All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 12 Lesson 4 Problem-Solving Investigation: Make an Organized List will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 12 Lesson 4 Problem-Solving Investigation: Make an Organized List
Learn the Strategy
Sebastian has 0.24 of a dollar. How many different combinations of coins could he have?
1. Understand
What facts do you know?
Sebastian has _______________ of a dollar.
What do you need to find?
the number of possible coin combinations
2. Plan
I will make an organized list to solve the problem.
3. Solve
0.24 of a dollar = 24¢
- 2 dimes, 4 pennies
- 1 dime, 2 nickels, 4 pennies
- 1 dime, 1 nickel, 9 pennies
- 4 nickels, 4 pennies
- 3 nickels, 9 pennies
- 2 nickels, 14 pennies
- 24 pennies
- 1 dime, 14 pennies
- 1 nickel, 19 pennies
There are ______________ different combinations.
4. Check
Does your answer make sense? Explain.
Answer:Â Sebastian has 0.24 of a dollar. There are 9 different combinations of coins he had.
Explanation: As given in the question,
Sebastian has 0.24 of a dollar.
Now, we will find the different combinations of a coins.
So, the value is 0.24 of a dollar = 24¢
2 dimes, 4 pennies = 2 x 10 + 4 x 1 = 20+4 =24
1 dime, 2 nickels, 4 pennies = 1 x 10 + 2 x 5 + 4 x 1 = 10+10+4 = 24
1 dime, 1 nickel, 9 pennies = 1 x 10 + 1 x 5 + 9 x 1 = 10+5+9 = 24
4 nickels, 4 pennies= 4 x 5 + 4 x 1 = 20+4 = 24
3 nickels, 9 pennies = 3 x 5 + 9 x 1 = 15+9 = 24
2 nickels, 14 pennies = 2 x 5 + 14 x 1 = 10+14 = 24
24 pennies= 24 x 1 = 24
1 dime, 14 pennies = 1 x10 + 14x 1 = 10+14 = 24
1 nickel, 19 pennies = 1 x 5 + 19 x 1 = 5+19 = 24.
Hence, the total number of different combinations are 9.
yes, our answer make sense. Because it is right way to calculate.
Practice the Strategy
Brody has three cats. One has a mass of 4,523 grams. One has a mass of 5,012 grams. One has a mass of 4,702 grams. If Brody picks up two of the cats at once, what are the possible total masses that Brody is carrying?
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: If brody picks up two of the cats at once then the total possible masses of brody carrying is 9535 grams, 9225 grams, and 9714
grams.
Explanation: Given that,
Brody has three cats. One has a mass of 4,523 grams.
One has a mass of 5,012 grams.
One has a mass of 4,702 grams.
Brody picks up two of the cats at once.
Now, we will find the total possible masses of brody carrying.
The total possible masses are,
4523 + 5012 =Â 9535 grams.
4523 + 4702 = 9225 grams
5012 + 4702 = 9714 grams.
Hence, the total possible masses of brody carrying is 9535 grams, 9225 grams, and 9714 grams.
Apply the Strategy
Solve each problem by making an organized list.
Question 1.
Mathematical PRACTICE Make a Plan Brianna has 0. 16 of a dollar. How many different combinations of coins could she have?
Answer: Given that,
Brianna has 0.16 of a dollar.
Now, we write the different combinations of coins she had.
The different combinations of coins she had been
1 dime, 1 nickel, 1 penny
3 nickels, 1 penny
1 dime, 6 pennies
2 nickels, 6 pennies
1 nickel, 11 pennies
Question 2.
There were three races at the track meet. The distances were 100 meters long, 800 meters long, and 3,200 meters long. Suppose Lucy ran two of the races. What are the possible total distances that she ran?
Answer: The possible total distance that she ran is 900 meters, 3300 meters and 4000 meters.
Explanation: Given that,
There were three races at the track meet.
The distances were 100 meters long, 800 meters long, and 3,200 meters long.
Now, we will find the possible distance.
The possible distance she ran is 100 and 800 meters long.
The total distance is 100 + 800 = 900 meters.
The another possible distance she ran is 100 and 3200 meters.
The total distance is 100 + 3200 = 3300 meters.
The other distance is 800 and 3200 meters. So, the total distance is 3200+800 = 4000 meters.
Question 3.
