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
|
|