What Can You Do With...
How Can You Show Me?

Years 1 - 6

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doug@blackdouglas.com.au

Summary

Learning is clearly turned over to the child in this activity. They are given two numbers and asked what they can do with them, with the help of their calculator in the first instance, then using Poly Plug and other material as a follow up. The justification and explanation of what they find out is as important as the exploration itself.

This activity builds on an idea from page 21, Calculators, Children and Mathematics and is suitable for threading.

 

Materials

  • One Poly Plug per pair
  • One calculator per pair

Procedure

One of the strengths of teachers in our network is encouraging children to explore in open ended situations then building on the children's discoveries. When threaded through the curriculum, this activity provides just those opportunities. It also:
  • combines calculator exploration with Poly Plug representation
  • encourages mental arithmetic and number sense
  • encourages recording in symbols and pictures
  • reinforces personal responsibility for learning with the question:
    Can you check it another way?
Children work in pairs. To begin, the teacher writes two numbers on the board and asks:

What can you do with ___ and ___ on the calculator?
 

Content

  • decimal calculations
  • decimal interpretation
  • decimal representation of a fraction
  • negative numbers
  • number line - ordering, operations
  • operations - whole number
  • order of operations
  • pattern generalisation
  • pattern interpretation
  • pattern recognition
  • properties of number
  • recording - calculator
  • recording - written

  • Pairs explore and record for a few minutes. Pairing is to promote discussion but some children may prefer to work alone, or with their own calculator even though they are working in a pair.
  • Share some of the results by asking children to record on the board. For example ask each group to write one of their examples on the board until no more ideas can be added.
Look for opportunities in groups, or with the class, to engage the children's number sense. The following example (Calculators, Children & Mathematics page 21) gives an idea of what might develop using the numbers 1 & 4:
Gus (age 7.5) recorded what he could do in a very systematic way; he wrote:
4 + 1 = 5 1 + 4 = 5
4 x 1 = 4 1 x 4 = 4
4 - 1 = 3 1 - 4 = -3
4 ÷ 1 = 4 1 ÷ 4 = 0·25
Then he said: I think a quarter is 0·25. And he checked it in two ways:
0·25 + 0·25 + 0·25 + 0·25 = 1
0·25 x 4 = 1

Variations & Extensions

  1. Why use single digit numbers just because the children are young? There is a related message in Jacki Healey's comments in Poly Plug Values.
    • I used 2 digits numbers from the beginning. My first example was 36 and 9.

  2. Add to What Can You Do With? by also asking How Can You Show Me? and How Can You Show Me Another Way? These questions lead to variations like:
    • Choose two of your equations and show me with your Poly Plug why they are true. ... Draw how you explained it to me.
    • Same idea but limit the operations, eg: What can you do with ___ and ___ using only the x and ÷ buttons?
    • How can you show me each of these as a number line story?
      (Students are expected to draw their own blank number line to start with, rather than be given one with a prescribed scale. Alternatively the teacher draws a blank line on the child's book and then asks the question.)
    • Some teachers use a playground number line (easily and quickly drawn with chalk) and ask children to demonstrate some of the ones recorded on the board.


Return to Calculating Changes Activities

Calculating Changes ... is a division of ... Mathematics Centre