Module 4 lesson 6 Engage NY Eureka Math 7th Grade Module 4 Lesson 6 Answer Key

Example 1: Mental Math and Percents
a. 75% of the students in Jesse’s class are 60 inches or taller. If there are 20 students in her class, how many students are 60 inches or taller?
→ Is this question a comparison of two separate quantities, or is it part of the whole? How do you know?
The problem says that the students make up 75% of Jesse’s class, which means they are part of the whole class; this is a part of the whole problem.

→ What numbers represent the part, whole, and percent?
The part is the number of students that are 60 inches or taller, the whole is the 20 students that make up Jesse’s class, and the percent is 75%.

Instruct students to discuss the problem with a partner; challenge them to solve it using mental math only. After 1–2 minutes of discussion, ask for students to share their mental strategies with the class.
Possible strategies:
75% is the same as $$\frac{3}{4}$$ of %; 20 → % and 20 = 4(5), so 3(5) = 15, which means 15 is $$\frac{3}{4}$$ of
% → 20
25% → 5
75% → 15
Have students write a description of how to mentally solve the problem (including the math involved) in their student materials.

The numbers involved in the problem shared factors with that were easy to work with.

b. Bobbie wants to leave a tip for her waitress equal to 15% of her bill. Bobbie’s bill for her lunch is $How much money represents 15% of the bill? Answer: → Is this question a comparison of two separate quantities, or is it part of a whole? How do you know? She is leaving a quantity that is equal to 15% of her bill, so this is a comparison of two separate quantities. → What numbers represent the part, the whole, and the percent? Is the part actually part of her lunch bill? The part is the amount that she plans to leave for her waitress and is not part of her lunch bill but is calculated as if it is a part of her bill; the whole is the$18 lunch bill, and the percent is 15%.

Instruct students to discuss the problem with a partner; challenge them to solve it using mental math only. After 1–2 minutes of discussion, ask for students to share their mental strategies with the class.
Possible strategy includes the following:
15% = 10%+5%; 10% of $18 is$; half of 10% is 5%, so 5% → 1/2( $) =$;
$+$ = $→ Was this problem easy to solve mentally? Why? The numbers involved in the problem shared factors with that were easy to work with. → Could you use this strategy to find 7% of Bobbie’s bill? Yes; 7% = 5%+2(1%); 1% of$18 is $, so 2% →$; $+$ = $, so 7% →$
Have students write a description of how to mentally solve the problem in their student materials including the math involved.

Exercise 1.
Express 9 hours as a percentage of 3 days.
3 days is the equivalent of 72 hours since 3(24) =
72 hours represents the whole.
Quantity = Percent × Whole. Let p represent the unknown percent.
9 = p(72)
$$\frac{1}{72}$$ (9) = p(72) ∙ $$\frac{1}{72}$$
$$\frac{9}{72}$$ = p(1)
$$\frac{1}{8}$$ = p
$$\frac{1}{8}$$ (%) = %

Exercise 2.
Richard works from a.m. to a.m. His dinner break is 75% of the way through his work shift. What time is Richard’s dinner break?
The total amount of time in Richard’s work shift is 16 hours since 1+12+3 =
16 hours represents the whole.
Quantity = Percent × Whole. Let b represent the number of hours until Richard’s dinner break.
b = (16)
b = 12
Richard’s dinner break is 12 hours after his shift begins.
12 hours after a.m. is p.m.
Richard’s dinner break is at p.m.

