Year 4

We can explain each step when we write addition calculations in columns using the expanded method

Year 4 Unit 11a

What we are learning:

• When developing a written column method for addition, children usually begin with an expanded method that allows them to see clearly the steps involved in the process. E.g. 276 + 489
  276
  489 +
  15 (6 + 9)
  150 (70 + 80)
  600 (200 + 400)
  765
  The numbers are added starting from the right (the units column here) and working to the left. This is in preparation for using the compact method of addition.
  In the example above, the stages are written in brackets at the side which may be helpful for your child. As they become more confident with the method this may not be necessary.
• Ensure that children have experience of adding more than two numbers together e.g. 342 + 158 + 417
• Ensure that children have experience of adding numbers with a different number of digits e.g. 542 + 76. This means that they have to think carefully in setting the calculation out to ensure they get the digits in the right columns.

Activities you can do at home:

• Explore the expanded method above together so that your child sees and can explain the steps involved in the process.
  Try with other numbers. 576 + 355, 286 + 547, 476 + 289, 354 + 557, 287 + 615, 315 + 367
  Make sure that your explanation is mathematical. So when adding the tens, say 70 add 80 are 150, not 7 add 8 is 15. Work on examples together.
  Estimate the answer first by rounding the number to the nearest 10 so 576 + 355 would be 580 + 360 which your child will be able to work out mentally so the estimate would be 940 and your child will know that their answer will be near this.
  Ask Will the answer be larger or smaller than 940? Why do you think that? Your child should be able to reason that that answer would will be smaller because both numbers have been rounded up for the estimate.
  When your child is confident adding two three-digit numbers, it should be easy to move to adding two four-digit numbers and mixed numbers.
  Try adding mixed numbers 376+ 85 + 454 + 18. Your child will need to make sure that when adding these vertically they line up the numbers correctly under each other. They should be able to do this on plain paper.
• Model one where you make a mistake and see if your child can spot the error. Tell your child that this is called ‘Spot the mistake’ Try an error where you line up the numbers incorrectly – use the following numbers
  472 + 76 + 18 + 185.
  Ask In what order would it be best to write these numbers vertically?
  Does this make the calculation easier/ harder? Why?

Good questions to ask:

As you are doing this calculation, can you explain how you are doing it?
What tips would you give to someone to help with this method?

If your child:

Gets confused by the expanded method and wants to go straight to a compact method
If the school has asked you to focus on the expanded method persevere with it as it forms the basis of your child’s understanding of the operation. Moving to a compact method is fine when your child is ready, but they are only ready when they can explain what each digit means in the calculation and how the numbers are being added. Children taught the compact method but who do not have this understanding often face difficulties later in maths when work gets more complex and they have little knowledge to fall back on.