unit 2 twmm 2013.docx.docx -...

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsCORE CONTENT

Enduring understanding (Big Idea): Students will model relationships with graphs and equations. The will use models to analyze situations and solve problems. Students will understand that solving multi-step equations connect through tables and graphs and students will understand the difference between a linear and a nonlinear function.

Essential Questions: What are the key variables in this situation? If there is a pattern relating variables, is it strong enough to allow me to make a predictions? What is the pattern relating the variables? What kind of equation will express the relationship? How can I use the equation to answer questions about the relationship?

BY THE END OF THIS UNIT:

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Models

Unit Plans Investigation Suggested ACE Questions

Standards 8.F.2; 8.F.3; 8.F.5; 8.SP.1Investigation 1Exploring Data Patterns

1.1 Bridge Thickness and Strength1.2 Bridge Length and Strength1.3 Custom Construction PartsMath ReflectionsCommon Core Mathematical Practices

1.1: ACE 1.2: ACE 1.3: ACE

Standards 8.EE.5; 8.EE.7b; 8.EE.8a; 8.EE.8c; 8.F.3; 8.F.4; 8.SP.2Investigation 2Linear Models and Equations

2.1 Modeling Linear Data Patterns2.2 Up and Down the Staircase2.3 Tree Top Fun2.4 Boat Rental Business2.5 Amusement Park or MoviesMath ReflectionsCommon Core Mathematical Practices

2.1: ACE 2.2: ACE 2.3: ACE 2.4: ACE 2.5: ACE

Standards 8.EE.5; 8.F.3; 8.F.5; 8.SP.1Investigation 3Inverse Variation

3.1 Rectangles With Fixed Area3.2 Distance, Speed, and Time3.3 Planning a Field Trip3.4 Modeling Data PatternsMath ReflectionsCommon Core Mathematical Practices

3.1: ACE 3.2: ACE 3.3: ACE 3.4: ACE

Standards 8.SP.1; 8.SP.2; 8.SP.3Investigation 5Variability and Associations in Categorical Data

5.1 Wood or Steel? That’s the Questions5.2 Politics of Girls and Boys5.3 After-School Jobs and HomeworkMath ReflectionsCommon Core Mathematical Practices

5.1: ACE 5.2: ACE 5.3: ACE

*The ACE will be completed when the teacher resources arrive.

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsCORE CONTENT

Cluster Title: Define, evaluate, and compare functions.

Standard 8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Concepts and Skills to Master

●Compare two linear functions each represented a different way and describe similarities and differences in slopes, y-intercepts, and values.

SUPPORTS FOR TEACHERSCritical Background Knowledge

●Determine slopes and y-intercepts.

Academic Vocabulary

slope, intercept, rate of change, function, linear, non-linear

Suggested Instructional Strategies

● Given one representation of a function, create the others.

● Put students in small groups. Give groups scenarios and ask each group to create a different representation of the scenario (table, equation, graph).

● Identify attributes (slope, y-intercept, values) of a function in its equation, graph, or a table.

Resources

Textbook Correlation● Thinking With Mathematical Models

○ Investigation 1 ● Say It With Symbols

○ Investigation 2

Helpful Websites / Resources○ Many links to appropriate resources connected to 8.F.2

- http://ccssmath.org/?page_id=715 ○ 8th Grade Common Core Math Wiki ○ Internet 4 Classroom Resources ○ Real World Situations - Comparing Functions ○ MARS Concept AssessmentTaskLessons (MS):

A05: Baseball Jerseys; A17: Linear Graphs, A19: Meal Out

○ MARS Concept Formative AssessmentLessons (MS): Modeling Situations With Linear

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Models○ CMP2 Resources ○ Texas Instrument 8.F.2

Lessons:http://education.ti.com/calculators/downloads/US/Activities/Search/Standards

○ YouTube Video: Algebra: Graphing Lines 1 ○ YouTube Video: Graphing Linear Equations

Sample Assessment Tasks

Skill-based Task

Is y=2(x+5) the same as the function described as “twice a quantity plus 5”?

Problem Task

Billy argues that the equation y=4x+5 is equivalent to the equation of the line that goes through (2,6) and (3,10). How did he arrive at this conclusion? Is he correct? Justify your answer.


