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DEKALB COUNTY SCHOOL
DISTRICT
RIGOROUS CURRICULUM DESIGN
UNIT PLANNING ORGANIZER
Subject(s) Mathematics
Grade and Course Grade 7
Unit of Study Unit 1: Operations with Rational Numbers
Pacing 5 weeks
“Unwrapped” Georgia Standards of Excellence
Skills and Concepts 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.
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“Unwrapped” Priority Standards
“Unwrapped” Concepts
(Students Need to Know)
“Unwrapped” Skills (Students Need
to Be Able to Do)
Bloom’s Taxonomy Levels
DOK (For Overall Standard)
MGSE7.NS.1
• APPLY AND EXTEND
• ADD & SUBTRACT
• REPRESENT
• Understandings of addition and subtraction.
• Rational numbers
• Addition and subtraction on a horizontal or vertical number line.
• 3 (Apply)
• 2 (Understand)
• 2 (Understand)
• 2 (Skills and Concepts)
MGSE7.NS.2
• APPLY AND EXTEND
• MULTIPLY AND DIVIDE
● Previous and understandings of multiplication and division of fractions
● Rational numbers
● 3 (Apply)
● 2 (Understand) ● 2 (Skills and
Concepts)
MGSE7.NS.3
● SOLVE
● Real-world and mathematical problems involving the four operations with rational numbers.
● 3 (Apply) ● 2 (Skills and
Concepts)
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Supporting Standards
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.
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Standards of 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.
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.
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Unit Assessments
Pre-Assessment Post-Assessment
Student Version:
Gr7_MATH_Unit1_Preassessment_Student
Teacher Version:
Gr7_MATH_Unit1_Preassessment_Teacher
Student Version:
DeKalb Gr7 Benchmark Assessment
Teacher Version:
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Performance Assessment
Engaging Scenario
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.
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Performance Task 1 In Detail
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
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Account Ledger
Date Transaction Description
Deposits (Credits)
Withdrawals (Debits)
Balance
In addition: 1. Use the table to determine the beginning and ending balance, and state if the company made
a profit or remained in debt. 2. What is the total running balance?
3. In what ways is it useful to develop an algorithm for adding and subtracting rational numbers?
4. How would you interpret the total running balance?
Task 1 Teacher Notes/Answer Key: Visual representations may be helpful as students begin this work. If
they do not have a visual to illustrate what is happening when they are adding and subtracting rational
numbers, they will get lost in the symbols and will not know how to combine the absolute value of the
rational numbers.
Differentiation: For advanced learners, students can create their own table to record the various
transactions. In addition, students can create a budget within a given income as an extension activity.
• Students may struggle with the vocabulary, since there are many different ways to debit your
account.
• For students that are demonstrating exemplary knowledge, have students create the ledger on
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Performance Task 1 Scoring Guide
4 Advanced 3 Proficient 2 Basic 1 Below Basic
All Proficient criteria plus: o Explains how
developing an
algorithm helps to
add and subtract
rational numbers and
provides example
using the task.
o Attends to precision
with all calculations
with the balances
after each
transaction.
o Provides an accurate
ending balance.
o Explains the
meaning of the
balance using
mathematical
terminology.
o Provides calculations
with errors for some
of the balances after
various transactions
with an error in the
ending balance.
o Explains the balance
without using
appropriate
mathematical
terminology.
o Provides
explanations and/or
mathematical
representations that
could not be clearly
understood or
interpreted.
their own.
Account Ledger
Date Transaction Description
Deposits (Credits)
Withdrawals (Debits)
Balance
8/15 Beginning Balance $50,000.00
8/16 Studio Rental $2,000.35 $47,999.65
8/16 Manufactured CD $162,050.03 -$114,050.38
8/16 Concert ticket sales $25,000.00 -$89,050.38
8/17 Endorsement $22,000.00 -$67,050.38
8/17 Clothing Allowance $3,350.00 -$70,400.38
8/18 Publishing $6,000.00 -$76,400.38
8/19 Downloads $5,098.99 -$71,301.39
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Performance Task 2 In Detail
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.
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Task 2 Teacher Notes:
Differentiation: Provide a table to organize calculations for students that require a visual aid.
Extension Activity: Negotiate with the record company whose offer you originally rejected, determine what
change in royalty percentages or ratios are necessary to make you select that particular company, and
write a counteroffer to present.
Answer A:
500,000($16) = $8,000,000 This represents the amount of money collected from CD sales.
$8,000,000(.11) = $880,000 This represents the amount each band member will receive in royalties.
$8,000,000(.3) = $2,400,000 This represents the amount the retailer will receive.
$8,000,000(.22) = $1,760,000 This represents the amount the distributor will receive.
$8,000,000(.04) = $320,000 This represents the amount the producer will receive.
Answer B:
500,000($15) = $7,500,000: This represent the amount of money collected from CD sales.
$7,500,000(1/8) = $937,500: This represent the amount each band member will receive in royalties.
$7,500,000(¼) = $1,875,000: This represents the amount the retailer will receive.
$7,500,000(1/5) = $1,500,000: This represent the amount the distributor will receive.
