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Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 6 Module 1
Bridges in Mathematics Grade 5 Home Connections Unit 6 Module 1 Session 2 Answer Key
Plotting Points on a Graph
Question 1.
Plot and label these points on the coordinate plane below. The first one has been done as an example.
(1, 3)
(2, 6)
(3, 9)
(4, 12)
(5, 15)
Answer:
Explanation:
Given from the above graph plotted the points on coordinate plane and completed the graph.
Question 2.
Amanda plotted 5 points on the coordinate plane to the right. What ordered pairs did Amanda plot?
Amanda’s ordered pairs: (1 , 2 ) (_________, _________) (_________, _________) (_________, _________) (_________, _________)
Answer:
Amanda’s ordered pairs : ( 1 , 2 ) ; ( 2 , 3 ) ; ( 3, 4 ) ; ( 4 , 5 ) ; ( 5 , 6 ),
Explanation:
The following are the ordered pairs plotted on the coordinate plane,
Question 3.
What is the next ordered pair if Amanda’s pattern continues? (_________, _________)
Answer:
The next ordered pair is (6 , 7) if Amanda’s pattern continues,
Explanation:
The Amanda’s pattern from the graph are (1,2) ; (2,3) ; (3,4) ; (4,5) ; (5,6) ; (6,7).
Question 4.
Zoe planted a walnut tree. Every week, she measures the tree and records its growth. On the first week, the tree was 27\(\frac{1}{2}\) inches tall. On the second week, it was 29\(\frac{1}{4}\) inches tall. On the third week, it was 31\(\frac{1}{3}\) inches tall. How much did the tree grow from the first week until it was measured on the third week? Show your work.
Answer:
The tree grew about 3.83 inches between first and third week,
Explanation:
Given that measure of records its growth in first week is 27 1/2 inches inches tall , measure of records its growth in second week is 29 1/4 inches and measure of records of growth in third week is 31 1/3 inches so therefore the length of tree grow from first week until it was measured on the third week is 3.83 inches.
Question 5.
CHALLENGE There are 8 people on a committee. Each time they meet, they shake hands with each other so that each person shakes everyone else’s hand once.
a. Each time they meet, how many handshakes are there? Use numbers, labeled sketches, or words to model and solve this problem. Show all your work.
Answer:
28 handshakes are there,
Explanation:
Given total number of people in a committee are 8, each person shakes everyone else hand once so,
b. Imagine that 3 committee members arrive late. The other 5 members have already shaken hands. How many handshakes will there be when the 3 late members arrive? Use numbers, labeled sketches, or words to model and solve this problem. Show all of your work.
Answer:
15 handshakes,
Explanation:
Given that number of committee members arrived late are 3 so that number of members have already shaken are 5 therefore number of handshakes are 3 X 5 = 15.
Bridges in Mathematics Grade 5 Home Connections Unit 6 Module 1 Session 4 Answer Key
More About the Short Towers Sequence
Question 1.
Here are the first 3 arrangements in the Short Towers cube sequence you worked with in class. Explain to an adult at home how the towers change from one arrangement to the next, and have the adult initial the sheet to show he or she understands.
Answer:
Explanation:
Given from the above arrangements the towers are increasing from one arrangement to the next in order that one cube is arranging below and number of cubes arranged to each arm and remaining cubes are arranged as shown in the initial sheet.
Question 2.
a. Here is the 4th arrangement in the sequence. How many cubes are in this arrangement?
Answer:
16 cubes,
Explanation:
Given from above arrangement the number of cubes are 16 as 1 cube in middle which is unseen and 5 arms are there which each arm has 3 cubes that is 16 cubes.
b. Shanda says you don’t have to count the cubes one by one to find out how many are in the 4th arrangement. She says there is 1 cube in the middle and then 5 arms of 3 cubes each.
Write an equation to show how Shanda figured out the number of cubes in the 4th arrangement.
Answer:
16 cubes,
Explanation:
Given from above figure 1 cube in middle and then 5 arms of 3 cubes each so the number of cubes in 4th arrangement which the equation is 1 + ( 5 X 3 ) = 1+15 = 16 cubes.
Question 3.
How many cubes are in the 5th arrangement? Use Shanda’s method or come up with one of your own to figure it out without counting one by one. Label the picture of arrangement 5 and write an equation to show your thinking.
Answer:
21 cubes,
Explanation:
Given from above 5th arrangement by using Shanda’s method the equation is 1 cube which is in middle and 5 arms and each arm has 4 cubes so the equation is 1 + ( 5 X 4) = 1 + 20 = 21 cubes.
Question 4.
How many cubes would it take to build the 23rd arrangement in this sequence? Show your thinking using numbers, words, or labeled sketches.
Answer:
111 cubes would it take to build the 23rd arrangement,
Explanation:
Given from above sequences the arrangements build by using Shanda’s method is that 1 cube is middle which hide and 5 arms in which each arm has 22 cubes and the equation is 1 + ( 5 X 22 ) = 1+110 = 111 cubes so, therefore number of cubes for 23rd arrangement are 111 cubes.
Question 5.
CHALLENGE A certain arrangement in this sequence takes 631 cubes to build. Which arrangement is it? Show your thinking using numbers, words, or labeled sketches.
