All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 8 Problem-Solving Investigation: Determine Reasonable Answers will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 8 Problem-Solving Investigation: Determine Reasonable Answers
1. Understand
What facts do you know?
Leandra feeds the rabbit the same amount every 
What do you need to find?
how much food she feeds her rabbit each
2. Plan
Use estimation to find a reasonable answer.
3. Solve.
Round each fraction to the nearest whole number. ‘
In one day, she feeds Bounce about 
cups of food.
So, Leandra feeds Bounce about 2 cups of food each day.
4. Check
Is my answer reasonable?
The estimate of 2 cups is close to the actual amount of 1\(\frac{3}{4}\) cups of food.
Practice the Strategy
Jonas needs to determine how much wood to buy at the store to make picture frames. The dimensions for each picture frame are listed in the table. About how many feet of wood does Jonas need to buy to build 5 frames?
1 Understand
What facts do you know?
Answer: Jonas uses the same amount of wood for each frame.
What do you need to find?
Answer: How much wood is needed to make 5 frames?
2 Plan
Answer: Use estimation to find a reasonable answer.
3 Solve
The above-given:
The top of the frame is 5/8 feet.
The bottom of the frame is 5/8 feet.
The left side of the frame is 3/4 feet.
The right side of the frame is 3/4 feet.
5/8 is pretty close to 1.
3/4 is pretty close to 1.
Therefore, for one frame he needs to buy 1 + 1+ 1 + 1 or 4 feet of wood.
for 5 frames, he needs to buy 4 x 5 = 20 feet of wood.
4. Check
Is my answer reasonable?
answer:
yes, the answer is reasonable.
5 x 1 = 5; 5 x 1 = 5; 5 x 1 = 5; 5 x 1 = 5
5 + 5 + 5 + 5 = 20
Therefore, the answer is reasonable.
Apply the Strategy
Determine a reasonable answer to solve each problem.
Question 1.
Use the table to determine whether 245 pounds, 260 pounds, or 263 pounds is the most reasonable estimate for how much more the ostrich weighs than the flamingo. Explain.
Answer:
The above-given:
The weight of the bird Flamingo = 9 1/10
The weight of the bird Ostrich = 253 1/2
What do we want to find?
We need to find out the number of pounds the ostrich weighs more than the flamingo.
Plan: Use estimation to find a reasonable answer.
Solve:
we can write 9 1/10 as 9
we can write 253 1/2 as 254.
To know the answer, we need to subtract.
Suppose, the answer is x.
x = 254 – 9
x = 245
Therefore, the answer is 245 pounds.
Question 2.
Mathematical PRACTICE 6 Explain to a Friend A grocer sells 12 pounds of apples. Of those, 5\(\frac{3}{4}\) pounds are green and 3\(\frac{1}{4}\) pounds are golden. The rest are red. Which is a more reasonable estimate for how many pounds of red apples the grocer sold: 3 pounds or 5 pounds? Explain.
Answer:
The above-given:
The number of a grocer sells = 12
The number of pounds is green apples = 5 3/4
The number of pounds is golden apples = 3 1/4
The number of pounds is red apples = x
Plan: Use estimation to find a reasonable answer.
Solve:
we can write 5 3/4 as 6. { 3/4 is pretty close to 1. Here we have 5 3/4 = 5 + 1 = 6}
We can write 3 1/4 as 3. { 1/4 is pretty close to 0. Here we have 3 1/4 = 3 + 0 = 3}
Combining both the grocer sold 6 + 3 = 9
That means he sold 6 pounds of green apples and 3 pounds of gold apples.
The remaining = total apples – (number of pounds of green apples and gold apples)
The remaining = 12 – 9
The remaining = 3
Therefore, the rest of the red apples are 3 pounds
Question 3.
A puzzle book costs $4.25. A novel costs $9.70 more than a puzzle book. Which is the most reasonable estimate for the total cost of both items: $14, $16, or $18?
Answer:
The above-given:
The cost of the puzzle book = $4.25
The cost of a novel = $9.70 + novel book
Plan: Use estimation to find a reasonable answer.
Solve:
we can write $4.25 as 4
We can write $9.70 as 10
Here, the novel book is $10 more than the puzzle book.
so, the cost of the novel book is 10 + 4 = $14
Finally, the total cost of both books = 14 + 4 = 18.
Therefore, the answer is $18.
Question 4.
Thirty students from the Netherlands set up a record of 1,500,000 dominoes. Of these, 1,138,101 were toppled by one push. Which is a more reasonable estimate for how many dominoes remained standing after that push: 350,000 or 400,000?
Answer:
The above-given:
The total number of students from the Netherlands is 30
The number of dominoes set up a record = 1,500,000
The number of dominoes was toppled = 1,138,101
Plane: Estimation
Solve:
1138101 can be written as 1,150,000
If we subtract these two values:
1500000 – 1150000 = 350000
The remaining dominoes are 350000 standing after that push.
Review the strategies
Use any strategy to solve each problem.
- Determie reasonable answers.
- Look for a pattern.