$7,500,000(1/20) = $375,000: This represent the amount the producer will receive.
Answer C:
As a result of disagreeing with this advice, the band should decide to sign with “Bling Records”, because
they will receive will $937,500 in royalties compared to New Edge Records. If the band chose New Edge
Records they will receive a royalty amount of $880,000, which is less than Bling Records, and would not
be the best decision. In addition, the band would receive $57,500 less by signing with New Edge
Records.
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Performance Task 2 Scoring Guide
4 Advanced 3 Proficient 2 Basic 1 Below Basic
All Proficient criteria plus: o Attends to precision
with the calculation
of the new
percentages and
ratios.
o Justifies with math
examples which
change in royalties
are necessary for
selection of a band.
o Attends to precision
with calculating the
amount of money
received by each
individual using
percentage.
o Attends to precision
with calculating the
amount of money
received by each
individual using a
fraction.
o Provides a viable
argument using
math examples to
justify the selection
of a record
company.
o Calculates most of
the amount of money
received by each
individual accurately
using a percent
and/or fraction.
o Provides an
explanation of the
selection of a record
company without any
math examples.
o Provides
explanations and/or
mathematical
representations that
could not be clearly
understood or
interpreted.
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Performance Task 3 In Detail
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).
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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.
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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.
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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.
o Calculates solutions
but has errors in
potential profit and/or
amount of time
required to eliminate
the debt for each
solution.
o Provides graphs that
are inaccurate.
o Provides
explanations and/or
mathematical
representations that
could not be clearly
understood or
interpreted.
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Performance Task 4 In Detail
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.
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The teacher may pose the following questions for students:
• How would you design a presentation to persuade a Board of Directors to select your proposal?
• How would you illustrate a trend for the company's income?
• Can you apply what you know to any other real-world problem?
• How would you collect the data for Bling Records' finances?
Performance Task 4 Scoring Guide
4 Advanced 3 Proficient 2 Basic 1 Below Basic
All Proficient criteria
plus:
o Provides examples and counterexamples to support the viable argument.
o Attends to precision
with all calculations
provided in the
justification.
o Provides a viable
argument with
mathematical
accuracy of
supporting details
(visuals, graphs,
calculations, etc.)
containing the
following:
1. The company's current financial balance (surplus or deficit).
2. The company’s finances.
3. The mathematical justification to sell digital downloads or ringtones.
o Provides an
explanation that
contains errors in
calculations,
supporting details
and/or mathematical
understanding of the
task.
o Demonstrates errors
in computation skills
and use of math
strategies.
o Provides
explanations and/or
mathematical
representations that
could not be clearly
understood or
interpreted.
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Instructional Strategies
Instructional Strategies
Research-Based Effective Teaching Strategies
21st Century Learning Skills
□ Learning Objectives (posted and referenced)
□ Identifying Similarities and Differences
□ Summarizing and Note Taking
□ Reinforcing Effort, Providing Recognition
□ Homework and Practice
□ Nonlinguistic Representations
□ Cooperative Learning
□ Purposeful small group instruction
□ Increased think time
□ Setting Objectives, Providing Feedback
□ Check for Understanding
□ Generating and Testing Hypotheses
□ Cues, Questions, and Advance Organizers
□ Interdisciplinary Non-Fiction Writing
□ 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
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Intervention Strategies Intervention Strategies
(Tiers 1, 2, 3) Additional Supports in
Classroom
Specially Designed Instruction for Special
Education Students
Strategies for English Language Learners
□ Re-voicing
□ Explaining
□ Prompting for participation
□ Challenging or countering
□ Asking “Why?” “How?”
□ Reread
□ Practice new academic vocab.
□ Assistive technology
□ Pre-teach & re-teach in a different way
□ Repetition
□ Use of manipulatives
□ Collaborative work
□ Direct/explicit instruction
□ “Chunking”
□ Accommodating different learning styles
□ Create differentiated text sets
□ Providing additional guided
practice
□ Conferencing
□ Additional time
□ Small group collaboration
□ Modify quantity of work
□ Take student’s dictation
□ Scaffold information
□ Differentiated content process or product
□ Consistent reward system
□ Refer to students’ IEP or 504 plan
□ Assistive technology
□ Visuals/Realia
□ Front-loading
□ Echoing/Choral response
□ Color-coding
□ Multiple exposures in different media
□ Pair-share
□ Modeling
□ Language scaffolds: eg, sentence frames
□ Deconstruct complex sentences and texts
□ L1 support
□ increased opportunities for student-student talk
□ Strategic vocabulary instruction
□ Additional think time
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Strategies for Gifted Learners
Tier 1: Low Preparation Tier 2: Medium Preparation
Flexible-Learning Groups by Readiness, Interest,
Learning Profiles
Gifted Education Cluster Classes
Choice of Books Gifted Education Collaboration Classes
Homework Options Tiered Activities and Products
Use of Reading Buddies Use of Literature Clubs
Various Journal Prompts Multiple Testing Options
Student/Teacher Goal Setting Multiple Texts
Varied Pacing with Anchor Options Alternative Assessments
Work Alone or Together Subject Advancement within class
Flexible Seating Curriculum Compacting
Varied Scaffolding Tiered Centers
Varied Computer Programs Spelling by Readiness
Design-A-DAY Varying Organizers
Varied Supplemental Materials Community Mentorships
Computer Mentors Stations
Think-Pair-Share by Readiness, Interest, Learning Profiles
Group Investigations
Open-ended Activities Students are Assessed in Multiple Ways
Explorations by Interest Student choice in selecting learning activities.