Exercise 3.
At a playoff basketball game, there were fans cheering for school A and fans cheering for school B.
a. Express the number of fans cheering for school A as a percent of the number of fans cheering for school B.
The number of fans for school B is the whole.
Quantity = Percent × Whole. Let p represent the unknown percent.
= p()
$$\frac{1}{}$$ () = p()$$\frac{1}{}$$
$$\frac{}{}$$ = p(1)
$$\frac{2}{3}$$ = p
$$\frac{2}{3}$$ (%) = 66$$\frac{2}{3}$$%
The number of fans cheering for school A is 66 2/3% of the number of fans cheering for school B.

b. Express the number of fans cheering for school B as a percent of the number of fans cheering for school A.
The number of fans cheering for school A is the whole.
Quantity = Percent × Whole. Let p represent the unknown percent.
= p()
$$\frac{1}{}$$ () = p()$$\frac{1}{}$$
$$\frac{}{}$$ = p(1)
$$\frac{3}{2}$$ = p
$$\frac{3}{2}$$ (%) = %
The number of fans cheering for school B is % of the number of fans cheering for school A.

c. What percent more fans were there for school B than for school A?
There were 50% more fans cheering for school B than for school A.

Exercise 4.
Rectangle A has a width of 8 cm and a length of 16 cm. Rectangle B has the same area as the first, but its width is % of the width of the first rectangle. Express the length of Rectangle B as a percent of the length of Rectangle A. What percent more or less is the length of Rectangle B than the length of Rectangle A?
To find the width of Rectangle B:
The width of Rectangle A is the whole.
Quantity = Percent × Whole. Let w represent the unknown width of Rectangle B.
w = (8) = 5
The width of Rectangle B is 5 cm.

To find the length of Rectangle B:
The area of Rectangle B is % of the area of Rectangle A because the problem says the areas are the same.
Area = Width × Length. Let A represent the unknown area of Rectangle A.
A = 8 cm(16 cm) = cm2
Area = Width × Length. Let l represent the unknown length of Rectangle B.
cm2 = 5 cm (l)
cm = l
The length of Rectangle B is cm.

To express the length of Rectangle B as a percent of the length of Rectangle A:
The length of Rectangle A is the whole.
Quantity = Percent × Whole. Let p represent the unknown percent.
cm = p(16 cm)
= p
(%) = %; The length of Rectangle B is % of the length of Rectangle A.

Therefore, the length of Rectangle B is 60% more than the length of Rectangle A.

Exercise 5.
A plant in Mikayla’s garden was 40 inches tall one day and was 4 feet tall one week later. By what percent did the plant’s height increase over one week?
4 feet is equivalent to 48 inches since 4(12) =
40 inches is the whole.
Quantity = Percent × Whole. Let p represent the unknown percent.
8 = p(40)
$$\frac{1}{5}$$ = p
$$\frac{1}{5}$$ = 20/ = 20%
The plant’s height increased by 20% in one week.

Exercise 6.
Loren must obtain a minimum number of signatures on a petition before it can be submitted. She was able to obtain signatures, which is 40% more than she needs. How many signatures does she need?
The number of signatures needed represents the whole.
Quantity = Percent × Whole. Let s represent the number of signatures needed.
= (s)
= s
Loren needs to obtain signatures on her petition.

Eureka Math Grade 7 Module 4 Lesson 6 Problem Set Answer Key

Question 1.
Micah has songs stored in his phone, which is 70% of the songs that Jorge has stored in his phone. How many songs are stored on Jorge’s phone?
Quantity = Percent × Whole. Let s represent the number of songs on Jorge’s phone.
= $$\frac{70}{}$$ ∙ s
= $$\frac{7}{10}$$ ∙ s
∙ $$\frac{10}{7}$$ = $$\frac{7}{10}$$ ∙ $$\frac{10}{7}$$ ∙ s
42 ∙ 10 = 1 ∙ s
= s
There are songs stored on Jorge’s phone.

Question 2.
Lisa sold 81 magazine subscriptions, which is 27% of her class’s fundraising goal. How many magazine subscriptions does her class hope to sell?
Quantity = Percent × Whole. Let s represent the number of magazine subscriptions Lisa’s class wants to sell.
81 = $$\frac{27}{}$$ ∙ s
81 ∙ $$\frac{}{27}$$ = $$\frac{27}{}$$ ∙ $$\frac{}{27}$$ ∙ s
3 ∙ = 1 ∙ s
= s
Lisa’s class hopes to sell magazine subscriptions.

