unit percents homework 3 answers 7th grade

Applying Percents Study Guide

What is a percent .

A percent is a way of expressing a number as a fraction of 100. The symbol "%" is used to denote a percent . For example, 25% means 25 out of 100.

Converting Between Percents , Decimals , and Fractions

To convert a percent to a decimal , divide the percent by 100. For example, 25% is equivalent to 0.25 as a decimal .

To convert a percent to a fraction , write the percent as a fraction with a denominator of 100 and simplify if possible. For example, 25% is equivalent to 25/100, which simplifies to 1/4.

To convert a decimal to a percent , multiply the decimal by 100. For example, 0.25 is equivalent to 25% as a percent .

To convert a decimal to a fraction , write the decimal as a fraction and simplify if possible. For example, 0.25 is equivalent to 25/100, which simplifies to 1/4.

Calculating Percentages

To calculate a percentage of a number, multiply the number by the decimal equivalent of the percentage. For example, to find 25% of 80, you would calculate 0.25 * 80 = 20.

Percent Increase and Decrease

To calculate a percent increase, first find the difference between the new and original values. Then, divide the difference by the original value and multiply by 100. For example, if the original value is 50 and the new value is 65, the percent increase is ((65-50)/50) * 100 = 30%.

To calculate a percent decrease, use the same process as for percent increase, but with the difference being the original value minus the new value.

Discounts and Markups

To calculate the sale price of an item after a discount, subtract the discount amount from the original price. For example, if an item is originally $80 and there is a 20% discount, the sale price would be $80 - (0.20 * $80) = $64.

To calculate the selling price of an item after a markup, add the markup amount to the original price. For example, if an item is originally $50 and there is a 25% markup, the selling price would be $50 + (0.25 * $50) = $62.50.

Word Problems

When solving percent word problems , it's important to carefully read the problem and identify the known values and the unknown value. Then, set up an equation and solve for the unknown value using the methods described above.

Practice Problems

• What is 30% as a decimal ?
• Convert 0.6 to a percent .
• Find 15% of 200.
• If the original price of a shirt is $40 and it is discounted by 20%, what is the sale price?
• If a computer is marked up by 35% to a selling price of $810, what was its original price?

Good luck with your study of applying percents !

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Eureka Math Grade 7 Module 4 Lesson 3 Answer Key

Engage ny eureka math 7th grade module 4 lesson 3 answer key, eureka math grade 7 module 4 lesson 3 example answer key.

Quantity = Percent × Whole Let p represent the unknown percent. 54 = p(300) \(\frac{1}{300}\) (54) = \(\frac{1}{300}\) (300)p \(\frac{54}{300}\) = 1p \(\frac{18}{100}\) = p \(\frac{18}{100}\) = 0.18 = 18% Anna and Emily were able to produce 18% of the total bracelets over the weekend.

b. Anna produced 32 of the 54 bracelets produced by Emily and Anna over the weekend. Write the number of bracelets that Emily produced as a percent of those that Anna produced. Answer: Arithmetic Method: 32 → 100% 1 → \(\frac{100}{32}\)% 22 → 22 ∙ \(\frac{100}{32}\)% 22 → 100 ∙ \(\frac{22}{32}\)% 22 → 100 ∙ 0.6875% 22 → 68.75%

Algebraic Method: Quantity = Percent × Whole Let p represent the unknown percent. 22 = p(32) \(\frac{1}{32}\) (22) = \(\frac{1}{32}\) (32)p \(\frac{22}{32}\) = 1p 0.6875 = p 0.6875 = 68.75%

22 bracelets are 68.75% of the number of bracelets that Anna produced. Emily produced 22 bracelets; therefore, she produced 68.75% of the number of bracelets that Anna produced.

c. Write the number of bracelets that Anna produced as a percent of those that Emily produced. Answer: Arithmetic Method: 22 → 100% 1 → \(\frac{100}{22}\)% 32 → 32 ∙ \(\frac{100}{22}\)% 32 → 100 ∙ \(\frac{32}{22}\)% 32 → 100 ∙ \(\frac{16}{11}\)% 32 → \(\frac{1600}{11}\)% 32 → 145 \(\frac{5}{11}\)%

Algebraic Method: Quantity = Percent × Whole Let p represent the unknown percent. 32 = p(22) \(\frac{1}{22}\) (32) = \(\frac{1}{22}\) (22)p \(\frac{32}{22}\) = 1p \(\frac{16}{11}\) = p 1 \(\frac{5}{11}\) = p 1 \(\frac{5}{11}\) = 1 \(\frac{5}{11}\) × 100% = 145 \(\frac{5}{11}\)%

32 bracelets are 145 \(\frac{5}{11}\)% of the number of bracelets that Emily produced. Anna produced 32 bracelets over the weekend, so Anna produced 145 \(\frac{5}{11}\)% of the number of bracelets that Emily produced.

Eureka Math Grade 7 Module 4 Lesson 3 Exercise Answer Key

Exercise 2. There are 750 students in the seventh – grade class and 625 students in the eighth – grade class at Kent Middle School. a. What percent is the seventh – grade class of the eighth – grade class at Kent Middle School? The number of eighth graders is the whole amount. Let p represent the percent of seventh graders compared to eighth graders. Quantity = Percent × Whole Let p represent the unknown percent. 750 = p(625) 750(\(\frac{1}{625}\)) = p(625)(\(\frac{1}{625}\)) 1.2 = p 1.2 = 120% The number of seventh graders is 120% of the number of eighth graders. There are 20% more seventh graders than eighth graders. Alternate solution: There are 125 more seventh graders. 125 = p(625), p = 0.20. There are 20% more seventh graders than eighth graders.

b. The principal will have to increase the number of eighth – grade teachers next year if the seventh – grade enrollment exceeds 110% of the current eighth – grade enrollment. Will she need to increase the number of teachers? Explain your reasoning. Answer: The principal will have to increase the number of teachers next year. In part (a), we found out that the seventh grade enrollment was 120% of the number of eighth graders, which is greater than 110%.