Aaron has 3,700 milliliters of lemonade in a pitcher. He has three cups. Their capacities are 320 milliliters, 495 milliliters, and 583 milliliters. Suppose Aaron fills two of the cups. What are the possible capacities of lemonade that he could have left in the pitcher?
Answer: The left of possible capacities of lemonade that he could have in the pitcher is 2885 mL, 2297 mL, 2622 mL.
Explanation: Given that,
Aaron has 3,700 milliliters of lemonade in a pitcher.
He has three cups the capacities are 320 milliliters, 495 milliliters, and 583 milliliters.
If Aaron fills two of the cups.
Now, we will find the left of possible capacities of lemonade that he could have in the pitcher.
The left of the possible capacities are,
3700-(320+495) = 2885
3700-(320+583) = 2297
3700-(495+583) = 2622.
So, the left of possible capacities of lemonade that he could have in the pitcher is 2885, 2297, 2622 mL.
Question 4.
Michael has 0.18 of a dollar. How many possible combinations of coins could he have?
Answer: Michael has 0.18 of a dollar. The possible combinations of coins could he have,
1 dime, 1 nickel, 3 penny = 0.10 + 0.5 + 3 x 0.1 = 0.18
3 nickel, 3 penny = 0.5 x 3 + 3 x 0.1 = 0.15 + 0.3 = 0.18
18 penny = 18 x 0.1 = 0.18
Question 5.
Dean has four pieces of clay to make a clay pot. The masses of the pieces are 10 grams, 15 grams, 20 grams, and 14 grams. If he uses three of the pieces, what are the possible total masses of the clay pot?
Answer: The possible total masses of the clay pot are 45 grams, 39 grams, 44 grams and 49 grams.
Explanation: Given that,
Dean has four pieces of clay to make a clay pot.
The masses of the pieces are 10 grams, 15 grams, 20 grams, and 14 grams.
If he uses three of the pieces, find the possible total masses of the clay pot.
The possible masses of the clay pot is,
10 + 15 + 20 = 45 grams.
10 + 15 + 14 = 39 grams.
10 + 20 + 14 =Â 44 grams
15 + 20 + 14 = 49 grams.
Hence, the possible total masses of the clay pot are 45 grams, 39 grams, 44 grams and 49 grams.
Review the Strategies
Use any strategy to solve each problem.
- Make an organized list.
- Guess, check, and revise.
- Find extra or missing information.
- Use logical reasoning.
Question 6.
There are three trees in the backyard. The second tree is half as tall as the first. The third tree is taller than the second tree and shorter than the first tree. The total height of the trees is 24 feet. What is the height of each tree?
Answer: The height of each tree is 10 ft, 5 ft and 9 ft.
Explanation: Given that,
There are three trees in the backyard. The second tree is half as tall as the first.
The third tree is taller than the second tree and shorter than the first tree.
The total height of the trees is 24 feet.
Now, we will find the height of each tree.
The height of first tree is 10 ft. So, the second tree is half as tall as the first i.e., 5 ft.
So, 10 ft + 5ft = 15ft.
Now, we will find the third tree height.
i.e., 24ft – 15 ft = 9 ft.
So, the height of each tree is 10ft, 5ft, 9 ft.
Question 7.
There are three lines. The first line is 3 times as long as the second. The second line is 4 meters longer than the third. The third line is 2 meters long. How long is the first line?
Answer: 12 meters long is the first line.
Explanation: Given that,
There are three lines. The first line is 3 times as long as the second.
The second line is 4 meters longer than the third. The third line is 2 meters long.
Now, we will find the how long is the first line.
So, the value of first line is 3 times as long as the second.
The value of second line is 4 meters.
Then 4 x 3 = 12 meters.
Hence, the first line long is 12 meters.
Question 8.
Darin has 5 coins that total 62¢. What are the coins?
Answer: Darin has 5 coins the total of this coins is 62¢. The coins are 2 quarter, 1 dime, 2 penny.
The values of quarter, dime, penny is
25, 10, 1
i.e., 2 x 25 + 1 x 10 + 2 x 1 = 50+ 10+2 = 62¢.
Question 9.
Mathematical PRACTICE Model Math Alfonso, Erik, Owen, and Alek are going hiking in pairs. How many different pairs of hiking partners are possible? List them.
Answer: There are 6 different pairs of hiking partners are possible. The pairs are listed below:
Alfonso, Erik
Alfonso, Owen
Alfonso, Alek
Erik, Owen
Erik, Alek
Owen, Alek
McGraw Hill My Math Grade 4 Chapter 12 Lesson 4 My Homework Answer Key
Problem Solving
Solve each problem by making an organized list.
