Moving Closer
Goals: To help students gauge the order of magnitude of different decimal numbers using concrete representations.
Year level:  Year 5 to 8
Group size: Whole class (in groups of 2-3)
Equipment:  MAB or LAB, 4 trays, a set of cards with decimal numbers written on one side and the letters A to D on the other, a chart like the one below for each group of students
Time: 5-10 minutes (good warm-up activity to have set up when students first come into class)


Activity Instructions:
 
1. Four different decimal numbers are represented by the teacher using the MAB (or LAB, even better) and labelled from A to D. (Use the large MAB block to represent one unit.) On the back of the labels (hidden from sight) write the actual decimal number.

2. Students stand at a distance (about 8m) and look at the blocks briefly. Enter their first estimate of each number and which is largest and smallest on their chart provided.

3. They then move closer (to a point specified by the teacher, about 5m) and write their revised estimates in the next row of the table. This may be repeated once more, moving closer still (to about 1-2m).

4. Students then write their ordering of the sets of blocks from largest to smallest. e.g. A, C, D, B

5. Cards are turned over and actual decimal numbers revealed and recorded, comparing them to the block ordering.
NB. The link between concrete and symbolic representations seems to be developed most strongly when students are asked to say the decimal number in terms of hundredths, tenths etc. For example, 0.45 is 4 tenths and 5 hundredths

6. Collect results and discuss, using both the blocks and the decimal numbers.

Teaching Notes:
Here is a list of numbers that would work well for discussion:

 

A

B

C

D
Game 1

2.0

2.01

0.3

1.99
Game 2

1.089

1.01

0.8

1.8
Game 3

0.578

0.001

0.6

1.0
Game 4

0.002

0.003

0.9

1.0
Game 5

0.56

0.987

1.0

0.1
 
Game 6

1.98

2.0

0.2

0.02

Comments:
As the students have been asked to estimate there are no correct answers, but obvious wrong answers should be commented on. What emerges is that the overall size of the number is determined by the largest blocks to be seen; the smaller blocks are not initially considered. This is the reason that when ordering numbers the columns are compared from left to right.

A pair of students might end up with a page like this:

A

B

C

D

Smallest

Largest

First estimate

5

1

2

2

B

A

Second estimate

5.3

1.3

2.5

2.5

B

A

Third estimate

5.3

1.31

2.63

2.64

B

A

Actual number

5.3

1.308

2.628

2.64

B

A