Shaquila is 57 inches tall. How tall is Shaquila in feet? Should you multiply or divide to solve this problem? Explain. Describe a number of different correct ways to write the answer to the conversion problem. Explain briefly why these different ways of writing the answer mean the same thing. Carlton used identical paper clips to measure the length of a piece of wood. He found that the wood is 35 paper clips long. Next, Carlton measured the length of the wood using identical rods. He found that 2 rods are as long as 5 paper clips. How many rods long is the wood? 2. Explain your reasoning. 3. Suppose that the students in your class want to have a party at which they will serve punch to drink. The punch that the children want to serve is sold in half-gallon containers. If 25 children attend the party and if each drinks 8 fluid ounces of punch, then how many containers of punch will you need? Describe several different ways that students could correctly solve this problem. For each method of solving the problem, explain simply and clearly why the method makes sense.
The Correct Answer and Explanation is:
1. Shaquila’s Height Conversion (Inches to Feet)
- Given: Shaquila is 57 inches tall.
- Question: How tall is she in feet?
Should you multiply or divide?
- Since 1 foot = 12 inches, to convert inches to feet, you divide the number of inches by 12. This is because feet are a larger unit than inches, so to find how many feet fit into 57 inches, divide 57 by 12.
Calculation:
57 inches÷12=4.75 feet57 \text{ inches} \div 12 = 4.75 \text{ feet}
Different correct ways to write the answer:
- 4.75 feet
- 4 feet 9 inches (because 0.75 feet × 12 inches/foot = 9 inches)
- 4 ft 9 in
- 4 and 3/4 feet (since 0.75 = 3/4)
Why do these mean the same thing?
All these expressions represent the same length, just in different formats:
- 4.75 feet is the decimal form.
- 4 feet 9 inches breaks the decimal feet into whole feet and leftover inches.
- 4 and 3/4 feet is the fractional equivalent of the decimal 0.75.
Each is just a different way to express the same measurement.
2. Carlton’s Paper Clips and Rods Problem
- Given: Wood length = 35 paper clips
- Also given: 2 rods = 5 paper clips
Find: Length of wood in rods.
Reasoning:
Since 2 rods = 5 paper clips, then
- 1 rod = 5/2 paper clips = 2.5 paper clips
To find the length of wood in rods, divide the total paper clips by the number of paper clips per rod: Length in rods=35 paper clips2.5 paper clips/rod=14 rods\text{Length in rods} = \frac{35 \text{ paper clips}}{2.5 \text{ paper clips/rod}} = 14 \text{ rods}
3. Punch Containers for Party
- Given:
- Number of children = 25
- Each drinks 8 fluid ounces
- Punch sold in half-gallon containers
- Goal: Find number of containers needed.
Step 1: Total ounces needed
25×8=200 fluid ounces25 \times 8 = 200 \text{ fluid ounces}
Step 2: Convert half-gallon containers to fluid ounces
- 1 gallon = 128 fluid ounces
- Half-gallon = 128 ÷ 2 = 64 fluid ounces
Step 3: Number of containers needed
200 ounces64 ounces/container≈3.125 containers\frac{200 \text{ ounces}}{64 \text{ ounces/container}} \approx 3.125 \text{ containers}
Since you can’t buy a fraction of a container, round up to 4 containers.
Different ways to solve the punch problem:
- Using direct multiplication and division:
- Multiply number of children by ounces per child to get total ounces.
- Divide total ounces by container size in ounces.
- Using unit rates:
- Calculate how many children can be served by one container: 64 ounces8 ounces per child=8 children per container\frac{64 \text{ ounces}}{8 \text{ ounces per child}} = 8 \text{ children per container}
- Divide total children by children per container: 258=3.125⇒4 containers\frac{25}{8} = 3.125 \Rightarrow 4 \text{ containers}
- Using fractions:
- Write ounces per child as fractions and multiply: 25×8=20025 \times 8 = 200
- Express container size as fraction of gallon and convert.
Why do these methods make sense?
- All methods calculate the total quantity needed and then compare it to the container size.
- Different approaches just rearrange or interpret the same numbers, but they all lead to the same conclusion: 4 containers are needed.
Summary of final answers:
- Shaquila is 4 feet 9 inches tall.
- The wood is 14 rods long.
- You need 4 half-gallon containers of punch.
Explanation
When converting Shaquila’s height from inches to feet, you divide by 12 because there are 12 inches in one foot. Dividing shows how many whole feet plus leftover inches she is tall. Expressing 4.75 feet as “4 feet 9 inches” or “4 and 3/4 feet” are just different formats representing the same measurement, using decimals, fractions, or mixed units.
For Carlton’s measurement problem, since 2 rods equal 5 paper clips, one rod equals 2.5 paper clips. To find how many rods make up 35 paper clips, dividing the total paper clips by paper clips per rod gives the length in rods. This approach translates a measurement from one unit to another by understanding the ratio between the two.
The punch container problem is solved by first calculating the total punch needed (number of children × ounces per child), then converting container sizes to ounces. Dividing total ounces by ounces per container yields how many containers are needed. Alternatively, determining how many children each container serves and dividing total children by this number gives the same answer. All methods rely on understanding unit conversions, multiplication, and division.
In all cases, the different ways to approach or write answers emphasize the flexibility of numbers and measurement units. Each method and expression is a valid way to communicate or solve the problem, which is essential for understanding and practical problem-solving in everyday life
