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Game of Circles and Stars |
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This
unit is a modification of a lesson by Marilyn Burns, described in her book Math
by all Means Multiplication Grade 3, Math Solutions Publications, 1991.
During
the lesson children work in pairs. They
need many loose blank sheets of paper, pencils, rulers, and calculators. They also need one die for each pair, and
later some lined paper for writing a report.
1. How the game is played.
There
are two "big figures", circles and squares, and several small figures
such as stars, X's, slashes, and dots. Each child in a pair chooses one big figure
and one small figure, for example, square and X.
A
sheet of paper is divided into two parts (neatly with a ruler) and both
children write their names on the top.
|
MARY |
PETER |
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Then
one child tosses the die and draws as many big figures as the die shows, on
his/her side. (For
example, 4.)
|
MARY |
PETER |
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The
same child tosses the die a second time and draws in each big figure as many small
ones as the die shows. (For example, 3.)
|
MARY |
PETER |
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The
child finds the total number of small figures (the other child checks the
calculation), and writes it next to his/her name.
|
MARY |
PETER 12 |
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Next,
the other child does the same on his/her side, and whoever has the bigger score
wins.
|
MARY |
PETER 12 |
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Mary
wins.
2. After the children get familiar with the game
(after they play it a few times) the whole class should discuss the topic: How to compute the total number of small
figures. The following methods must be
included (Peter's example):
Mental,
(1) Simple counting, 1 2 3 4 5 6 7 8 9 10 11 12.
(2) Skip counting, 3 6 9 12.
With
a calculator,
(3) Skip counting, [3][+][=][=][=][=]
(4) Multiplication, [4][*][3][=]
Children
should be encouraged to use all the methods.
3. After each pair has played at least 6 times,
the teacher asks what numbers were obtained and how, and writes the results on
the blackboard.
(The
numbers are provided by children.)
| Number of small figures: | How it was obtained: |
| 1 | 1*1 |
| 2 | 1*2 2*1 |
| 3 | 1*3 3*1 |
| 4 | 1*4 2*2 4*1 |
| 5 | 1*5 5*1 |
| 6 | 1*6 2*3 3*2 6*1 |
| 8 | 2*4 4*2 |
| 9 | 3*3 |
| 10 | 2*5 5*2 |
| 12 | 2*6 6*2 3*4 4*3 |
| 15 | 3*5 5*3 |
| 16 | 4*4 |
| 18 | 3*6 6*3 |
| 20 | 4*5 5*4 |
| 24 | 4*6 6*4 |
| 30 | 5*6 6*5 |
| 36 | 6*6 |
The
question, "Are some other combinations possible?" should be
discussed.
Also
it may be worthwhile to tally how often each number comes up and see that it is
proportional to the number of combinations in the right column.(6 occurs most
often, roughly four times more often than 1 or 36). Next the children should be
allowed to play again.
4. Finally each pair should be asked to write
two essays titled:
"How to play the Circles and Stars
game" and "How to compute the total number of small figures." At least some
of the essays should be read and discussed in class.
Remarks.
(1) This unit should be spread over several days.
(2) The unit does not attempt to teach children
multiplication facts, so memorization of them should not be encouraged.
(3) The write-ups should be as complete as
possible; children should be asked the questions, "Did you write
everything?" and "What is still missing from your description?"
Lesson Index