(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.
- 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.
- 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

**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
- 5/8 (24) = 15 boys

3/8 (24) = 9 + 6 = 15 girls - 30 students total
- 5/8 (32) = 20 boys

3/8 (32) = 12 + 6 = 18 girls - 38 students total
- 5/8 (40) = 25 boys

3/8 (40) = 15 + 6 = 21 girls - 46 students total
- 5/8 (48) = 30 boys

3/8 (48) = 18 + 6 = 24 girls - 54 students total
- 5/8 (56) = 35 boys

3/8 (56) = 21 + 6 = 27 girls - 62 students total
- 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
- 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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