Adding Within 20 Using Ten Frames

Think of an egg box that holds ten eggs, or a baking tray with ten spots for cookies — two rows of five. With one quick look you can tell it's nearly full, or half empty, without counting every egg. That handy picture has a name in maths: a ten frame, and it makes adding something you can see.

A ten frame is a little grid: two rows of five boxes, which makes ten cells in all. You drop one counter into each cell, and that simple picture turns counting into seeing. At a glance you can tell how many counters are inside and — just as useful — how many empty cells are left. A completely full frame is always 10.

Here is the number 8 shown on a ten frame — eight cells filled, two still empty:

Two empty cells means 8 is just two away from a full ten.

You do not need to count the dots one by one. The top row is already five, so eight is "a full top row and three more" — 5 + 3. The frame is built so your eyes do the adding for you.

A single line of ten dots is hard to read — you would have to count along it every time. Splitting it into five and five gives your eyes an anchor: a full top row is always five, so anything above five you read as "five and a bit". That is why a ten frame is two short rows, not one long one. Five is also how many fingers are on one hand — so the rows match the hands you already count with.

See it: two numbers, two frames

When you add, you can lay each number out on its own ten frame and then read the total. Press Refresh to roll a brand-new sum, and look first at the empty cells in the first frame — those tell you how many counters from the second frame you would slide across to make a ten.

Make a ten, then add the rest

Adding numbers that cross ten — like 8 + 5 — is easier if you first make a ten. Start with 8, then use just enough of the 5 to fill the frame:

8 needs 2 more to make ten, so take 2 from the 5. The first frame is now full, and 3 are left over for a second frame:

The two faded counters are the ones that slid across from the 5 to top up the first frame. A full ten and three more is 13:

8 + 5 = 8 + 2 + 3 = 10 + 3 = 13

That is the whole trick: split the second number so part of it tops up the first number to ten, because adding to a ten and then a few more is quick to see and easy to count.

Two more worked examples

Once you have the idea, every "make a ten" sum follows the same three beats: how far to ten? take that much · fill the frame · count on the leftovers.

9 + 4. Nine has only one empty cell, so it needs just 1 more. Take 1 from the 4, fill the frame, and 3 are left:

9 + 4 = 9 + 1 + 3 = 10 + 3 = 13

7 + 6. Seven needs 3 to reach ten. Take 3 from the 6, which leaves 3:

7 + 6 = 7 + 3 + 3 = 10 + 3 = 13

Notice all three sums landed on 13 — but you never had to cross ten in your head. You only ever made a tidy ten and then added a small leftover.

Two traps to dodge with ten frames:

A full frame is ten, not "lots". Don't recount the full frame dot by dot — count the empty cells instead, because they tell you exactly how many more you need to make ten.
After you make a ten, count on from ten — say "ten… eleven, twelve, thirteen" — don't go back and recount everything from one. The whole point of making a ten is to skip that slow counting.

Imagine a baking tray with ten spots for cookies, arranged two rows of five — that is a ten frame you can eat! a cookie If seven cookies are baked, you can see without counting that three spots are empty — so the tray is three cookies short of full. Snacks, eggs in a box, buttons on a card: any "ten spaces" object is secretly a ten frame, and the empty spaces always whisper how far you are from ten.

If a sum like 9 + 8 fills the first frame and spills a near-full second frame, you have one full ten and seven more — 17. Two completely full frames would be 10 + 10 = 20, which is the most two ten frames can hold. That is exactly why this lesson is "adding within 20": two ten frames have room for twenty counters and not one more.