CORE CONTENTCluster Title: Define, evaluate, and compare functions.

Standard 8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.


● Distinguish between linear and non-linear functions given their algebraic expression, a table, or a graph. ● Recognize that functions written in the form y = mx + b are linear and that every linear function can be written in the form y= mx +

b

SUPPORTS FOR TEACHERS

Critical Background Knowledge

● Generate and plot ordered pairs from an equation. ● Understand linear slope as a constant rate of change.

Academic Vocabulary

collinear, linear, nonlinear


● Examine constant and non-constant rates of change in tables of values.

● Explore growing patterns generated from a variety of contexts to explore linear and nonlinear relationships.

Resources


○ Investigation 2

Helpful Websites / Resources● Many links to appropriate resources connected to 8.F.3

- http://ccssmath.org/?page_id=717 ● Grapher ● Line Plots ● MARS Concept AssessmentTaskLessons (MS):

○ A05: Baseball Jerseys ; A17: Linear Graphs, A19: Meal Out

● CMP2 Resources ● MARS Concept Formative AssessmentLessons (MS):

○ Modeling Situations With Linear ● Texas Instrument 8.F.3 Lessons:

http://education.ti.com/calculators/downloads/US/Activities/Search/Standards

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsSample Assessment Tasks

Skill-based Task

Determine which of the following equations are linear:a) y = 3x + 1 b) y = x c) 2x – y = 5

d) y = 2x e) 2y + 5x² = 0

Problem Task

Hermione argues that the table below represents a linear function. Is she correct? How do you know?

x 10 8 6 2 0

y -1 3 7 15 19

CORE CONTENTSupport for Teachers

Cluster Title: Use functions to model relationships between quantities.

Standard 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x , y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.


○ Determine and interpret the initial value and rate of change given two points, a graph, and a table of values, a geometric representation, or a story problem (verbal description) of a linear relationship.

○ Write the equation of a line given two points, a graph, a table of values, a geometric representation, or a story problem (verbal description) of a linear relationship.


●Understand the meaning of slope and y-intercept; Write an equation as y = mx + b given a graph.

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsAcademic Vocabulary

Linear relationship, y-intercept, slope


● Use a real-world application to generate a table of values.

● Use the table to construct a function that models the relationship.

● Connect to other standards in the Expressions and Equations Domain.

Resources


○ Investigations 1 and 2

Helpful Websites / Resources● Many links to appropriate resources connected to 8.F.4 -

http://ccssmath.org/?page_id=719 ● YouTube Video:Algebra - Find the Equation of a Line

Given Two Points Intuitive Math Help● CMP2 Resources ● MARS Concept AssessmentTaskLessons (MS): ● A05: Baseball Jerseys ; A17: Linear Graphs, A19: Meal

Out● MARS Concept Formative AssessmentLessons (MS): ● Modeling Situations With Linear ● Texas Instrument 8.F.4 Lessons:

http://education.ti.com/calculators/downloads/US/Activities/Search/Standards

● Video Streaming ● Baseball Cards ● Chicken and Steak, variation 1


Skill-based Task

● The student council is planning a ski trip to Sundance. There is a $220 deposit for the lodge and the tickets will cost $70 per student. Construct a function, build a table, and graph the data showing how much it will cost for the students’ trip.

● Find the equation of the line that goes through (3,5) and (-5,7).

Problem Task

Michael says that the equation of a line that passes through the points (2,4) and (-4 , -6) is y = -2x + 2. Is he correct? Explain why or why not.

Wally created the table below for a function he knows to be linear. He thinks something must be wrong with his table because he can’t find the original function from the table. Find the error and the original function. Explain your strategy for finding the error. 3.2 6.4 9.6 12.8 16 19.2 22.4 25.617.8 30.6 43.4 56.2 66 81.8 94.6 107.4


CORE CONTENTCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

Standard 7.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.


● Ability to apply and extend previous understanding to represent addition and subtraction problems of rational numbers with a horizontal or vertical number line.

