1 of 14 7.MATH.APT.Unit 3
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Rigorous Curriculum Design Authentic Performance Tasks
Subject Unit 3
Grade/Course 7th Grade
Unit of Study Unit 3 – Expressions and Equations
Duration of Unit 4 weeks
Engaging Scenario S Student Council has been given a $1,000 budget for a school garden. C Students need to calculate total number of apple and orange trees to be purchased staying within the $1,000 budget. R Student council Treasurer spending $1,000 on fruit trees. A student body, teacher, and administration P Student Council has been given $1,000 to start a school garden. As the student council Treasurer you must purchase apple and orange trees with this money while staying within your budget.
Priority Standards Expressions and Equations 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 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.
Supporting Standards 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Interdisciplinary Connections
Language arts Science Technology
“Unwrapped” Concepts (students need to know)
“Unwrapped” Skills (students need to be able to do)
DOK Levels
Apply 7.EE.1 *to Add 7.EE.1 Subtract Factor Expand 7.EE.1
Use 7.EE.4 Construct 7.EE.4
Properties of operations as strategies 7.EE.1 Linear expressions with coefficients
Variables 7.EE.1 *to represent quantities Simple equations and inequalities *to solve problems * by reasoning about the quantities
7.EE.4
1 1 1 2
Unit Vocabulary Terms “Unwrapped” Priority Standards Concepts Supporting Standards Concepts
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Expressions Equations Inequalities Coefficients Properties of Operations
Area
Performance Task Synopses Task 1: Students need to calculate how many apple and orange trees to purchase staying within $1,000 budget.
Task 2: Students will make a diagram of how the trees should be planted. Task 3: Students will write expressions representing the total amount of fruit produced from the trees in a single season. Task 4: Students will have to adjust total purchase of fruit trees to meet the need of equal distribution of fruit to the entire student body.
Performance Task # 1 In Detail S: Which standard(s) (priority/supporting) will the task address? 7.EE. 1, 7.EE.4, 7.EE.2 Q: What essential Question(s) and corresponding Big Idea(s) will this task target?
Corresponding Big Ideas Essential Questions
Properties of operations can be used to create equivalent expressions. 7.EE.1 Variables represent unknown parts of a problem that can be put into equations and inequalities to solve. 7.EE.4
What do you do with coefficients to create equivalent linear expressions? 7.EE.1 How can you create an equation or inequality to solve a real-life problem? 7.EE.4 Susan paid $5.50 and a bought pie crust for $1.75 and some apples for $0.75 each. Create an equation that will help you find the number of apples Susan bought. 7.EE.4
U: Which “unwrapped” specific concepts and skills will this task target? Apply 7.EE.1 properties of operations as strategies 7.EE.1 Use 7.EE.4 Variables 7.EE.1 Construct 7.EE.4 Simple equations and inequalities to solve problems by reasoning about the quantities 7.EE.4 A: How will the students apply the concepts and skills? What will they do and/or produce? Students will use expressions, equations, and inequalities to calculate the total amount of apple and orange trees to purchase staying within their budget. R: What resources, instruction, and information will students need in order to complete the task? Materials to complete task, equations, expressions, and inequalities instruction E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills – the standard(s)? 1. Students meet “Proficient” level on task 1 rubric 2. Students respond to “Big Ideas” in written or formal format D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students can use calculators and will be allowed extra time.
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Task 1 Full Description: Student Council has been given $1,000 to start a school garden. As the student council Treasurer you must purchase apple and orange trees with this money while staying within your budget. Student Council has given you this information: Fuji Apple Trees, x, cost $32.99 each Washington Navel Orange Trees, y, cost $29.99 each Student council has $500 to spend on apple trees and $500 to spend on orange trees.
1) Determine the max number of apple and orange trees that can be purchased without going over
budget:
A. Write an equation showing how to solve each amount. Apple:____________________ Orange: _______________________
B. How many apple and orange trees can the school purchase? Apple:____________________ Orange: _______________________
C. How much money will be spent on each? Apple:____________________ Orange: _______________________
David in your class says that student council can purchase 16 apple trees. Is he correct? Circle: Yes or No
Performance Task # 1 Scoring Guide
Goal/Proficient
Correctly writes and solves two equations
Correctly computes total number of trees.
