6th Grade

Elementary School Mathematics

Teaching Plan

Kozo Tsubota, Vice-Principal, University of Tsukuba Elementary SchoolResearchConsidering How to Use Percentage

Theme
1. Teaching Material: Use of Percentages
2. Research ThemeIn this class, we shall think about "probability" as an extension to learning about"percentages".
Concretely, we will think about the probability of picking out two balls from a numberof balls.
Place six white balls and two red balls in a box.
Pick out two balls at the same time from the box. Two red balls result in 1st prize, one
red ball and one white ball result in 2nd prize, and two white balls result in third prize.
Have the children think about the frequencies of these various combinations.
First, the children must figure out the total number of possible scenarios.
The children are expected to think about using listing all the possible cases when
picking out two balls.
For example, they can write a different number on each of the balls, allowing easy
identification of all the ball pairs. Other possible approaches include developing a table
to count the number of matches in the case of a round-robin tournament involving eightteams, or by representing the teams as eight points in a
diagram, linking up all possible pairs of points the possible
pairs of points and then counting the total number of lines.
The goal is to obtain the percentage by thinking about thenumber of a given combination in relation to the total
number of combinations.
In this case, the first prize = 1/28, the second prize is 12/28,
and the third prize is 15/28.
3. Objective
Find ways to think about the number of possible cases.
4. Guidance Plan: Handling of Special 1-Hour Session
5. Implementation of this Class○○○○○○●●○
3 3 3 3 3 2 2○
3 3 3 3 2 2○
3 3 3 2 2○
3 3 2 2
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3 2 2
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2 2●
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(1) Objective: To find ways to count the total number of possible cases and figure out thepercentage of a given case.
(2) Implementation
Learning Activity

Guidance Points

1. Verify that the box contains 8 balls.

① Using the example of a lottery, let the？

children see the balls being placed inthe box.

2.

Thinkaboutball② Have the children think about the casecombinations when 2 balls are picked

when 2 balls are picked out of the box.

out of the box.

Have them think in terms of receiving

White & White

thepossible

White & Red

Red & Redeither the 1st, 2nd, or 3rd prize

○ ●

● ●

depending on the combination of balls○ ○that is picked out.
3. Think about how to figure out thepercentage of each combination.

③ Have the children find ways to thinkabout

thepercentageofeach・Use a tournament table.

combination while remembering what

・Use lines linking the points.

they have already learned.

4. Obtain the various percentages from all
the possible cases.

④ Have the children think about the○○→15÷28×100＝ approx. 54 (%)

percentages○●→

12÷28×100＝approx. 43 (%)

combinations while looking at a table,●●→

1÷28×100＝approx. 3 (%)

etc.

forallthepossible⑤ While actually drawing lots, have the5. Investigate the probability of each casethrough actual experimentation.

children check whether the results
approximate the assumed values.
⑥ Ask the children to comment by

6. Compare the actual experiment resultswith the results calculated based onassumptions.

lookingatexperiment.

theresultsofthe