For parents
2, 5 and 10 times tables: spot the patterns
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Does your child understand equal groups but lose track of times-table facts? Choose one step size: 2, 5 or 10. Each new total comes from adding one more equal group. Explore where the answer comes from before practising recall.
Make a set of dot cards
You need paper and a pencil. Make five cards showing two dots, five showing five dots and five showing ten dots, arranged in two rows of five. Use one set at a time; there is no need to cover all three tables in one sitting. The NCETM resource below explains the role of understanding equal groups before learning times-table facts. The activity here is a suggested home game.
Build four fives, one card at a time
Put down one five-dot card: the total is 5. Add a second to make 10, a third to make 15 and a fourth to make 20. Touch a whole card as you say each total: 5, 10, 15, 20. Four groups of five give 4 × 5 = 20. Identify the number of groups, the number in each group and the total separately. A fifth card would add 5 more, giving 25.
Compare steps of 2, 5 and 10
Two-dot cards give 2, 4, 6, 8, 10. These totals are even: all the dots can be paired. Five-dot cards give 5, 10, 15, 20, 25, ending in 5 or 0. Ten-dot cards give 10, 20, 30, 40, 50, all ending in 0. These patterns concern multiplication by non-negative whole numbers. A final digit alone does not identify the answer: 4 × 5 is 20, not just any number ending in zero.
Connect fives and tens
Lay out four five-dot cards. Place a second five-dot card below each one. Every column now has ten dots, and the total has grown from 20 to 40. For the same number of groups, multiplying by 10 gives twice the result of multiplying by 5: 4 × 10 = 40. Point to the groups to explain why, rather than relying only on an instruction to write a zero.
Play missing stop
Write 5, 10, 15, 20, 25 on five pieces of paper to make a road. Cover 15. Your child finds the missing stop by adding 5 to 10 or subtracting 5 from 20. Shuffle the cards and rebuild the road. Another round can use 2, 4, 6, 8, 10 or 10, 20, 30, 40, 50. Move a paper car along the road and say how many groups it has passed.
Practice with explained answers
3 × 2 = 6: three pairs make six. 5 × 5 = 25: add one more five to four fives, or 20. 4 × 10 = 40: four tens. In 10, 20, __, 40, the missing number is 30 because the step is 10. If 6 × 5 = 30, then 6 × 10 = 60 because each of the six groups doubles in size. Offer one question at a time and reveal its answer after your child tries.
Common mix-ups and a next step
If your child says 4 × 5 = 9, compare adding 4 and 5 with making four groups of five. If counting begins at 0, show that zero means no groups; the first card already gives 5. Skip the timer and finish with an answer your child can explain. A parent can later choose the Multiplication Tables book in Otto Math on iPhone or iPad. The first five routes in each book are free; further routes require Otto Plus.