Correctly computes amounts for both.
Correctly answers questions regarding David’s response
Justification supports your answer.
Basic
Meets _3-4__ of the “Goal” criteria Below Basic
Meets fewer than _0-2_ of the “Goal” criteria
If David is correct, justify your answer:
If David is incorrect, justify your answer:
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Interdisciplinary Connections and Related Priority Standards Specific to Task #1
21st Century Learning Skills Specific to Task #1
Language Arts Check all those that apply for each task:
❑ Teamwork and Collaboration
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
Critical thinking and Problem Solving
❑ Flexibility and Adaptability
Effective Oral and Written Communication Accessing and Analyzing Information
❑ Other
Performance Task # 2 In Detail S: Which standard(s) (priority/supporting) will the task address? 7.EE. 1, 7.EE.4, 7.EE.2 Q: What essential Question(s) and corresponding Big Idea(s) will this task target?
Corresponding Big Ideas Essential Questions
Properties of operations can be used to create equivalent expressions. 7.EE.1 Variables represent unknown parts of a problem that can be put into equations and inequalities to solve. 7.EE.4
What do you do with coefficients to create equivalent linear expressions? 7.EE.1 How can you create an equation or inequality to solve a real-life problem? 7.EE.4 Susan paid $5.50 and a bought pie crust for $1.75 and some apples for $0.75 each. Create an equation that will help you find the number of apples Susan bought. 7.EE.4
U: Which “unwrapped “specific concepts and skills will this task target? Apply 7.EE.1 properties of operations as strategies 7.EE.1 Use 7.EE.4 Variables 7.EE.1 Construct 7.EE.4 Simple equations and inequalities to solve problems by reasoning about the quantities 7.EE.4 A: How will the students apply the concepts and skills? What will they do and/or produce? Students will apply concepts by solving inequalities to determine maximum amount of orange trees to purchase. Students will also create a diagram of how the trees should be planted. R: What resources, instruction, and information will students need in order to complete the task? Materials to complete task, equations, expressions, and inequalities instruction E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills – the standard(s)? 1. Students meet “Proficient” level on task 1 rubric 2. Students respond to “Big Ideas” in written or formal format D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students will be allowed use of calculators and will be given more time. Task 2 Full Description: 1. Student Council just found out that the orange trees have to be delivered. The nursery delivery charge
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is a one-time fee of $50.
A. Which inequality will determine the maximum number of orange trees the school can purchase, along with the delivery fee, without going over their budget? Check all that apply.
o 29.99y – 50 > 500
o 29.99y + 50 < 500
o 500 – 50 > 29.99y
o 50y + 29.99 > 500
B. Solve the inequality showing the maximum number of orange trees to be purchased. (Round to the nearest whole number)
C. Graph the solution to part B on a number line. D. What is the new amount of orange trees the school can purchase? _____________
2. The area to plant the trees is sixty feet by seventy-two feet. Each tree needs to be planted 12 feet apart. A. How many trees can be planted in each row? ______________
B. How many total rows can be planted? ______________
C. Using the space below, draw a diagram of how the trees should be planted. Make sure to make a key representing the apple trees and the distance between each.
Performance Task # 2 Scoring Guide Goal
Selects correct inequalities
Correctly solves inequality
Graph correctly reflects inequality
Correctly computes new amount
Correctly determines number of trees
Correctly determines number of rows
Diagram includes “key” and distance between trees
60
ft
72 ft
Key
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Proficient
Meets _6-7__ of the “Goal” criteria Basic
Meets _4-5__ of the “Goal” criteria Below Basic
Meets fewer than _3_ of the “Goal” criteria
Interdisciplinary Connections and Related Priority Standards Specific to Task #2
21st Century Learning Skills Specific to Task #2
Science Language Arts Technology
Check all those that apply for each task:
❑ Teamwork and Collaboration
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
Critical thinking and Problem Solving
❑ Flexibility and Adaptability
Effective Oral and Written Communication Accessing and Analyzing Information
❑ Other
Performance Task # 3 In Detail
S: Which standard(s) (priority/supporting) will the task address? 7.EE. 1, 7.EE.4, 7.EE.2 Q: What essential Question(s) and corresponding Big Idea(s) will this task target?
