Number Slider Years K - 6

Summary There is much more to place value and operations that depend on it than tens and ones. Apart from recognising the importance and process of grouping in sets of ten, children must be able to decompose and recompose numbers in ways that suit the problem. Number Slider is a tool that helps children explore the richness of our number system, and operations within it, in a way that encourages the development of 'aha' moments. On the other hand traditional teaching of this topic tends to atomise it into a myriad of 'safe' bits; as a result children often don't have sufficient data to make correct connections between the bits. Suitable for threading. Materials Two Poly Plug sets between 2 - 4 students. Number Slider frame. This is a 2 page document. Print both pages, trim and tape to make the frame as shown. Two red boards should fit neatly on the frame. Notes: We suggest you save this file to your hard drive before printing. Printing from the browser may alter proportions a little. If you use US paper you may have to rescale printing to produce a Slider that fits the plug frame. Acknowledgement Number Slider is a work in progress. It has been placed on the Calculating Changes site through the generosity of Alistair McIntosh, University of Tasmania, who developed the idea within the Mental Computation Project in Tasmania. In the Mental Computation Project the Number Slider is called a Place Value Board. With Alistair's permission the idea is included here for our network to explore. It has been modified from the sheet provided by the Mental Computation Project to allow teachers to use Poly Plug to present it in a more colourful, tactile way.

Please explore the 'device' and its associated ideas with your classes and, in the tradition of this site, feed back anything that could add value to the current information. For example:

• How do you adapt/adopt the idea in your classroom?
• How do the students respond to the material?
• Does the Poly Plug presentation help? If so, can you identify why?
• What learning can you identify as a result of using the Number Slider?
• How do you combine Number Slider with your calculators?

Responses should be directed to: Doug Williams - doug@blackdouglas.com.au

Procedure The following ideas are starting points. Please develop them, thread them into your curriculum, and let us know what learning develops. What numbers are hiding under the plugs? How do you know?

Content addition facts beyond 10 addition facts to 10 complementary addition exploring large numbers group (or skip) counting making/recording groups of 10 operations - whole number place value problem solving subtraction visual and kinaesthetic representation of number

One yellow plug has replaced the two blue plugs above. How were the blue numbers combined to make the yellow number?

One yellow plug has replaced the two blue plugs above. How were the blue numbers combined to make the yellow number?

Now the Number Slider can be used to show big numbers What number is it showing at the moment? What is the biggest number it can show like this? How would you make the Slider show an even bigger number?

What do you add to make this number into 66? Explain how you worked it out. Can you check this answer another way?

What do you subtract to make this number into 37? Explain how you worked it out. Can you check this answer another way?

From the Mental Computation Project

MAKING ONE-DIGIT NUMBERS

1. Make 3. Make 5. Make 8. Make 0.
2. Make 3 with 2 counters. Make 5 with 2 counters. Make 8 with 2 counters.
3. Make 9 with 2 counters in different ways.
4. In how many different ways can you make 4 with 2 counters?

5. Make 30. Make 50. Make 80.
6. Make 30 with 2 counters. Make 50 with 2 counters. Make 80 with 2 counters.
7. Make 90 with 2 counters in different ways.
8. In how many different ways can you make 60 with 2 counters?

9. Make 300. Make 500. Make 800.
10. Make 300 with 2 counters. Make 500 with 2 counters. Make 800 with 2 counters.
11. Make 900 with 2 counters in different ways.
12. In how many different ways can you make 700 with 2 counters?

13. Make 23 with 2 counters. Make 47 with 2 counters. Make 50 with 1 counter ...with 2 counters.
14. Make 35 with 2 counters...with 3 counters.
15. How many ways can you make 42 with 3 counters?
16. What is the least number of counters to represent 3, ...7, ..any l-digit number?
17. What is the least number of counters to represent 25, ...83, ...any 2-digit number?
18. What is the least number of counters to represent 247, ...906, ...any 3-digit number?

19. Make 14 with 2 counters. What would you move to change it into 15? ...18? ...12?
20. Make 47 with 2 counters. What would you move to change it into 67? ...97? ...17?
21. Make 38 with 2 counters. Add 1. Subtract 7. Add 6.
22. Make 38 with 2 counters. Add 20. Add 40. Subtract 30.
23. Make 32 with 2 counters. Add 11. Add 35.

1. A number is represented by not more than 1 counter in any row.
2. You can replace any two counters with an equivalent counter (for example you can replace 3 and 4 with 7, or 20 and 40 with 60).
3. You can replace any two counters with two equivalent counters (for example you can replace 7 and 9 with 10 and 6, or 30 and 40 with 50 and 10).

24. Place one counter to make 8 and one counter to make 6. 'Add' them: that is, use Rules B and C so that the final result satisfies Rule A. Explain what you did.
25. Place two counters to make 32 and two more counters to make 25. 'Add' them: that is, use Rules B and C so that the final result satisfies Rule A. Explain what you did.
26. Place two counters to make 49 and two more counters to make 36. 'Add' them: that is, use Rules B and C so that the final result satisfies Rule A. Explain what you did.
27. Place two counters to make 87 and two more counters to make 54. 'Add' them: that is, use Rules B and C so that the final result satisfies Rule A. Explain what you did.
28. Add 267 and 428. Add 173 and 457. Add 876 and 654. Add 348 and 652.
29. Use the board to help you find pairs of numbers with a sum of 100, ...a sum of 1000.

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