How to Teach Addition to Kids: A Stage-by-Stage Guide

Put three toy cars on the table, then two more a little apart. Ask your child, “How many cars are there now?” and let them push the groups together and count. That small moment is addition, and it’s the right place to start today.

The stages below suit ages 4 to 8, roughly preschool to grade 2. Ages are a rough guide only. Some children take a week per stage and others take months, and both are fine.

What order should you teach addition in?

These four ways of adding build on each other, and US school standards (the Common Core) follow the same order: adding with objects in kindergarten, counting on and making ten in grade 1, and sums from memory by the end of grade 2. Each way is quicker than the one before, so let your child keep the old way until the new one feels safe.

You don’t need to name the stages. Watch what your child does, and offer the next way when the current one looks easy.

Before addition: what does your child need first?

Addition rests on counting. Before you add, your child should be able to count a small group, touching each object once, and know that the last number said tells how many there are. If that isn’t steady yet, start with how to teach counting to preschoolers and come back in a few weeks.

Two more things help. One is seeing small amounts at a glance, like knowing three dots is three without counting. Dice and dominoes build this.

The other is the language of putting together: words like “and”, “more”, “altogether” and “in all” used during play. “You have 2 blocks. Here are 3 more. How many altogether?”

These are the words the plus sign will stand for later.

Stage 1: count all (ages 4 to 5)

In this stage your child makes both groups, puts them together and counts everything from 1. For 3 + 2 they count three blocks, two blocks, then all five: “1, 2, 3, 4, 5.”

It’s slow, but it shows the real meaning of addition: two groups joined make one bigger group. Kindergarten standards start here, with addition shown “with objects, fingers, mental images, drawings” and other concrete ways (K.OA.A.1).

Things to use:

• Small toys or snacks. Grapes, buttons, toy animals. Anything your child can move.
• Two plates. One group on each plate, then slide both onto a third plate.
• Fingers. Three on one hand, two on the other, then count all the fingers that are up.

Keep totals to 5 at first, then 10. In kindergarten, US standards have children add within 10 using objects or drawings, and add within 5 fluently by the end of the year (K.OA.A.2 and K.OA.A.5). For more ideas at this age, see these kindergarten math games.

Stage 2: count on (ages 5 to 7)

Counting on means starting at one number and counting forward. For 5 + 3, your child says “five” and then counts three more: “six, seven, eight.” Some children start this late in kindergarten. US standards put it in grade 1, where children relate counting to addition, for example by counting on 2 to add 2 (1.OA.C.5).

To get there, hide the first group. Put five buttons under a cup and say, “There are five under here.” Then add three buttons you can see. The hidden ones can’t be counted, so your child is nudged to start at five.

The next step is starting from the bigger number. For 2 + 7, counting on from 2 takes seven counts. Counting on from 7 takes only two: “eight, nine.” Point out that both ways give 9, and let your child pick the shorter one.

A number line makes counting on visible. Start on the first number and make one hop for each number you add. Your child can see that 5 + 3 is three hops that land on 8.

Try it below: drag the dot, choose how many hops, and tap Hop. Keep the Add button on for now.

Stage 3: how does make 10 help? (ages 6 to 7)

Counting on works well for 5 + 3, but 9 + 5 means counting five more and keeping track. Make 10 is faster. Your child knows that 9 needs 1 more to make 10, so they split 5 into 1 and 4: 9 + 1 = 10, then 10 + 4 = 14.

This rests on knowing the pairs that make 10, like 7 and 3 or 6 and 4, which in turn grow out of the smaller pairs that make 5. If those aren’t quick yet, spend time on them first. Our guide to number bonds explained shows how to teach the pairs with objects and ten frames.

Ten frames show this well. Fill the first frame with 8 counters and put 5 in the second. Move 2 counters across to fill the first frame. Now there’s a full ten and 3 more, so 8 + 5 = 13.

Grade 1 standards list making ten as one strategy for adding within 20 (1.OA.C.6). Start with a 9 or an 8, because they need only 1 or 2 to fill the ten.