Exercise 3. At Kent Middle School, there are 104 students in the band and 80 students in the choir. What percent of the number of students in the choir is the number of students in the band? Answer: The number of students in the choir is the whole. Quantity = Percent × Whole Let p represent the unknown percent. 104 = p(80) p = 1.3 1.3 = 130% The number of students in the band is 130% of the number of students in the choir.

Teacher may ask students what percent less than the cost of lunch is the cost of breakfast. The cost of breakfast is 66\(\frac{2}{3}\)% less than the cost of lunch.

Exercise 5. Describe a real – world situation that could be modeled using the equation 398.4 = 0.83(x). Describe how the elements of the equation correspond with the real – world quantities in your problem. Then, solve your problem. Answer: Word problems will vary. Sample problem: A new tablet is on sale for 83% of its original sale price. The tablet is currently priced at $398.40. What was the original price of the tablet?

0.83 = \(\frac{83}{100}\) = 83%, so 0.83 represents the percent that corresponds with the current price. The current price ($398.40) is part of the original price; therefore, it is represented by 398.4. The original price is represented by x and is the whole quantity in this problem. 398.4 = 0.83x \(\frac{1}{0.83}\) (398.4) = \(\frac{1}{0.83}\) (0.83)x \(\frac{398.4}{0.83}\) = 1x 480 = x The original price of the tablet was $480.00.

Eureka Math Grade 7 Module 4 Lesson 3 Problem Set Answer Key

Question 1. Solve each problem using an equation. a. 49.5 is what percent of 33? Answer: 49.5 = p(33) p = 1.5 = 150%

b. 72 is what percent of 180? Answer: 72 = p(180) p = 0.4 = 40%

c. What percent of 80 is 90? Answer: 90 = p(80) p = 1.125 = 112.5%

Question 2. This year, Benny is 12 years old, and his mom is 48 years old. a. What percent of his mom’s age is Benny’s age? Answer: Let p represent the percent of Benny’s age to his mom’s age. 12 = p(48) p = 0.25 = 25% Benny’s age is 25% of his mom’s age.

b. What percent of Benny’s age is his mom’s age? Answer: Let p represent the percent of his mom’s age to Benny’s age. 48 = p(12) p = 4 = 400% Benny’s mom’s age is 400% of Benny’s age.

c. In two years, what percent of his age will Benny’s mom’s age be at that time? Answer: In two years, Benny will be 14, and his mom will be 50. 14 → 100% 1 → (\(\frac{100}{14}\))% 50 → 50(\(\frac{100}{14}\)% 50 → 25(\(\frac{100}{7}\))% 50 → (\(\frac{2500}{7}\))% 50 → 357 \(\frac{1}{7}\)% His mom’s age will be 357 \(\frac{1}{7}\)% of Benny’s age at that time.

d. In 10 years, what percent will Benny’s mom’s age be of his age? Answer: In 10 years, Benny will be 22 years old, and his mom will be 58 years old. 22 → 100% 1 → \(\frac{100}{22}\)% 58 → 58(\(\frac{100}{22}\))% 58 → 29(\(\frac{100}{11}\))% 58 → \(\frac{2900}{11}\)% 58 → 263 \(\frac{7}{11}\)% In 10 years, Benny’s mom’s age will be 263 \(\frac{7}{11}\)% of Benny’s age at that time.

e. In how many years will Benny be 50% of his mom’s age? Answer: Benny will be 50% of his mom’s age when she is 200% of his age (or twice his age). Benny and his mom are always 36 years apart. When Benny is 36, his mom will be 72, and he will be 50% of her age. So, in 24 years, Benny will be 50% of his mom’s age.

d. As Benny and his mom get older, Benny thinks that the percent of difference between their ages will decrease as well. Do you agree or disagree? Explain your reasoning. Answer: Student responses will vary. Some students might argue that they are not getting closer since they are always 36 years apart. However, if you compare the percents, you can see that Benny‘s age is getting closer to 100% of his mom’s age, even though their ages are not getting any closer.

Question 3. This year, Benny is 12 years old. His brother Lenny’s age is 175% of Benny’s age. How old is Lenny? Answer: Let L represent Lenny’s age. Benny’s age is the whole. L = 1.75(12) L = 21 Lenny is 21 years old.

Question 4. When Benny’s sister Penny is 24, Benny’s age will be 125% of her age. a. How old will Benny be then? Answer: Let b represent Benny’s age when Penny is 24. b = 1.25(24) b = 30 When Penny is 24, Benny will be 30.

b. If Benny is 12 years old now, how old is Penny now? Explain your reasoning. Answer: Penny is 6 years younger than Benny. If Benny is 12 now, then Penny is 6.

Question 5. Benny’s age is currently 200% of his sister Jenny’s age. What percent of Benny’s age will Jenny’s age be in 4 years? If Benny is 200% of Jenny’s age, then he is twice her age, and she is half of his age. Half of 12 is 6. Jenny is currently 6 years old. In 4 years, Answer: Jenny will be 10 years old, and Benny will be 16 years old. Quantity = Percent × Whole. Let p represent the unknown percent. Benny’s age is the whole. 10 = p(16) p = \(\frac{10}{16}\) p = \(\frac{5}{8}\) p = 0.625 = 62.5% In 4 years, Jenny will be 62.5% of Benny’s age.

