All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 11 Lesson 10 Problem-Solving Investigation: Guess, Check and Revise will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 11 Lesson 10 Problem-Solving Investigation: Guess, Check and Revise
Learn the Strategy
Three elk are walking in the mountains. Two of the elk weigh the same amount. The other elk weighs 150 pounds more than the other two. If the total weight of the three elk is 1,650 pounds, how much does each elk weigh?
1. Understand
What facts do you know?
Two elk weigh the same amount. A third elk weighs 150 pounds more than the other two.
The total weight of the three elk is ______________ pounds.
What do you need to find?
the weight of each elk
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
So, two of the elk weigh ______________ pounds. The third elk weighs ______________ + 150, or ______________ pounds.
4. Check
Does your answer make sense? Explain.
Answer:
Given that: The total weight of the three elk is 1,650 pounds. Two of the elk weigh the same amount. The other elk weighs 150 pounds more than the other two.
As the third elk is 150 pounds more than the other two, first we will subtract this extra weight from the total, which will be 1650-150=1500.
After removing the extra weight, all the three elk will be of same weight. Therefore, 1500÷3=500.
First and second elk will weigh 500 pounds each.
Third elk will weigh around 500+150=650 pounds.
Practice the Strategy
Corrinne is making twice as much fruit punch as lemonade. She is making 12 gallons total. How many gallons will be fruit punch and how many will be lemonade?
1. Understand
What facts do you know?
What do you need to find?
2. Plan
3. Solve
4. Check
Does your answer make sense? Explain.
Answer:
1. Understand
What facts do you know?
Corrinne is making twice as much fruit punch as lemonade.
She is making 12 gallons in total.
What do you need to find?
Quantity of fruit punch and lemonade in gallons.
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
4. Check
Corrinne is making twice as much fruit punch as lemonade.
We need to estimate the two numbers such that one number is twice the other and their sum equals to 12.
Let us assume 4 as the first number, 4 times 2 is 8.
So, 4 and 8 can be the two numbers whose sum equals to 12 and one number is twice of the other.
Therefore, it will be 4 gallons of fruit punch and 8 gallons of lemonade.
Apply the Strategy
Guess, check, and revise to solve each problem.
Question 1.
Mathematical PRACTICE Draw a Conclusion Theo lives twice as far from Cassidy as Jarvis. How far do Theo and Jarvis live from Cassidy?
Answer:
1. Understand
What facts do you know?
Theo lives twice as far from Cassidy as Jarvis.
What do you need to find?
How far do Theo and Jarvis live from Cassidy?
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
4. Check
Given that: Theo lives twice as far from Cassidy as Jarvis.
We need to estimate the two numbers such that one number is twice the other and their sum equals to 9.
Let us assume 3 as the first number, 3 times 2 is 6.
So, 3 and 6 are the two numbers, when added gives 9 and one is twice the other.
Therefore, we can estiamte that Jarvis lives 3 miles away from Cassidy and Theo lives 6 miles away.
Question 2.
Jorge and his two brothers each water the plants. Jorge’s watering can holds half as much water as his older brother’s watering can. His younger brother’s watering can holds 8 cups. Altogether, the watering cans hold 2 gallons. How many cups does Jorge’s watering can hold?
Answer:
1. Understand
What facts do you know?
Jorge’s watering can holds half as much water as his older brother’s watering can. His younger brother’s watering can holds 8 cups.
What do you need to find?
How many cups does Jorge’s watering can hold
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
4. Check
1 gallon equals 16 cups.
Watering cans hold 2 gallons of water or 2×16=32 cups of water.
His younger brother’s watering can holds 8 cups.
So, Jorge’s watering can and his older brother’s watering can hold 32-8=24 cups of water.
Jorge’s watering can hold half as much water as his older brother’s watering can.
Let us assume 8 as the first number, 8 times 2 is 16.
So, 8 and 16 can be the two numbers whose sum equals to 24 and one number is twice of the other.
Therefore, Jorge’s watering can hold 8 cups of water.
Question 3.
Mathematical PRACTICE Make Sense of Problems Rhonda filled her aquarium with water. Then, she took out 3 gallons to make room for the gravel and fish. She added 2 quarts back in. Then, she added 4 fish. Each fish was in a separate bag with 1 pint of water. If she has a 20-gallon aquarium, how many pints are in the aquarium now?
Answer:
1. Understand
What facts do you know?
Rhonda filled her aquarium with water. Then, she took out 3 gallons to make room for the gravel and fish. She added 2 quarts back in. Then, she added 4 fish. Each fish was in a separate bag with 1 pint of water.
What do you need to find?
Number of pints in the aquarium now.
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
She has 20-gallon aquarium. Out of 20 gallons, she took out 3 gallons to make room for the gravel and fish.
So, now the aquarium will have 20-3=17 gallons of water in it.
1 gallon equals 8 pints. Therefore, 17 gallons will be equal to 17×8=136 pints of water.
She added 2 quarts in it. 1 quart equals 2 pints. 2 quarts will be equal to 2×2=4 pints of water.
Now, the amount of water in aquarium will be 136+4=140 pints of water.
Then, she added 4 fish. Each fish was in a separate bag with 1 pint of water. 4 fishes will be having 4 pints of water.
Therefore, the number of pints in the aquarium now will be 140+4=144 pints of water.
4. Check
Does your answer make sense? Explain.
Total capacity of aquarium, 20 gallons of water equals 20×8=160 pits.
She removed 3 gallons or 3×8=24 pits of water.
Total water removed will be 24 pits.
She added 2 quarts and 4 fishes, each with 1 pit of water. 2 quarts equals 4 pits of water.
