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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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Video transcript
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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'' -.
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Chapter 1: Ratios and Rates; Lesson 5: Graph Ratio Tables. Please share this page with your friends on FaceBook. Question 6 ... 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. ... Math Practice 101 ...
Ratio tables. Pat can drive 36 kilometers for every 3 liters of gas they put in their car. Complete the table using equivalent ratios. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class ...
Lesson 5: Graph Ratio Tables. Chapter 1, Lesson 5.wmv. ... Pause the Video & Complete the Practice Problems. Once you are done, resume the video and I will share the answers so you can check your work. ... After solving the Guided Practice Problems on page 50, enter the ANSWERS into the Google Form found in our Classroom. Here is the link to ...
This is a 6th grade math tutorial video on graphing ratio tables.
Lesson 5 Homework Practice Graph Ratio Tables - Free download as PDF File (.pdf), Text File (.txt) or read online for free.
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.
Lesson 5 Problem-Solving Practice Graph Ratio Tables PHOTOGRAPHY A photography store sells black and white film. The cost of 1, 2, and 3 ... the graph. EXERCISE The table shows the time it takes Bernard to jog 1, 2, 3, and 4 laps around the track. Number of Times Around Track Total Time (min) 15 210 315 420 3. List this information as ordered pairs
The ratio 3 to 5 or 3/5 is the same thing as 12 to 20, is the same thing as 24 to 40, is the same thing as 48 to 80. Let's make sure we got the right answer. Let's do a couple more of these. The following table shows equivalent fractions to 27/75. So then they wrote all of the different equivalent fractions.
Lesson 5 Homework Practice Graph Ratio Tables Graph and label each point on the coordinate plane at the right. 1. N (8, 6) 2. P (0, 8) 3. R (4, 8) 4. S (3, 4) 5. T (6, 8) 6. ... Then describe the graph. 10. ERASERS Erasers cost 5 cents each at the school store. The table shows this relationship. a. List this information as ordered pairs (number ...
Let's solve a few ratio problems with ratio tables and without. ... Lesson Summary. A ratio table is a structured list of ... Comparing Ratios Using Tables & Graphs; Practice Problems for ...
• I can use various operations to create tables of equivalent ratios. • I can use ratio tables to solve ratio problems. 5.1 Completing Ratio Tables Work with a partner. Use the ratio tables shown. x 5 y 1 x 1 — 4 y 1 — 2 a. Complete the fi rst ratio table using multiple operations. Use the same operations to complete the second ratio ...
About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...
Equivalent Ratios and Tables Unit 1 Lesson 3 Math 6 . Equivalent Ratios and Tables Students will be able to: ... Equivalent Ratios and Tables Sample Problem 5: Mark can type 30 words per minute. Complete the table of ... graph should be a straight line. Example:
Pizza. 5. 16. 20 The snack bar at the soccer field is charging $12 for 9 hamburgers. At that rate, how many hamburgers could you get for $20? A fast typist can type 120 words in 100 seconds. At that rate, how many seconds would it take to type 258 words? The ratio of oil to vinegar in a certain salad dressing is 8:5.
Ratios, Rates, Tables, and Graphs Practice and Problem Solving: D Use the table to complete Exercises 1-6. The table shows information about the number of tires needed for a number of cars. 1. Complete the table. The first one is done for you. 2. Write the rule for the table. _____ 3. Find the rate of tires needed for one car. Start with a ...
Equivalent ratios displayed on a graph maintain a linear relationship that passes through the origin and can be used to make predictions regarding other equivalent ratios. Activity 5.3: Using Ratio Graphs to Solve Problems Asynchronous Facilitation Notes In this activity, students use a ratio to generate values in a table, then use the table to ...
LESSON 5: Ratios and Tables Ratios and Tables - Graphing Ratios on the Coordinate Plane (CP, WG, M, GP, IP) S44 (Answers on T98.) M, GP, WG, CP: Have students turn to S44 in their books. Make sure students know their designation as Partner A or Partner B. Students will be graphing the information from the ratio table on S43.
This lesson combines creating ratio tables with graphing on the coordinate plane. To start the Intro to New Material section, I have students create a ratio table to represent the situation. Students may ask if they can create a tape diagram as the visual. Because we're working with multiple equivalent ratios, I want them to use a table.
About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...
Ratio Tables. Find More…. Tags: Ratio tables worksheets with answers, Grade 5 Math Ratio table word problems, Ratios and rates worksheets, Understanding ratios 5th grade, Ratios and proportional relationships 5th grade worksheets, Equivalent ratios and graphs.
Ratios, Rates, Tables, and Graphs Reading Strategy: Read a Table ... Practice and Problem Solving: C Find the unknown value in each proportion. Round to the nearest tenth if needed. 1. 2 3 = 7.5 2. 7 ... LESSON 7-2 8 11 33 x =, x = 24; The width should be 24 in. 200 mi.
Lesson 5 Problem-Solving Practice Compare Properties of Functions 1. Anne kept track of the number of steps she took in a day using a pedometer. The average number of steps she took y per hour x can be represented by the function y = 700 x. The table below shows the number of steps per hour that Elyse walked. Compare the functions for
Lesson5 Homework Practice Graph Ratio Tables - Displaying top 8 worksheets found for this concept. ... 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. ...