Corresponding Big Ideas Essential Questions
Properties of operations can be used to create equivalent expressions. 7.EE.1 Variables represent unknown parts of a problem that can be put into equations and inequalities to solve. 7.EE.4
What do you do with coefficients to create equivalent linear expressions? 7.EE.1 How can you create an equation or inequality to solve a real-life problem? 7.EE.4 Susan paid $5.50 and a bought pie crust for $1.75 and some apples for $0.75 each. Create an equation that will help you find the number of apples Susan bought. 7.EE.4
U: Which “unwrapped “specific concepts and skills will this task target? Apply 7.EE.1 properties of operations as strategies 7.EE.1 Use 7.EE.4 Variables 7.EE.1 Construct 7.EE.4 Simple equations and inequalities to solve problems by reasoning about the quantities 7.EE.4 A: How will the students apply the concepts and skills? What will they do and/or produce? Students will use expressions to calculate total number of apples and oranges that will be produced during one season. They will also use expressions and equations to find the total number of apples and oranges each student will receive. R: What resources, instruction, and information will students need in order to complete the task? Materials to complete task, equations, expressions, and inequalities instruction E: What evidence of learning will I look for to show that I know all of my students have conceptually
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learned the concepts and skills – the standard(s)? 1. Students meet “Proficient” level on task 1 rubric 2. Students respond to “Big Ideas” in written or formal format D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students will be allowed use of calculators and will be given more time. Task 3 Full Description: Part 1: Your teacher has done some research and has found that each apple tree, x, can produce approximately 500 apples and each orange tree, y, can produce approximately 150 oranges in a single season.
1. Using x to represent apple trees and y to represent orange trees, write an expression showing the total amount of apples and oranges produced in a single season.
2. How many total apples will be produced from all the apple trees? Justify your answer.
3. How many total oranges will be produced from all the orange trees? Justify your answer. Comparing apples to oranges: Complete the chart
Fruit Tree Amount of fruit produced per
tree
Total purchased tree
Total amount of fruit per season
Apple 500
Orange 150
Part 2: 1. Using the chart, if the apples are divided equally among the 705 students how many apples would each student
receive. Justify your answer.
Apples:
Oranges:
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Performance Task # 3 Scoring Guide Goal
Student derived the correct expression and correctly solved for total number of apples.
Student derived the correct expression and correctly solved for total number of oranges.
Completed chart containing four correct responses.
Student derived the correct expression and correctly solved for how many apples each student would receive.
Student derived the correct expression and correctly solved for total number of oranges each student would receive.
Reasoning supports student’s answer to agree or disagree. Proficient
Meets _5-6__ of the “Goal” criteria Basic
Meets _3-4__ of the “Goal” criteria Below Basic
Meets fewer than _2_ of the “Goal” criteria
Interdisciplinary Connections and Related Priority Standards Specific to Task #3
21st Century Learning Skills Specific to Task #3
Language Arts Check all those that apply for each task:
❑ Teamwork and Collaboration
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
Critical thinking and Problem Solving
❑ Flexibility and Adaptability
Effective Oral and Written Communication Accessing and Analyzing Information
❑ Other
Performance Task # 4 In Detail [District Scored PT]
2. Using the chart, if the oranges are divided equally among the 705 students how many oranges would each student receive. Justify your answer.
3. From your data Student Council has decided that more orange trees than apple trees need to be planted in order for students to receive the same amount of apples and oranges. Do you agree or disagree? Explain your reasoning. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________
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S: Which standard(s) (priority/supporting)will the task address? 7.EE. 1, 7.EE.4, 7.EE.2 Q: What essential Question(s) and corresponding Big Idea(s) will this task target?
