All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 12 Lesson 8 Problem-Solving Investigation: Solve a Simpler Problem will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 12 Lesson 8 Problem-Solving Investigation: Solve a Simpler Problem
Learn the Strategy
Shane rolls a 0-5 number cube and a 5-10 number cube together twenty times. The greatest possible sum is 15. Shane estimates that half of his rolls will have a sum of 15. Is his estimate reaso-nable?
1. Understand
What facts do you know?
the number of times he will roll the number cubes
Shane is estimating that half of the rolls will give a sum of _____________.
Answer:
Shane is estimating that half of the rolls will give a sum of 15.
What do you need to find?
if his estimate is ________________
Answer:
His estimate is reasonable.
2. Plan
I will collect and organize the data in a line plot. Then I will decide if Shane’s estimate is ________________.
Answer:
I will collect and organize the data in a line plot. Then I will decide if Shane’s estimate is reasonable.
3. Solve
Make a line plot. Roll the number cubes together. Record each sum with an X.
Half of 20 rolls are 10 rolls.
Shane only rolled 15 ________________ times.
His estimate was ______________ reasonable.
Answer:
Shane only rolled 15 two times.
His estimate was not reasonable.
4. Check
Does your answer make sense? Explain.
Answer:
Yes,because he only rolled 15 twice.
Practice the Strategy
Julina estimated that she needs to make 100 favors for the family reunion. Is this a reasonable estimate if 62 relatives come on Friday and half that many come on Saturday?
1. Understand
What facts do you know?
Answer:
From the given data, we know that Julina needs to make 100 favors for the family reunion and also about the estimate of relatives coming on friday and saturday.
What do you need to find?
Answer:
We need to find the total number of relatives coming.
2. Plan
Answer:
Determine the total number of relatives coming.Add the relatives coming on friday and saturday and compare that too 100.
3. Solve
Answer:
Count of relatives coming on friday=62
Count of relatives coming on saturday = half the count of friday=62÷2=31
Therefore, the total count of relatives will be = 62+31=93
4. Check
Does your answer make sense? Explain.
Answer:
Total 93 relatives will be attending, 93 is less than 100.So, Julina’s estimation of making 100 favors for the family reunion is resonable.
Apply the Strategy
Solve each problem by first solving a simpler problem.
Question 1.
Mathematical PRACTICE Be Precise Michael received a mixed-up box of T-shirts for the four teams he is coaching. He needs four of each number 1-5. He wrote down each number in a frequency table. Make a line plot to determine if he has enough of each number.
Does Michael have enough of each number? Explain.
Answer:
Michael needs four of each number 1-5. But, he has 4 t-shirts for number 1 and 3 only. He needs 1 more t-shirt of number 2, 2 more t-shirts of number 4 and 1 more t-shirt of number 5.
Question 2.
Aubrey’s class earned a reward for good behavior. The tally chart shows their votes. Put the data in a bar graph to determine if about half of the class voted for read-aloud time.
Is it reasonable to say that half the class voted for read-aloud time?
Answer:
From the above data, the total number of students are 6+3+8+10=27
It is not reasonable to say that half the class voted for read-aloud time,because only 10 students voted for read-aloud time.
Review the Strategies
Use any strategy to solve each problem.
- Solve a simpler problem.
- Determine reasonable answers.
- Make a table.
Question 3.
Draw an example of a tally chart that may have been used to organize the data in the vertical bar graph below.
Answer:
How many people were surveyed for this graph? Explain.
Answer:
From the data above, we can calculate the total number of people surveyed for this graph.
The total number of people who like Tomato salsa flavour are 10.
The total number of people who like Mango salsa flavour are 5.
The total number of people who like Pineapple salsa flavour are 7.
Therefore, the total will be 10+5+7=22
From the above data,
How many fewer people chose mango salsa than pineapple or tomato salsa combined?
Answer:
The total number of people who like pineapple or tomato salsa combined will be 7+10=17
The fewer people who choose mango salsa than pineapple or tomato salsa combined will be 17-5=12
Question 4.
The graph shows the number of people in each car that drove by Niguel’s house. What is the total number of people who drove by?
Answer:
7 cars drove only 1 people.So, the total number of people will be 7×1=7
9 cars drove 2 people.So, the total number of people will be 9×2=18
3 cars drove 3 people.So, the total number of people will be 3×3=9
8 cars drove 4 people.So, the total number of people will be 8×4=32
1 car drove 5 people.So, the total number of people will be 1×5=5
1 car drove 6 people.So, the total number of people will be 1×6=6
The total number of people who drove by Niguel’s house will be the sum of all the above people,
7+18+9+32+5+6=77 people.
How many more cars had either 1 or 2 people rather than 4 people?
Answer:
Number of cars who had either 1 or 2 people will be 7+9=16
Number of cars who had either 4 people will be 8
Therefore, the number of cars who had either 1 or 2 people rather than 4 people will be 16-8=8
Question 5.
Mathematical PRACTICE Reason Is it reasonable to say that about twice as many cars had 1 passenger than 3 passengers? Explain.
Answer:
Yes, that is reasonable to say because the number of cars with 1 passenger is 7 and twice of 3 passengers is 6.
As 7 is greater than 6, the given statement is reasonable.
McGraw Hill My Math Grade 3 Chapter 12 Lesson 8 My Homework Answer Key
Problem Solving
Question 1.
What activity do Jaime’s friends want to do most? Solve a simpler problem first by organizing the data in a tally chart.
Jaime and his friends will _______________.
Answer:
Jaime’s friends like the swim activity than the other two activities.
Solve each problem by first solving a simpler problem.
Question 2.
Elizabeth surveyed her friends. She asked them to name their favorite sport. Is it reasonable to say that Elizabeth surveyed about 30 of her friends? First solve a simpler problem by making a bar graph.
Answer:
The total number of friends Elizabeth surveyed will be 6+4+8+10=28
As 28 is closer to estimate of 30.So, it is reasonable to say that Elizabeth surveyed about 30 of her friends.
Question 3.
Mathematical PRACTICE Make Sense of Problems Look at Exercise 2. What is the simpler problem you solved first?
Answer:
The first simpler problem solved is to find out if the estimate is reasonable.I had to find the actual number of friends Elizabeth survyed.
Question 4.
How many more students chose football and baseball together than basketball? Write an equation.
Answer:
The number of students who chose football and baseball together are 8+4=12
The number of students who chose basketball are 10
Therefore, the number of students chose football and baseball together than basketball will be 12-10=2
Let ‘a’ be the number of students chose football and baseball together than basketball. So, the equation will be 12-10=a=2
Question 5.
Mathematical PRACTICE Model Math Write a problem about the data above that would take two steps to solve. Then solve.
Answer:
Is it reasonable to say that the number of Elizabeth’s friends who like football are twice that of baseball?
From the above data, we know that the number of Elizabeth’s friends who like football are 8.
The number of Elizabeth’s friends who like baseball are 4. As twice of 4 (2×4=8) is 8, the estimate is reasonable.