Addition within 20

Many of the techniques used for addition and subtraction within 20 will be the same as those the children learned for Addition within 10 and Subtraction within 10 - such as "counting on" - and other previous sections. Children should by now be very familiar with adding numbers up to 10 and number bonds up to 10. However, one of the most important skills for mental maths and for much of what comes later will also be learned here - that of adding by grouping or "making 10". We've provided plenty of ways to practise and ideas for making it interesting below. Or scroll down to find our printable resources.

We look at 3 different techniques for adding within 20 here:

1. Adding by counting on
2. Adding by making 10
3. Adding by adding units

Making It Real

• Kitchen fun. Anything edible makes maths fun! Grab a packet of cookies, a container of small sweets or similar and start by placing 8 in front of your child. Count them. Now put 3 more down on the table. Count again. So 8 + 3 makes 11. Try the same thing but this time start with 9 (count) and add a larger number like 7 or 8 (count again). Discuss with your child how slow this counting process can be!

• 10 plus. Using our Numbers to 20 Frames or Numbers to 20 Towers and a stack of counters, fill up the first 10 and then practice adding 1, 2, 3 or more counters to make 11, 12, 13 and so on. Use story language such as "We have 10 counters. Now we add 2 counters. 10 counters plus 2 counters makes 12 counters." Most children will find addition sums starting with 10 relatively easy to grasp at this stage. Our 10 Plus Facts Worksheets and Count on from 10 Worksheets Set 3 below provide printable practice at this skill, and our Teen Facts Addition Poster (with fill-in-the-blank version) can be used for display.

1. Adding By Counting On

Counting on is a useful skill when adding a small number (1, 2, 3 or maybe 4) to a larger number. Many children struggle with counting on, however, because they start by counting the big number rather than counting on to the next. It can be useful, therefore, to start by physically keeping the big number to one side and the smaller number to the other side, as in the ideas below. Once your child becomes familiar with the technique, the separation will no longer be necessary.

• Finger hopping. Put 8 items (manipulatives, sweets etc) on the table, slightly to the left of your child. Now line up 3 of the same items, slightly to the right of your child. Point to the group of 8 and count them. Now, make exaggerated hops with your finger as you count on.

• Use number lines. Start with your finger on the first number and "hop" along counting 1, 2, 3 or 4 to get your answer.
• Which is easier? Is it easier to add 9 + 2 or 2 + 9 using counting on? Try this by finger hopping with a number line. Start with a finger on 9 and then hop along counting 1, 2 to get to the answer. Now start on 2 and hop along counting 1, 2, 3, 4, 5, 6, 7, 8, 9. Try this with 3 + 8 and 8 + 3 and other combinations of numbers.
• Head and fingers. Some children will be able to add 2, 3 or 4 by counting on in their head without extra help. For those who need extra help, show children how to use "head and fingers". What is 9 plus 2? Show the child how to point to their head with their non-dominant hand, saying 9. Now count on 2 using the fingers of the other hand - 10, 11. The answer is 11. What is 9 plus 3? Point to the head - 9 - and count on 3 on the fingers - 10, 11, 12. The answer is 12. Try to do this in a rythm and make a game out of it. For example: 11 plus 2 is 11 (head) 12 (finger) 13 (finger) - with emphasis on the 13! After a while you can suggest that the child "holds" the first number in their head rather than pointing to their head.
• Worksheets. You will find our "Addition by Counting On" and "Addition to 20 Using Number Lines" worksheets in the Resources section below.

2. Adding By Making 10

Counting on and number lines are a good way to get children started on adding bigger numbers, but both have their limitations. Counting on gets tricky when you are adding bigger numbers together, and number lines aren't always available or practical! One strategy to help children add 2 numbers, when the first number is less than 10, is to redistribute the number to "make 10" and then add 10 to the remainder. Adding by making 10 is a really useful skill for much that comes later as well as having many real life uses, so the more practice the children get at this stage, the better.

• Revise. Children who have easy and instant recall of Number Bonds to 10 will have an advantage here, so you might want to revise these by playing Snap Challenge, or going back to look at more ideas for learning these essential maths facts. Also, all the work you did on Counting on from 10 and "looping" skills comes into its own now! You might want to go back and print out some of our worksheets for some quick revision.
• 10+. Children should by now be able to quickly answer any addition sum up to 20 that starts with a 10 - for example, 10 + 5 = 15 or 10 + 7 = 17. If not, now is the time to practice. We have 2 simple worksheets below for extra help.
• Ten frames. Gather 2 Ten Frames - or better still, our Numbers to 20 Frames or Numbers to 20 Towers - and a stack of counters. Put 8 or 9 counters on one frame, and 3 or 4 counters on the other. Now experiment with your child to find different ways of counting the combined counters. You could start by counting on. Now try moving counters from the second frame onto the first to fill it up, or "make 10". Now count the extras and add to 10. Much quicker! Some children will realise that they are using their knowledge of Number Bonds to 10 and will grasp this concept quickly while others will need plenty of hands-on practice, moving counters from one frame to another and re-counting the counters each time.
• Worksheets. You can use our set of Add by Making 10 worksheets to practice this skill, together with a printable of the illustration below, in the Resources section.

We have a printable of this illustration available below.

Watch this method and our worksheets in action as Shelly teachers her son how to add by "making 10".

3. Adding by Adding Units

If one of the 2 numbers to be added is greater than 10, children can make use this third method. This process builds on our Loop 10 and Count Worksheets set 1, so you might want to go back to these for revision first.  It's a very useful skill to practice for mental maths agility later, and also introduces the concept of "tens" and "units" - without specifying them as such - to the children for the first time. The larger number is split into one "ten" and a number units. The units are added together, and that total is added to 10. So, for example:

13 + 5 becomes 10 + 3 + 5 or 10 + 8, or 18.

Use manipulatives to practice this until your child is confident. We also have a printable version of this diagram, and two sets of worksheets using this addition method below.

Our Addition Within 20 Resources

All the resources mentioned above, together with other printables you may find useful when learning addition and subtraction within 20, can be explored by clicking the links below. They are in alphabetical rather than suggested-use order.