you. Look at the two sets of numbers below.

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

7 (10) 3        8 (14) 6

Left number + right number
EDDIE SAYS
Could you identify the pattern? If we look at the first set of numbers: 7 (10) 3, how do the outside numbers (7 and 3) make the inside number (10)? We add the outside numbers to make the inside number: 7 + 3 = 10 This also works for the second set of numbers: 8 + 6 = 14. Keep those eyes peeled for more pattern spotting.
• Question 3

Look at the two sets of numbers below.

Which rule creates the inside number by using the outside numbers?

4 (5) 20        5 (6) 30

Right number ÷ left number
EDDIE SAYS
Did you spot the rule here? How do the numbers 4 and 20 make an answer of 5? 20 ÷ 4 = 5 So, the rule here is 'right number ÷ left number'. Let's just check that it works for the second set of numbers: 30 ÷ 5 = 6 . It does - terrific work, detective!
• Question 4

Are you getting the hang of these yet, detective?

Which rule helps you create the middle numbers here using their outside numbers?

15 (4) 11        20 (11) 9

Left number - right number
EDDIE SAYS
Did you spot the rule here? To create the number on the inside of the brackets, we need to take the right number away from the left number. 15 (left number) - 11 (right number) = 4 (middle number). This makes the rule: left number - right number. Does it work for the second set of numbers? 20 - 9 = 11 It does!
• Question 5

Match the sets of numbers below to their rules.

The rules tell us how to make the middle numbers.

Column B

5 (15) 3
Left number x right number
3 (13) 16
Right number - left number
4 (6) 24
Right number ÷ left number
7 (13) 6
Left number + right number
EDDIE SAYS
How many matches did you find here, detective? Let's look at each number set: 5 (15) 3 --> Left number x right number: 5 x 3 = 15 3 (13) 16 --> Right number - left number: 16 - 3 = 13 4 (6) 24 --> Right number ÷ left number: 24 ÷ 4 = 6 7 (13) 6 --> Left number + right number: 7 + 6 = 13 It's time to ramp things up for your next mission!
• Question 6

Now we have a mystery number for you to find!

Look at the number sets below:

5 (14) 9      6 (14) 8        7 (?) 10

The rule for the first two sets of numbers is 'left number + right number'.

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

17
seventeen
EDDIE SAYS
If we use the rule 'left number + right number', we can work out the mystery number here. 7 (left number) + 10 (right number) = 17 (mystery middle number). Now it's time for you to work out the rules yourself! I think you're ready!
• Question 7

Look at the sets of numbers below.

Work out the rule to make the middle number in the first two number sets.

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

5 (20) 4        7 (21) 3        8 (?) 2

16
sixteen
EDDIE SAYS
Did you spot the rule here? Let's focus on the first set of numbers to help us figure out the rule. How do the outside numbers (5 and 4) create the inside number (20)? 5 x 4 = 20 The rule here is left number x right number. Let's check if it works for the second set: 7 x 3 = 21...yes it works! Now we know the rule, we have to follow this with the third set of numbers to work out the mystery number: 8 (left number) x 2 (right number) = 16 (mystery number).
• Question 8

Ready for another one, number detective?

Look at the number sets below.

21 (18) 3        20 (17) 3       34 (?) 2

Work out the rule for the first two sets of numbers and use this rule to work out the mystery number in the final set.

32
EDDIE SAYS
How do the numbers on the outside of the brackets create the numbers on the inside of the brackets here? Let's look at the first set of numbers: 21 (18) 3 How do the numbers 21 and 3 create an answer of 18? 21 - 3 = 18. This makes the rule 'left number - right number = middle number'. Can you check if this rule works for the second set of numbers too? Now let's follow this rule for the third set of numbers: 34 - 2 = 32. 32 is our missing number. Are you finding this getting easier with practice?
• Question 9

Here's another number puzzle for you to solve.

Work out the rule for the first two sets of numbers and use this rule to work out the missing number in the final set.

4 (7) 28        8 (4) 32        3 (?) 27

9
EDDIE SAYS
Did you notice that we divide the numbers on the right by the numbers on the left? Remember: right is this way ----> left is this way <---- Let's follow this rule with the final set of numbers: 27 ÷ 3 = 9. This makes 9 the mystery number. Are you ready for the final challenge, number detective?
• Question 10

It's time for your final, and most challenging, number puzzle!

Work out the rule that makes the middle numbers using the outside numbers.

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

7 (21) 3        9 (36) 4        10 (?) 11

110
EDDIE SAYS
Did you work out the rule to make the middle numbers here? We need to times the number on the left by the number on the right. Let's do this with the final set: 10 x 11 = 110. Great number puzzle-solving today, detective! You should now feel confident when asked to identify number rules that use basic operations.
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