● Ability to understand the relationship between a positive number and its opposite● Ability to write mathematics sentences to show relationships● Ability to use appropriate notations to indicate positive and negative numbers



Conceptual● Understand how to model addition and subtraction of

integers using distance/direction on a number line and using chips.

● Understand that the Commutative Property holds for addition of rational numbers.

● Understand and use the relationship between addition and subtraction to simplify computation by changing subtraction problems to addition and vice versa.

● Understand and use the relationship between addition and subtraction found in fact families.

Procedural● Develop algorithms for adding and subtracting integers.● Recognize and solve problems involving addition and

subtraction of integers.● Use the Distributive Property to solve problems.● Solve simple equations with missing facts by using fact

families

Academic Vocabulary

Additive inverse, rational numbers

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsSuggested Instructional Strategies

● To introduce students to adding integers, discuss examples of saving and spending.

● Start the lesson by showing students the addition of two positive numbers. Then show that addition of two negative numbers follow a similar pattern. Focus your presentation on integers with different signs. Use the number line to model.

● To introduce students to subtracting integers, ask them to

explain how they would subtract a greater number from a lesser number.

● To introduce subtraction of integers, relate negative integers to borrowing money to buy something you do not have enough money for.

Resources

Textbook Correlation● Accentuate the Negative

○ Investigations 1, 2, and 4

Helpful Websites / Resources● Many links to appropriate resources connected to

7.NS.1c - http://ccssmath.org/?page_id=616 ● MARS Task: ● A11: Division● E03: A Day Out● E11: Taxi Cabs● Texas Instruments Lessons:● Adding Integers – A Modeling Approach● Adding Integers Exploration● Getting Negative● Integer Subtraction – What’s the Difference?● Integers● Number Line Activity – Adding Integers● http://mathstar.lacoe.edu/lessonlinks/integers/

integers_adding_main.html● http://mathstar.lacoe.edu/lessonlinks/integers/

integers_subtracting_main.html● http://www.uen.org/Lessonplan/preview?LPid=23406


Skill-based Task

Morgan has $4 and she needs to pay a friend $3. How much will Morgan have after paying her friend?

Problem Task

The Ravens started their possession on the 20 yard line. On 1st down, they gained 4 yards. On 2nd down they lost 9 yards. What is their total yardage so far?



Standard 7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.

Concepts and Skills to Master:

● Ability to apply and extend previous understanding to represent addition and subtraction problems of rational numbers with a horizontal or vertical number line.

● Ability to understand the relationship between a positive number and its opposite● Ability to write mathematics sentences to show relationships● Ability to use appropriate notations to indicate positive and negative numbers



Conceptual● Understand how to model addition and subtraction of

integers using distance/direction on a number line and using chips.

● Understand that the Commutative Property holds for addition of rational numbers.

● Understand and use the relationship between addition and subtraction to simplify computation by changing subtraction problems to addition and vice versa.

● Understand and use the relationship between addition and subtraction found in fact families.

Procedural● Develop algorithms for adding and subtracting

integers.● Recognize and solve problems involving addition and

subtraction of integers.● Use the Distributive Property to solve problems.● Solve simple equations with missing facts by using

fact families

Academic Vocabulary: Additive inverse, rational numbers


● To introduce students to adding integers, discuss examples of saving and spending.

Resources



● Start the lesson by showing students the addition of two positive numbers. Then show that addition of two negative numbers follow a similar pattern. Focus your presentation on integers with different signs. Use the number line to model.

● To introduce students to subtracting integers, ask them to explain how they would subtract a greater number from a lesser number.

● To introduce subtraction of integers, relate negative integers to borrowing money to buy something you do not have enough money for.