Options for Competition Simulations
Tier 3: High Tier 4: Advanced/Autonomous
Advanced Content English/language arts, mathematics, science and/or social studies courses
Above grade level accelerated English/language arts, mathematics, science and/or social studies courses
Resource Classes Advanced Placement Classes
Independent/Directed Study International Baccalaureate Classes
Socratic Seminars Internship/Mentorships
Whole Grade Acceleration
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Instructional Resources and Materials Suggested Resources Suggested Technology Resources
Math Tools:
o Number line o Double Number Line o Virtual Manipulatives o Two-color counters o Tiles o Area Model o Arrays o Fraction Manipulatives
Explanation of Standards:
GADOE Grade Level Curriculum Overview Seventh Grade
GADOE Grade 7 Framework Unit 1
Carnegie Learning Textbook – Chapters 1 and 4 Example of a Checkbook Ledger
http://www.activitiesforkids.com/afkpdf/printable-check-register.pdf Virtual Manipulatives
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
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
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Unit Vocabulary
Unit Vocabulary Terms Interdisciplinary Connections
Academic / Tier 2 Unit-Specific / Domain / Tier 3
Balance Bankruptcy Credit Debt Debit Deposits Distributor Expense Income Inherit Ledger Producer Profit Retailer Revenue Royalty Transaction Trend
Additive Inverse Multiplicative Inverse Absolute Value Integers Long Division Natural Numbers Negative Numbers Opposite Numbers Positive Numbers Rational Numbers Repeating Decimal Terminating Decimal Zero Pair
ELAGSE7W2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and
analysis of relevant content. Banking Engineering Construction Weather Stock Market Accounting
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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)
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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.
Week 1
MGSE7.NS.1 MGSE7.NS.3 MGSE7.NS.1a MGSE7.NS.1b MGSE7.NS.1c MGSE7.NS.1d
Intro Engaging Scenario
o Review Adding and
Subtracting Integers
Adding and Subtracting Rational Numbers
o Carnegie Learning Chapter 4, Lessons 4.1 and 4.2
o Georgia Framework Task:
o Show Me Your Sign 1
o Show Me Your Sign 2
o Subtracting Integers
o Hot Air Balloon o https://learnzillion.com/les
son_plans/4001-2-use-distance-and-direction-to-find-sums-of-integers-fp
o Interactive Math Journals
o Number Talk o Math Talk
Pre-Assessment (Unit Pre-Assessment) Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions
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Week 2
MGSE7.NS.1 MGSE7.NS.3 MGSE7.NS.1a MGSE7.NS.1b MGSE7.NS.1c MGSE7.NS.1d
Task 1: Balance ledger Formative Assessment Lesson: Using Positive and Negative Numbers http://map.mathshell.org/lessons.php?unit=7105&collection=8
o Adding and Subtracting Rational Numbers
o Carnegie Learning Chapter 4, Lessons 4.3, 4.4 and 4.5
o Georgia Framework Task:
o Debits and Credits o Interactive Math
Journals o Number Talk o Math Talk
Task 1 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions
Week 3
MGSE7.NS.1 MGSE7.NS.2 MGSE7.NS.2a MGSE7.NS.2b MGSE7.NS.2c MGSE7.NS.2d MGSE7.NS.3
Task 2: Compare and contrast company’s royalty offers.
o https://learnzillion.com/lesson_plans/3921-7-use-properties-to-multiply-rational-numbers-fp
GADOE Gr. 7 Unit 1: Multiplying Integers GADOE Gr. 7 Unit 1: Do it Yourself Revisited o o Multiplying and Dividing
Rational Numbers o Carnegie
Learning Chapter 5
Task 2 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions
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Week 4
MGSE7.NS.2 MGSE7.NS.3 MGSE7.NS.2a MGSE7.NS.2b MGSE7.NS.2c MGSE7.NS.2d
Task 3: Analyze two business solutions.
o Multiplying and Dividing rational Numbers
o Carnegie Learning Chapter 5
o Georgia Framework Task:
o Converting Fractions to Decimals
o Interactive Math Journals
o Number Talk o Math Talk
Task 3 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions
Week 5
MGSE7.NS.1 MGSE7.NS.2 MGSE7.NS.3 MGSE7.NS.1a MGSE7.NS.1b MGSE7.NS.1b MGSE7.NS.1c MGSE7.NS.1d MGSE7.NS.2a MGSE7.NS.2b MGSE7.NS.2c MGSE7.NS.2d
Task 4: Create persuasive proposal.
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
Post Assessment (District Benchmark)