Total water added will be 4+4=8 pits.
Remaning water in aquarium will be 160-24+8=144 pits of water.
Review the Strategies
Use any strategy to solve each problem.
- Guess, check, and revise.
- Find extra or missing information.
- Use logical reasoning.
- Look for a pattern.
Question 4.
The distance from Ian’s home to the museum is 2,640 yards. Is it reasonable to say that Ian’s home is more than 9,000 feet away from the museum? (Hint: 3 feet = 1 yard)
Answer:
Given that: The distance from Ian’s home to the museum is 2,640 yards.
1 yard equals 3 feet.
2,640 yards will be equal to 2640×3=7920 feet.
No, it is not reasonable to say that Ian’s home is more than 9,000 feet away from the museum as 7920 is less than 9000 feet.
Question 5.
Mathematical PRACTICE Use Math Tools One seal weighs 22 pounds. Another seal weighs three times as much. How much do the seals weigh altogether?
Answer:
Given that: One seal weighs 22 pounds. Another seal weighs three times as much.
Weight of another seals = 22×3 = 66 pounds.
Total weight of seals will be 22+66 = 88 pounds.
Question 6.
Mathematical PRACTICE Model Math Mario wants to download 12 songs on his digital music player. He has only 5 minutes to download the songs. If it takes 30 seconds for Mario to download one song, will he have enough time to download all of the songs? Explain.
Answer:
Mario wants to download 12 songs on his digital music player.
Time taken to download one song is 30 seconds.
Therefore, the time taken to download 12 songs will be 12×30 = 360 seconds or 360÷60 = 6 minutes.
As he has only 5 minutes to download the songs, it will be not enough. He will require 6 minutes to download all of the songs.
Question 7.
A stunt person jumps from the roof of a 54-foot building. A skydiver jumps from a plane that is 186 times as high. From what height did the skydiver jump?
Answer:
Given that: A stunt person jumps from the roof of a 54-foot building.
A skydiver jumps from a plane that is 186 times as high.
186 × 54 = 10044 foot.
Thus, the skydiver will jump from 10044 foot height.
McGraw Hill My Math Grade 4 Chapter 11 Lesson 10 My Homework Answer Key
Problem Solving
Guess, check, and revise to solve each problem.
Question 1.
Max was on vacation twice as long as Jared and half as long as Wesley. The boys were on vacation a total of 3 weeks. How many days was each boy on vacation?
Answer:
1)Guess
The boys were on vacation a total of 3 weeks or 3×7=21 days.
Max was on vacation twice as long as Jared and half as long as Wesley.
Let us assume Max’s vacation as V, Wesley’s vacation will be 2V and Jared will be \(\frac{1}{2}\)V days.
Now we need to estimate the value of V such that the sum of V + 2V + \(\frac{1}{2}\)V = 12.
From the above relation, we can say that the value of V should be even, as it needs to be exactly divisible by 2.
It cannot be 2 as it will give very less value. Also it should be less than 8 as double of 8 is 16, 16+8=24.Whereas the sum should be 21.
So, my guess is 4 or 6.
2)Check
Let us check for V as 4, 4+8+2=14
V as 6, 6+12+3 = 21
3)Revise
Max has 6 days of vacation, Wesley’s vacation has twice as of Max, 6×2=12 days and Jerrad has half as of Max 6÷2=3-day vacation.
Question 2.
Anu drinks 2 cups of water each day. Jan drinks twice as much water as Anu. How many fluid ounces does Jan drink?
Answer:
1)Guess
Anu drinks 2 cups of water each day. Jan drinks twice as much water as Anu. Thus, Jan drinks 4 cups of water each day.
2)Check
1 cup equals 8 fluid ounces.
4 cups of water equals 4×8=32 fluid ounces.
3)Revise
Anu drinks 2 cups of water each day, 2 × 8 = 16 fluid ounces.
Jan drinks twice as much water as Anu. Thus, Jan drinks 16 × 2 = 32 fluid ounces of water.
Question 3.
Mathematical PRACTICE Plan Your Solution Casey likes to run. She runs an additional \(\frac{1}{4}\) mile each day. On the last day, she ran 1\(\frac{1}{4}\) miles. If she ran \(\frac{1}{2}\) mile her first day, for how many days has she been running?
Answer:
Casey ran 1\(\frac{1}{4}\) miles or \(\frac{5}{4}\) on the last day.
On first day she ran \(\frac{1}{2}\) or \(\frac{2}{4}\) miles.
On second day, she would have ran \(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)miles.
On third day, she would have ran \(\frac{3}{4}\) + \(\frac{1}{4}\) = \(\frac{4}{4}\)miles.
On fourth day, she would have ran \(\frac{4}{4}\) + \(\frac{1}{4}\) = \(\frac{5}{4}\) or 1\(\frac{1}{4}\) miles.
Question 4.
There are 4 semi-trailer trucks parked in a line at the rest stop. After the first truck, each truck in the line weighs 2 tons more than the truck before it. The trucks weigh a total of 32 tons. How many pounds does .each truck weigh?
Answer:
The total weight of 4 trucks is 32 tons.
Let the weight of first truck be w, then the weight of second truck will be w+2.
Weight of third truck will be w+2+2=w+4
Weight of fourth truck will be w+4+2=w+6
The sequence will be w, w+2, w+4 and w+6.
The sum of the sequence should be 32, as the total weight of trucks is 2 tons.
Check:
5+(5+2)+(5+4)+(5+6)=32
5+7+9+11=32
Thus, the weight of first truck will be 5, second truck will be 7, third truck will be 9 and fourth truck will be 11.