Rigorous Curriculum Design Authentic Performance Tasks · 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” Interdisciplinary Connections Language

1 of 14 7.MATH.APT.Unit 3

ⓒ Leadership and Learning Center. All rights reserved. Last revised: September 2014

Greenfield/Rosedale/Fruitvale/Norris

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




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.




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:




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?




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




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




Proficient

Meets _6-7__ of the “Goal” criteria Basic


Meets fewer than _3_ of the “Goal” criteria



Science Language Arts Technology

Check all those that apply for each task:








❑ 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?




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




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:




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













❑ 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. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________




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?




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.




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]















❑ 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.




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




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:




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

Documents

Rigorous Curriculum Design Authentic Performance Tasks · 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” Interdisciplinary Connections Language