Students in the Class
(Source: Mathematics Teaching in the Middle School)
Five-eighths of the students
in a class are boys. After six girls join the class, the number
of boys and girls in the class is the same. How many students
are in the class now?
What do you know?
5/8 of total is boys
6 girls join
NOW, # boys = # girls
What do you need to know?
# of students in class now
How should you solve this
problem? Use the 4-Step Plan for Problem Solving.
- Explore: What do you know? What do you want
to find out?
- If you know 5/8 of the students
are boys, you should also know that 3/8 of the students are girls.
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- Since we are trying to find
out the number of students in the class now, wouldn't it be feasible
to say that a normal class size is between 20 and 35 (depending
on the location and demographics of the school)...I think so.
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- By listing the multiples
of 8 (this is a good problem to use when discussing the least
common denominator or least common multiple), one can begin the
process of elimination. 8: 8, 16, 24, 32, 40, 48, 56, 64, 72,
80, 88, 96, 104, 112,120
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- Plan: Estimate your answer. Make a list
of data that pertains to the problem and see if it would be reasonable.
If the problem does not make sense, try to solve a simpler problem...or
try solving it in another way!!!
- 5/8 (8) = 5 boys
- 3/8 (8) = 3 + 6 = 9 girls
- 14 students total
-
- 5/8 (16) = 10 boys
3/8 (16) = 6 + 6 = 12 girls
- 22 students total
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- 5/8 (24) = 15 boys
3/8 (24) = 9 + 6 = 15 girls
- 30 students total
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- 5/8 (32) = 20 boys
3/8 (32) = 12 + 6 = 18 girls
- 38 students total
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- 5/8 (40) = 25 boys
3/8 (40) = 15 + 6 = 21 girls
- 46 students total
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- 5/8 (48) = 30 boys
3/8 (48) = 18 + 6 = 24 girls
- 54 students total
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- 5/8 (56) = 35 boys
3/8 (56) = 21 + 6 = 27 girls
- 62 students total
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- 5/8 (64) = 40
3/8 (64) = 24 + 6 = 30
- 70 students total
- Solve: SOLVE the problem.
- 5/8 (24) = 15 boys
3/8 (24) = 9 + 6 = 15 girls
- 30 students total
- Examine: How does your plan relate to your
solved problem? Is it reasonable? Do you need to make corrections?
- Because the problem asked
for the total number of students in the class now after these
6 girls joined the class, AND the fact that the total number
of boys equaled the total number of girls, one can see from the
list of data that the only REASONABLE answer would be:
-
- 24 students started out in
the class
- there were 15 boys and 9
girls
- 6 girls joined the group,
making the total girls increase to 15
- the total number of boys
never changed
- the new group total is now
30 students...with 15 boys and 15 girls
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- No other numbers could work
for this problem because as the the total number of girls increased
by 3 and the total number of students increased by 8, the difference
between the total boys and total girls was -4, -2, 0, 2, 4, 6,
8, 10, 12, ..., respectively. Only when the difference is 0,
does the equation fit the problem.
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