Helpful Websites / Resources● Many links to appropriate resources connected to 7.NS.1d -

http://ccssmath.org/?page_id=618 ● MARS Task: ● A11: Division● E03: A Day Out● E11: Taxi Cabs● Texas Instruments Lessons:● Adding Integers – A Modeling Approach● Adding Integers Exploration● Getting Negative● Integer Subtraction – What’s the Difference?● Integers● Number Line Activity – Adding Integers● http://mathstar.lacoe.edu/lessonlinks/integers/

integers_adding_main.html● http://mathstar.lacoe.edu/lessonlinks/integers/

integers_subtracting_main.html● http://www.uen.org/Lessonplan/preview?LPid=23406


Skill-based Task

1. On 3rd down of the same possession they lost 7 more yards. What is their total yardage now?

Problem Task

Introduce the situation: Chris, Rob, Amy and Melissa are arguing over which day of their skiing trip the temperature dropped the most. Below are the scenarios for each of the 4 days of their trip and who picked each day as the greatest drop in temperature.

a. Rob: On Friday, when they hit the slopes in the morning the temperature was 12.5°F. When they finally called it quits that evening, the temperature had dropped to -3.5°F. (16°F)

b. Melissa: On Saturday when they got to the ice skating rink in the morning, the temperature was -11.5°. When they were having hot cocoa that evening the temperature had dropped to -17.25°F. (5.75°F)

c. Amy: On Sunday morning when they left the hotel to go snowboarding the temperature outside was 5.75°F. When they stopped for dinner that evening, the temperature had dropped

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Modelsto -7.5°F. (13.25°F)

d. Chris: On Monday morning as they were hitting the slopes on the last day of their trip, the temperature was -2.25°F. When they finally left the slopes that evening to go home and pack, the temperature had dropped to -21.5°F. (19.25°F)


Standard 7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.


● Ability to identify and apply the following properties: Multiplicative Inverse, Commutative Property of Multiplication, Associative Property of Multiplication, Identity Property of Multiplication.

● Ability to recognize that rules for multiplying signed numbers remain the same for all rational numbers.● Ability to explore and justify the result of division by 0.

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Models● Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to

extend to multiplication and division.● Ability to use patterns and concrete models to devise a general rule for dividing integers.● Ability to identify and apply the following properties: Distributive Property, Associative Property, Commutative Properties, and

Identity Properties.



Conceptual● Understand how to use a number line/motion model to

develop the relationship between repeated addition and multiplication with integers.

● Understand and use the relationship between multiplication and division found in fact families.

Procedural● Develop and use algorithms for multiplying and dividing

integers.● Examine number patters to confirm the algorithm for

multiplication.● Recognize and solve problems involving multiplication and

division of integers

Academic Vocabulary: Additive Inverse, Algorithm, Commutative Property, Distributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers, Rational Numbers


Discuss how the “product” and “quotient” compare to the “factors” and “divisors” and “dividends.” Will the answers be larger or smaller? Why is that?Introduce by using basic multiplication with rational number before doing negatives

Resources




7.NS.2 - http://ccssmath.org/?page_id=620 Resource for Modeling Multiplication and Division:

● http://www.teachfind.com/national-strategies/models- and-images-multiplication-and-division

● http://www.lessonplanspage.com/ mathmultiplyingfractionsmanipulatives46-htm/

Dividing Fractions with Visual Models● http://www.teachfind.com/national-strategies/models-

and-images-multiplication-and-division

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsSample Assessment Tasks

Skill-based Task

Which of the following fractions is equivalent to -4/5? Explain your reasoning.

a. 4/-5 b. -16/20 c. -4/-5

Problem Task

Write the equation that represents the following:

Forgiving 3 debts of $2.00 each


Standard 7.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.

Concepts and Skills to Master:

●Ability to identify and apply the following properties: Multiplicative Inverse, Commutative Property of Multiplication, Associative Property of Multiplication, Identity Property of Multiplication.●Ability to recognize that rules for multiplying signed numbers remain the same for all rational numbers.●Ability to explore and justify the result of division by 0.●Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to

extend to multiplication and division.●Ability to use patterns and concrete models to devise a general rule for dividing integers.●Ability to identify and apply the following properties: Distributive Property, Associative Property, Commutative Properties, and









multiplication.● Recognize and solve problems involving multiplication

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Modelsand division of integers

Academic Vocabulary: Additive Inverse, Algorithm, Commutative Property, Distributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers, Rational Numbers


● Before beginning this investigation, you may want to review: the difference between irrational and rational numbers; the difference between a terminating and a repeating decimal; how to change a fraction to a decimal and vice versa.