Question 3.
Theresa and Isaiah are comparing the number of pages that they read for pleasure over the summer. Theresa read 2, pages, which was 85% of the number of pages that Isaiah read. How many pages did Isaiah read?
Quantity = Percent × Whole. Let p represent the number of pages that Isaiah read.
2, = $$\frac{85}{}$$ ∙ p
2, = $$\frac{17}{20}$$ ∙ p
2, ∙ $$\frac{20}{17}$$ = $$\frac{17}{20}$$ ∙ $$\frac{20}{17}$$ ∙ p
∙ 20 = 1 ∙ p
2, = p
Isaiah read 2, pages over the summer.

Question 4.
In a parking garage, the number of SUVs is 40% greater than the number of non-SUVs. Gina counted 98 SUVs in the parking garage. How many vehicles were parked in the garage?
40% greater means % of the non-SUVs plus another 40% of that number, or %.
Quantity = Percent × Whole. Let d represent the number of non-SUVs in the parking garage.
98 = $$\frac{}{}$$ ∙ d
98 = $$\frac{7}{5}$$ ∙ d
98 ∙ $$\frac{5}{7}$$ = $$\frac{7}{5}$$ ∙ $$\frac{5}{7}$$ ∙ d
14 ∙ 5 = 1 ∙ d
70 = d
There are 70 non-SUVs in the parking garage.
The total number of vehicles is the sum of the number of the SUVs and non-SUVs.
70+98 = There is a total of vehicles in the parking garage.

Question 5.
The price of a tent was decreased by 15% and sold for $What was the original price of the tent in dollars? Answer: If the price was decreased by 15%, then the sale price is 15% less than % of the original price, or 85%. Quantity = Percent × Whole. Let t represent the original price of the tent. = $$\frac{85}{}$$ ∙ t = $$\frac{17}{20}$$ ∙ t ∙ $$\frac{20}{17}$$ = $$\frac{17}{20}$$ ∙ $$\frac{20}{17}$$ ∙ t $$\frac{1,}{17}$$ = 1 ∙ t ≈ t Because this quantity represents money, the original price was$ after rounding to the nearest hundredth.

Question 6.
40% of the students at Rockledge Middle School are musicians. 75% of those musicians have to read sheet music when they play their instruments. If 38 of the students can play their instruments without reading sheet music, how many students are there at Rockledge Middle School?
Let m represent the number of musicians at the school, and let s represent the total number of students. There are two whole quantities in this problem. The first whole quantity is the number of musicians. The 38 students who can play an instrument without reading sheet music represent 25% of the musicians.
Quantity = Percent × Whole
38 = 25/ ∙ m
38 = $$\frac{1}{4}$$ ∙ m
38 ∙ $$\frac{4}{1}$$ = $$\frac{1}{4}$$ ∙ $$\frac{4}{1}$$ ∙ m
$$\frac{}{1}$$ = 1 ∙ m
= m
There are musicians in the school.

Quantity = Percent × Whole
= $$\frac{40}{}$$ ∙ s
= $$\frac{2}{5}$$ ∙ s
∙ $$\frac{5}{2}$$ = $$\frac{2}{5}$$ ∙ $$\frac{5}{2}$$ ∙ s
$$\frac{}{2}$$ = 1 ∙ s
= s
There are students at Rockledge Middle School.

Question 7.
At Longbridge Middle School, students said that they are an only child, which is 48% of the school’s student enrollment. How many students attend Longbridge Middle School?
Quantity → %
→ 48%
$$\frac{}{48}$$ → 1%
$$\frac{}{48}$$ () → %
5() → %
→ %
There are students attending Longbridge Middle School.

