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“Unwrapped” Priority Georgia Standards of Excellence
Skills and Concepts
Use properties of operations to generate equivalent expressions. MGSE7.EE.1 APPLY properties of operations as strategies to add, subtract, factor, and EXPAND linear expressions with rational coefficients. MGSE 7.EE.4 USE variables to REPRESENT quantities in a real world or mathematical problem, and CONSTRUCT simple equations and inequalities to SOLVE problems by reasoning about the quantities.
Use properties of operations to generate equivalent expressions. MGSE7.EE.2 Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related. For example a + 0.05a = 1.05a means that adding a 5% tax to a total is the same as multiplying the total by 1.05. MGSE7.EE.3 Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. For example: • If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. • If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. MGSE7.EE.4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
MGSE7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. MGSE7.EE.4b Solve real-world and mathematical problems by writing and solving equations of the form x+p = q and px = q in which p and q are rational numbers.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. (Daily) 2. Reason abstractly and quantitatively. (Daily) 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. (Daily) 7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
1. How can we represent quantities using variables? 2. What properties are required in order to rewrite and evaluate algebraic expressions and solve equations? 3. What similarities and differences exist between equations and inequalities?
1. Variables can be used to represent numbers in any type mathematical problem.
2. Properties of real numbers are used to write and solve multi-step equations consisting of rational numbers.
3. Similarities and differences exist between equations and inequalities which help to define the solution set to a given mathematical problem.
Current Situation: You just landed at Hartsfield-Jackson International Airport from your Spring Break Trip to the Bahamas. You had an awesome time; although, your flight arrived later than expected. Due to your late arrival, you were unable to find someone to pick you up from the airport. You have to make a decision as to whether or not you are going to catch a taxi or use Uber. During your research, you determine that other companies exist that might be more economical. Your mother decided to give you $20 a month so that you will never find yourself in that situation again. Your frustration caused you to start your own transportation company. Create a speech to present to city officials as to why your company is the best. Include evidence stating which is better and why. Develop an advertisement for your own company that is a better deal than any of the other transportation services.
Student Challenge: During your research, you determine that other companies exist that might be more economical. Your mother decided to give you $20 a month so that you will never find yourself in that situation again. Your frustration caused you to start your own transportation company. Create a speech to present to city officials as to why your company is the best. Include evidence stating which is better and why. Develop an advertisement for your own company that is a better deal than any of the other transportation services.
Student Role: Complete the following tasks: Write an expression to represent the amount of money need to take a taxi or take Uber, create a table to determine cost, compare modes of transportation.
Intended Audience: Students will present speech to city officials promoting your company.
Product of Performance: Develop an advertisement for your own company that outlining cost and comparisons to other companies and construct viable arguments.
Performance Task Synopses
Task 1: MGSE7.EE.1, MGSE7.EE.2 Students will write and evaluate an expression to represent the amount of money need to take a Taxi or Uber for an unknown number of miles. Task 2: MGSE7.EE.3, MGSE7.EE.4 Student will write and solve equations to determine which transportation company will allow you to travel the greatest number of miles. Task 3: MGSE7.EE.3, MGSE7.EE.4 Students will write, solve and graph inequalities give a maximum number of miles that you can travel within a month. Task 4: MGSE7.EE.1, MGSE7.EE.2, MGSE7.EE.3, MGSE7.EE.4 Students will write a speech and create an advertisement to convince citizens to use their newly developed company.