Question 6. At the animal shelter, there are 15 dogs, 12 cats, 3 snakes, and 5 parakeets. a. What percent of the number of cats is the number of dogs? Answer: \(\frac{15}{12}\) = 1.25. That is 125%. The number of dogs is 125% the number of cats.

b. What percent of the number of cats is the number of snakes? Answer: \(\frac{3}{12}\) = \(\frac{1}{4}\) = 0.25. There are 25% as many snakes as cats.

c. What percent less parakeets are there than dogs? Answer: \(\frac{5}{15}\) = \(\frac{1}{3}\). That is 33 \(\frac{1}{3}\)%. There are 66 \(\frac{2}{3}\)% less parakeets than dogs.

d. Which animal has 80% of the number of another animal? Answer: \(\frac{12}{15}\) = \(\frac{4}{5}\) = \(\frac{8}{10}\) = 0.80. The number of cats is 80% the number of dogs.

e. Which animal makes up approximately 14% of the animals in the shelter? Answer: Quantity = Percent × Whole. The total number of animals is the whole. q = 0.14(35) q = 4.9 The quantity closest to 4.9 is 5, the number of parakeets.

Question 7. Is 2 hours and 30 minutes more or less than 10% of a day? Explain your answer. Answer: 2 hr.30 min. → 2.5 hr.; 24 hours is a whole day and represents the whole quantity in this problem. 10% of 24 hours is 2.4 hours. 2.5 > 2.4, so 2 hours and 30 minutes is more than 10% of a day.

Question 8. A club’s membership increased from 25 to 30 members. a. Express the new membership as a percent of the old membership. Answer: The old membership is the whole. Quantity = Percent × Whole. Let p represent the unknown percent. 30 = p(25) p = 1.2 = 120% The new membership is 120% of the old membership.

b. Express the old membership as a percent of the new membership. Answer: The new membership is the whole. 30 → 100% 1 → \(\frac{100}{30}\)% 25 → 25 ∙ \(\frac{100}{30}\)% 25 → 5 ∙ 1\(\frac{100}{6}\)% 25 → \(\frac{500}{6}\)% = 83 \(\frac{1}{3}\)% The old membership is 83 \(\frac{1}{3}\)% of the new membership.

Question 9. The number of boys in a school is 120% the number of girls at the school. a. Find the number of boys if there are 320 girls. Answer: The number of girls is the whole. Quantity = Percent × Whole. Let b represent the unknown number of boys at the school. b = 1.2(320) b = 384 If there are 320 girls, then there are 384 boys at the school.

b. Find the number of girls if there are 360 boys. Answer: The number of girls is still the whole. Quantity = Percent × Whole. Let g represent the unknown number of girls at the school. 360 = 1.2(g) g = 300 If there are 360 boys at the school, then there are 300 girls.

Question 10. The price of a bicycle was increased from $300 to $450. a. What percent of the original price is the increased price? Answer: The original price is the whole. Quantity = Percent × Whole. Let p represent the unknown percent. 450 = p(300) p = 1.5 1.5 = \(\frac{150}{100}\) = 150% The increased price is 150% of the original price.

b. What percent of the increased price is the original price? Answer: The increased price, $450, is the whole. 450 → 100% 1 → \(\frac{100}{450}\)% 300 → 300(\(\frac{100}{450}\))% 300 → 2(\(\frac{100}{3}\))% 300 → \(\frac{200}{3}\)% 300 → 66 \(\frac{2}{3}\)% The original price is 66 \(\frac{2}{3}\)% of the increased price.

Question 11. The population of Appleton is 175% of the population of Cherryton. a. Find the population in Appleton if the population in Cherryton is 4,000 people. Answer: The population of Cherryton is the whole. Quantity = Percent × Whole. Let a represent the unknown population of Appleton. a = 1.75(4,000) a = 7,000 If the population of Cherryton is 4,000 people, then the population of Appleton is 7,000 people.

b. Find the population in Cherryton if the population in Appleton is 10,500 people. Answer: The population of Cherryton is still the whole. Quantity = Percent × Whole. Let c represent the unknown population of Cherryton. 10,500 = 1.75c c = 10,500÷1.75 c = 6,000 If the population of Appleton is 10,500 people, then the population of Cherryton is 6,000 people.

c. Locate all points on the graph that would represent classrooms in which the number of girls y is 100% of the number of boys x. Describe the pattern that these points make. Answer: The points lie on a line that includes the origin; therefore, it is a proportional relationship.

d. Which points represent the classrooms in which the number of girls as a percent of the number of boys is greater than 100%? Which points represent the classrooms in which the number of girls as a percent of the number of boys is less than 100%? Describe the locations of the points in relation to the points in part (c). Answer: All points where y > x are above the line and represent classrooms where the number of girls is greater than 100% of the number of boys. All points where y < x are below the line and represent classrooms where the number of girls is less than 100% of the boys.

e. Find three ordered pairs from your table representing classrooms where the number of girls is the same percent of the number of boys. Do these points represent a proportional relationship? Explain your reasoning. Answer: There are two sets of points that satisfy this question: {(3,6), (5,10), and (11,22)}: The points do represent a proportional relationship because there is a constant of proportionality k = \(\frac{y}{x}\) = 2. {(4,2), (10,5), and (14,7)}: The points do represent a proportional relationship because there is a constant of proportionality k = \(\frac{y}{x}\) = \(\frac{1}{2}\).

g. What is the constant of proportionality in your equation(s), and what does it tell us about the number of girls and the number of boys at each point on the graph that represents it? What does the constant of proportionality represent in the table in part (a)? Answer: In the equation y = 2x, the constant of proportionality is 2, and it tells us that the number of girls will be twice the number of boys, or 200% of the number of boys, as shown in the table in part (a). In the equation y = 1/2 x, the constant of proportionality is 1/2, and it tells us that the number of girls will be half the number of boys, or 50% of the number of boys, as shown in the table in part (a).

