lesson 5 problem solving practice graph ratio tables

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• Grade 6 McGraw Hill Glencoe - Answer Keys

Explanation:

Reason Inductively the distance around a circle is also called the circumference. The diameter of a circle is the distance across the circle through its center.

a. The table shows the circumference and diameter for different circles. Complete the table by estimating the ratio \(\frac{c}{d}\) for each circle.

b. The ratio \(\frac{c}{d}\) is representing by the Greek letter \(\pi\), which is called pi. Describe the ratio \(\frac{c}{d}\) for the value you calculated.

c. Make a Prediction Find two circular objects. Measure the diameter and then make a prediction about the circumference of each circle. How could you check your prediction?

• Type below:

d. Use the Internet or another media source to research pi. Write a few sentence about you learned.

H.O.T. Problems Higher Order Thinking

Model with Mathematics Write a real-world problem using ratios or rates that could be represented on the coordinate plane.

Persevere with Problems Give the coordinates of the point located halfway between (2, 1) and (2, 4).

Persevere with Problems The graph below shows the cost of purchasing pencils from the school office. The graph is missing a point to indicate the cost of 12 pencils. Complete the graph by plotting the missing information. Explain your answer.

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Curriculum  /  Math  /  7th Grade  /  Unit 1: Proportional Relationships  /  Lesson 5

Proportional Relationships

Lesson 5 of 18

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Write equations for proportional relationships from word problems.

Common Core Standards

Core standards.

The core standards covered in this lesson

Ratios and Proportional Relationships

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

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.

Foundational Standards

The foundational standards covered in this lesson

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.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Recall that a ratio relationship $$A:B$$  has two unit rates, $$A/B$$  and $$B/A$$ .
• Find the constant of proportionality from a situation (not a table) by finding the value of $$y/x$$ ,  where $$y$$  is the dependent variable and $$x$$  is the independent variable. 
• Write an equation using the constant of proportionality for a proportional relationship.
• Use an equation to solve problems.
• Decontextualize situations to represent them as equations and re-contextualize equations to explain their meanings as they relate to situations (MP.2).

Suggestions for teachers to help them teach this lesson

Lesson Materials

• Calculators (1 per student)

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

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

A repair technician replaces cracked screens on phones. He can replace 5 screens in 3 hours. 

a.   Write an equation you can use to determine how long it takes to replace any number of screens.

b.   Write an equation you can use to determine how many screens can be replaced in a certain number of hours.

c.   Use one of your equations to determine how long it would take to replace 30 screens.

d.   Use one of your equations to determine how many screens could be replaced in 12 hours.

Guiding Questions

A train traveling from Boston to New York moves at a constant speed. The train covers 260 miles in 3.25 hours. 

Write an equation that represents this relationship. Explain what your equation tells you about the train.

Deli turkey meat is on sale at two different grocery stores, as represented below.

What is the unit price of turkey per pound at each store? Which store has the better sale?

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

The 7th graders at Wilson Middle School are taking a field trip to the science museum. So far, 12 students have turned in a total of $81 to pay for their ticket.

a.   Write an equation to represent the cost, $$c$$ , for  $$t$$  tickets.

b.   If all 72 students turn in their ticket money, how much money will be collected?

Student Response

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Challenge: The average person uses about 90 gallons of water per day. At this rate, how long would it take a family of 4 to use enough water to fill an average-size swimming pool? An olympic-size swimming pool?
• EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 8 — Problem Set 1-4; Do not include any questions with graphs as these will be addressed in upcoming lessons.
• Open Up Resources Grade 7 Unit 2 Practice Problems — Lesson 5
• EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 9 — Example 1, Problem Set 1 and 3
• Illustrative Mathematics Sore Throats, Variation 1
• RDA Performance Task Bank Grade 7 Mathematics Sample SR Item

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

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

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Course: 6th grade   >   Unit 1

• Ratio tables

Solving ratio problems with tables

• Equivalent ratios
• Equivalent ratios: recipe
• Equivalent ratio word problems
• Understanding equivalent ratios
• Equivalent ratios in the real world
• Interpreting unequal ratios
• Understand equivalent ratios in the real world

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Lesson5 Homework Practice Graph Ratio Tables

Lesson5 Homework Practice Graph Ratio Tables - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Tteeaacchheerrss gguuiiddee, Lesson 6 comparing ratios using ratio tables, Name date period lesson 7 homework practice, Ratios rates unit rates, Homework practice and problem solving practice workbook, Writing linear equations module 5, Ratios and proportional relationships lessons 1 6, Just the maths.

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1. TTEEAACCHHEERRSS GGUUIIDDEE

2. lesson 6: comparing ratios using ratio tables, 3. name date period lesson 7 homework practice, 4. ratios, rates & unit rates, 5. homework practice and problem-solving practice workbook, 6. writing linear equations module 5, 7. ratios and proportional relationships: lessons 1-6, 8. ''just the maths'' -.