All the solutions provided in McGraw Hill Math Grade 3 Answer Key PDF Chapter 4 Lesson 6 Use Multiplication to Find Combinations will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 4 Lesson 6 Use Multiplication to Find Combinations
Math in My World
Example 1
Amos’ team has 3 jersey colors: green, red, and yellow. They can wear orange or black shorts. Find all of the jersey and short combinations for the team.
1. Color the first jersey m green, the second one red, and the last yellow.
2. Color 1 pair of 43 shorts orange and 1 pair of shorts black below each jersey.
Answer:
Explanation:
Amos’ team has 3 jersey colors: green, red, and yellow
They can wear orange or black shorts
There are 3 jersey colors x 2 shorts colors = 6 jersey and shorts combinations are possible.
1st combination is green jersey and orange shorts, 2nd combination is green jersey and black shorts, 3rd combination is red jersey and orange shorts, 4th combination is red jersey and black shorts, 5th combination is yellow jersey and orange shorts and 6th combination is yellow jersey and black shorts
In this way we will get 6 combinations.
Another way to find combinations is to use a tree diagram.
A tree diagram uses “branches” to show all possible combinations.
Example 2
What are all the possible fruit sorbet combinations if you choose one flavor and one fruit to add in?
Complete the tree diagram.
Check Multiply to find the number of possible combinations.
Answer:
Explanation:
3 fruits X 3 flavors = 9 possible combinations
1st combination is mango and banana, 2nd combination is mango and berries, 3rd combination is mango and peach, 4th combination is strawberry and banana, 5th combination is strawberry and berries, 6th combination is strawberry and peach, 7th combination is vanilla and banana, 8th combination is vanilla and berries and9th combination is vanilla and peach
In this way every fruit will combine with 3 flavors
So, there are 9 possible combinations.
Guided Practice
Question 1.
Refer to Example 2. How would the possible number of combinations change if one more flavor was added? Write the multiplication sentence
multiplication sentence:
Answer:
3 fruits X 4 flavors = 12 possible combinations
Explanation:
In example 2, We used 3 flavors and 3 fruits
Here we added 1 flavor
So for example if mango will combine with 4 flavors , we can get 4 combinations
In this way other 2 fruits also combine with 4 flavors
One fruit will get 4 combinations
Here we are using 3 fruits
So, there are 12 possible combinations.
Talk Math
Explain how a tree diagram helps you find all the possible combinations without repeating any.
Answer:
A tree diagram is a visual representation of all possible future outcomes and the associated probabilities of a random variable. Tree diagrams are particularly useful when we have several possible outcomes. They can help you record all the possibilities in a clear, uncomplicated manner.
Independent Practice
Find all the possible combinations. Write a multiplication sentence to check.
Question 2.
Jackie is playing a card game with triangles and circles. Each shape can be blue, red, yellow, or green. How many different cards are there?
Answer:
Explanation:
Multiplication sentence : 2 shapes X 4 color = 8 different card combinations.
So there are 8 different card combinations possible
Here we take 2 shapes and 4 colors
So every shape will combine with 4 cards. Like wise triangle will combine with 4 colors means blue, red, yellow or green
So we get 4 different card combinations they are triangle blue card, triangle red card, triangle yellow card and triangle green card.
In this way if circle also combine with 4 colors, then we get 4 different combinations of cards
Now, if we add triangle combinations and circle combinations together we get 8 different combinations of cards.
List all of the 2-digit numbers that can be made with 3 or 4 as the tens digit and 1, 6, 7, 8, or 9 as the ones digit number
Answer:
Multiplication sentence:2 tens digit numbers X 5 ones digit numbers = 10 two digit numbers .
There are 10 two digit numbers possible
Explanation:
In this problem their are 2 tens digit numbers and 5 ones digit numbers
Here 3 and 4 are tens digit numbers
1, 6, 7, 8, 9 are ones digit numbers
Here both tens digit numbers 3 and 4 will combine with 1, 6, 7, 8, 9 numbers means
If 3 will combine with 1 then we get 31, like wise it will combine with 6, 7, 8, 9 then we get 36 , 37 , 38 ,39 numbers
Number 4 also combine with 1, 6, 7, 8, 9 then we get 41, 46, 47,48, 49 numbers. every tens digit number will combine with these 5 numbers . then we can get 5 combinations with each number. here we have two numbers
So there are 10 two digit numbers possible
The numbers are 31 , 36 , 37 , 38 ,39 , 41 , 46 , 47 , 48 , 49.