Eureka Math Grade 7 Module 4 Lesson 3 Exit Ticket Answer Key

Solve each problem below using at least two different approaches. Question 1. Jenny’s great – grandmother is 90 years old. Jenny is 12 years old. What percent of Jenny’s great – grandmother’s age is Jenny’s age? Answer: Algebraic Solution: Quantity = Percent × Whole. Let p represent the unknown percent. Jenny’s great – grandmother’s age is the whole. 12 = p(90) 12 ∙ \(\frac{1}{90}\) = p(90) ∙ \(\frac{1}{90}\) 2 ∙ \(\frac{1}{15}\) = p(1) \(\frac{2}{15}\) = p \(\frac{2}{15}\) = \(\frac{2}{15}\) (100%) = 13 \(\frac{1}{3}\)% Jenny’s age is 13 1/3% of her great – grandmother’s age.

Numeric Solution: 90 → 100% 1 → \(\frac{100}{90}\)% 12 → (12 ∙ \(\frac{100}{90}\))% 12 → (100 ∙ \(\frac{12}{90}\))% 12 → 100(\(\frac{2}{15}\))% 12 → 20(\(\frac{2}{3}\))% 12 → (\(\frac{40}{3}\))% 12 → 13 \(\frac{1}{3}\)%

Alternative Numeric Solution: 90 → 100% 9 → 10% 3 → \(\frac{10}{3}\)% 12 → 4(\(\frac{10}{3}\))% 12 → (\(\frac{40}{3}\))% 12 → 13 \(\frac{1}{3}\)%

Question 2. Jenny’s mom is 36 years old. What percent of Jenny’s mother’s age is Jenny’s great – grandmother’s age? Answer: Quantity = Percent × Whole. Let p represent the unknown percent. Jenny’s mother’s age is the whole. 90 = p(36) 90 ∙ \(\frac{1}{36}\) = p(36) ∙ \(\frac{1}{36}\) 5 ∙ \(\frac{1}{2}\) = p(1) 2.5 = p 2.5 = 250% Jenny’s great grandmother’s age is 250% of Jenny’s mother’s age.

Eureka Math Grade 7 Module 4 Lesson 3 Part, Whole, or Percent—Round 1 Answer Key

Eureka Math Grade 7 Module 4 Lesson 3 Part, Whole, or Percent—Round 2 Answer Key

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Math  /  7th Grade  /  Unit 1: Proportional Relationships

Proportional Relationships

Students deepen their understanding of ratios to investigate proportional relationships, in order to solve multi-step, real-world ratio problems using new strategies that rely on proportional reasoning.

Unit Summary

In Unit 1, 7th grade students deepen their understanding of ratios to investigate and analyze proportional relationships. They begin the unit by looking at how proportional relationships are represented in tables, equations, and graphs. As they analyze each representation, students continue to internalize what proportionality means, and how concepts like the constant of proportionality are visible in different ways. Students then spend time comparing examples of proportional and non-proportional associations, and studying how all the representations are connected to one another. Finally, in this unit, students will solve multi-step, real-world ratio and rate problems using efficient strategies and representations that rely on proportional reasoning (MP.4). These new strategies and representations, such as setting up and solving a proportion, are added to students’ growing list of approaches to solve problems. Throughout the unit, students will engage with MP.2 and MP.6. Translating between equations, graphs, tables, and written explanations requires students to reason both abstractly and quantitatively, and to pay precise attention to units, calculations, and forms of communication throughout their work. 

In 6th grade , students were introduced to the concept of ratios and rates. They learned several strategies to represent ratios and to solve problems, including using concrete drawings, double number lines, tables, tape diagrams, and graphs. They defined and found unit rates and applied this to measurement conversion problems. 7th grade students will draw on these conceptual understandings to fully understand proportional relationships.

Beyond this unit, in Unit 5 , students will re-engage with proportional reasoning, solving percent problems and investigating how proportional reasoning applies to scale drawings. In eighth grade, students connect unit rate to slope, and they compare proportional relationships across different representations. They expand their understanding of non-proportional relationships to study linear functions in the form of $$y=mx+b$$ , and compare these to non-linear functions, such as  $$y=6x^2$$ .

Pacing: 22 instructional days (18 lessons, 3 flex days, 1 assessment day)

Fishtank Plus for Math

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

The following assessments accompany Unit 1.

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Pre-Unit Student Self-Assessment

Have students complete the Mid-Unit Assessment after lesson 9.

Use the resources below to assess student understanding of the unit content and action plan for future units.

Post-Unit Assessment

Post-Unit Assessment Answer Key

Post-Unit Student Self-Assessment

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Intellectual Prep

Suggestions for how to prepare to teach this unit

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

Internalization of Standards via the Post-Unit Assessment

• Standards that each question aligns to
• Strategies and representations used in daily lessons
• Relationship to Essential Understandings of unit 
• Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

• Read and annotate the Unit Summary.
• Notice the progression of concepts through the unit using the Lesson Map.

Essential Understandings

• Connection to Post-Unit Assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

• Read Progressions for the Common Core State Standards in Mathematics, 6-7, Ratios and Proportional Relationships  to gain a better understanding of what students have learned in sixth grade and what is expected in seventh grade.
• The UnboundEd  Ratios: Unbound: A Guide to Grade 7 Mathematics Standards  is also a great read.
• Read the following table that includes models used throughout the unit:

The graph below shows the relationship between the cost of gas and the number of gallons of gas purchased at a gas station. 

The central mathematical concepts that students will come to understand in this unit

• A proportional relationship between two quantities is a collection of equivalent ratios, related to each other by a constant of proportionality. 
• Proportional relationships can be represented in different, related ways, including a table, equation, graph, and written description. Knowing one representation provides the information needed to represent the relationship in a different way. 
• A unit rate, associated with a ratio $$a:b$$ , is $$a/b$$ or $$b/a$$ units of one quantity per 1 unit of another quantity. Unit rates are represented in equations of the form $${y=kx}$$ and in graphs of proportional relationships as the ordered pair $$(1, r)$$ .
• There are many applications that can be solved using proportional reasoning, including problems with price increases and decreases, commissions, fees, unit prices, and constant speed.