● To review operation sign rules, have students think through a solution as well as a picture (number line, etc.) to represent each of these scenarios:a. iTunes sells 4 iPhone apps at the cost of $2 per

app (4 x 2 = 8).b. You spend $3 each on 4 bottles of Gatorade.

(4 x -3 = -12).c. Your brother owes $6 to each of 4 friends,

(-6 x 4 = -24).d. You tell 3 of your friends not to worry about

paying you the $6 each that they owe you. (-3 x -6 = 18).

Resources




7.NS.2a - http://ccssmath.org/?page_id=623 Resource for Modeling Multiplication and Division:

● http://www.teachfind.com/national-strategies/models-and- images-multiplication-and-division


Dividing Fractions with Visual Models● http://www.teachfind.com/national-strategies/models-and-

images-multiplication-and-division



Skill-based Task

−25 x

23

Problem Task

Kenny buys a huge 1-foot (12-inch) Toblerone candy bar and breaks it in half. He decides to eat only 1/6 of one of the halves of the candy bar today, because it is so big. How much of the original candy bar will he have left over for tomorrow, in inches?



Standard 7.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.



● Ability to recognize that rules for multiplying signed numbers remains the same for all rational numbers.● Ability to explore and justify the result of division by 0.● Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to










multiplication.● Recognize and solve problems involving multiplication

and division of integers

Academic Vocabulary: Additive Inverse, Algorithm, Commutative Property, Distributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers,

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsRational Numbers


● Before beginning this investigation, you may want to review: the difference between irrational and rational numbers; the difference between a terminating and a repeating decimal; how to change a fraction to a decimal and vice versa.

● Describe how you multiply two integers. What strategies do you use?

● What connection can you make between multiplying and dividing integers?

● What are some similarities and difference between dividing and subtracting integers?

● What other connections can we make between integers and our own life?

Resources




7.NS.2b - http://ccssmath.org/?page_id=625Resource for Modeling Multiplication and Division:



● Texas InstrumentsMath Nspired: Order and Inequalities: Multiplication by Negative NumbersInvestigate the effect of multiplying the numbers on a number line by a negative number. Device: TI-Nspire(TM) CAS, TI-Nspire(TM)




Skill-based Task

Using long division, express the following fractions as decimals. Which of the following fractions will result in terminating decimals; which will result in repeating decimals?

Identify which fractions will terminate (the denominator of the fraction in reduced form only has factors of 2 and/or 5)

Problem Task

A trail is 13.5 miles long. There are markers every 0.25 mile along the trail, including at the end of the trail. How many markers are there in all? Show your work.



Standard 7.NS.2c: Apply properties of operations as strategies to multiply and divide rational numbers



● Ability to recognize that rules for multiplying signed numbers remain the same for all rational numbers.● Ability to explore and justify the result of division by 0.● Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to










multiplication.● Recognize and solve problems involving multiplication and

division of integers

Academic Vocabulary:

Additive Inverse, Algorithm, Commutative Property, Distributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers, Rational Numbers

Suggested Instructional Strategies Resources

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Models● Before beginning this investigation, you may want to

review: the difference between irrational and rational numbers; the difference between a terminating and a repeating decimal; how to change a fraction to a decimal and vice versa.

● Describe how you multiply two integers. What strategies do you use?

● What connection can you make between multiplying and dividing integers?

● What are some similarities and difference between dividing and subtracting integers?

● What other connections can we make between integers and our own life?




7.NS.2c - http://ccssmath.org/?page_id=627 Resource for Modeling Multiplication and Division:



● Texas InstrumentsMath Nspired: Order and Inequalities: Multiplication by Negative NumbersInvestigate the effect of multiplying the numbers on a number line by a negative number. Device: TI-Nspire(TM) CAS, TI-Nspire(TM)




Skill-based Task

The numerical expression is equal to 5/6 - 2/3(6-1/2) + 3/4

Problem Task

The drama club has $500 to put on the play. The club can spend up to 3/8 of the money on new costumes. How much money can they spend on other supplies?


Core ContentCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

Standard 7.NS.2.d: 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


●Ability to recognize that a terminating decimal or repeating decimal is a rational number.●Ability to recognize that when rational numbers in fractional form are converted to decimals, they either terminate or repeat.