Question 1.
Paul’s bathtub is clogged. He has to empty 30 liters of water by hand. Paul has a 3-liter, a 4-liter, and a 5-liter bucket. If Paul carries two buckets each trip, what combinations of sizes allow him to empty the bathtub in exactly four trips?
Answer: The combinations of sizes allow him to empty the bathtub in exactly four trips is 5 liter bucket with the 3 liter bucket twice, and then use the 3 liter bucket and the 4 liter bucket twice.
Explanation: Given that,
Paul’s bathtub is clogged. He has to empty 30 liters of water by hand.
Paul has a 3-liter, a 4-liter, and a 5-liter bucket. If Paul carries two buckets each trip,
Now, we will find the combinations of sizes allow him to empty the bathtub in exactly four trips.
The combinations are 5 and 3 = 8 liters , 5 and 4 = 9 liters, and 3 and 4 = 7 liters.
So, the values 8 + 7 + 8 + 7 = 30 liters. Using this combination we can empty the bathtub.
Therefore, he can take the 5 liter and 3 liter bucket twice, and then use the 3 liter and 4 liter bucket twice.
Question 2.
Tyra is training for a bicycle race. Each week she rides a total distance greater than 10 kilometers and less than or equal to 30 kilometers. If the distance is always an even number and a multiple of 3, what are the possible distances Tyra rides in one week?
Answer: The possible distances Tyra rides in one week is 12 km, 18km, 24km, or 30 km.
Explanation: Given that,
Tyra is training for a bicycle race.
Each week she rides a total distance greater than 10 kilometers and less than or equal to 30 kilometers.
If the distance is always an even number and a multiple of 3.
Now, we will find the possible distances Tyra rides in one week.
The multiples of 3 in a even number is, 6, 12, 18, 24, 30.
But the distance is greater than 10km and less than equal to 30 km.
So, the values is 12, 18, 24, and 30.
Hence, the possible distances she rides in one week is 12 km, 18km, 24km, or 30 km.
Question 3.
Mathematical PRACTICE Keep Trying Lexi’s bulletin board is 40 centimeters wide. Each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. What combinations of ribbons and photos will fit side by side with no overlap on Lexi’s bulletin board?
Answer: The combinations of ribbons and photos will fit side by side with no overlap on lexi’s bulletin board is 27.
Explanation: As given in the question,
Lexi’s bulletin board is 40 centimeters wide.
Each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide.
Now, we will find the combinations of ribbons and photos will fit side by side with no overlap on Lexi’s bulletin board.
Let see the ways 40 divides in 12 and 4 to get the combinations of ribbons and photos.
(i)The ways are, 7 ribbons and 1 photo.
i,e., 7 x 4 cm + 1 x 12 cm = 28 + 12 = 40. It will arranged as,
8!/(7! x 1!) = 8 x 7! / 7! = 8.
(ii)The second way is, 4 ribbons and 2 photo.
i,e., 4 x 4 cm + 2 x 12 cm = 16 + 24 = 40. It will arranged as,
6!/(4! x 2!) = 6 x 5 x 4! / 4! x 2 x 1 = 15.
(iii)The third way is 1 ribbon and 3 photo.
i,e., 1 x 4 cm + 3 x 12 cm = 4 + 36 = 40. It will arranged as,
4!/(3! x 1!) = 4 x 3! / 3! x 1 = 4.
Hence, the total combinations of ribbons and photos are 8 + 15 + 4 = 27.
Question 4.
Carmen buys a pack of crackers for 75 cents from the vending machine. She puts a $1 -bill in the machine. What combination of coins, excluding pennies, could Carmen get in change?
Answer: The combination of coins excluding pennies, could carmen get in change is 1 quarter,
1 dime, 3 nickel.
2 dime, 1 nickel.
5 nickel.
Explanation: Given that,
Carmen buys a pack of crackers for 75 cents from the vending machine.
She puts a $1 -bill in the machine.
Now, find the combination of coins, excluding pennies, could Carmen get in change.
1 dollar = 100 cents.
So, subtract 100 – 75 = 25 cents.
Now, we will write the combinations of change carmen gets.
Hence, we get the combination of coins excluding pennies, could carmen get in change is 1 quarter, (1 dime, 3 nickel), (2 dime, 1 nickel), 5 nickel.