Question 8.
Grace and her father spent 4 1/2 hours over the weekend restoring their fishing boat. This time makes up 6% of the time needed to fully restore the boat. How much total time is needed to fully restore the boat?
Quantity → %
4 $$\frac{1}{2}$$ → 6%
$$\frac{\frac{9}{2}}{6}$$ → 6%
$$\frac{\frac{9}{2}}{6}$$ → 1%
$$\frac{\frac{9}{2}}{6}$$ () → %
($$\frac{9}{2}$$)($$\frac{1}{6}$$) → %
($$\frac{9}{12}$$) → %
($$\frac{3}{4}$$) → %
/4 → %
75 → %
The total amount of time to restore the boat is 75 hours.

Question 9.
Bethany’s mother was upset with her because Bethany’s text messages from the previous month were % of the amount allowed at no extra cost under her phone plan. Her mother had to pay for each text message over the allowance. Bethany had 5, text messages last month. How many text messages is she allowed under her phone plan at no extra cost?
Quantity → %
5, → %
$$\frac{5,}{}$$ → 1%
$$\frac{5,}{}$$ () → %
25() → %
2, → %
Bethany is allowed 2, text messages without extra cost.

Question
Harry used 84% of the money in his savings account to buy a used dirt bike that cost him $1, How much money is left in Harry’s savings account? Answer: Quantity → % 1, → 84% $$\frac{1,}{84}$$ → 1% $$\frac{1,}{84}$$ () → % () → % 1, → % Harry started with$1, in his account but then spent $1, of it on the dirt bike. 1,, = Harry has$ left in his savings account.

Question
15% of the students in Mr. Riley’s social studies classes watch the local news every night. Mr. Riley found that of his students do not watch the local news. How many students are in Mr. Riley’s social studies classes?
If 15% of his students do watch their local news, then 85% do not.
Quantity → %
→ 85%
$$\frac{}{85}$$ → 1%
($$\frac{}{85}$$)() → %
() → %
→ %
There are total students in Mr. Riley’s social studies classes.

Question
Grandma Bailey and her children represent about % of the Bailey family. If Grandma Bailey has 12 children, how many members are there in the Bailey family?
Quantity → %
13 → %
($$\frac{1}{}$$)(13) → 1%
($$\frac{13}{}$$) → %
$$\frac{1,}{}$$ → %
&#;…&#; → %
The Bailey family has members.

Question
Shelley earned 20% more money in tips waitressing this week than last week. This week she earned $in tips waitressing. How much money did Shelley earn last week in tips? Answer: Quantity = Percent × Whole. Let m represent the number of dollars Shelley earned waitressing last week. 72 = $$\frac{}{}$$ m 72($$\frac{}{}$$) = $$\frac{}{}$$ ($$\frac{}{}$$)m 60 = m Shelley earned$60 waitressing last week.

Question
Lucy’s savings account has 35% more money than her sister Edy’s. Together, the girls have saved a total of $How much money has each girl saved? Answer: The money in Edy’s account corresponds to %. Lucy has 35% more than Edy, so the money in Lucy’s account corresponds to %. Together, the girls have a total of$, which is % of Edy’s account balance.
Quantity = Pecent × Whole. Let b represent Edy’s savings account balance in dollars.
= $$\frac{}{}$$ ∙ b
= $$\frac{47}{20}$$ ∙ b
∙ $$\frac{20}{47}$$ = $$\frac{47}{20}$$ ∙ $$\frac{20}{47}$$ ∙ b
$$\frac{4,}{47}$$ = 1 ∙ b
88 = b
Edy has saved $88 in her account. Lucy has saved the remainder of the$, so =
Therefore, Lucy has $saved in her account. Question Bella spent 15% of her paycheck at the mall, and 40% of that was spent at the movie theater. Bella spent a total of$ at the movie theater for her movie ticket, popcorn, and a soft drink. How much money was in Bella’s paycheck?
$→ 40%$ → 10%
$→ % Bella spent$ at the mall.
$→ 15%$ → 5%
$→ % Bella’s paycheck was$

