Addition
Addition puts two amounts together into one: four and three make seven, however you look at it. Once you can count on from either number, you will never count from one again.
The addition tool
Two frames, one total
Tap a square to set each number
0 0 0
Fill both frames to see the total.
How addition works
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Start from the bigger number
Say the larger addend out loud, then count on the smaller one. For 8 + 3, say eight, then count three more: nine, ten, eleven. Starting from the bigger number is the same amount of work as adding 3 + 8, so it takes no longer.
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Keep the starting number as your first count
Eight is already counted before you begin, so the next word you say is nine, not eight. If you say eight again you will land one short: 8 + 3 would come out as ten. Say the starting number once, firmly, and then move on.
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Make ten when the sum crosses ten
For 8 + 5, give two of the five to the eight to complete a ten, leaving three. Now the sum is 10 + 3, which is thirteen. Making ten turns a hard sum into an easy one and is the same idea you will use later when you carry.
Worked examples
7 + 3
Ten. Say seven, then count on three: eight, nine, ten. Both addends are close to ten here, so you can also make ten directly: 7 + 3 fills the frame exactly.
8 + 5
Thirteen. Give two of the five to the eight, making 10, and three are left. So 8 + 5 = 10 + 3 = 13. Eight and five are one apart from ten and three, and the total does not change.
9 + 6
Fifteen. Take one from the six to complete the nine into a ten, leaving five: 10 + 5 = 15. Check by counting on: nine, then ten, eleven, twelve, thirteen, fourteen, fifteen.
Where it goes wrong
- Counting from one every time Counting 1, 2, 3, 4, 5, 6, 7 for 4 + 3 is reliable but slow, and it hides the amount you already know. Count on from the larger addend instead: say four, then five, six, seven.
- Recounting the starting number Counting on from eight as eight, nine, ten for 8 + 3 gives ten instead of eleven, because the starting eight was counted as the first of the three. Eight is already on the table: say it once, then count three more words — nine, ten, eleven.
- Adding the digits and losing a ten When a sum crosses ten it is easy to add the parts separately and lose the ten: 5 + 7 is not 2. Make ten first, 5 + 7 = 10 + 2, and answer twelve.
Questions
Why count on instead of counting everything from one?
Counting everything works, but it carries no information from one sum to the next: 7 + 2 takes as long as 5 + 4. Counting on uses the amount you already know as a starting point, so it is quicker, and it is the same movement along the number line you will use for subtraction.
What is making ten, and why does it matter?
Making ten means splitting one addend so the other reaches exactly ten, then adding what is left: 8 + 5 becomes 8 + 2 + 3, which is 10 + 3, which is thirteen. Ten is the easy landmark in our number system, and this habit is what you will use when you carry tens in column addition.
Why is 4 + 3 the same as 3 + 4?
Both put the same seven things together. Picture two piles of counters and push them into one pile: the total is seven whichever pile you slide across first. Only the order of the addends changed; the amount did not.
Should children still use their fingers for addition?
Fingers are a fine tool for counting on, and they keep the counting physical. The goal is not to ban them but to move past needing them: when making ten and doubles become familiar, 8 + 5 stops being a count and becomes a fact you simply know.
How quick should sums to twenty be before moving on?
A useful marker is about two or three seconds for any sum to twenty, using counting on, doubles or making ten. Nothing has to be instant yet — the point of Level 2 is that the strategy is reliable. Speed follows from using it often, and practice at the right level is where it comes from.