McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 Answer Key Problem-Solving Investigation: Use Logical Reasoning

All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 8 Solve Two-Step Word Problems will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 9 Problem-Solving Investigation: Use Logical Reasoning

Learn the Strategy

Sara, Barb, and Erin each wrote a different expression. The expressions were 3 + 5 × 2, (3 + 5) × 2, and 3 × 5 + 2. The value of Barb’s expression is 13. The value of Erin’s expression is an even number. Which expression did each person write?
1. Understand
What facts do you know?
The value of Barb’s expression is ____________.
The value of Erin’s expression is an ______________ number.
What do you need to find?
which expression each person wrote

2. Plan
I will use logical reasoning to solve the problem.

3. Solve
Find the value of each expression.
McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 Answer Key Problem-Solving Investigation Use Logical Reasoning 1

4. Check
Does your answer make sense? Explain.
Answer: Yes, The answer is reasonable.

Explanation:
Given, 3 + 5 × 2 = 13,
This is Barb’s expression.
( 3 + 5 ) × 2 = 16,
16 is an even number So, This is Erin’s expression
3 × 5 + 2 = 17.

Practice the Strategy

Caleb, This, Joyce, and Lawanda each have one of four pets. This does not have a dog or a fish. Joyce does not have a bird or a fish. Caleb has a cat. What pet does each person have?
McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 Answer Key Problem-Solving Investigation Use Logical Reasoning 2
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: Caleb has a cat.
This has a bird,
Joyce has a dog,
Lawanda has a fish.

Explanation:
Caleb, This, Joyce, and Lawanda each have one of four pets.
This does not have a dog or a fish.
Joyce does not have a bird or a fish. Caleb has a cat.
Here, Caleb has a cat.
This does not have a dog or a fish. means she has a bird
Joyce does not have a bird or a fish. means she has a dog
Finally Lawanda owns a fish as a pet.

Check ,
Caleb has a cat.
This has a bird,
Joyce has a dog,
Lawanda has a fish.
All of them have each pet .
So, yes answer is reasonable.

Apply the Strategy

Solve each problem by using logical reasoning.

Question 1.
Marilee places her language book next to her science book. Her math book is next to her reading book, which is next to her language book. What is one possible order?
Answer: The possible order is math book, reading book, language book , science book.

Explanation:
Given, Marilee places her language book next to her science book.
Her math book is next to her reading book, which is next to her language book.
Use logical thinking,
Here, the fixed book place is for science book,
The order goes as follows,
Math book next to the reading book next to the language book next to the science book,
That means, math book, reading book, language book , science book.
So, The possible order is math book, reading book, language book , science book.

Question 2.
Mathematical PRACTICE Reason Three friends will put their money together to buy a game that costs $5. Dexter has 5 quarters and 6 dimes. Belle has 6 quarters and 8 dimes. Emmett has 5 coins. If they have 10
Answer: Yes, the answer is reasonable

Explanation:
Given, Three friends will put their money together to buy a game that costs $5.
Dexter has 5 quarters and 6 dimes.
Belle has 6 quarters and 8 dimes. Emmett has 5 coins.
Here, one dime is equals to 10 cents
Dexter had $1 , Belle had $2 ,and Emmett has $3
Altogether they had $5 to purchased the game.
So, the answer is reasonable.

Question 3.
Rod is less than 17 years old. The sum of the two digits in his age is even and greater than 4, but both digits are odd. How old is Rod?
Answer: Rod is 15 years old

Explanation:
Given, Rod is less than 17 years old.
The sum of the two digits in his age is even and greater than 4, but both digits are odd.
let the digits be 1 and 5
Because, both are odd numbers ,
Their sum is 1 + 5 = 6
And 15 is less than 17
So, Rod is 15 years old

Question 4.
Jan is 3 inches taller than Dan. Ellie is 2 inches taller than Jan. If Ellie is 54 inches tall, how tall are Jan and Dan?
McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 Answer Key Problem-Solving Investigation Use Logical Reasoning 3
Answer: Jan is 52 inches and Dan is 49 inches tall.

Explanation:
Given, Jan is 3 inches taller than Dan.
Ellie is 2 inches taller than Jan.
If Ellie is 54 inches tall,
Then, Jan will be 54 – 2 = 52 inches
Then Dan will be  52 – 3 = 49 inches tall
So, Jan is 52 inches and Dan is 49 inches tall.

Review the Strategies

Use any strategy to solve each problem.

  • Determine extra or missing information.
  • Make a table.
  • Look for a pattern.
  • Use models.

