Rigorous Curriculum Design Unit Planning Organizer Blank ... · Rigorous Curriculum Design—Unit Planning Organizer Blank ... REPRESENT addition and subtraction on a horizontal or
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Apply and Extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers MGSE7.NS.1a Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00. MGSE7.NS.1b Understand p + q as the number located a distance from p, in the positive or negative direction depending on whether q is positive or negative. Interpret sums of rational numbers by describing real world contexts. MGSE7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (– q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐ world contexts. MGSE7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. MGSE7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (- 1) (– 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐ world contexts. MGSE7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐ zero divisor) is a rational number. If p and q are integers, then – (p/q) = (– p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐ world contexts. MGSE7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. MGSE7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
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.
Essential Questions Corresponding Big Ideas
1. Why are properties important when solving positive and negative rational numbers problems?
2. What strategies are most useful in helping develop algorithms for adding, subtracting, multiplying, and dividing positive and negative rational numbers?
3. How can we apply number relationships to develop efficient strategies for solving problems in everyday life?
1. The properties are used to provide multiple ways to solve positive and negative numbers and promote computational fluency.
2. Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.
3. Positive and negative rational numbers are often used to solve problems in everyday life.
Current Situation: After gaining the new position as Chief Financial Officer for “Bling Records”, you noticed that the company’s accounting books show a balance of $50,000 due to the lack of organization in the finance department.
Student Challenge: In order to prevent “Bling Records” from filing bankruptcy, you have a responsibility to analyze the current financial situation. First, you will need to balance the accounting ledger for “Bling Records”. Next, you will need to compare and contrast “Bling Records” royalties offer to a competing company. Then, you will compare two business solutions and determine the best solution for Bling Records. Finally, you will create a proposal outlining your final decision to correct the financial instability. Your proposal must show how Bling Records should generate income by creating growth.
Student Role: Students are Chief Financial Officers of a major music label company.
Intended Audience: Students will present their finding to the Board of Directors.
Product or Performance: Persuasive proposal that includes: the current balance, revenue and
expenses, discusses the best options to generate income.
Performance Task Synopses
Task 1: MGSE7NS1, MGSE7NS1a-d The students will use a table (or check register) to record debits
and credits and calculate a running total balance.
Task 2: MGSE7NS2a-d The students will compare and contrast the dollar amounts after converting the
rational numbers of each record company, and will determine the amount of royalties that will be
generated based on the amount of CD sales. Also, students will identify which company will generate the
greatest royalties.
Task 3: MGSE7NS1, MGSE7NS2, MGSE7NS2 a- d The students will analyze two business solutions in
order to eliminate "Bling Record’s" debt, determine the best solution, and justify their decision.
Task 4: MGSE7NS1, MGSE7NS2, MGSE7NS3 Create a multimedia proposal to justify your plan to the
board of directors using the information in Task 1 – 3.
Apply and Extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers MGSE7NS1, MGSE7NS1a-d: APPLY and EXTEND previous understandings of addition and subtraction to ADD and SUBTRACT rational numbers; REPRESENT addition and subtraction on a horizontal or vertical number line diagram. MGSE7.NS.1a Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00. MGSE7.NS.1b Understand p + q as the number located a distance from p, in the positive or negative direction depending on whether q is positive or negative. Interpret sums of rational numbers by describing real world contexts. MGSE7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (– q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts.
MGSE7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. Circumstances of Performance: In Class (Approximate Time 20 – 30 minutes)
Task 1 Student Directions: Create a table to sort and organize the expenses and income of "Bling
Records". There are two types of transactions that may take place, (1) deposits (money the company
receives), and (2) debits/payments (money which the company spends and withdrawal from the account). If
the total amount of credits is more than debits, the account balance is positive. If the total amount of debits
are more than credits, the account balance is in debt and shows a negative cash value.
Use the table record each transaction:
• Transactions (Determine if the transaction is a withdrawal or deposit)
• On August 15, the beginning balance was $50,000.00
• On August 16, paid for rental of studio time $2,000.35
• On August 16, paid for manufactured CD $162,050.03
• On August 16, received proceeds from concert ticket sales $25,000
• On August 17, received $22,000 in endorsements
• On August 17, paid for artist clothing allowance $3,350.00
• On August 18, paid for publishing $6,000
• On August 19, received proceed from download $5,098.99
Apply and Extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers MGSE7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (- 1) (– 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐ world contexts. MGSE7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐ zero divisor) is a rational number. If p and q are integers, then – (p/q) = (– p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐ world contexts. MGSE7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
MGSE7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Circumstances of Performance: In-Class (Approximate Time 60 – 70 minutes)
Task 2 Student Directions:
A new band is trying to decide if they are going to sign with your company or "New Edge Records." A band of 4 that writes their own material, and they must determine which company's offer is the best deal.