Problem Solving
Write a multiplication sentence to solve the problem.
Question 4.
Madison needs to choose 1 breakfast item and 1 drink. Find the number of possible combinations.
Answer:
Multiplication sentence : 2 break fast items X 2 drinks = 4 possible combinations.
There are 4 possible combinations in breakfast .
Explanation:
Here there are 2 breakfast items and 2 drinks
Every breakfast item will combine with 2 drinks , then we can get 2 different combinations with each breakfast item
Pan cakes and bread toast as breakfast items, milk and juice are drinks
Now we get 2 combinations with pan cakes they are
pancakes and milk , pancakes and juice
Also we get 2 combinations with bread toast they are
bread toast and milk , bread toast and juice
In this way there are 4 possible combinations.
Suppose hot chocolate was added to the drink menu. How would the number of combinations change?
Answer:
Multiplication sentence: 2 breakfast items X 3 drinks = 6 possible combinations.
So there are 6 possible combinations.
Explanation:
To the above example if w e add hot chocolate to the drink menu
Every breakfast item will combine with 3 drinks
The combinations are pancakes and milk, pancakes and juice, pancakes and hot chocolate, bread toast and milk, bread toast and juice, bread toast and hot chocolate
In this way the number of possible combinations will be 6.
HOT Problems
Question 5.
Mathematical PRACTICE 5 Use Math Tools Write a real-world combination problem for the multiplication sentence 4 × 2 = 
. Ask a classmate to solve with a tree diagram. Then find the unknown.
Answer:
Explanation:
Multiplication sentence: 4 different shapes X 2 different colors = 8 different combinations.
There are 4 different shapes like circle, oval, triangle, square and 2 different colors are blue and pink. So every shape will combine with 2 colors
That is circle with blue and circle with pink, oval with blue and oval with pink, triangle with blue and triangle with pink, square with blue and square with pink. In this way every shape will combine with each color. So, we get 8 possible combinations like blue circle, pink circle, blue oval, pink oval, blue triangle, pink triangle, blue square , pink square
So there are 8 different combinations possible.
Question 6.
? Building on the Essential Question How can multiplication help to find combinations?
Answer:
Using multiplication can help us to find the combinations
For example their are two shirts and 4 trousers with John the number of combinations that he can make using them can be found by multiplying them
That is 2 x 4 = 8
Therefore, 8 will the number of combinations that John can make with 2 shirts and 4 trousers.
McGraw Hill My Math Grade 3 Chapter 4 Lesson 6 My Homework Answer Key
Practice
Question 1.
Diana can take 1 pencil and 1 eraser to school. Her choices are shown. How many different pencil and eraser combinations are there? Complete the tree diagram. Write a multiplication sentence.
Answer:
Multiplication sentence : 1 pencil X 1 eraser = 1 possible combination.
Explanation:
Multiplication sentence : 1 pencil X 1 eraser = 1 possible combination.
Here there are 2 items only
If 1 pencil will combine with 1 eraser then the number of possible combinations is only 1
So there is only one possible combination.
Question 2.
Mathematical PRACTICE 7 Identify Structure For a snack. Randy can choose from peanuts, carrots, or popcorn. He can have water or juice to drink How many snack and drink combinations are there? Complete the tree diagram. Write a multiplication sentence.
Answer:
Explanation:
Multiplication sentence : 3 snack item X 2 drinks = 6 possible combinations
Here there are 3 snack items like peanuts, carrots, popcorn and 2 drinks like water and juice
If every snack item will combine with each drink
Like peanuts with water and juice , carrots with water and juice , popcorn with water and juice
We get 6 possible combinations like peanuts and water , peanuts and juice , carrots and water , carrots and juice , popcorn and water and popcorn and juice
So there are 6 combinations possible.
Vocabulary Check
Question 3.
Write the correct vocabulary word(s) in each space to complete the sentence.
Combination tree diagram
Each branch of a —– shows a possible —- of items.
Answer:
Each branch of a tree diagram shows a possible combination of items.
Test Practice
Question 4.
Amanda bought 4 pairs of shoes and 5 purses. Which number sentence shows the number of different shoes and purse combinations that Amanda can make?
A. 4 + 5 = 9
B. 5 × 8 = 40
C. 4 + 4 + 4 + 4 = 16
D. 4 × 5 = 20
Answers:
D. 4 × 5 = 20
Explanation:
D Is answer because if 4 pairs of shoes will combine with 5 purses then
Multiplication sentence: 4 pairs of shoes X 5 purses = 20 combinations
So there are 20 possible combinations