Use properties of operations to generate equivalent expressions. MGSE7.EE.1 APPLY properties of operations as strategies to add, subtract, factor, and EXPAND linear expressions with rational coefficients. MGSE7.EE.2 Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related. Circumstances of Performance: In-Class (Approximate Time 30 – 45 minutes) Task 1 Student Directions: The taxi fare in Atlanta is $2.40 for the first 1/2 miles and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. The Uber base fare is $1. There is a charge of $1.05 per mile. You also plan to give the driver a $2 tip. Write an expression to represent the amount of money need to take a taxi or take Uber. (x = the number of miles.) Create a table to determine how much it will cost to go 12 miles, 20 miles and 50 miles. Which mode of transportation is better, use information from the table to support your answer? Task 1 Teacher Notes: Answer: The minimum charge is for 1/2 mile, so let x be the number of miles we can travel in the taxi past the first half mile. Each additional tenth of a mile costs 20 cents so each additional mile costs $2. So it costs 2x dollars to travel the x miles beyond the first half mile. Since the first half mile costs $2.40 and the tip will be $2.00, the total cost of the trip is 2x+2.40+2.00 or
Taxi Expression: 2x+4.40 Let x be the number of miles we can travel using Uber. Each mile cost $1.05. So it cost 1.05x to travel x miles. Since the base fare is $1.00 and the tip will be $2.00, the total cost of the trip 1.05x + 1.00 + 2.00 or
Uber Expression: 1.05x +3.00
Taxi Uber
X (miles)
2x+4.40
X (miles)
1.05x + 3.00
12 $28.40 12 $15.60
20 $44.40 20 $24.00
50 $104.40 50 $55.50
Advanced Criteria: Students must also create a graph with the information. Students must correctly graph the information. Students’ answers will vary.
Use properties of operations to generate equivalent expressions. MGSE7.EE.3 Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. MGSE 7.EE.4 USE variables to REPRESENT quantities in a real world or mathematical problem, and CONSTRUCT simple equations and inequalities to SOLVE problems by reasoning about the quantities. Circumstances of Performance: In-Class (Approximate Time 15 – 20 minutes) Task 2 Student Directions: While trying to determine which mode of transportation you were going to use in leaving the airport, you discovered Lyft was another mode of transportation. The base fare for Lyft is $1.35 and $0.95 per mile. You plan to give the Lyft driver a tip of $2. Determine the expression that represents the amount of money needed to use Lyft as your transportation service. (x = the number of miles). You realize that you only have $10.00 left from you trip. You are trying to determine whether or not you have enough money to make it home using either Uber or Lyft service. Remember the expression for using Uber is 1.05x + 3.00. Write and solve an equation to determine the number of miles you can travel using Lyft and Uber. Which company will allow you to travel the greatest number of miles? Task 2 Teacher Notes: Let x be the number of miles we can travel using Lyft. Each mile cost $0.95. So it
cost 0.95x to travel x miles. Since the base fare is $1.35 and the tip will be $2.00, the total cost of the trip 0.95x +
1.35 + 2.00 or
Lyft Expression: 0.95x + 3.35
Uber Lyft 1.05x + 3 = 10 0.95x + 3.45 = 10 -3 -3 -3.45 -3.35 1.05x = 7 0.95x = 6.65 x = 6 2/3 miles x = 7 miles The person can travel 7 miles using Lyft and 6 2/3 miles using Uber. You can travel the greatest distance using Lyft. Advanced Learner: How many miles can you travel if you have $15 or $23?
Performance Task 2 Scoring Guide
4 Advanced 3 Proficient 2 Basic 1 Below Basic
All Proficient criteria plus: o Correctly determines
the number of miles you can travel with $15 and $23 with each company.
o Provides a detailed explanation of when
o Writes an accurate expression to represent the fees involved with Lyft.
o Writes and solves the equation for Uber.
o Determines which service would yield
o Writes the correct expression for Lyft or the equation for Uber.
o Compares the 2 companies but does not discuss which would yield the greater distance.
o Provided explanations and/or mathematical representations that could not be clearly understood or interpreted.
comparing the 2 companies which would give you the greatest distance for the money spent.
the greatest distance traveled based on parameters.
Performance Task 3 In Detail
Use properties of operations to generate equivalent expressions. MGSE7.EE.3 Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. MGSE 7.EE.4 USE variables to REPRESENT quantities in a real world or mathematical problem, and CONSTRUCT simple equations and inequalities to SOLVE problems by reasoning about the quantities. Circumstances of Performance: In-Class (Approximate Time 20 – 30 minutes) Task 3 Student Directions: You were able to safely make it home from the airport. Your mother decided to give you $20 in January on your Lyft account so that you will not be in the same situation again. Each mile cost $0.95. The base fare is $1.35 and the tip will be $2.00 per trip.
