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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the s...

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Mathematics
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Activity/Lab
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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
03/17/2013
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: If 100 dollars in one year gain $3\frac12$ dollars interest, what sum will gain \38.50 cents in one year and a quarter?... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 08/01/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use. Subject: Ratios and Proportions Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 08/06/2015 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The taxi fare in Gotham City is \2.40 for the first $\frac{1}{2}$ mile and additional mileage charged at the rate \0.20 for each additional 0.1 mile.... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/17/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Jamaican sprinter Usain Bolt won the 100 meter sprint gold medal in the 2012 Summer Olympics. He ran the 100 meter race in 9.63 seconds. There are abou... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 05/28/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Inflation is a term used to describe how prices rise over time. The rise in prices is in relation to the amount of money you have. The table below show... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/25/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are 180 students at Winthrop Middle School, where the ra... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/17/2013 Read the Fine Print Rating 0.0 stars This lesson is about trying to get students to make connections between ideas about equations, inequalities, and expressions. The lesson is designed to give students opportunities to use mathematical vocabulary for a purpose to describe, discuss, and work with these symbol strings.The idea is for students to start gathering global information by looking at the whole number string rather than thinking only about individual procedures or steps. Hopefully students will begin to see the symbol strings as mathematical objects with their own unique set of attributes. (7th Grade Math) Subject: Algebra Numbers and Operations Material Type: Activity/Lab Lecture Lesson Plan Teaching/Learning Strategy Provider: Noyce Foundation Provider Set: Inside Mathematics Author: Disston, Jacob Date Added: 11/30/2011 Read the Fine Print Some Rights Reserved Rating 0.0 stars Ratio errors confuse a dodgeball coach as two teams face off in an epic tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion. Subject: Mathematics Material Type: Lecture Provider: Learning Games Lab Author: NMSU Learning Gams Lab Date Added: 07/15/2015 Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars Baby Proportions is an activity designed to challenge students to compare body measurement proportions of adults, students and infants. They then use these proportions to create a scale drawing of themselves and an infant enlarged to be their same height. The idea is to use real world measurements in practicing proportional relationship skills while creating an interesting image when finished. Subject: Measurement and Data Ratios and Proportions Material Type: Lesson Plan Author: Katie Barngrover Date Added: 11/21/2019 Read the Fine Print Some Rights Reserved Rating 0.0 stars True love has the right ratio. In this humorous animation, the number of words spoken by each partner predicts whether a date goes well or horribly. What do you do when someone asks if you listen to country music backwards, but won't let you get a word in edgewise? Subject: Mathematics Material Type: Lecture Provider: Learning Games Lab Author: NMSU Learning Games Lab Date Added: 07/15/2015 Conditional Remix & Share Permitted CC BY-NC-SA Rating 0.0 stars This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses. Subject: Ratios and Proportions Material Type: Activity/Lab Lesson Plan Provider: National Association of State Directors of Career Technical Education Consortium Provider Set: Career Technical Education Date Added: 07/26/2012 Conditional Remix & Share Permitted CC BY-NC-SA Rating 3.25 stars This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses. Subject: Architecture and Design Geometry Ratios and Proportions Material Type: Activity/Lab Assessment Homework/Assignment Lesson Plan Provider: National Association of State Directors of Career Technical Education Consortium Provider Set: Career Technical Education Date Added: 03/05/2012 Unrestricted Use CC BY Rating 0.0 stars This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations. Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 05/01/2012 Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars In this interactive unit, students are introduced to the various factors and elements that contribute to a company's success by creating a product to sell. Students participate in a mock business venture from beginning to end - from making the product (a candy bar) to selling the product. Some math concepts and principles include:using proportional relationshipssolving multistep problemsdetermining percents, markup, and taxFurther, students apply English Language Arts standards to their finished product, including:designing a marketing posterwriting, recording, and presenting a sales pitch Subject: English Language Arts Mathematics Material Type: Lesson Plan Author: Cathryn Chellis Blended Learning Teacher Practice Network Date Added: 11/12/2018 Unrestricted Use CC BY Rating 0.0 stars Many students will not know that when comparing two quantities, the percent decrease between the larger and smaller value is not equal to the percent increase between the smaller and larger value. Students would benefit from exploring this phenomenon with a problem that uses smaller values before working on this one. Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 05/01/2012 Read the Fine Print Educational Use Rating 0.0 stars Engineering analysis distinguishes true engineering design from "tinkering." In this activity, students are guided through an example engineering analysis scenario for a scooter. Then they perform a similar analysis on the design solutions they brainstormed in the previous activity in this unit. At activity conclusion, students should be able to defend one most-promising possible solution to their design challenge. (Note: Conduct this activity in the context of a design project that students are working on; this activity is Step 4 in a series of six that guide students through the engineering design loop.) Subject: Engineering Material Type: Activity/Lab Provider: TeachEngineering Provider Set: TeachEngineering Author: Denise W. Carlson Lauren Cooper Malinda Schaefer Zarske Date Added: 09/18/2014 Only Sharing Permitted CC BY-NC-ND Rating 5.0 stars This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller. Subject: Numbers and Operations Material Type: Assessment Lesson Plan Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Date Added: 04/26/2013 Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars In this problem-based learning module, students will explore the importance of sleep and the impact sleep has on their lives. During the launch phase students can choose to record sleep data via downloaded apps or in a sleep diary. Days 2 through 4 have students explore the concept and necessity of living organisms need to sleep. On day 2 the participants will take a series of cognitive test for baseline data. Through station rotation and a jigsaw activity learners will become familiar with circadian rhythm and sleeping disorders. Finally, days 5-7 have the students produce a video or infographic to communicate the importance of sleep and its relationship to performance both physically and academically. Subject: English Language Arts Life Science Mathematics Material Type: Lesson Plan Author: Blended Learning Teacher Practice Network Date Added: 07/27/2018 Only Sharing Permitted CC BY-NC-ND Rating 4.5 stars This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units. Subject: Algebra Geometry Ratios and Proportions Material Type: Assessment Lesson Plan Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Date Added: 04/26/2013 Conditional Remix & Share Permitted CC BY-NC-SA Rating 0.0 stars Students will be using real-life energy use data to learn how to use spreadsheets and create graphs to better organize and view data. Discussions can then follow to analyze the data and explain the usage. Real rates are then provided, and students can use the electricity consumed data to create a utility bill for the consumer and compare the standard Residential Service charges to if the member were instead billed by the “Time of Use” rate. Subject: Measurement and Data Numbers and Operations Material Type: Activity/Lab Data Set Lesson Plan Primary Source Date Added: 08/15/2017 Only Sharing Permitted CC BY-NC-ND Rating 4.0 stars This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table. Subject: Education Geometry Measurement and Data Ratios and Proportions Material Type: Assessment Lecture Notes Lesson Plan Teaching/Learning Strategy Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Author: http://map.mathshell.org/ Date Added: 04/26/2013 Unrestricted Use CC BY Rating 0.0 stars This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally. Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 05/01/2012 Conditional Remix & Share Permitted CC BY-NC-SA Rating 0.0 stars In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing. Subject: Ratios and Proportions Material Type: Module Provider: New York State Education Department Provider Set: EngageNY Date Added: 05/14/2013 Conditional Remix & Share Permitted CC BY-NC-SA Rating 0.0 stars In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations. Material in early lessons is designed to reinforce students understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students use visual models and equations, building on their earlier work with these. As the lessons and topics progress and students solve multi-step percent problems algebraically with numbers that are not as compatible, teachers may let students use calculators so that their computational work does not become a distraction. Subject: Ratios and Proportions Material Type: Module Provider: New York State Education Department Provider Set: EngageNY Date Added: 01/02/2014 Only Sharing Permitted CC BY-NC-ND Rating 4.0 stars This lesson unit is intended to help teachers assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties: translating between percents, decimals, and fractions; representing percent increase and decrease as multiplication; and recognizing the relationship between increases and decreases. Subject: Ratios and Proportions Material Type: Assessment Lesson Plan Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Date Added: 04/26/2013 Read the Fine Print Educational Use Rating 0.0 stars In this activity, students gain first-hand experience with the mechanical advantage of pulleys. Students are given the challenge of helping save a whale by moving it from an aquarium back to its natural habitat into the ocean. They set up different pulley systems, compare the theoretical and actual mechanical advantage of each and discuss their recommendations as a class. Subject: Engineering Physics Material Type: Activity/Lab Provider: TeachEngineering Provider Set: TeachEngineering Author: Jake Lewis Janet Yowell Malinda Schaefer Zarske Michael Bendewald Date Added: 10/14/2015 Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset. Subject: Mathematics Material Type: Full Course Provider: Pearson Date Added: 10/06/2016 Rating 0.0 stars Getting Started Type of Unit: Introduction Prior Knowledge Students should be able to: Understand ratio concepts and use ratios. Use ratio and rate reasoning to solve real-world problems. Identify and use the multiplication property of equality. Lesson Flow This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students will use throughout the year. An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. Students learn how to present their work to the class, the importance of students’ taking responsibility for their own learning, and how to effectively participate in the classroom math community. Students then work on Gallery problems, to further explore the resources and tools and to learn how to organize their work. The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students use the multiplication property of equality to justify solutions to real-world ratio problems. Subject: Mathematics Material Type: Unit of Study Provider: Pearson Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars Review the multiplication property of equality. Demonstrate the use of “ask myself” questions to understand a problem before solving it. Have students discuss the strategies that they can use when they feel stuck on a problem. Direct partners to solve a problem using a ratio table and equations, and then justify their solution in a presentation using the multiplication property of equality. Have each student write a Summary of the Mathematics in the lesson and work together to create a classroom summary.Key ConceptsStudents