Conceptual● Understand the connection between decimals and fractions.● Understands how to make connections between decimals

and fractions represented in real world situations.● Understand terminating and repeating decimals.● Understand rational and irrational numbers.

Procedural● Ability to convert fractions to decimals.● Ability to convert decimals to fractions.●Ability to apply algorithms for dividing integers

Academic Vocabulary: Terminating decimals, repeating decimals, irrational numbers, rational numbers, positive numbers, negative numbers


Before beginning this investigation, you may want to review: the difference between irrational and rational numbers; the difference between a terminating and a repeating decimal; how to change a fraction to a decimal and vice versa.

Resources


○ Investigations 3


7.NS.2d - http://ccssmath.org/?page_id=629 ● MARS Task:● E11: Taxi Cabs● A12: Fencing● Texas Instruments Lessons:

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Models● Repeating Decimals and Fractions● Fractions to Decimals Form


Skill-based Task

Write 27

as a decimal.

Which is greater? -18/25 or -0.72727272…

Problem Task

You are tutoring a younger student. How would you explain rational numbers, irrational numbers, and how are they different?


CORE CONTENTCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers

Standard 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers


● Ability to describe and identify complex fractions.● Ability to apply knowledge of Order of Operations



Conceptual● Understand the order of operations to order computation in

problems.Procedural● Ability to use the Distributive Property to solve problems.

Academic Vocabulary: Distributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers, Rational Numbers


Review with students the order of operations. Place the acronym on the board: PEMDAS. Have students come up with their own words to remember the acronym. Have students share with the class.

Resources




7.NS.3 - http://ccssmath.org/?page_id=631 ● Texas Instruments Lessons:

○ Number Sense○ Oops! Order of Operations and the TI graphing

calculator○ Order Some Ops○ What’s Your Address?


Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical ModelsSkill-based Task

What is the simplified form of (6² + 4) – 15?

Problem Task

Consider the expression (1 + 5)² - (18 ÷ 3). Can you perform the operations in different orders and still get the correct answer? Explain your reasoning.


CORE CONTENTCluster Title: Solve real-life mathematical problems using numerical and algebraic expressions and equations.

Standard 7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies


● Ability to draw visuals to represent fractions, decimals and percents as evidence that the answers are reasonable.● Ability to understand linear expression terminology: sum, difference, term, product, factor, quotient, coefficient.● Ability to factor by using division to express a linear expression by its factors; i.e., 2x – 6 = 2 (x – 3)● Ability to expand by using multiplication to rewrite the factors in a linear expression as a product; i.e., 5 (x + 12) = 5x + 60● Ability to utilize Properties of Operations in order to rewrite expression in different forms.● Ability to develop understanding of equivalent forms of numbers, their various uses and relationships, and how they apply to a

problem



Conceptual● Understand how to identify and apply the following

properties: Distributive Property, Associative Property, Commutative Properties, and Identity Properties.

● Understand the order of operations to order computation in problems.

Procedural● Ability to identify and apply the following properties:

Multiplicative Inverse, Commutative Property of Multiplication, Associative Property of Multiplication, Identity Property of Multiplication.

● Ability to apply properties of operations using mental math and calculators.

Academic Vocabulary: Terminating decimals, repeating decimals, irrational numbers, rational numbers, positive numbers, negative numbers


● Review combining like terms.● Review combining like terms by using the distributive

property of multiplication over addition.● Review combining like terms by using the distributive

Resources


○ Investigations 1, 2, and 3● Variables and Patterns

Course Name: Eight Grade Math Unit # 2 Unit Title: Thinking With Mathematical Modelsproperty of multiplication over subtraction. ○ Investigation 3


7.EE.3 - http://ccssmath.org/?page_id=637


Skill-based Task

Lissette’s age is 3 years less than twice the age of her sister Francesca. Lissette is 13. How old is Francesca?

Problem Task

The perimeter of a rectangle is equal to twice the sum of its length and its width. One rectangle has a length of 13 ⅛ inches and a perimeter of 42 ½ inches. Write an equation that can be used to find the width, w, of the rectangle. What is the width of the rectangle?

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