Question 5.
Mathematical PRACTICE Plan a Solution Hailey planted 30 tomato seeds. Three out of every 5 seeds grew into tomato plants. How many tomato plants does Hailey have?
Answer: Hailey have 18 tomato plants

Explanation:
Given, Hailey planted 30 tomato seeds.
Three out of every 5 seeds grew into tomato plants.
Let us make an row of seeds each having 5 seed
Like wise 6 rows are there for a total of 30 seeds
Here from every 5 seeds 3 seeds are grown, making for the 6 rows as 6 × 3 = 18
So, Hailey have 18 tomato plants.

Question 6.
There are 11 scouts in a troop. Their van has 4 rows of seats, and each row holds 3 scouts. How many scouts can the van hold?
Answer: The van can hold 12 scouts.

Explanation:
Given, There are 11 scouts in a troop.
Their van has 4 rows of seats, and each row holds 3 scouts.
then it will be, 4 × 3 = 12.
So, The van can hold 12 scouts.

Question 7.
Mathematical PRACTICE Use Number Sense The amusement park sold ride tickets in packs of 5, 10, 15, and 20 tickets. What would a packet of 5 tickets cost if 20 tickets cost $4?
Answer: a packet of 5 tickets cost $1

Explanation:
Given, The amusement park sold ride tickets in packs of 5, 10, 15, and 20 tickets.
a packet of 5 tickets cost if 20 tickets cost $4
Then it will be, a packet of 5 tickets cost $1.
So, a packet of 5 tickets cost $1.

Question 8.
Morgan buys 8 packages of 5 bookmarks. Each package costs $2. How much did she spend on the bookmarks?
Answer: He spent $80 on bookmarks.

Explanation:
Given, Morgan buys 8 packages of 5 bookmarks.
Each package costs $2.
Then, 8 × 5 = 40
40 × 2 = 80
So, He spent $80 on bookmarks.

Question 9.
Mathematical PRACTICE Make a Plan Madison can make two apple pies with the apples shown. If she has 9 times as many apples, how many pies can she make?
McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 Answer Key Problem-Solving Investigation Use Logical Reasoning 4
Answer:  She can make 18 pies.

Explanation:
Given, Madison can make two apple pies with the apples shown.
If she has 9 times as many apples, how many pies can she make,
Then, for ten apples she can make 2 pies
For, 9 × 10  = 90 apples
for 90 apples she can make 18 pies.
So, She can make 18 apples.

McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 My Homework Answer Key

Problem Solving

Mathematical PRACTICE Reason Solve each problem using logical reasoning.

Question 1.
Granola bars cost 45¢, gum costs 35¢, and crackers cost 50¢. Lauren buys two different items. She pays with a $1 bill and receives 3 of the same type of coin as change. What did Lauren buy, and what did she receive as change?
Answer:  She bought Granola bar and gum and She received 3 dimes as change.

Explanation:
Given, Granola bars cost 45¢, gum costs 35¢, and crackers cost 50¢.
Lauren buys two different items.
She pays with a $1 bill and receives 3 of the same type of coin as change.
She bought Granola bar and gum
making 4 5 + 35 = 70cents
it will give us the change of 30 cents means 3 dimes,
So, She received 3 dimes as change.

Question 2.
There are four cars parked next to each other. The blue car is not in the fourth space. The silver car is in the third space. The black car is two spaces in front of the red car. In what order are the cars parked?
Answer:  The order of the cars parked next to each other is black car, blue car, silver car, red car.

Explanation:
Given, There are four cars parked next to each other.
The blue car is not in the fourth space. The silver car is in the third space.
The black car is two spaces in front of the red car.
Here, The silver car is in the third space. it is fixed
The black car is two spaces in front of the red car., means first car is black and the fourth car is red
as, it satisfies the condition given,
The blue car is not in the fourth space., Then it will be in second place.
Then the order will be black, blue, silver, red
So, The order of the cars parked next to each other is black car, blue car, silver car, red car.

Question 3.
There are 21 wheels at the bike shop. The wheels will be used to build tricycles and bicycles. There will be half as many tricycles as bicycles. How many of each type of bike will be built?
Answer: There will be 3 tricycles and 6 bicycles.

Explanation:
Given, There are 21 wheels at the bike shop.
The wheels will be used to build tricycles and bicycles.
There will be half as many tricycles as bicycles.
Here, 3 × 3 = 9
9 wheels can make 3 tricycles
6 × 2 = 12
12 wheels can make 6 bicycles
So, There will be 3 tricycles and 6 bicycles.

Question 4.
Mitchell has $18 to spend. What is the greatest number of any one item he can buy?
McGraw Hill My Math Grade 3 Chapter 9 Lesson 9 Answer Key Problem-Solving Investigation Use Logical Reasoning 5
Answer: Mitchel can buy one item in greater number that is baseball.

Explanation:
Given, Mitchell has $18 to spend.
He can buy baseball because it cost $10 and it is highest of all the given items,
So, Mitchel can buy one item in greater number that is baseball.

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