- Solve a simpler problem.
- Find an estimate or exact answer.
Question 5.
Use the graph below. Is 21 inches, 24 inches, or 25 inches a more reasonable total amount of rain that fell in May, June, and July?
Answer:
The above-given:
The rainfall in may = 6.2
The rainfall in June = 9
The rainfall in July = 5.9
The total rainfall = x
Plan: Estimation
solve:
we can estimate 6.2 as 6
We can estimate 5.9 as 6
x = 6 + 9 + 6
x = 21
Therefore, the total rainfall in those three months is 21 inches.
Question 6.
Mathematical PRACTICE 5 Use Math Tools Draw the next figure in the pattern.
Answer:
In the first diagram, the arrow represents left
In the second diagram, the arrow represents down.
In the third diagram, the arrow represents the right.
In the fourth diagram, the arrow represents the up.
And, in the next diagram, the arrow represents the left and the process so on…
Question 7.
A high jumper starts the bar at 48 inches and raises the bar \(\frac{1}{2}\) inch after each jump. How high will the bar be after the seventh jump?
Answer:
The above-given:
The number of inches a high jumper starts the bar = 48
The number of inches raises after each jump = 1/2
The number of inches raises after the seventh jump = x
Solve:
we can write up to seven jumps:
48, 48.5, 49, 49.5, 50, 50.5, 51, 51.5
The seventh jump is 51.5
Therefore, the value of the x is 51.5
Question 8.
Ms. Kennedy wants to buy a new interactive whiteboard for her classroom that costs $989. So far, Ms. Kennedy has collected $485 in donations, and $106 in fundraising. About how much more money does she need to buy the interactive whiteboard?
Answer:
The above-given:
The cost of the whiteboard = $989
The amount she collected in donations = $485
The fund she collected = $106
The amount she needed to buy the interactive whiteboard = x
Solve:
add: 485 + 106 = 591
The total amount she has = $591
The remaining amount = cost of the whiteboard – the amount she has
The remaining amount = $989 – $591
The remaining amount = $398.
Therefore, she needs $398 more to buy an interactive whiteboard.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 8 My Homework Answer Key
Problem Solving
Mathematical PRACTICE 3 Check for Reasonableness Determine a reasonable answer to solve each problem.
Question 1.
Alyssa needs 7\(\frac{5}{8}\) inches of ribbon for one project and 4\(\frac{7}{8}\) inches of ribbon for another project. If she has 11 inches of ribbon, will she have enough to complete both projects? Explain.
Answer:
The above-given:
The number of inches of ribbon Alyssa needs for one project = 7 5/8
The number of inches of ribbon Alyssa needs for another project = 4 7/8
We need to find out if she has enough to complete both projects = x
Plan: Estimate
Solve:
We can write 7 5/8 as 8
We can write 4 7/8 as 5
The above-given 11 inches.
Now add: 8 + 5 = 13
For both projects, she needs 13 inches of ribbon but she only has 11 inches.
Therefore, she does not have enough ribbon with her.
Question 2.
Josiah has a piece of wood that measures 10\(\frac{1}{8}\)– feet. He wants to make 5 shelves. If each shelf is 1\(\frac{3}{4}\) feet long, does he have enough to make 5 shelves? Explain.
Answer:
The above-given:
The number of feet Josiah has a piece of wood = 10 1/8
The number of shelves he wants to make is 5
The number of feet long a feet shelf = 1 3/4
Plan: Estimate
Solve:
we can write 10 1/8 as 10
we can write 1 3/4 as 1.
10/5 = 2
Yes, (2 > 1) he has enough wood to make 5 shelves.
Question 3.
After school, Philipe spent 1\(\frac{3}{4}\)– hours at baseball practice, 2\(\frac{1}{4}\) hours on homework, and \(\frac{1}{4}\) hour getting ready for bed. Which is the most reasonable estimate for how long he spent on his activities: 3 hours, 4 hours, or 5 hours? Explain.
Answer:
The above-given:
The number of hours Philipe spent at basketball practice = 1 3/4
The number of hours he spent on homework = 2 1/4
The number of hours he spent on getting ready for bed = 1/4
The total hours he spent on his activities = x
Plan: Estimate
Solve:
we can write 1 3/4 as 2
We can write 2 1/4 as 2
we can write 1/4 as 0.
x = 2 + 2 + 0
x = 4
Therefore, he spent 4 hours on his activities.
Question 4.
Kimani and a friend picked apples. Kimani picked 4\(\frac{2}{3}\) pounds and his friend picked 5\(\frac{5}{6}\) pounds. Which is the most reasonable estimate for how many pounds they picked altogether: 9 pounds, 11 pounds, or 12 pounds?
Answer:
The above-given:
The number of pounds of apples Kimani picked = 4 2/3
The number of pounds of apples his friend picked = 5 5/6
The number of pounds of apples they picked together = x
Plan: Estimate
Solve:
We can write 4 2/3 as 5
We can write 5 5/6 as 5
x = 5 + 6
x = 11
Therefore, they picked 11 pounds of apples.