Addition and subtraction within 10 — a parents guide

Adding and taking away within 10 is the first proper mathematical step before school. It is best learned not formally on paper but through real situations with real objects.

Age milestones

Age 4: understands "give me one more" and "put one back". Starts intuitively adding and subtracting tiny numbers (within 3) by manipulating real objects.
Age 5: adds and subtracts up to 5 with concrete objects. Begins to grasp that adding makes more and subtracting makes less.
Age 6: just before school, your child should manage addition and subtraction within 10 with visual support (fingers, blocks). Some easy combinations (1+1, 2+2, 5+5) are usually known by heart.

Three strategies that work

Concrete objects first. Always start with real things — blocks, buttons, apples. Once your child understands the operation, move to pictures and only then to numbers.
Counting on / counting back. For 3 + 2, ask your child to say "three" and then count on by two: "four, five". They don't need to count from one.
Decomposing 5 and 10. Teach number bonds — 5 = 4 + 1, 5 = 3 + 2. These pairs are the building blocks of all later arithmetic.

Everyday situations

In the kitchen: we have 3 apples, I bought 4 more — how many now?
While playing: you built a tower of 6 blocks, then knocked one over — how many are left?
Outside: 2 pigeons sit on the bench, then 1 more flies over — how many?

The "story problem" principle

Children grasp the idea better when the example is told as a short story:

"We had 5 spades, 2 got lost. How many do we have now?"

With formal "5 – 2 = ?" many 5-year-olds still hesitate. With a story, they answer "three" right away.

Common mistakes and how to handle them

Counting themselves twice when counting on. For 3 + 2 they say "1, 2, 3" then "4". Solution: show your child a hand — "three fingers, two more: four, five".
Mixing up + and –. Young children may not yet see the difference between the symbols. Always say what you're doing aloud: "we are adding" or "we are taking away".
Trouble when the answer is 0. "We had 3 and you eat them all" — some children stall here. Explain that zero means "nothing left".

Games that help

Domino with dots — sum the dots on the two ends.
Dice: roll two and add the spots.
Block towers: add and remove storeys.
Online exercises like Adding pictures, Cross out and Addition and subtraction (level "up to 10") are designed for this age.

When to seek professional advice

If, just before starting school, your child still cannot move past 1 + 1 and 2 + 1 even with visual support, it is worth talking to a child psychologist. Sometimes a specific exercise for visual perception or working memory helps a lot.

The most important thing is that math stays a game. Pressure always slows learning down.