A) New Edge Records will sell each CD for $16. Your deal is to receive a royalty rate of 11% per band member. The retailer receives 30%, the distributor receives 22% and the producer receives 4%. If you sell 500,000 records, how much will each individual receive?
B) Bling Records will sell each CD for $15. Our deal is to receive a royalty rate of 1/8 of sales per band member. The retailer receives ¼, the distributor receives 1/5, and the producer receives 1/20 of the sales. If you sell 500,000 CDs, how much will each individual receive?
C) Some band members are having a difficult time deciding which company to choose, and a representative approached one member from New Edge Records. The smooth-talking representative suggests to him that the band should sign with their company because they sell each CD for more money than Bling Records; therefore, you will make more money. Do you agree or disagree with this advice? Explain why you agree or disagree using your calculations from each company to justify your position.
M Apply and Extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers.
M MGSE7.NS.1: APPLY and EXTEND previous understandings of addition and subtraction to ADD and SUBTRACT rational numbers; REPRESENT addition and subtraction on a horizontal or vertical number line diagram.
MGSE7.NS.2: APPLY and EXTEND previous understandings of multiplication and division of fractions to
MULTIPLY and DIVIDE rational numbers.
MGSE7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (- 1) (– 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐ world contexts. MGSE7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐ zero divisor) is a rational number. If p and q are integers, then – (p/q) = (– p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐ world contexts. MGSE7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
MGSE7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Circumstances of Performances: In Class (Approximate Time 55 – 60 minutes)
Task 3 Student Directions: Your company's research and development department discovered two possible solutions to eliminate the debt over time, and generate revenue. The possible solutions are either selling digital releases of sounds through iTunes, or selling your songs as ringtones through major cell phone providers. Determine the best solution if given a 36-month timeframe to get out of debt and make a profit. Then, justify your decision using your data and calculations.
Solution 1: Digital Downloads and Releases
The cost for a digital release is $0.09 per song that must be paid to the songwriter and iTunes. "Bling Records" decided to sell each artist's song for $1.99.
a. What is the potential profit per digital release?
b. How much is your potential profit per month?
c. If your average sales per month are 2,525 songs, how long will it take to eliminate the debt of $71,301.39? (Round answer to nearest whole number).
d. At the end of the 36 months, how much is your potential revenue?
e. Chart the quarterly trend for the possible revenue of selling digital releases over a 36-month timeframe.
Solution 2: Ringtones
The cost for producing a ringtone is $0.24 that must be paid to the songwriter and the cell phone provider. "Bling Records" decided to sell each ringtone $0.99.
a. What is the potential profit per sale of ringtone?
b. How much is your potential profit per month?
c. If you sell 3,750 ringtones per month on average, how long with it take to eliminate the debt of $71,301.39? (Round answer to the nearest whole number).
d. At the end of the 36 months, how much is your potential revenue?
e. Chart the quarterly trend for the possible revenue of selling ringtones over a 36-month timeframe.
Which solution would you choose to help eliminate the company's debt and generate a profit? Justify your decision.
Task 3 Teacher Notes: Students may have difficulty with question d for both solutions, it would be
helpful to discuss how many months it took to eliminate the debt and break even at zero dollars. Then,
students must subtract the time it takes to eliminate the debt from 36 months, in order to calculate the
profit at the end of the timeframe. The concept of changing a percent to a decimal will need to be
explored before administering this task. (See GDOE Framework Task Unit 1) A math talk discussing the
various ways data can be displayed will be needed along with proper labels on graphs.
Differentiation:
• A calculator may be provided to complete this task.
• Visuals and/or videos about digital downloads and ringtones may be helpful to grasp students'
attention and to conceptualize the importance of the task.
• Teacher may provide students with graph paper in order to chart the trends for both solutions, or
students can utilize Microsoft Excel to create both graphs.
Teacher may ask students the following questions to summarize, analyze, organize, or evaluate:
• What is a better solution to help eliminate the company's debt, and generate revenue?
• How would you defend your position about the particular solution you determined to be best in
the company's interest?
Teacher may ask students the following questions to apply or relate:
• How would you interpret the trends for both solutions over a course of 3 years?
Teacher may ask students the following questions to recall facts, make observations, or demonstrate
understanding:
• What did you observe about the length of time that was required to eliminate the company's debt
for each possible solution?
Answer Key
Solution 1: Digital Downloads and Releases
The cost for a digital release is $0.09 that must be paid to the songwriter and iTunes. "Bling Records" decided to sell each artist's song for $1.99.
a. What is the potential profit per digital release? Answer: $1.90
b. If your average sales per month is 2525 songs, how long will it take to eliminate the debt of $71,301.39? Answer: 15 months.
c. How much is your potential profit per month? Answer: $4797.50 a month
d. At the end of the 36 months, how much is your potential revenue? Answer: $100,747.50
e. Chart the trend for the possible revenue of selling digital releases over a 36-month timeframe.
