1 Access Points

Access Point
 MAFS.7.NS.1.AP.3a: Solve realworld and mathematical problems involving the four operations with rational numbers from 100 to 100.

Lesson Plan

Predicting the decimal equivalent for a fraction  terminating or repeating?: This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization. 
Wallpaper Woes Money Math: Lessons for Life: Students hear a story about a middleschool student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs. 
Using Positive and Negative Numbers in Context: This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the following structures:  starting temperature + change in temperature = final temperature
 final temperature – change in temperature = starting temperature
 final temperature – starting temperature = change in temperature

Increasing and Decreasing Quantities by a Percent: This lesson unit is intended to help you 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
 recognizing the relationship between increases and decreases

Pricing The Twelve Days of Christmas: Students will discover how much the items in the classic song, "The Twelve Days of Christmas," would cost in the current year; and then they will update the list for modern times. 
Run For Your Life!: Based on a studentfocused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space. 
Which van is the best buy?: The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase. 
Future Homes for America: The students will need to look at data and make good decisions on which model home will be constructed for victims hurt by natural disasters. 
Zany's Joke Shop Dilemma: The main problem is that students will help rank products offered at Zany Joke Shop. They will be ranking the products from best overall to least. By helping rank the products, the student will help create a purchase order for the store. They will be expected to create a device to rank the products offered from best to worst. Students will be given tables that show: cost per product, customer rating, profits made and affordability. The second letter offers students a twist since new products are being introduced for the store to sell and a budget constraint will be introduced. 
Whirl Wind: The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job. 
Cool Uniforms: Students are asked to rank fabrics designated for a new women's volleyball team. Students must take into account the uniform color, Ultraviolet Protection Factor, weight of the fabric availability of material and cost. They will compare and contrast fabrics on these factors and calculate yardage needed to manufacture the team's 24 uniforms. 
Forever Green Landscaping: Students are asked to rank different types of mulch for a Landscaping company. 
Ranking Banking: In this activity, the students are given specifics and data tables to figure out which banking institution best fits the needs of the customer. Student have to figure out the company's monthly banking activities and use this information to rank the banks provided in the table(s) to determine which bank will give them the most service for the least cost. The twist adds a new situation to take into consideration that may or may not change their original recommendation. 
All Around Fences: Students use problem solving skills to determine how much fencing is needed and the type of fencing in order to secure a pool and recreational area. 
We're Going on Vacation!: Teams of students act as travel agents in order to plan a vacation package for a family of 5. The students must create four vacation packages that include: hotel, car rental, and visits to three theme parks. 
Where in the world?: This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase. 
Best Chicken Franchise for Me: In this MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise. 
Batteries Included: This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from EZ Go Taxi Cab Service to evaluate several batteries and help them decide which battery they should purchase. 
Say Cheese!: This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Simple Photography Classes to evaluate several digital cameras and help them decide which one they should purchase. 
Along for the Ride!: This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Cut It Out Section of the Building and Grounds Maintenance Department of a school district to evaluate several lawn tractor models and help them decide which unit they should purchase. 
Laura’s Babysitting Job: In this 7^{th} grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking. 
Johansson Family Travel Plans: In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation. 
Rocket Repair: Students will select the best type of coating for rockets given a set of data which will include temperature, hardness, resistance to corrosion and drag. 
MEA NASA Salaries: This is a NASAthemed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of $500,000. The students’ original decision (and “twist”) will be based on information from the client’s letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.

Unit/Lesson Sequence

Money Matters: Integers are Integral: "In this fourlesson unit, students will design and develop a working budget for a onemonth period after learning to add and subtract integers. Within that budget, students will utilize integers to maintain an accurate account of money saved and spent over that time. Students will explore addition and subtraction of integers with various strategies and manipulatives along the way." (from NSA.gov) 
ProblemSolving Task

Classic MiddleGrades Problems for the Classroom: This lesson will have students applying, adapting, and communicating a variety of strategies to mathematical problem solving.
Two classic word problems are presented, the Mangoes Problem and Sailors and Coconuts, both of which can be represented and solved in several different ways. The four methods explained here include guess and check, draw a picture, working backwards, and write an equation.
(from NCTM Illuminations) 
Space Math: Lunar Cratering: Students explore the formation of craters on the lunar surface using real world imaging data and mathematical reasoning. Students make observations and inferences about the time that impact craters were formed using probability and percentages.

Sharing Prize Money: This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense. 
Teaching Idea

Feeding TimeSeaWorld Classroom Activity: Students determine the cost to feed a group of ocean animals in captivity, thus solving a reallife problem. 
Formative Assessment

A Rational Number Expression: Students are given a numerical expression to evaluate. 
Monitoring Water Temperatures: Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.