use the multiplication property of equality to justify their solution to a ratio problem.Goals and Learning ObjectivesBefore starting to work on a problem, make sense of the problem by using “ask myself” questions.Persevere in solving a problem even when feeling stuck.Solve a ratio problem using two different strategies.Link arithmetic and algebraic methods to solve a ratio problem.Use the multiplication property of equality to solve ratio problems Subject: Ratios and Proportions Material Type: Lesson Plan Provider: Pearson Date Added: 09/21/2015 Rating 0.0 stars Proportional Relationships Type of Unit: Concept Prior Knowledge Students should be able to: Understand what a rate and ratio are. Make a ratio table. Make a graph using values from a ratio table. Lesson Flow Students start the unit by predicting what will happen in certain situations. They intuitively discover they can predict the situations that are proportional and might have a hard time predicting the ones that are not. In Lessons 2–4, students use the same three situations to explore proportional relationships. Two of the relationships are proportional and one is not. They look at these situations in tables, equations, and graphs. After Lesson 4, students realize a proportional relationship is represented on a graph as a straight line that passes through the origin. In Lesson 5, they look at straight lines that do not represent a proportional relationship. Lesson 6 focuses on the idea of how a proportion that they solved in sixth grade relates to a proportional relationship. They follow that by looking at rates expressed as fractions, finding the unit rate (the constant of proportionality), and then using the constant of proportionality to solve a problem. In Lesson 8, students fine-tune their definition of proportional relationship by looking at situations and determining if they represent proportional relationships and justifying their reasoning. They then apply what they have learned to a situation about flags and stars and extend that thinking to comparing two prices—examining the equations and the graphs. The Putting It Together lesson has them solve two problems and then critique other student work. Gallery 1 provides students with additional proportional relationship problems. The second part of the unit works with percents. First, percents are tied to proportional relationships, and then students examine percent situations as formulas, graphs, and tables. They then move to a new context—salary increase—and see the similarities with sales taxes. Next, students explore percent decrease, and then they analyze inaccurate statements involving percents, explaining why the statements are incorrect. Students end this sequence of lessons with a formative assessment that focuses on percent increase and percent decrease and ties it to decimals. Students have ample opportunities to check, deepen, and apply their understanding of proportional relationships, including percents, with the selection of problems in Gallery 2. Subject: Mathematics Ratios and Proportions Material Type: Unit of Study Provider: Pearson Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars Students connect percent to proportional relationships in the context of sales tax.Key ConceptsWhen there is a constant tax percent, the total cost for items purchase—including the price and the tax—is proportional to the price.To find the cost, c , multiply the price of the item, p, by (1 + t), where t is the tax percent, written as a decimal: c = p(1 + t).The constant of proportionality is (1 + t) because of the structure of the situation:c = p + tp = p(1 + t).Because of the distributive property, multiplying the price by (1 + t) means multiplying the price by 1, then multiplying the price by t, and then taking the sum of these products.Goals and Learning ObjectivesFind the total cost in a sales tax situation.Understand that a proportional relationship only exists between the price of an item and the total cost of the item if the sales tax is constant.Find the constant of proportionality in a sales tax situation.Make a graph of an equation showing the relationship between the price of an item and the total amount paid. Subject: Ratios and Proportions Material Type: Lesson Plan Provider: Pearson Date Added: 09/21/2015 Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars Students create equations, tables, and graphs to show the proportional relationships in sales tax situations.Key ConceptsThe quantities—price, tax, and total cost—can each be known or unknown in a given situation, but if you know two quantities, you can figure out the missing quantity using the structure of the relationship among them.If either the price or the total cost are unknown, you can write an equation of the form y = kx, with k as the known value (1 + tax), and solve for x or y.If the tax is the unknown value, you can write an equation of the form y = kx and solve for k, and then subtract 1 from this value to find the tax (as a decimal value).Building a general model for the relationship among all three quantities helps you sort out what you know and what you need to find out.Goals and Learning ObjectivesMake a table to organize known and unknown quantities in a sales tax problem.Write and solve an equation to find an unknown quantity in a sales tax problem.Make a graph to represent a table of values.Determine the unknown amount—either the price of an item, the amount of the sales tax, or the total cost—in a sales tax situation when given the other two amounts. Subject: Ratios and Proportions Material Type: Lesson Plan Provider: Pearson Date Added: 09/21/2015 Conditional Remix & Share Permitted CC BY-NC Rating 0.0 stars Students are given a collection of statements that are incorrect. Their task is to construct arguments about why the statements are flawed and then correct the flawed statements.Key ConceptsPercent change is a rate of change of an original amount.In two situations with the same percent change but different original amounts, the percent amount will be different because the percent amount depends directly on the original amount. For example: 50% of 20 is 10. 50% of 10 is 5.Similarly, in two situations with the same amount of increase but different original amounts, the percent change of each amount is different. For example: Suppose two amounts increase by5. If one original amount is $20, the increase is 25%. If the other original amount is$25, the increase is 20%.Goals and Learning ObjectivesIdentify errors in reasoning in percent situations.Use examples to explain why the reasoning is incorrect.

Subject:
Ratios and Proportions
Material Type:
Lesson Plan
Provider:
Pearson