Write and solve the inequality for each situation. Graph the solution to the inequality and write a sentence to describe the meaning of the solution. Round to the nearest hundredth.
1. What is the greatest number of miles that you travel in January for one trip?
The local university decided to ban Lyft from coming on campus. You decided to use Uber instead. Your mother decided to continue to add $20 to your account each month. Let x equal the number of miles you can travel using Uber. Each mile cost $1.05. The base fare is $1.00 and the tip will be $2.00 for each trip.
Write and solve the inequality for each situation. Graph the solution to the inequality and write a sentence to describe the meaning of the solution. Round to the nearest hundredth.
3. What is the greatest number of miles that you travel in January for one trip?
Sentence _________________________________________________________ 4. What is the greatest number of miles that you can travel in January for two trips?
Sentence: I cannot travel more than 17.53 miles for one trip.
2. Inequality 0.95x + 6.70 ≤ 20 (Note: Multiply the base fare and the tip by 2 because two trips were taken) Solution x ≤ 14 14 Sentence: I cannot travel more than 14 miles for two trips.
Solution x ≤ 16.19 16.19 Sentence: I cannot travel more than 16.19 miles for one trip.
4. Inequality 1.05x + 6 ≤ 20 (Note: Multiply the base fare and the tip by 2 because two trips were taken) Solution x ≤13.33 13.33 Sentence: I cannot travel more than 13.33 miles for two trips.
Extension: Give the students a budget and have them research transportation companies and how many miles they would be able to travel and still remain within their budget. What would be the cheapest company? What would be the most expensive?
Performance Task 3 Scoring Guide
4 Advanced 3 Proficient 2 Basic .1 Below Basic
All Proficient criteria plus: o Researched a
transportation company and determined how many miles they could travel and remain in budget.
o Attends to precision when calculating the cheapest company and the most expensive company.
o Writes an accurate inequality for each situation.
o Attends to precision when solving the inequality.
o Graphs the inequality on the number line justifying the solution set.
o Provides an explanation of the solution using the details from the graphs and inequality to justify answers.
o Provides inequalities and graphs, but errors exist in one or more representations.
o Explains solutions but is unable to justify data from the representations provided.
o Provided explanations and/or mathematical representations that could not be clearly understood or interpreted.
Use properties of operations to generate equivalent expressions. MGSE7.EE.3 Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. MGSE 7.EE.4 USE variables to REPRESENT quantities in a real world or mathematical problem, and CONSTRUCT simple equations and inequalities to SOLVE problems by reasoning about the quantities. Circumstances of Performance: In-Class (Approximate Time 50 – 75 minutes) Task 4 Student Directions: The citizens must vote on which transportation company is best to service the citizens of the city. You have to convince the citizens to choose your company. In order to do that you will have to create an advertisement for you company and deliver a speech convincing the citizens to select your company. As you prepare for both, use the data and information from the previous task to assist you.
o Include the cost per mile, base fair and recommended tip amount per trip for your company.
o Create a table for each company that will make it easy for consumers to determine the cost per trip.
o Justify and support mathematically why your company is better than both Uber and Lyft.
Uber Lyft Your Company
____________________
The Uber base fare is $1.00. There is a charge of $1.05 per mile and the tip will be $2.00 per trip.
Number of Miles
Cost of the Trip
5
10
15
20
25
Each mile cost $0.95. The base fare is $1.35 and the tip will be $2.00 per trip.
Number of Miles
Cost of the Trip
5
10
15
20
25
Cost per mile: _____________ Base fare: ________________ Tip Amount: ______________
Answers will vary for the student’s company that they create.
Enrichment: Create a website promoting your new company.
Performance Task 4 Scoring Guide
4 Advanced 3 Proficient 2 Basic 1 Below Basic
All proficient criteria plus: o Designs a website
that includes the cost per trip, cost per mile, recommended tip amount, and the table with rates.
o Attends to precision calculating the cost per trip for Uber and Lyft.
o Provides the cost per trip for the newly created company.
o Creates a detailed advertisement which includes the cost analysis using the data from the tables.
o Exhibited mathematical thinking in speech when comparing the new company to both Uber and Lyft and justifies why this company is better using the data from tables.
o Provided calculations that were inaccurate.
o Explains solutions but is unable to justify data from the representations provided.
o Provided explanations and/or mathematical representations that could not be clearly understood or interpreted.