Trail Mix Munchies: Students are asked to solve a word problem involving division of fractions. 
Complex Fractions: Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Positive and Negative Fractions: Students are asked to add, subtract, multiply, and divide positive and negative fractions.
Related Resource Types
 + Classic MiddleGrades Problems for the Classroom + : This lesson will have students applying, adapting, and communicating a variety of strategies to mathematical problem solving.<br /><br />Two classic word problems are presented, the <i>Mangoes Problem</i> and <i>Sailors and Coconuts</i>, both of which can be represented and solved in several different ways. The four methods explained here include <i>guess and check, draw a picture, working backwards, and write an equation</i>.<br />(from NCTM Illuminations)
 + Money Matters: Integers are Integral + : "In this fourlesson unit, students will design and develop a working budget for a onemonth period after learning to add and subtract integers. Within that budget, students will utilize integers to maintain an accurate account of money saved and spent over that time. Students will explore addition and subtraction of integers with various strategies and manipulatives along the way." (from NSA.gov)
 + Predicting the decimal equivalent for a fraction  terminating or repeating? + : This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization.
 + Wallpaper Woes Money Math: Lessons for Life + : Students hear a story about a middleschool student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.
 + Feeding TimeSeaWorld Classroom Activity + : Students determine the cost to feed a group of ocean animals in captivity, thus solving a reallife problem.
 + Using Positive and Negative Numbers in Context + : This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the following structures: <br /><ul><li>starting temperature + change in temperature = final temperature</li><li>final temperature – change in temperature = starting temperature</li><li>final temperature – starting temperature = change in temperature</li></ul>
 + Increasing and Decreasing Quantities by a Percent + : This lesson unit is intended to help you 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:<br /><ul><li>translating between percents</li><li>decimals and fractions</li><li>representing percent increase and decrease as multiplication</li><li>recognizing the relationship between increases and decreases</li></ul>
 + Space Math: Lunar Cratering + : <p>Students explore the formation of craters on the lunar surface using real world imaging data and mathematical reasoning. Students make observations and inferences about the time that impact craters were formed using probability and percentages.</p>
 + Sharing Prize Money + : This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense.
 + Pricing The Twelve Days of Christmas + : Students will discover how much the items in the classic song, "The Twelve Days of Christmas," would cost in the current year; and then they will update the list for modern times.
 + Run For Your Life! + : Based on a studentfocused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space.
 + Which van is the best buy? + : The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase.
 + Future Homes for America + : The students will need to look at data and make good decisions on which model home will be constructed for victims hurt by natural disasters.
 + Zany's Joke Shop Dilemma + : The main problem is that students will help rank products offered at Zany Joke Shop. They will be ranking the products from best overall to least. By helping rank the products, the student will help create a purchase order for the store. They will be expected to create a device to rank the products offered from best to worst. Students will be given tables that show: cost per product, customer rating, profits made and affordability. The second letter offers students a twist since new products are being introduced for the store to sell and a budget constraint will be introduced.
 + Whirl Wind + : The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job.
 + Cool Uniforms + : Students are asked to rank fabrics designated for a new women's volleyball team. Students must take into account the uniform color, Ultraviolet Protection Factor, weight of the fabric availability of material and cost. They will compare and contrast fabrics on these factors and calculate yardage needed to manufacture the team's 24 uniforms.
 + Forever Green Landscaping + : Students are asked to rank different types of mulch for a Landscaping company.
 + Ranking Banking + : In this activity, the students are given specifics and data tables to figure out which banking institution best fits the needs of the customer. Student have to figure out the company's monthly banking activities and use this information to rank the banks provided in the table(s) to determine which bank will give them the most service for the least cost. The twist adds a new situation to take into consideration that may or may not change their original recommendation.
 + All Around Fences + : Students use problem solving skills to determine how much fencing is needed and the type of fencing in order to secure a pool and recreational area.
 + We're Going on Vacation! + : Teams of students act as travel agents in order to plan a vacation package for a family of 5. The students must create four vacation packages that include: hotel, car rental, and visits to three theme parks.
 + Where in the world? + : This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.
 + Best Chicken Franchise for Me + : In this MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise.
 + Batteries Included + : This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from EZ Go Taxi Cab Service to evaluate several batteries and help them decide which battery they should purchase.
 + Say Cheese! + : This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Simple Photography Classes to evaluate several digital cameras and help them decide which one they should purchase.
 + Along for the Ride! + : This resource provides a ModelEliciting Activity where students will analyze a realworld scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Cut It Out Section of the Building and Grounds Maintenance Department of a school district to evaluate several lawn tractor models and help them decide which unit they should purchase.
 + Laura’s Babysitting Job + : In this 7<sup>th</sup> grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.
 + Johansson Family Travel Plans + : In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation.
 + Rocket Repair + : Students will select the best type of coating for rockets given a set of data which will include temperature, hardness, resistance to corrosion and drag.
 + MEA NASA Salaries + : <p>This is a NASAthemed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of $500,000. The students’ original decision (and “twist”) will be based on information from the client’s letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.</p> <p> </p>
 + A Rational Number Expression + : Students are given a numerical expression to evaluate.
 + Monitoring Water Temperatures + : <p>Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.</p>
 + Trail Mix Munchies + : Students are asked to solve a word problem involving division of fractions.
 + Complex Fractions + : <p>Students are asked to rewrite complex fractions as simple fractions in lowest terms.</p>
 + Positive and Negative Fractions + : <p>Students are asked to add, subtract, multiply, and divide positive and negative fractions.</p>
1 Student Resources
 Sharing Prize Money: This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense.
1 Parent Resources
 Sharing Prize Money: This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense.
Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Remarks/Examples
 Examples of Opportunities for InDepth Focus
When students work toward meeting this standard (which is closely connected to 7.NS.1.1 and 7.NS.1.2), they consolidate their skill and understanding of addition, subtraction, multiplication and division of rational numbers.
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