Stage 4: how do kids learn addition facts? (ages 6 to 8)

Facts are sums your child knows without working them out, like 4 + 4 = 8. The aim isn’t to skip the earlier stages. A child who understands the stages can always rebuild a fact they forget.

There are 100 facts from 0 + 0 to 9 + 9, but your child doesn’t need to learn 100 separate things:

• Turnarounds. 3 + 8 and 8 + 3 have the same answer. Counting each pair once leaves 55 facts.
• Adding 0 and adding 1. The answer is the same number or the next one, so these come quickly. They cover 36 of the 100 facts.
• Doubles. There are only ten of them up to 10 + 10, and matching fingers on two hands show each one.

Doubles open up near doubles. If your child knows 6 + 6 = 12, then 6 + 7 is one more: 13. Using a fact you know to find one you don’t is called a derived fact.

In a study of 44 children aged 6 to 7, Dowker (2014) found that derived fact strategies, such as using “one more” or swapping the order of a sum, differed greatly in difficulty. Because of that, we suggest introducing them one at a time and showing each one with objects.

US standards expect fluency within 10 in grade 1 and all sums of two one-digit numbers from memory by the end of grade 2 (1.OA.C.6 and 2.OA.B.2).

We suggest short, frequent practice rather than long sessions. A few minutes on most days is plenty: a few sums at dinner, or a quick card game. Stop while it’s still fun. Our list of math games for kids has several that use addition.

How do you move from objects to written sums?

Written sums come after your child can add with objects, not before. Make the switch slowly:

1. Objects and words. “Three cars and two more cars make five cars.”
2. Drawings. Your child draws three circles and two circles, then counts.
3. Numbers under the drawing. Write 3 and 2 under the circles, and 5 under all of them.
4. The full sum. Now write 3 + 2 = 5 and read it as “three and two make five.”

The equals sign needs care. Watch for a child who reads it as “the answer comes next,” and explain that it means “is the same amount as.”

Show it with a balance or two equal towers of blocks: 3 + 2 on one side and 5 on the other. Grade 1 standards ask children to decide if sums like 5 + 2 = 2 + 5 are true or false (1.OA.D.7).

Little stories make the symbols mean something. “Pip has 4 berries and finds 3 more. How many does Pip have now?” Let your child act it out with real objects first.

Vary the story. “Putting together” joins two groups: 2 red apples and 5 green apples make 7 apples. A missing part is harder: Pip had 4 berries and now has 7, so how many did Pip find? US grade 1 standards include each of these story types (1.OA.A.1). Save the missing part until the first two feel easy.

If you’d like a game for this stage, math board games for kids explains how dice and a number track turn counting on into a race.

What are common addition mistakes, and how do you fix them?

• Counting the starting number twice. For 5 + 3 your child says “five, six, seven” and answers 7. They counted the 5 as one of the hops. On the number line, show that you stand on 5 and only count when you land.
• Always counting from 1. It works, so it sticks. Hide the first group under a cup to nudge them toward counting on.
• Starting from the smaller number. For 2 + 9 they count nine more. Line up the two groups and ask which looks bigger. Start there.
• Losing track while counting on. Your child doesn’t know when to stop. Have them raise one finger per count, and stop when the fingers match the number added.
• Guessing. This usually means the step is too big. Go back a stage for a few days, use smaller numbers, and end on a sum your child gets right.

The short version

Teach addition in four steps: count all, count on, make 10, then facts. Use real objects at every new step, and keep sessions short. Move on when the current way looks easy, and go back a step whenever guessing creeps in. Once addition within 20 feels steady, the same ideas carry over to how to teach multiplication, which builds on adding equal groups.

Once hands-on adding feels easy and you want more practice with number sentences, Math Learner is a math practice app for children aged 3 to 10. Its Addition world uses number sentences with four answer choices, and the early levels never need carrying across ten. Each level has eight questions, and a wrong answer shows the right one. The first 15 levels of each world are free, one lesson a day.

It has no ads, no account and no tracking tools. You can download it here and try a level together.