Terms and notation that students learn or use in the unit

constant of proportionality

dependent variable

equivalent ratio

independent variable

part to whole ratio

part to part ratio

proportional relationship

To see all the vocabulary for Unit 1, view our 7th Grade Vocabulary Glossary .

The materials, representations, and tools teachers and students will need for this unit

• Calculators (1 per student)
• Graph Paper (2-3 sheets per student)
• Ruler (1 per student)

To see all the materials needed for this course, view our 7th Grade Course Material Overview .

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Solve ratio and rate problems using double number lines, tables, and unit rate.

7.RP.A.1 7.RP.A.2

Represent proportional relationships in tables, and define the constant of proportionality.

7.RP.A.2 7.RP.A.2.B

Determine the constant of proportionality in tables, and use it to find missing values.

7.RP.A.2.A 7.RP.A.2.B

Write equations for proportional relationships presented in tables.

7.RP.A.2.B 7.RP.A.2.C

Write equations for proportional relationships from word problems.

7.RP.A.2 7.RP.A.2.C

Represent proportional relationships in graphs.

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D

Interpret proportional relationships represented in graphs.

7.RP.A.2 7.RP.A.2.D

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Topic B: Non-Proportional Relationships

Compare proportional and non-proportional relationships.

Determine if relationships are proportional or non-proportional.

Topic C: Connecting Everything Together

Make connections between the four representations of proportional relationships (Part 1).

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Make connections between the four representations of proportional relationships (Part 2).

Use different strategies to represent and recognize proportional relationships.

Topic D: Solving Ratio & Rate Problems with Fractions

Find the unit rate of ratios involving fractions.

Find the unit rate and use it to solve problems.

7.RP.A.1 7.RP.A.3

Solve ratio and rate problems by setting up a proportion.

Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.

Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.

Use proportional reasoning to solve real-world, multi-step problems.

7.RP.A.1 7.RP.A.2 7.RP.A.3

Common Core Standards

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Ratios and Proportional Relationships

7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

7.RP.A.2.A — Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Foundational Standards

Standards covered in previous units or grades that are important background for the current unit

Expressions and Equations

6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.C.9 — Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Number and Operations—Fractions

5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

6.RP.A.2 — Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Expectations for unit rates in this grade are limited to non-complex fractions. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."

6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.A.3.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.A.3.B — Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

The Number System

6.NS.A.1 — Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Future Standards

Standards in future grades or units that connect to the content in this unit

8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.

8.F.A.2 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.A.3 — Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.5 — Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 — Attend to precision.

CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Operations with Rational Numbers

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7th Grade Math Percents Unit Test

# 1 of 6 : spicy, # 2 of 6 : spicy, # 3 of 6 : medium, # 4 of 6 : medium, # 5 of 6 : spicy, # 6 of 6 : mild.

A percentage refers to a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. Students must take a 7 grade math unit test to check their understanding of percentage and enhance their knowledge. 

Teachers can assign this percentage practice test in the classroom to assess students’ percentage knowledge. 

A percentage refers to a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. Students must take ...

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Circles Angle Relationships Expressions, Equations, And Inequalities Probability Rates And Proportional Relationships Signed Number Operations

Lesson 3. 5

Application of percents, videos & guided notes.

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Home / United States / Math Classes / Worksheets / 7th Grade Ratio And Proportions Worksheets

• 7th Grade Ratio And Proportions Worksheets

7th Grade Ratio and Proportion Worksheets help students learn to compare two similar sizes by giving them a ratio. When both ratios are the same in an equation, they are called proportions. Ratio and proportions are based on numbers and fractions and are the basis for several mathematical concepts. Ratios and Proportion Worksheets help 7th graders understand concepts such as how to express ratios in their simplest form, compare ratios, arrange ratios in ascending or descending order, proportions, and the proportional mean between numbers. Practice questions feature  tables, graphs, word problems, and stimulating visuals to keep students engaged while learning. ...Read More Read Less

• Interactive Worksheets
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Choose Math Worksheets by Grade

Choose math worksheets by topic, benefits of 7th grade ratio and proportions worksheets.

The Ratio and Proportion Worksheets are essential learning materials for 7th graders. Regular practice with these worksheets can help students increase their understanding of these crucial topics. 

Instilling reasoning using logic:

Children can develop a keen sense of reasoning as they practice and solve problems using the Online Ratio and Proportion Worksheets. The printable worksheets cover various topics to help students understand the basics of rations and proportions and learn to use what they have learned in their daily life. 

Approaching cautiously :

The step-by-step 7th Grade Ratio and Proportions worksheets start with simple tasks that gradually increase in difficulty level. Students learn to solve these problems at their own pace and apply the concepts to real life situations.  

Studying in their own time:

The Ratio and Proportion Worksheets provide children with multi-level problems they can do either in the classroom or at home to help them understand the concepts of this topic.

Trying different formats:

7th Grade Online Ratios and Proportions Worksheets were designed to keep students engaged and eliminate monotonous studying. Worksheets are interactive, and give students interesting visual examples to help them understand the concepts being reviewed and build their confidence. 

Grade 7 Ratio and Proportions Worksheets Explained

Ratio proportion worksheets for 7 th grade are designed to teach young students the basics of ratio and proportions quickly and effectively. Worksheets often contain tables of equivalent rates with two rows. Each row represents values for an item.

Below is a basic table where students need to figure out proportions and ratios from two given Kilometer and Hour values. The worksheets are arranged in order of difficulty, so the first worksheet will feature simpler problems to introduce these concepts. The proportion/ratio is defined in the beginning of the worksheets.

