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Change Missing Number Problems into Algebra (1)

In this worksheet, students express missing number problems algebraically.

'Change Missing Number Problems into Algebra (1)' worksheet

Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Express Problems Algebraically

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

When we use algebra, we use letters to stand for numbers that we are trying to find.

Algebra is like a language with its own rules.

 

a stands for a number.

 

a + 2 is 2 more than the number.

a - 7 is 7 less than the number.

5a is 5 times the number. (N.B. We don't use the × sign in algebra because it looks like the letter x.)

a/4 or ¼a is a quarter of the number or the number divided by 4. (N.B. We don't use the ÷ sign in algebra.)

 

 

Example

I think of a number.

I double it and take away 5.

I get 21.

 

Write this using algebra.

Use n for the number I think of.

 

Answer

n is the number I think of.

Double it to get 2n.

Take away 5 to get 2n - 5.

This equals 21.

So we write:

2n - 5 = 21

I think of a number.

I double it and add 5.

I get 21.

 

Write this using algebra.

Use n for the number I think of.

5n + 2 = 21

5n - 2 = 21

2n + 5 = 21

2n - 5 = 21

I think of a number.

I multiply it by 5 and add 2.

I get 22.

 

Write this using algebra.

Use n for the number I think of.

5n + 2 = 22

5n - 2 = 22

2n + 5 = 22

2n - 5 = 22

I think of a number.

I divide it by 5 and add 2.

I get 6.

 

Write this using algebra.

Use n for the number I think of.

5n + 2 = 6

6n + 2 = 5

n/5 + 2 = 6

5n ÷ 6 = 2

I think of a number.

I divide it by 2 and add 2.

I get 12.

 

Write this using algebra.

Use n for the number I think of.

2n + 2 = 12

12n + 2 = 2

n/2 - 2 = 12

½n + 2 = 12

I think of a number.

I treble it and subtract 2.

I get 16.

 

Write this using algebra.

Use n for the number I think of.

16n + 2 = 3

3n + 2 = 16

2n + 16 = 3

3n - 2 = 16

I think of a number.

I multiply it by 5 and subtract 5.

I get 5.

 

Sajid thinks that the answer is  5n x 5 - 5 = 5

 

Is he correct?

Yes

No

This is the equation

 

n/3 - 2 = 7

 

Which of the descriptions below match this equation?

 

I think of a number. I divide it by 3 and subtract 1. I get 7.

I think of a number. I divide it by 3 and subtract 2. I get 7

I think of a number. I divide it by 3 and subtract 2. I get 5.

I think of a number. I divide it by 2 and subtract 2. I get 7

I think of a number.

I divide it by 4 and add 4.

I get 4.

 

4n + 4 = 4

4n + ¼ = 4

n/4 - 4 = 4

¼n + 4 = 4

Here is the answer to the puzzle.

 

n/4 + 12 = 12

 

What was the question?

 

I think of a number. I divide it by 8 and add 12. I get 12.

12n + 4 = 4I think of a number. I divide it by 4 and add 12. I get 11

I think of a number. I divide it by 2 and add 12. I get 12

I think of a number. I divide it by 4 and add 12. I get 12

I think of a number.

I multiply it by 12 and add 12.

I get 12.

 

12n + 12 = n

12n - 12 = n

12n + 12 = 12

12n - 12 = 0

  • Question 1

I think of a number.

I double it and add 5.

I get 21.

 

Write this using algebra.

Use n for the number I think of.

CORRECT ANSWER
2n + 5 = 21
EDDIE SAYS
In algebra, we use n to represent a number when we don't know what its real value is. In this case, we know that a number doubled with 5 added to it = 21. 2n (2 times n or double n) + 5 = 21 Did you follow that? Double n and add 5 to get 21.
  • Question 2

I think of a number.

I multiply it by 5 and add 2.

I get 22.

 

Write this using algebra.

Use n for the number I think of.

CORRECT ANSWER
5n + 2 = 22
EDDIE SAYS
How did you do? Remember n just substitutes a number when we are unsure of its actual value. Five times n (5n) and add 2 to get 22. Are you keeping up with this?
  • Question 3

I think of a number.

I divide it by 5 and add 2.

I get 6.

 

Write this using algebra.

Use n for the number I think of.

CORRECT ANSWER
n/5 + 2 = 6
EDDIE SAYS
We simply need to put n into the sum that we are reading, rather than 'think of a number'. Write out the exact sum with n in place and this gives us n/5 + 2 = 6.
  • Question 4

I think of a number.

I divide it by 2 and add 2.

I get 12.

 

Write this using algebra.

Use n for the number I think of.

CORRECT ANSWER
½n + 2 = 12
EDDIE SAYS
Halve n and add 2 to get 12.
  • Question 5

I think of a number.

I treble it and subtract 2.

I get 16.

 

Write this using algebra.

Use n for the number I think of.

CORRECT ANSWER
3n - 2 = 16
EDDIE SAYS
Multiply n by 3 and subtract 2 to get 16.
  • Question 6

I think of a number.

I multiply it by 5 and subtract 5.

I get 5.

 

Sajid thinks that the answer is  5n x 5 - 5 = 5

 

Is he correct?

CORRECT ANSWER
No
EDDIE SAYS
Sajid is incorrect as he has added one too many 5's into his equation. The correct answer should have been 5n - 5 = 5. Remember 5n means 5 x n, it is just the way that mathematicians write it!
  • Question 7

This is the equation

 

n/3 - 2 = 7

 

Which of the descriptions below match this equation?

 

CORRECT ANSWER
I think of a number. I divide it by 3 and subtract 2. I get 7
EDDIE SAYS
How did you get on with this one? It's just a case of the question flipping around. You have the answer so now you need to work backwards.
  • Question 8

I think of a number.

I divide it by 4 and add 4.

I get 4.

 

CORRECT ANSWER
¼n + 4 = 4
EDDIE SAYS
Find a quarter of n and add 4 to get 4.
  • Question 9

Here is the answer to the puzzle.

 

n/4 + 12 = 12

 

What was the question?

 

CORRECT ANSWER
I think of a number. I divide it by 4 and add 12. I get 12
EDDIE SAYS
Divide n by 4 and add 12 to get 12.
  • Question 10

I think of a number.

I multiply it by 12 and add 12.

I get 12.

 

CORRECT ANSWER
12n + 12 = 12
EDDIE SAYS
12 times n and add 12 to get 12.
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