Corresponding Big Ideas Essential Questions
Properties of operations can be used to create equivalent expressions. 7.EE.1 Variables represent unknown parts of a problem that can be put into equations and inequalities to solve. 7.EE.4
What do you do with coefficients to create equivalent linear expressions? 7.EE.1 How can you create an equation or inequality to solve a real-life problem? 7.EE.4 Susan paid $5.50 and a bought pie crust for $1.75 and some apples for $0.75 each. Create an equation that will help you find the number of apples Susan bought. 7.EE.4
Apply 7.EE.1 properties of operations as strategies 7.EE.1 Use 7.EE.4 Variables 7.EE.1 Construct 7.EE.4 Simple equations and inequalities to solve problems by reasoning about the quantities 7.EE.4 A: How will the students apply the concepts and skills? What will they do and/or produce? Students will use diagrams, equations, charts, etc to justify new total amount of fruit trees to be purchased. R: What resources, instruction, and information will students need in order to complete the task? Materials to complete task, equations, expressions, and inequalities instruction E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills – the standard(s)? 1. Students meet “Proficient” level on task 1 rubric 2. Students respond to “Big Ideas” in written or formal format D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students will be allowed use of calculators, will be given more time, and check students IEP/504 plan. Task 4 Full Description:
1. Student Council wants to make sure that each student receives equal amounts of apples and oranges. Using diagrams, equations, charts, etc, justify the new total amount of fruit trees that need to be purchased without going over the budget of $1,000 and keeping with a total of 30 trees purchased. (Get as close as possible to total amount of fruit.)
2. How much will be spent on orange trees ($29.99)? _____________ How much will be spent on apple trees (32.99)? _____________
3. Write and solve an inequality justifying that you are still within budget. . (Remember to include the one-time $50 delivery fee.)
4. What is the new total amount of apples all 705 students can receive? Show all work.
5. What is the new total amount of oranges all 705 students can receive? Show all work.
6. Complete the table with the new amount of apple and orange trees.
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7. Your principal looks over the new plan and concludes that all 705 students will receive one apple and one orange once a week over a course of 9 weeks. Is he correct?
Circle: Yes or No If your answer is yes, provide justification. If your answer is no, provide justification.
Fruit Tree Amount of fruit produced per
tree
Total purchased tree
Total Amount of Fruit
Total fruit per student
Apple 500
Orange 150
Performance Task # 4 Scoring Guide [District Scored PT] Goal
Adequately justifies the new number of fruit trees that needs to be purchased without going over the $1,000 budget.
Correctly identifies how much money will be spent on the orange and apple trees.
Write and solves an inequality to show that student is staying within budget, remembering to include $50 one-time delivery fee.
Correctly determines the new total amount of apples; shows all work.
Correctly determines the new total amount of oranges; shows all work.
Table contains six correct responses.
Correctly answers questions regarding principal.
Justifies answer regarding principal. Proficient [Score: 8]
Meets _7-8__ of the “Goal” criteria Basic [Score: 6]
Meets _5-6__ of the “Goal” criteria Below Basic [4 points]
Meets fewer than _3-4_ of the “Goal” criteria Far Below Basic [2 points]
Meets fewer than _1-2_ of the “Goal” criteria No Response [0 points]
Meets fewer than _0_ of the “Goal” criteria
Interdisciplinary Connections and Related Priority Standards Specific to Task #4
21st Century Learning Skills Specific to Task #4
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Language Arts Check all those that apply for each task:
❑ Teamwork and Collaboration
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
Critical thinking and Problem Solving
❑ Flexibility and Adaptability
Effective Oral and Written Communication Accessing and Analyzing Information
❑ Other
Answer key
Student Council has been given $1,000 to start a school garden. They have asked
your class for some help. They want to purchase apple and orange trees with this
money for the garden but do not know how many trees to buy.
Part 1
Student Council has given you this information:
Fuji Apple Trees, x, cost $32.99 each
Washington Navel Orange Trees, y, cost $29.99 each
Student count wants to spend, as close as possible, equal amount of money on the two
different trees.
1. What is the max number of apple and orange trees that can be purchased without
going over budget?