Weekly Planner Course: Grade 7 Mathematics Unit: Unit 2: Expressions and Equations
Pacing Priority (in bold) and Supporting Standards
Engaging Learning Experiences
Core Instruction (in bold) and additional resources
Formative Assessments
Mathematical Literacy: The ability to read, listen, think creatively, and communicate about problem situations, mathematical representations, and the validation of solutions will help students to develop and deepen their understanding of mathematics. (National Council of Teachers of Mathematics, 2000)
6 weeks Make modifications to the
pacing based upon student pre-assessment results and the daily analysis of
student work.
See CAAG for a listing of all standards. Instruction should be supported with the implementation of the Standards for Mathematical Practice (SMP).
Students should complete the listed experiences to support understanding and mastery of the math standards. Students are expected to exhibit the SMP.
Teachers should implement the listed experiences to support core instruction on the math standards. Teachers should model the SMP during the 3-Part Lesson Structure.
Teachers should use the assessments to support student learning at all levels. The unit pre-assessment should be administered prior to unit instruction for diagnostic purposes.
o Differentiate instruction based upon the pre-assessment results. o Make modifications to the pacing based upon student pre-assessment results and the daily analysis of student work. o Implement the Formative Assessment Lesson (FAL) to monitor the progress of students during the instructional unit. o Introduce the learning targets on a daily basis in kid friendly language using “I Can” statements. o Provide instruction using the Concrete-Representational-Abstract (CRA) sequence of instruction. o Utilize the Gradual Release Model of Responsibility (I do, We do, You do) during instruction to support student learning of
concepts/skills. o Use UPS Check and the 3 Read Protocol for the Problem Solving Process. o Use Newman’s Prompt to diagnose the hurdles students face while problem solving. o Incorporate Mathematical Visualization to model math concepts, skills, and problem solving.
o Remind students that mistakes are respected, expected, and inspected in the mathematics classroom.
Pacing Priority (in bold) and Supporting Standards
Engaging Learning Experiences
Core Instruction (in bold) and additional resources
Formative Assessments
Unit Expectations o Performance Assessment (4 Tasks and Scoring Guide) o Formative Assessment Lessons o GADOE Instructional Tasks
Weekly core instruction should include the implementation of instructional tasks from the Georgia Department of Education (GADOE) located at www.georgiastandards.org along with other district and supplemental instructional resources. Included in the planner are possible suggestions for GADOE tasks.
Week 1
MGSE7.EE.1 MGSE7.EE.2
Intro Engaging Scenario GADOE Gr. 7 Unit 2: Distributing and Factoring Using Area
Apply number properties (distributive, commutative and associative) to write and evaluate expressions and equations. Carnegie Learning Chapter 6 Carnegie Learning Chapter 6 Assessment Items Number Talks Interactive Notebooks https://learnzillion.com/lesson_plans/51-represent-real-life-scenarios-by-writing-numerical-and-algebraic-expressions
Pre-Assessment (Unit Pre-Assessment) Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions
Week 2 MGSE7.EE.1 MGSE7.EE.2
Task 1: Evaluate expressions for a given variable. GADOE Gr. 7 Unit 2: Area and Algebra
Apply number properties (distributive, commutative and associative) to write and evaluate expressions and equations. Carnegie Learning Chapter 6 Carnegie Learning Chapter 6 Assessment Items
Task 1 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions
Pacing Priority (in bold) and Supporting Standards
Engaging Learning Experiences
Core Instruction (in bold) and additional resources
Formative Assessments
Week 5 MGSE7.EE.3 MGSE7.EE.4
GADOE Gr. 7 Unit 2: T.V. Time and Video Games Task 4: Write a speech and create an advertisement to convince citizens to use their newly developed company.