Simple formulae: find n: what children learn
In this game children solve equations and match each to the value of n that makes it true, such as 3n = 21 with n = 7. Every equation has one answer, and children can check each match by putting the number back in.
Supports part of Common Core 6.EE.B.7: solving equations such as x + p = q and px = q. Some two-step equations go beyond Grade 6.
Common Core connection: 6.EE.B.7. This is focused practice for part of the standard.
How to play
Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.
Step by step
- Read the letter as a number. 3n means 3 × n. n ÷ 2 means a number divided by 2.
- Undo the operation. To solve n + 9 = 20, undo the + 9 by subtracting 9: n = 11. To solve 3n = 21, undo the × 3 by dividing by 3: n = 7.
- Two steps: undo in reverse. For 2n + 1 = 9, first undo the + 1 (2n = 8), then undo the × 2 (n = 4).
- Check by substituting. Put the answer back in: if n = 4, then 2 × 4 + 1 = 9. It works.
Worked examples
Example 1: Solve n − 4 = 9.
Working: Add 4 to both sides: 9 + 4 = 13.
Answer: n = 13
Example 2: Solve 4n − 3 = 9.
Working: Add 3: 4n = 12. Divide by 4: n = 3.
Answer: n = 3
Example 3: Solve n ÷ 3 = 4.
Working: Multiply by 3: 4 × 3 = 12.
Answer: n = 12
Common mistakes and how to fix them
- Reading 3n as 30-something, such as 3n = 35 meaning n = 5. 3n means 3 × n, not a two-digit number.
- Doing the same operation instead of the opposite, so n + 9 = 20 gives n = 29. Ask what would undo the operation: + is undone by −, × by ÷.
- Undoing steps in the wrong order. Undo the last thing done to n first: for 2n + 1, undo the + 1 before the × 2.
Activities to try at home
- Play 'I'm thinking of a number': 'I double it and add 1 and get 15. What is my number?'
- Write a simple formula for the cost of tickets: cost = 5 × number of people.
- Use a formula to work out cooking times.
Ideas for the classroom
- Use bar models to show equations such as 2n + 1 = 9.
- Students write their own 'think of a number' problems as equations for a partner.
- Use formulae such as perimeter = 2 × (l + w) with real measurements.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
How should I choose this game for my learner?
Supports part of Common Core 6.EE.B.7: solving equations such as x + p = q and px = q. Some two-step equations go beyond Grade 6.
What is the difference between an equation and a formula?
An equation says two things are equal, such as 3n = 21. A formula shows how one amount is worked out from others, such as area = length × width.
Why always n?
Any letter can stand for an unknown number. Using one letter in this game keeps the focus on solving.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it, then pick its partner.