7th Grade Ratio and Proportion worksheets challenge students to figure out the equivalent values for one of the items across multiple, equal proportions or ratios.

Moving up in difficulty,  the table's structure stays the same, but the provided values move to the middle of the table.

The most complex problems on the worksheets feature some values in one of the rows and some in the other. Again, students need to understand the unit rates to complete these.

Some ratio proportion worksheets may contain traditional mathematical problems. These are designed to reflect real-life situations as much as possible. This helps students learn perspective and apply mathematics in practical life problems.

• 7 th Grade Ratio and Proportion worksheets feature problems such as:

Q1: If x: y = 2:3, then what should be 2x + 3y: 4x + 5y?

Answer: If x: y = 2:3, then x/y = 2/3, or 3x = 2y, or x = 2y/3.

Applying this formula to the bigger ratio, 2x + 3y = (2 x 2y/3) + 3y = 13y/3

And 4x + 5y = (4 x 2y/3) + 5y = 23y/3

So 2x + 3y: 4x + 5y = 13y/3 / 23y/3 = 13/23 = 13:23

Q2: If a 6 feet tall tree casts a shadow of 15 meters, how tall a shadow will a pole 30 meters high cast?

Here, the proportion of the tree’s height to its shadow is 6:15, which can be simplified to 2:5.

So, we present this equivalency problem as:

2:5 = 30:x (assuming x is the height of the shadow cast)

or, 2/5 = 30/x

or, x/30 = 5/2

or, x = 30 x 5/2 = 75

The answer is 75 meters.

By practicing using Grade 7 Ratio and Proportions Worksheets, students are encouraged to solve these expressive problems in simpler forms, find the difference between ratios, order ratios in either up or down formation, and proportionally average between numbers. The worksheets also illustrate problems that use algebraic variables that relate to real world mathematical problems.

What are 7th grade ratio and proportions worksheets about?

The 7th grade ratio and proportions worksheets are free fun and interactive printable worksheets that contain questions and stepwise solutions based on ratio and proportion that enhance the knowledge about the concept and self assessment skill.

What is the difference between ratio and proportion?

The ratio is the mathematical term to represent the comparison of two numbers and it is represented by either a/b or a : b but proportion is the equation that tells whether the two ratios are equal or not.

What are equivalent ratios?

The equivalent ratios are the ratios that describe the same relationship between numbers. The value of equivalent ratios is equivalent.

How can we find whether the ratios are proportional?

The ratios, whether proportional or not can be determined in three ways, first is finding the values of the ratios, second is using cross product property, and third is using the equivalent ratio table. You will find good practice questions in grade 7 ratio and proportions worksheets.

How are grade 7 ratio and proportions worksheets beneficial for students?

The 7th-grade ratio and proportions worksheets for students are free and printable worksheets which means the student can appear for the worksheets as many times as he/she wants and can print them also so, no need for internet connectivity for solving worksheets. The worksheet has questions based on ratio and proportion that will reinforce the knowledge of the topic and by solving real-life questions students can also apply the concept to real-life needs. In worksheets, there are different types of questions, solving those questions students have an encouraging feeling and can trace their progress. That will help in analytical thinking skill.

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Percents Activity Bundle 7th Grade

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This Percents Activity Bundle includes 8 classroom activities to support solving real-life proportions, solving percent problems, percent of change, percent error, and simple interest.

These hands-on and engaging activities are all easy to prep! Students are able to practice and apply concepts with these percents activities, while collaborating and having fun!  Math can be fun and interactive!

Standards: CCSS (7.RP.2, 7.RP.3) and TEKS (7.4D)

What is included in the 7th grade Percents Activity Bundle?

Eight hands-on activities that can be utilized in pairs or groups of 3-4. All activities include any necessary recording sheets and answer keys.

• Scavenger Hunt:  solving proportions review
• Cut and Paste:  percent proportions
• Task Cards:  percent mark up and discount
• Class Demonstration:  percent change
• Solve and Color:  percent error
• Spinner Activity:  simple interest
• Performance Task: percents
• Find It, Fix It:  percents unit review

How to use this resource:

• Use as a whole group classroom activity
• Use in a small group for additional remediation, tutoring, or enrichment
• Use as an alternative homework or independent practice assignment
• Incorporate within our CCSS-Aligned Percents Unit or   TEKS-Aligned Proportionality Unit  to support the mastery of concepts and skills.

Time to Complete:

• Most activities can be utilized within one class period. Performance tasks summarize the entire unit and may need 2-3 class periods. However, feel free to review the activities and select specific problems to meet your students’ needs and time specifications. There are multiple problems to practice the same concepts, so you can adjust as needed.

Looking for more 7 th Grade Math Material? Join our All Access Membership Community! You can reach your students without the “I still have to prep for tomorrow” stress, the constant overwhelm of teaching multiple preps, and the hamster wheel demands of creating your own teaching materials.

• Grade Level Curriculum
• Supplemental Digital Components
• Complete and Comprehensive Student Video Library 

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Digital Math Activity Bundle 7th Grade

Percents Unit 7th Grade CCSS

Proportionality Unit 7th Grade TEKS

Free Printable Percents Worksheets for 7th Grade

Percents made accessible! Discover a vast collection of free printable math worksheets tailored for Grade 7 students, designed to enhance their understanding of percentages. Dive into the world of math with Quizizz!

Recommended Topics for you

• Converting Percents, Decimals, and Fractions
• Percent Problems

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Percents worksheets for Grade 7 are an essential resource for teachers looking to help their students master the concepts of Math, Percents, Ratios, and Rates. These worksheets provide a variety of exercises and problems that cover topics such as calculating percentages, finding equivalent ratios, and determining rates. By incorporating these worksheets into their lesson plans, teachers can ensure that their Grade 7 students have a strong foundation in these critical mathematical concepts. Furthermore, these percents worksheets for Grade 7 are designed to be engaging and challenging, keeping students interested in the material while also promoting a deeper understanding of the subject matter.

