Adding Within Five

Now we put two groups together.

What we're learning

That joining two groups gives us a bigger group
The plus sign (+) and the equals sign (=)
How to write addition sentences for sums up to 5

Start with objects, not symbols

Before any math symbols come out, we want your child to feel the action of addition.

Get a small handful of pennies (or anything small). Make a pile of 2 on the left. Make a pile of 3 on the right. Ask: "How many altogether?"

Your child will probably push them together and count. That's exactly right. Pushing things together IS what addition means.

Do this several times with different small numbers (1+1, 2+2, 1+3, 2+3, 4+1) before you ever write down a symbol.

Introducing the plus sign

Once they've felt the action a dozen times, you can introduce the symbol.

Write 2 + 3 = 5 on a piece of paper. Read it aloud as you point: "Two plus three equals five."

Then make the situation real: 2 pennies, plus 3 pennies, equals 5 pennies. The symbol on the page is just shorthand for what just happened with the pennies.

The five facts

There are exactly fifteen addition facts that make sums of 5 or less:

0+0  0+1  0+2  0+3  0+4  0+5
     1+1  1+2  1+3  1+4
          2+2  2+3
               3+3

(Plus their commutative twins: 1+0, 2+1, etc.)

These are the building blocks for everything that follows. Most kindergarteners can memorize them within a few weeks of regular practice — if they truly understand what addition means first. Memorizing without understanding is brittle and gets harder later.

Try it together

Roll two dice (or pull two cards 1-5 from a deck). Add them. Let your child use fingers, pennies, or a number line — whatever helps.
Keep a running list of "facts you know cold" on the fridge. Add to it as your child masters them.

Watch for

Counting all instead of counting on: A child computing 4 + 2 by counting "1, 2, 3, 4… 5, 6" is using the count all strategy. A more efficient strategy is count on: start at 4 and say "5, 6." Both get the right answer; counting on is a sign of growth.
Reluctance to use fingers: Some children get told fingers are "for babies." They are not. Fingers are a portable tool. Use them as long as they help.

Where this is going

Once sums to 5 are solid, we extend to sums to 10, then to 20, then to "make a ten" strategies (e.g., 8+5 → 8+2+3 → 10+3 → 13). Each layer reuses what came before.