Solution 2: Ringtones
The cost for producing a ringtone is $0.24 that must be paid to the songwriter and the cell phone provider. "Bling Records" decided to sell each ringtone $0.99.
a. What is the potential profit per sale of ringtone? Answer: $0.75
b. If you sell 3,750 ringtones per month on average, how long with it take to eliminate the debt of $71,301.39? Answer: 25 months.
c. How much is your potential profit per month? Answer: $2812.50 a month
d. At the end of the 36 months, how much is your potential revenue? Answer: $30,937.50
e. Chart the trend for the possible revenue of selling ringtones over a 36-month timeframe.
Which solution would you choose to help eliminate the company's debt and generate a profit? Justify your decision. Students should state they would choose solution one, digital downloads and releases, because they earned more money overall. In addition, students should state that the digital downloads and releases required the least amount of time.
Performance Task 3 Scoring Guide
4 Advanced 3 Proficient 2 Basic 1 Below Basic
All Proficient criteria plus: o Justifies solution to
include words and a
visual (table/chart)
that shows the
potential for profit,
the amount of time to
eliminate each debt
with specific
examples from the
task.
o Attends to precision
with calculating…
1. The potential profit
for each solution.
2. The amount of
time required
eliminating the
debt for each
solution.
3. The amount of
potential profit per
month for each
solution.
4. The amount of
potential revenue
for each solution.
o Graphs the trends for each solution with correct amounts and values over the 30-month period.
o Graphs with precision intervals, a title, labeled axes for each solution.
Ap Apply and Extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers.
M MGSE7.NS.1: APPLY and EXTEND previous understandings of addition and subtraction to ADD and
SUBTRACT rational numbers; REPRESENT addition and subtraction on a horizontal or vertical number line diagram.
MGSE7.NS.2: APPLY and EXTEND previous understandings of multiplication and division of fractions to
MULTIPLY and DIVIDE rational numbers.
MGSE7.NS.3: SOLVE real-world and mathematical problems involving the four operations with rational numbers.
Circumstances of Performance: In-Class (Approximate Time 75 – 120 minutes)
Task 4 Student Directions: You have the choice of creating the following: A Prezi, PowerPoint Presentation, or a persuasive letter to justify your plan to the Board of Directors. Your detailed plan must contain the following:
• Discuss the company's current financial balance.
• Summarize the company's revenues and expenses.
• Discuss the company's options to generate revenue and reduce debt.
• Justify your position about which solution best meets the needs of "Bling Records" current financial status.
• Use appropriate visuals, charts, and/or figures to support your proposal.
• Mathematical evidence/calculations to support your proposal.
Task 4 Teacher Notes: The teacher may want to provide students with a handout that summarizes the
completed solutions from the previous tasks, as this particular task is focusing on creating a proposal.
Technology Resources: GADOE Grade Level Curriculum Overview -Grade 7 Illustrative Mathematics https://www.illustrativemathematics.org/7.NS Math Shell – Using Positive and Negative Numbers in context http://map.mathshell.org/lessons.php?unit=7105&collection=8 Unit 1 Framework https://www.georgiastandards.org/Georgia-Standards/Frameworks/7th-Math-Unit-1.pdf Khan Academy – Adding and Subtracting Negative Numbers https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-sub-neg-intro/v/adding-and-subtracting-negative-number-examples Negative Number Word Problems https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-sub-word-problems-w-negatives/v/negative-number-word-problems-1 Modeling Integer Multiplication http://www.brainingcamp.com/legacy/content/concepts/integer-multiplication/lesson.php How to Start and Run a Record Label http://smallbusiness.chron.com/start-run-record-label-4755.html
Weekly Planner Course: Grade 7 Mathematics Unit: Unit 1: Operations with Rational Numbers
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. Unit Expectations
o Performance Assessment (4 Tasks and Scoring Guide) Weekly core instruction should include the implementation of instructional tasks from the Georgia Department of Education (GADOE)
o Formative Assessment Lessons o GADOE Instructional Tasks
located at www.georgiastandards.org along with other district and supplemental instructional resources. Included in the planner are possible suggestions for GADOE tasks.
o Review Multiplication and Division of Rational Numbers
o Carnegie Learning Chapter 5
o Georgia Framework Task:
o The Repeater vs. Terminator
o A Poster o Whodunit? The
undoing of (-7) o Interactive Math
Journals o Number Talk
o Math Talk
Task 4 Scoring Guide Post Assessment Chapter 4 and Chapter 5 Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions Parking Lot Students’ Presentation KWL