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Skip-counting


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Last updated 26 October 2012 15:30 by NZTecAdmin
Skip-counting (PDF, 40 KB)

Multiplicative Strategies progression, 2nd step

The purpose of the activity

In this activity, the learners develop their understanding of multiplication by skip-counting in twos, threes and fives to solve simple problems. By doing this, they begin to learn the 2, 3 and 5 times tables.

The teaching points

  • Multiplication involves counting groups of a like size to find out how many there are altogether.
  • Multiplication and division are connected. Multiplication names the product of two factors. Division finds a missing factor when the product and the other factor are known.
  • The usual convention is that 4 x 2 refers to four sets of 2 rather than 2 sets of 4, although there is no reason to be rigid about this. The important idea is that the learners can relate the factors in the equation to the problem context.
  • Discuss the ways learners can use skipcounting in everyday situations.

Resources

  • A 10 x 10 grid numbered from 1 to 100.
  • Highlighters.

The guided teaching and learning sequence

1. Ask the learners to work out how many human legs there are in the classroom (for this example, assume there are 14 people in the room).

“There are 14 of us in the room. How many legs are there altogether?”

2. Tell the learners to stand. Ask:

“How can we count legs to solve the problem?”

3. If a learner suggests counting in ones, do that by asking each person in turn to count their legs and then sit down. For example, the first person counts “1, 2” (then sits down), the second person counts “3, 4” (then sits down) and so on to 28.

4. Hopefully someone will suggest counting in twos. Once more, ask the learners to stand and take turns ‘skip-counting’ in twos. For example, the first learner says 2 (then sits down), the second leaner says 4 (then sits down) and so on to 28.

5. Give each learner a 10 x 10 grid and ask them to use a highlighter to shade in the multiples of 2 starting from 2.

6. When they have finished, ask:

“What do you notice about the numbers when you count (or skip-count) in twos?”

  • They all end in 0, 2, 4, 6, or 8 (that is, even numbers).
  • They form columns on the chart.

7. “How could you use this chart to work out 7 lots of 2?” (Use the chart to help keep track of the count of twos)

8. Ask the learners to work in pairs to solve the following problems by skip-counting in twos. Encourage them to use the chart they developed earlier if they have difficulty keeping track of the number of twos they have counted.

  • 3 lots of 2
  • 8 lots of 2
  • 20 lots of 2
  • 33 lots of 2.

The next section of this guided learning sequence repeats the above steps with skip-counts of 5. This could be taken as a separate teaching session.

9. Ask the learners to work out how much money you would need to give everyone in the room $5.

“There are 14 of us in the room. How much money would I need if I were to give you each $5?”

10. Tell the learners to stand. Ask:

“How can we count to solve the problem?”

11. If a learner suggests counting in ones, do that by asking each person in turn to count five and then sit down. For example, the first person counts “1, 2, 3, 4, 5” (then sits down), the second person counts “6, 7, 8, 9, 10” (then sits down) and so on to 70.

12. Hopefully someone will suggest counting in fives. Once more ask the learners to stand and take turns ‘skip-counting’ in fives. For example, the first learner says “5” (then sits down), the second leaner says “10” (then sits down) and so on to 70.

13. Ask the learners to use a different-coloured highlighter to shade in the skip-counts of 5 starting from 5 on the 10 x 10 grid.

14. When they have finished ask:

“What do you notice about the numbers when you count (or skip-count) in fives?”

  • They all end in 5 or 0.
  • They form two columns on the chart.

15. How could you use this chart to help you work out 5 lots of 5. (You could use the chart to help keep track of the count of fives.)

16. Ask the learners to work in pairs to solve the following problems by skip-counting in fives. Encourage them to use the chart if they have difficulty keeping track of the number of fives they have counted.

  • 13 lots of 5
  • 6 lots of 5
  • 20 lots of 5
  • 9 lots of 5.

The final section in this guided learning sequence repeats the above steps with skip-counts of 3. This could be taken as a separate teaching session.

17. Ask the learners to suggest situations where you need to be able to count in threes. Use one of these suggestions as the context for the problems posed. For example, wheels on a tricycle.

18. Pose the problem:

“How many wheels do you need for 14 tricycles?”

19. Tell the learners to stand, ask:

“How can we count to solve the problem?”

20. Given the experience of the twos and fives, you would expect the learners to suggest counting in threes. If someone volunteers counting in ones, ask if they can think of a quicker way of counting.

21. Once more ask the learners to stand and take turns ‘skip-counting’ in threes. For example, the first learner says “3” (then sits down), the second leaner says “6” (then sits down) and so on to 42.

22. Give the learners a third coloured highlighter and ask them to shade in the skip-counts of 3 starting from 3 on the 10 x 10 grid.

23. When they have finished ask:

“What do you notice about the numbers when you skip-count in threes?” (They form diagonals on the chart. Some overlap with the twos or the fives.)

24. How could you use this chart to help you work out nine lots of three. (Use the chart to help keep track of the count of threes.)

25. Ask the learners to work in pairs to solve the following problems by skip-counting in threes. Encourage them to use the chart if they have difficulty keeping track of the number of threes they have counted.

  • 13 lots of 3
  • 7 lots of 3
  • 16 lots of 3
  • 4 lots of 3.

Follow-up activity

Give the learners a blank 10 x 10 grid and ask them to highlight the skip-counts of 4 starting from 4. Ask them to write and solve skip-counts of fours problems, using the chart.

For example:

  • 14 lots of 4 is 56
  • 2 lots of 4 is 8
  • 15 lots of 4 is 60.

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