Number Patterns Game

Number patterns are lists of numbers that follow a rule, and spotting that rule is one of the first real pieces of reasoning in school math. This game shows five numbers in a row and asks what comes next. It starts with counting on by ones for kindergarten and works up to doubling, halving and square numbers by Grade 5, so the same page grows with a child, and it works just as well as a few minutes of math patterns practice at the start of a lesson.

How to Play Number Patterns

Press Start. Each question shows five numbers that follow one rule, with a question mark where the sixth belongs. Tap the number that comes next from the four choices, or press 1, 2, 3 or 4 on a keyboard. There is nothing else to press: the answer is checked the moment you choose it.

Right or wrong, the game then shows the working, such as 47 + 1 = 48, and names the rule, such as Add 1 each time, so every question teaches something. The next question follows by itself. A round is 15 questions, and there is no clock: this is a game for thinking, not a race.

Choosing a Grade and a Difficulty

Pick a grade from K to 5. Each grade follows what the US Common Core standards expect at that grade, and the line under the buttons says what it practices:

• Kindergarten: Count on by 1s to 100, and count by 10s. (K.CC.A.1, K.CC.A.2)
• Grade 1: Count on by 1s and 10s to 120, and count back by 1s and 10s. (1.NBT.A.1, 1.NBT.C.5)
• Grade 2: Skip count by 2s, 5s and 10s within 100, and by 100s to 1000. (2.NBT.A.2)
• Grade 3: Add or take away the same number each time: 3 to 9, then 25s and 50s. (3.OA.D.9)
• Grade 4: Follow a rule: add or take away, double, triple, halve, growing gaps. (4.OA.C.5)
• Grade 5: Rules that add, take away, multiply or divide, growing gaps and square numbers. (5.OA.B.3)

Then pick a difficulty. Harder levels bring new kinds of rules, not bigger numbers, so the reasoning gets harder while the arithmetic stays comfortable. Easy counts forward from friendly numbers, such as counting in fives from 15. Medium adds counting back, starting anywhere and bigger steps. Hard adds the rest of the grade, such as tripling and halving at Grade 4, or growing gaps and square numbers at Grade 5. Numbers stay within 100 up to Grade 2 and within 300 after that, apart from counting by 100s in Grade 2, which is exactly what that grade practices. Every game starts on Easy so the first round feels like a win.

Tips for Spotting the Rule

Start with the gap between the first two numbers, then check it against the next pair. If the gap stays the same, the rule adds or takes away that amount, and the next number is one more gap along.

If the numbers climb faster and faster, the gap is growing. Check whether each number is double the one before, or whether the gap itself goes up by the same amount each time, as in 3, 5, 8, 12, where the gaps are 2, 3 and 4.

When the numbers go down, say the rule as taking away rather than adding. Children often spot a falling pattern and then add the gap out of habit, which is the most common wrong answer in this game.

Why Number Patterns Help

Counting in 2s, 5s and 10s is the times tables before anyone calls them that, and a child who can see the pattern in 7, 14, 21, 28 already knows most of the seven times table. For more practice on the same idea, our times tables game turns those patterns into quick facts.

Finding a rule and using it to predict the next number is also early algebra. It is why Common Core asks third graders to explain patterns and fourth graders to follow a given rule, long before they meet letters standing for numbers.

For practice away from a screen, the number patterns worksheet has missing numbers to fill in and rules to find, with an answer key.

Younger children who are still learning to count in steps can start with the skip counting worksheet, which counts by 2s, 5s and 10s along a number line.

Questions Parents and Teachers Ask