A. Write an equation showing how to solve each amount.
Apple: 32.99x = 500 Orange: 29.99y = 500
B. How many apple and orange trees can the school purchase?
Apple: 15
Orange: 16
C. How much money will be spent on each?
Apple: 495.85 Orange: 479.84
David in your class says that student council can purchase 16 apple trees. Is he correct?
Circle: Yes or No
Part 2
If David is correct, justify your answer:
If David is incorrect, justify your answer: David is rounding incorrectly. The
answer is approximately 15.16, and should be rounded down, not up.
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Student Council just found out that the orange trees have to be delivered. The nursery
delivery charge is a one-time fee of $50.
1. Which inequality will determine the maximum number of orange trees the school can
purchase, along with the delivery fee, without going over their budget? Check all that
apply.
o 29.99n – 50 > 500
o 29.99n + 50 < 500
o 500 – 50 > 29.99n
o 50n + 29.99 > 500
2. What is the new amount of orange trees the school can purchase? __15___________
3. Graph the inequality showing the maximum number of orange trees to be purchased.
(Round to the nearest whole number)
The area to plant the trees is sixty feet by seventy-two feet. Each tree needs to be planted
12 feet apart.
1. How many trees can be planted in each row? __6____________
2. How many total rows can be planted? _____5_________
3. Using the space below, draw a diagram of how the trees should be planted. Make
sure to make a key representing the apple trees and the distance between each.
Part 3
1. Using x to represent apple trees and y to represent orange trees, write an expression
showing the total amount of apples and oranges produced in a single season.
2. How many total apples will be produced from all the apple trees? Justify your answer.
3. How many total oranges will be produced from all the apple trees? Justify your
answer.
Comparing apples to oranges: Complete the chart
Check Students work
150(15) = 2250
12 13 14 15
Apples:
500x
Oranges:
150y
500(15) = 7500
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Fruit Tree Amount of fruit
produced per tree
Total purchased
tree
Total amount of fruit
Apple 500 15 7500
Orange 150 15 2250
Using the chart, if the school has 705 students, write and solve an expression that shows x,
how many apples, and y, how many oranges each student would receive.
From your data Student Council has decided that more orange trees than apple trees need to
be planted. Do you agree or disagree? Explain your reasoning.
Yes, more orange trees need to be purchased because students will receive approximately
2/3 more apples than oranges
Part 4
1. Student Council wants to make sure that each student receives equal amounts of
apples and oranges. Using diagrams, equations, charts, etc, justify the new total
amount of fruit trees that need to be purchased without going over the budget of
$1,000 and keeping with a total of 30 trees purchased. (Get as close as possible to
total amount of fruit.)
Possible solution, check student
Apples Oranges
15x = 7500 15y = 2250
14x = 7000 16y = 2400
13x = 6500 17y = 2550
10x = 5000 20y = 3000
8x = 4000 22y = 3300
7x = 3500 23y = 3450
Apples:
Oranges:
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6x = 3000 24y = 3600
1. How much will be spent on orange trees? 23(29.99) = $689.77 How much will be
spent on apple trees? 7(32.99) = 230.93
2. Write and solve an inequality justifying that you are still within budget. (Remember to
include the one-time $50 delivery fee.)
7x + 23y + 50 < 1000 7(32.99) + 23(29.99) + 50< 1000
230.93 + 689.77+ 50 < 1000
970.70 < 1000
3. What is the new total amount of apples all 705 students can receive? Show all work.
7(500) = 3500
4. What is the new total amount of oranges all 705 students can receive? Show all work.
23(150) = 3450
Complete the table with the new amount of apple and orange trees.
Your
princip
al looks
over
the
new
plan
and
conclud
es that
all 705 students will receive one apple and one orange once a week over a course of 9
weeks. Is he correct?
Circle: Yes or No
If your answer is yes, provide justification.
If your answer is no, provide justification.
Since each student will receive 4 apples and 4 oranges they can only receive one
apple and one orange over a course of four weeks.
Fruit Tree Amount of fruit
produced per tree
Total purchased
tree
Total Amount of Fruit
Total fruit per student
Apple 500 7 3500 4
Orange 150 23 3450 4