2nd Grade algebra · Ages 7–8
Number Machines
Put a number in, the machine does the same thing every time, a new number comes out. That is a function — in Grade 2.
The one idea
A rule is a machine: the same thing happens to every number that goes in.
Ready?
2nd Grade algebra · Number Machines
Put a number in, the machine does the same thing every time, a new number comes out. That is a function — in Grade 2.
Full screen — no distractions
For grown-ups: 2nd Grade algebra
Number machines are how functions start. The big leap this year is running the machine backwards — if 15 came out of a “+ 6” machine, what went in? That is the idea of undoing, and every equation they ever solve depends on it.
This page is the right one if they can already…
- Adds and subtracts within 20 quickly
- Skip-counts by 2s, 5s and 10s
- Finds the missing number in 3 + □ = 7
Not yet? Start at 1st Grade: The Same As — algebra only works one rung at a time.
🏠 Try it at home
In, rule, out
Be the machine. Your child calls out a number; you secretly add 2 and say the answer. Can they guess your rule?
Find the rule
Play “guess my rule” with + and − rules. Whoever guesses in fewest tries wins.
Run the machine backwards
Walk forward 6 steps from a mark, then walk back 6. Where do you end up? Undoing brings you home.
Patterns that grow
Count fingers on hands round the table: 5, 10, 15… How many for 6 people?
The words, in plain English
- Rule
- What happens to every number.
- + 3 is a rule.
- Input
- The number that goes in.
- 4 goes in.
- Output
- The number that comes out.
- 7 comes out.
- Opposite
- The move that undoes another move.
- − 6 undoes + 6.
- Growing pattern
- Gets bigger by the same amount each time.
- 5, 10, 15, 20
🌍 Algebra in an ordinary day
- Every person gets 2 cookies — how many for 4 people?
- Coins: every nickel is 5 cents, so 3 nickels is…
- Working backwards: “I spent 6 and have 9 left. What did I start with?”
🏁 By the end of 2nd Grade
- Finds the output of a + or − machine
- Finds the rule from a table and tests it on every row
- Runs a machine backwards using the opposite operation
- Continues and extends growing patterns
Where this fits
One idea, twelve rungs. The hiding spot just gets cleverer.
Frequently Asked Questions
What algebra should a 2nd Grade child learn?
A rule is a machine: the same thing happens to every number that goes in. By the end of the year they should be able to: finds the output of a + or − machine; finds the rule from a table and tests it on every row; runs a machine backwards using the opposite operation; continues and extends growing patterns.
Isn’t 2nd Grade too early for algebra?
Not the way it is taught here. Algebra is finding a number that is hiding, and at this age the hiding spot is ? — something a child can point at. There are no letters, and the ideas match what 2nd grade maths already covers.
What is the most common 2nd Grade algebra mistake?
Finds a rule from the first row and stops. 2 → 7 could be + 5 — but a child might also guess “add 3 then add 2” or something that only works once. The fix: A rule has to work for every row. Test it on all of them before you trust it.
What if my child is stuck?
Go down one rung. Every lesson here builds on the 1st Grade page, and the “ready for this page if” list at the top tells you exactly what they need first. In practice, a wrong answer gives a hint, and a second wrong answer shows the full worked solution.
Is it free?
Yes. All 4 lessons, the pictures, the worked examples, the balance scale and the practice questions are free with no signup. The practice never runs out — every question is generated fresh and checked.