Question
On a road trip, Sara’s brother drove % of the trip, and Sara drove 80% of the remainder. If Sara drove for 4 hours and 12 minutes, how long was the road trip?
There are two whole quantities in this problem. First, Sara drove 80% of the remainder of the trip; the remainder is the first whole quantity. 4 hr min. is equivalent to 4 12/60 hr. = hr.
Quantity → %
→ 80%
$$\frac{}{80}$$ → 1%
$$\frac{}{80}$$ () → %
$$\frac{}{80}$$ → %
$$\frac{42}{8}$$ → %
→ %
The remainder of the trip that Sara’s brother did not drive was hours. He drove % of the trip, so the remainder of the trip was % of the trip, and the whole quantity is the time for the whole road trip.
Quantity → %
→ %
$$\frac{}{}$$ → 1%
($$\frac{}{}$$)() → %
$$\frac{}{}$$ → %
10 → %
The road trip was a total of 10 hours.

Eureka Math Grade 7 Module 4 Lesson 6 Exit Ticket Answer Key

Question 1.
Parker was able to pay for 44% of his college tuition with his scholarship. The remaining $10, he paid for with a student loan. What was the cost of Parker’s tuition? Answer: Parker’s tuition is the whole; 56% represents the amount paid by a student loan. Quantity = Percent × Whole. Let t represent the cost of Parker’s tuition. 10, = (t) $$\frac{10,}{}$$ = t 17, = t Parker’s tuition was$17,

Question 2.
Two bags contain marbles. Bag A contains marbles, and Bag B contains marbles. What percent fewer marbles does Bag A have than Bag B?
The number of marbles in Bag B is the whole.
There are 28 fewer marbles in Bag A.
Quantity = Percent × Whole. Let p represent the unknown percent.
28 = p()
$$\frac{2}{10}$$ = p
$$\frac{2}{10}$$ = $$\frac{20}{}$$ = 20%
Bag A contains 20% fewer marbles than Bag B.

Question 3.
There are 42 students on a large bus, and the rest are on a smaller bus. If 40% of the students are on the smaller bus, how many total students are on the two buses?
The 42 students on the larger bus represent 60% of the students. If I divide both 60% and 42 by 6, then I get 7 → 10%. Multiplying both by 10, I get 70 → %. There are 70 total students on the buses.

Eureka Math Grade 7 Module 4 Lesson 6 Percent More or Less—Round 1 Answer Key

Directions: Find each missing value.  Eureka Math Grade 7 Module 4 Lesson 6 Percent More or Less—Round 2 Answer Key

Directions: Find each missing value.  Teachers, save “Math: Module 4 Lesson 6 (Kindergarten Eu…” to assign it to your class.

1) Press the picture to watch the video. 2) Press the X when the video is done. 3) Press 4) Use the or tools to finish the problems. 5) When you finish page one, press page two and do it also. (Page two is up in the top right corner.) 6) Press twice to send your work to your teacher. Kindergarten, Math  Compatible with: Chromebooks, computers, iPads, iPhones, Android tablets, Android phones, Kindle Fire
Sours: https://app.seesaw.me/activities/2w39my/math-modulelessonkindergarten-eureka

Algebra I Module 4, Topic A, Lesson 6 Student Outcomes

• Students use appropriate and efficient strategies to find solutions to basic quadratic equations.
• Students interpret the verbal description of a problem and its solutions in context and then justify the solutions using algebraic reasoning.

Resources may contain links to sites external to the EngageNY.org website. These sites may not be within the jurisdiction of NYSED and in such cases NYSED is not responsible for its content.

Common Core Learning Standards

CCLS State Standard
A.REIb Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the
Sours: https://www.engageny.org/resource/algebra-i-moduletopic-lesson-6

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6 lesson module 4

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EngageNY Grade 4 Module 4 Lesson 6

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