What are equations?

What are equations?
We explain what equations are and how children are taught to solve equations in KS1 and KS2, as well as how the topic of algebra is introduced.

What are equations?

An equation is a number sentence where one side equals the other, for example:

In this case, we know that 4 + 4 = 8 and 10 - 2 = 8, so both sides of this equation are equal, which means it is correct.

Equations in KS2 SATs

Children are often given equations with numbers missing in SATs tests, for example this question may be given to a child in Year 4 or 5:

Children need plenty of practice in these, as they need to be aware that the process involves understanding the inverse. For the above equation, a child would need to work out that 90 - 2 is 88. They would then need to think about what they should add to 50 to make 88 (or work out 88 - 50 = 38).

They may also be given equations involving multiplication and division, for example:

They would need to work out 39 + 6 which is 45, then divide 45 by 9 to make 5, which is the number that goes in the gap.

Harder equations may have gaps on both sides, for example:

In this case, there will be more than one answer and various ways of approaching finding an answer.

  • A child could put any number into the second gap, for example: 80 - 70 which would equal 10.
  • They would then need to think about whether they could multiply 4 by any number to make 10.
  • Once they realised this was not possible they would need to find a number to take away from 80 that would produce a multiple of 4.
  • So they could do 80 - 60 which equals 20, then work out that 20 divided by 4 is 5 and therefore put 5 in the other gap.

Some teachers will encourage children to see how many different possibilities they can find to complete the above equation, which helps to develop children's investigative skills in maths.

Algebra in KS2

Often SATs papers from Year 4 onwards will include questions that introduce children to the beginnings of algebra, for example:

  • In this case, a child would need to work out the left hand side of the equation, which is 40.
  • They would then need to work out that to find the value of the triangles, they would need to calculate 40 minus the star, which is 20, so the value of the two triangles together is 20.
  • Since half of 20 is 10, the value of the triangle is 10.

Under the new curriculum, children in Year 6 learn algebra. They will be required to work out equations such as the following:

Very similar to the equations with gaps above, they would need to work out 6 x 3 = 18 and then take 8 away from 18 to find y, which equals 10.

These equations may then get harder:

In algebra, when a number is placed next to a letter this means the letter and number need to be multiplied. Therefore to calculate 8y a child would need to work out 8 x 10 = 80. Then they would need to take 5 away from 80 to make 75, therefore b is 75.

More able Year 6 children may start to do more complicated algebraic equations, such as the following:

  • In this case, they would need to work out the value of the left-hand side of the equation first: 9 x 5 + 6 which equals 51.
  • They would then need to remember that the right-hand side of the equation also has to equal 51, so they would know that 4b is 51 + 5, which equals 56.
  • They would then need to divide 56 by 4 to find b, which is 14.

It is always a good idea to write the answers into the equation and work it out again to check you are correct:

An important rule of algebra is that when you see a multiplication in an equation along with an addition or subtraction, the multiplication must be done first, so this number sentence:

would equal 17, not 26, because the 4 x 2 is done first, then the 9 is added.

If you are required to carry out an addition or subtraction first, this will be put in brackets, so for the above number sentence, if we are required to work out 9 + 4 first, these would be put in brackets, then the 2 would be put next to them at the beginning, to show that we needed to find two lots of 9 + 4:

The rules about the order in which to complete calculations are taught as BODMAS (Brackers, Other / Indices, Division, Multiplication, Addition and Subtraction).