In addition to traditional worksheets, teachers can also utilize Quizizz, an online platform that offers interactive quizzes and games related to Math, Percents, Ratios, and Rates for Grade 7 students. This platform allows teachers to create customized quizzes and assignments, making it easy to incorporate the concepts covered in percents worksheets for Grade 7 into a more interactive and engaging format. Quizizz also provides teachers with valuable data and insights on student performance, allowing them to identify areas where students may need additional support or practice. By combining the use of percents worksheets for Grade 7 with the innovative tools and resources offered by Quizizz, teachers can create a comprehensive and effective learning experience for their students.

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Unit 3: Unit rates and percentages

Lesson 4: converting units.

• Ratios and measurement (Opens a modal)
• Ratios and units of measurement Get 3 of 4 questions to level up!

Lesson 5: Comparing speeds and prices

• Comparing rates example (Opens a modal)
• Comparing rates Get 3 of 4 questions to level up!

Lesson 6: Interpreting ratios

• Solving unit rate problem (Opens a modal)

Lesson 9: Solving rate problems

• Rate review (Opens a modal)

Lesson 12: Percentages and tape diagrams

• Finding the whole with a tape diagram (Opens a modal)
• Percents from tape diagrams Get 3 of 4 questions to level up!
• Find percents visually Get 5 of 7 questions to level up!

Lesson 13: Benchmark percentages

• No videos or articles available in this lesson
• Percents from fraction models Get 3 of 4 questions to level up!
• Benchmark percents Get 5 of 7 questions to level up!

Lesson 14: Solving percentage problems

• Finding a percent (Opens a modal)
• Finding percents Get 5 of 7 questions to level up!

Lesson 15: Finding this percent of that

• Percent of a whole number (Opens a modal)
• Equivalent representations of percent problems Get 3 of 4 questions to level up!

Lesson 16: Finding the percentage

• Percent word problem: recycling cans (Opens a modal)
• Percent word problems Get 5 of 7 questions to level up!

7th Grade Ratios, Proportions, Percents, and Similar Figures Math Unit

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Description

I am excited to introduce this 7th grade NO PREP math product. It is a great way to cover percent, ratio, and proportion concepts. Similar figures are also introduced to reinforce these concepts. Included in this unit are notes, practice pages, quizzes, and a test to assess students. Answer keys are included! All you have to do is print the pages for your students.

An overview of the unit and a sample day-by-day lesson plans are included as well. Obviously this can be adjusted based on how much time you have to teach each day.

ALL chapters include:

• Practice Pages

• Answer Keys

Chapter 1 (Percents) includes:

• Equivalent fraction, decimal, and percent conversions
• Percent of a number
• Markup, discount, and tax
• Percent of change
• percent equations

Chapter 2 (Ratios and Proportions) includes:

• Proportions using scale factor
• Proportions using cross products
• Solving proportions (using equations)
• Proportional relationships

Chapter 3 (Similar Figures) includes:

• Congruent and similar shapes
• Finding missing side lengths of similar shapes using scale factor
• Finding missing side lengths using proportions
• Finding missing side lengths in nested triangles
• How scale factor affects: sides, perimeter, area, and corresponding angles

There is also an assessment (quiz) over each chapter and a test over the entire Unit! There is a review for each of the quizzes as well. These are also in Google!

There is also an End of the Year review activity that goes along with this unit.

*This is the same product as 7th Grade Unit 3 Percents, Ratios, Proportions, and Similar Figures Using Google except this is the PDF version and NOT on Google!

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Concepts and Explanations | Worked Homework Examples | Math Background

The Problems of this Unit explore properties of polygons. Through work on tasks that require drawing, building, measuring, and reasoning about the size and shape of polygons, your student will learn:

• How to sort polygons into classes according to the number, size, and relationships of their sides and angles
• How to find angle measures by estimation, by use of tools like protractors and angle rulers, and by reasoning with variables and equations
• Formulas for finding the sum of the interior and exterior angles in any polygon
• The relationships of complementary and supplementary pairs of angles, such as those formed by interior and exterior angles of polygons, and in figures where parallel lines are cut by transversals
• How to apply and design angle-side measurement conditions needed for drawing triangles and quadrilaterals with specific properties
• The symmetry, tiling, and rigidity or flexibility properties of polygons that make them useful in buildings, tools, art and craft designs, and natural objects

As your child works on the Problems in this Unit, ask questions about situations that involve shapes such as:

• What do these polygons have in common? How do they differ from each other?
• When should I use estimation, freehand drawing, or special tools to measure and construct angles and polygons?
• How do the side lengths and angles of polygons determine their shapes?
• Why do certain polygons appear so often in buildings, artistic designs, and natural objects?
• How can I give directions for constructing polygons that meet conditions of any given problem?

7-2 Accentuate the Negative

Concepts and Explanations | Worked Homework Examples Math Background

In Accentuate the Negative , your student(s) will extend their knowledge of negative numbers. They will use negative numbers to solve problems. They will learn how to:

• Use appropriate notation to indicate positive and negative numbers and zero
• Compare and order rational numbers and locate them on a number line
• Understand the relationship between a number and its opposite (additive inverse)
• Relate direction and distance to the number line
• Develop and use different models (number line, chip model) for representing addition, subtraction, multiplication, and division
• Develop algorithms for adding, subtracting, multiplying, and dividing positive and negative numbers
• Interpret and write mathematical sentences to show relationships and solve problems
• Write and use related fact families for addition/subtraction and multiplication/division to solve simple equations
• Use parentheses and the Order of Operations in computations
• Use the commutative properties of addition and multiplication
• Apply the Distributive Property to simplify expressions and solve problems
• Use models and rational numbers to represent and solve problems

When your child encounters a new problem, it is a good idea to ask questions such as:

• How do negative and positive numbers and zero help describe the situation?
• What will addition, subtraction, multiplication, or division of rational numbers tell about the problem?
• What model(s) for positive and negative numbers and zero help show relationships in the problem situation?

