Addition and subtraction within 20 — for parents

Adding and subtracting within 20 is the central skill of first-grade arithmetic. By the end of the year, most curricula expect a child to do these calculations fluently — without counting on fingers for the simplest ones — and to handle problems that cross over ten.

What "crossing the ten" means

Take 8 + 5. The two numbers do not just sit nicely below ten; the answer (13) jumps over it. Children who only add by counting on fingers can still do this — slowly. The "make-ten" strategy turns it into two easier hops:

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

Once a child sees this trick a few times, mental arithmetic gets dramatically faster.

Why this matters

If a child reaches 2nd grade still counting every sum on fingers, the next steps (adding within 100, then column addition) will feel exhausting. A few months of careful practice with the make-ten and down-to-ten strategies pays off for years.

Things you can do at home

• Talk about everyday additions: "we had 6 strawberries and bought 4 more — how many?"
• Play "what is missing": "I have 11 stickers, I want 15. How many more?"
• Roll two dice, add the numbers. Once that is easy, add three dice — now answers go past 10 naturally.
• Use the bottom row of a number line up to 20 (we have one in the Number line exercise).
• Make a paper pyramid and play Pyramid together. The "pyramid2" level is just right for first-graders.

Common difficulties

• Reverting to counting one-by-one. Encourage starting from the bigger number.
• Always counting on fingers — fine for the first months. Around mid-year, gently nudge toward the make-ten trick.
• Confusing 13 − 8 with 8 − 13. Read the problem aloud as a story to anchor the order.
• Getting tired and making careless mistakes. Short, daily 5-minute sessions beat one long Saturday push.

When to move on

Your child is ready for second-grade arithmetic (working within 100) when they can:

• compute any sum within 20 in under five seconds,
• explain how they got the answer (not just say it),
• solve a small word problem with one operation.

Until then, keep playing — math at this age is best when it tastes like a game.

← Worked examples