Linear number sequences: what children learn
In this game children find the rule for sequences and sort them into groups. Some sequences count back past zero into negative numbers, and some go up in decimals or in steps of 25, so children need to look closely at the difference between each pair of terms.
Supports part of Common Core 5.OA.B.3: generating patterns from a rule. Sequences that cross zero go beyond Grade 5.
Common Core connection: 5.OA.B.3. This is focused practice for part of the standard.
How to play
Sort the cards into the right groups. Tap a card, then its group. You can also drag a card, or press the number on its group. Each game has 3 rounds with no timer. Every card is checked as soon as you place it: a card in the wrong group comes back with a hint, and you get a point for each card you place right first time. For a quicker go, choose Quick quiz: 10 multiple-choice questions in 150 seconds (choose Relaxed for more time).
Step by step
- Find the difference. Work out how much the sequence changes from one number to the next: 5 − 2 = 3, 8 − 5 = 3.
- Going up or down?. If the numbers get bigger the rule is add; if they get smaller the rule is subtract.
- Check every step. The rule must work for every pair, not just the first two.
- Watch for zero. Sequences can cross zero: 7, 4, 1, −2 is still subtract 3.
Worked examples
Example 1: What is the rule for 1, 5, 9, 13, …?
Working: 5 − 1 = 4, 9 − 5 = 4.
Answer: add 4
Example 2: What is the rule for 20, 15, 10, 5, …?
Working: Each number is 5 less.
Answer: subtract 5
Example 3: What is the rule for 2, 2.5, 3, 3.5, …?
Working: 2.5 − 2 = 0.5.
Answer: add 0.5
Common mistakes and how to fix them
- Thinking a sequence that goes below zero has stopped working. Use a number line: from 1, subtract 3 to land on −2.
- Writing the rule as the first number rather than the step. The rule is the change between terms, not where the sequence starts.
- Thinking 2, 2.5, 3 is add 5. Look at the place value: the step is five tenths, which is 0.5.
Activities to try at home
- Count in 25s like coins in a money box: 25, 50, 75, 100.
- Spot sequences in house numbers on one side of a street: 1, 3, 5, 7.
- Take turns making a sequence for the other person to find the rule.
Ideas for the classroom
- Students build sequences with cubes and describe how each step grows.
- Give the 1st and 4th terms and ask students to find the rule.
- Use temperatures that fall below zero to make subtracting sequences.
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 5.OA.B.3: generating patterns from a rule. Sequences that cross zero go beyond Grade 5.
What does linear mean?
Linear means the step is always the same, so the numbers would make a straight line on a graph.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it up, then choose the group it belongs in.