7-3 Stretching and Shrinking

Concepts and Explanations Worked Homework Examples Math Background

In Stretching and Shrinking , your child will learn the mathematical meaning of similarity, explore the properties of similar figures, and use similarity to solve problems. Your student will learn how to:

• Identify similar figures by comparing corresponding sides and angles
• Use scale factors and ratios to describe relationships among the side lengths, perimeters, and areas of similar figures
• Construct similar figures (scale drawings) using informal methods, scale factors, and geometric tools
• Use algebraic rules to produce similar figures and recognize when a rule shrinks or enlarges a figure
• Predict the ways that stretching or shrinking a figure will affect side lengths, angle measures, perimeters, and areas
• Use the properties of similarity to find distances and heights that cannot be measured directly
• Use scale factors or ratios to find missing side lengths in a pair of similar figures
• What determines whether two shapes are similar?
• What is the same and what is different about two similar figures?
• When figures are similar, how are the side lengths, areas, and scale factors related?
• How can I use similar figures to find missing measurements?

7-4 Comparing and Scaling

Concepts and Explanations   Worked Homework Examples Math Background

In this Unit, your student(s) will extend their knowledge of ratios, proportions, and proportional reasoning. They will learn how to:

• Analyze comparison statements for correctness and quality;
• Use ratios, rates, and percents to write comparison statements;
• Distinguish between and use part-to-part and part-to-whole ratios to make comparisons;
• Scale a ratio, rate, or percent to solve a problem;
• Set up and solve proportions;
• Find unit rates and use them to solve problems;
• Recognize proportional situations from a table, graph, or equation;
• Connect a unit rate and a constant of proportionality to a table, graph, or equation representing a situation.

As you work on the Problems in this Unit, ask yourself these questions about situations that involve comparisons.

• What quantities are being compared?
• Why does the situation involve a proportional relationship (or not)?
• How might ratios, rates, or a proportion be used to solve the problem?

7-5 Moving Straight Ahead

Concepts and Explanations   > Worked Homework Examples Math Background

In Moving Straight Ahead , your child will explore properties of linear relationships and linear equations, and will learn how to:

• Recognize problem situations that involve linear relationships
• Construct tables, graphs, and symbolic equations that represent linear relationships
• Translate information about linear relations given in a verbal description, a table, a graph, or an equation to one of the other forms
• Connect equations that represent linear relationships to the patterns in tables and graphs of those equations
• Identify the rate of change, slope, and y-intercept from the graph of a linear relationship
• Solve linear equations
• Write and interpret equivalent expressions as well as determine whether two or more expressions are equivalent
• Solve problems and make decisions about linear relationships using information given in tables, graphs, and equations
• Solve problems that can be modeled with inequalities and graph the solution set
• What are the variables in the problem?
• Do the variables in the problem have a linear relationship to each other?
• What patterns in the problem suggest that the relationship is linear?
• How can the linear relationship in a situation be represented with a verbal description, a table, a graph, or an equation?
• How do changes in one variable affect changes in a related variable?
• How are these changes captured in a table, a graph, or an equation?
• How can tables, graphs, and equations of linear relationships be used to answer questions?

7-6 What Do You Expect?

In this Unit, your child will deepen their understanding of basic probability concepts and will learn about the expected value of situations involving chance. They will learn how to :

• Use probabilities to predict what will happen over the long run
• Distinguish between equally likely events and those that are not equally likely
• Use strategies for identifying possible outcomes and analyzing probabilities, such as using lists or tree diagrams
• Gather data from experiments (experimental probability)
• Analyze possible outcomes (theoretical probability)
• Understand that experimental probabilities are better estimates of theoretical probabilities when they are based on larger numbers of trials
• Determine if a game is fair or unfair
• Use models to analyze situations that involve two stages (or actions)
• Determine the expected value of a chance situation
• Analyze situations that involve binomial outcomes
• Interpret statements of probability to make decisions and answer questions

As you work on Problems in this Unit, ask your child questions about situations that involve analyzing probabilities:

• What are the possible outcomes for the event(s) in this situation?
• Are these outcomes equally likely?
• Is this a fair or unfair situation?
• Can I compute the theoretical probabilities or do I conduct an experiment?
• How can I determine the probability of one event followed by a second event: two-stage probabilities?
• How can I use expected value to help me make decisions?

7-7 Filling and Wrapping

In Filling and Wrapping , your child will explore surface area and volume of three-dimensional objects, and will learn how to:

• Develop the ability to visualize and draw three-dimensional shapes
• Develop strategies for finding volumes of three-dimensional objects, including prisms, cylinders, pyramids, cones, and spheres
• Design and use nets to develop formulas for finding surface areas of prisms and cylinders
• Develop formulas and strategies for finding the area and circumference of a circle
• Explore patterns relating the volumes of prisms, cylinders, cones, spheres, and pyramids
• Understand that three-dimensional figures may have the same volume but different surface areas
• Investigate the effects of scaling dimensions of figures on the volume and surface area
• Recognize and solve problems involving volume and surface area
• What are the shapes and properties of the figures in the problem?
• Which measures of a figure are involved—length, surface area, or volume?
• What measurement strategies or formulas might help in using given information to find unknown measurements?

7-8 Samples and Populations

In Samples and Populations , your student(s) will learn about different ways to collect and analyze data in order to make comparisons and draw conclusions. They will learn how to:

• What is the population?
• What is the sample?
• Is the sample a representative sample?
• How can I describe the data I collected?
• How can I use my results to draw conclusions about the population?
• How can I use samples to compare two or more populations?