Answer:
The 127th arrangement,
Explanation:
Given from above that the arrangement for 631 cubes that 1 cube will hide so that 631-1 = 630. That means there are 630 cubes 5 arms plus after taking the one extra away so, the number of cubes in an arm is 630 / 5 = 126. The arrangement is always the number of cubes in an arm +1, so this is the 126 + 1 = 127th arrangement.
Bridges in Mathematics Grade 5 Home Connections Unit 6 Module 1 Session 6 Answer Key
The Lemonade Stand
Troy and his little sister are going to sell lemonade to earn money for the wildlife refuge near their home. Troy’s parents have agreed to pay for the ingredients and the cups. The kids are going to charge 50¢ a glass for their lemonade.
Question 1.
Fill in the table below to show how much money they’ll earn.
Answer:
Explanation:
Given from above table cost of 1 glass sold is $0.50 ; for 2 glasses sold is 2 X $0.50 = $1.00; for 4 glasses sold is 4 X $0.50 =$2.00; for 5 glasses sold is 5 X $0.50 = $2.50; for 6 glasses sold is 6 X $0.50 = $3.00; for 7 glasses sold is 7 X $0.50 = $ 3.50 ;for 8 glasses sold is 8 x $0.50 = $4.00 ; for 8 glasses sold is 9 X $0.50 = $4.50; for 10 glasses sold is 10 X $ 0.50 = $5.00.
Question 2.
Use the grid below to graph the amount of money they’ll earn as they sell glasses of lemonade. Give your graph a good title.
Answer:
Explanation:
Given from above completed the graph of money earned to number of glasses sold.
Question 3.
Why do the points on the graph form a straight line?
Answer:
Because the rate increases for each glasses sold so, as number of glasses increases the money earned for each glass also increases then the graph form a straight line.
Question 4.
The first day they opened their lemonade stand it was really hot. Troy and his sister sold 24 glasses of lemonade between noon and 3:00 pm. How much money did they make? Show your work.
Answer:
They made $12.00,
Explanation:
Given from above money earned for 1 glass of lemonade is $0.50 so, money earned for 24 glasses of lemonade is 24 X $0.50 = $12.00 therefore troy and his sister made money is $12.00.
Question 5.
Between 1:00 pm and 5:00 pm on the second day, they made $14.50. How many glasses of lemonade did they sell during those 4 hours? Show your work.
Answer:
29 glasses of lemonade they sold during those 4 hours,
Explanation:
Given that from above for 1 glass of lemonade money earned is $0.50 so for $14.50 the number of glasses made is,
Question 6.
What do you have to do to figure out how much money they’ll earn for selling any number of glasses of lemonade? Give your answer in words, and then write an equation to match.
Answer:
The equation is M = G X 0.50 ,
Explanation:
As we know that from above divide the number of glasses in half that is Money earned (M) = Number of Glasses (G) / 2 so, the equation is that multiply the number of glasses by $0.50: M = G X $ 0.50.
Question 7.
Their goal is to earn $75.00 for the wildlife refuge. How many glasses of lemonade will they need to sell to reach their goal? Show your work.
Answer:
150 glasses of lemonade will need to reach their goal ,
Explanation:
Given that the number of glasses for $75.00 is $75.00 divides $0.50 so that (75/100) X (100/50) = 75/50 = 150 glasses of lemonade need to reach their goal.
Question 8.
Here is a recipe for 1 glass of lemonade:
1\(\frac{1}{2}\) tablespoons lemon juice
\(\frac{1}{4}\) cup sugar
1 cup of water
The pitcher the kids were using held 8 glasses of lemonade. How much lemon juice, sugar, and water did it take to make enough lemonade to fill the pitcher? Show your work.
Answer:
12 table spoons of lemon juice ; 2 cups of sugar ; 8 cups water ,
Explanation:
Given that for 1 glass of lemonade need (3/2) tablespoons of lemon juice , 1/4 of cup sugar and 1 cup of water so for 8 glasses of lemonade 8 X (3/2) =24/2 = 12 tablespoons of lemon juice ; 8 X (1/4) = 8/4 = 2 cups sugar and 8 X 1 cup of water = 8 cups of water need to fill the pitcher.
Question 9.
CHALLENGE Use your answer to problem 7, along with the information below, to figure out how much it cost Troy’s parents to buy the ingredients for all the lemonade they sold. (The kids did reach their goal of earning $75.00 exactly.) Show all of your work.
- A 1-quart bottle of lemon juice costs $2.95.
- There are 16 tablespoons in a cup and 4 cups in a quart.
- A 5-pound bag of sugar costs $3.29.
- There are 11\(\frac{1}{4}\) cups of sugar in a 5-pound bag.
Answer:
They spent total of $24.96,
Explanation:
Given from above that for 1 glass of lemonade 3/2 tablespoons of lemon juice needed so for 150 glasses that is 150 X (3/2) = 150 X 1.5 = 225 so, 225 tablespoons of lemon juice needed and 1/4 cups of sugar for 1 glass of lemonade so, for 150 /4 = 37.5 so 37(1/2) cups of sugar so, 4 bags of sugar 4 X $3.29 = $13.16 and for 225 tablespoons of lemon juice so, they needed 4 bottles of lemon juice 4 X $2.95 = $11.80 total they spent is $13.16 + $11.80 = $24.96.