Course Name: Seventh Grade Honors Unit # 7 Unit Title: Moving Straight Ahead
BY THE END OF THIS UNIT:
Course Name: Seventh Grade Honors Unit # 7 Unit Title: Moving Straight Ahead
Unit Plans / Investigation / Suggested ACE QuestionsStandard 7.EE.3, 7.EE4a
Investigation 1
Walking Rates / 1.1 Walking Marathons
1.2 Walking Rates and Linear Relationships
1.3 Raising Money
1.4 Using the Walkathon Money
Math Reflections
Understanding the Independent and Dependent Variable / 1.1: ACE 1-2, 15-18
1.2: ACE 3-5, 19-22, 30
1.3: ACE 6-9,23-26, 31-32
1.4: ACE 10-14, 27-29, 33
Standard 7.EE.3, 7.EE4a, 7.EE.4b
Investigation 2
Exploring Linear Functions with Graphs and Tables / 2.1 Walking to Win
2.2 Crossing the Line
2.3 Comparing Costs
2.4 Connecting Tables, Graphs and Equations
Math Reflections
Understanding the relationship represented by y = mx + b
Looking Back Looking Ahead
Algebraic Reasoning (1.a-f) / 2.1 ACE 1, 29-34, 42
2.2 ACE 2-5, 35-37, 43
2.3 ACE 6-14,38, 39, 43
2.4 ACE 15-28, 40, 41
Standard 7.EE.1, 7.EE3, 7.EE.4
Investigation 3
Solving Equations /
3.1 Solving Equations Using Tables and Graphs
3.2 Exploring Equality
3.3 From Pouches to Variables
3.4 Solving Linear Equations
3.5 Finding the Point of Intersection
Math Reflections
Application of the Symbolic MethodLooking Back Looking Ahead
Relationship of Income and Expenses (2.a-c)
/ 3.1 ACE 1-4, 28-30, 413.2 ACE 5-9, 31-33, 38
3.3 ACE 10-14, 39-40, 43
3.4 ACE 15-23, 34-37, 44-45
3.5 ACE 24-27, 42, 46
Standard 7.EE.1, 7.EE3, 7.EE.4a,4b
Investigation 4
Exploring Slope / 4.1 Climbing Stairs
4.2 Finding the Slope of a Line
4.3 Exploring Patterns with Lines
4.4 Pulling It All Together
Math Reflections
Understanding of Slope and the Y-intercept
Looking Back and Looking Ahead
Variables, Linear Relationships and Representation (3-8) / 4.1 ACE 1, 36-38, 42
4.2 ACE 2-15, 39, 43, 45
4.3 ACE 16-31, 40, 44
4.4 ACE 32-35, 41, 46, 47
HONORS SECTION ALGEBRA 1 FOUNDATIONS TEXTBOOK
Standard 8.F.5 / 4-1 / Problems 1-3, Exs. 5-17, 19-27
Standard 8.F.4 / 4-2 / Problems 1-2, Exs. 6-15, 17-25
Standard 8.F.3 / 4-3 / Problems 1-3, Exs. 6-26
Standard 8.F.4 / 4-4 / Problems 1-4 Exs. 9-29 odd, 31-54
Standard 8.F.3, 8.F.5 / 4-5 / Problems 1-3, Exs. 8-26, 28-51
Standard 8.F.1, 8.F.2 / 4-6 / Part A Problems 1-3 Exs. 7-17, 20
Part B Problems 4-5 Exs. 3-19
Standard 7.RP.2, Standard 8.EE.5, Standard 8.F.2 / 5-1 / Problems 1-4 Exs. 6-12, 13-33 odd, 34-40 even, 41-56
Standard 8.EE.6, Standard 7.RP.2, Standard 8.F.5 / 5-2 / Problems 1-4, Exs 7-23 odd, 24-32, 38, 40-52
CORE CONTENT
Cluster Title: Use properties of operations to generate equivalent expressions.Standard: 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Concepts and Skills to Master:
· 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; 5(x+ 12) = 5x + 60
SUPPORTS FOR TEACHERS
Critical Background KnowledgeConceptual
· Understands the distributive property, associative and commutative properties
· Understands how to translate real life situations into expressions and equations
· Understands the difference between factors and multiples
Procedural
· Ability to distribute and combine like terms using inverse operations.
· Ability to solve two step equations
Academic Vocabulary
Properties of equality, break-even point, point of intersection, solutions, symbolic method
Suggested Instructional Strategies:
· Examine the problems of the month from the link listed below: These problems are specifically aligned with the common core and they allow a spiraling range of difficulty to reinforce algebraic thinking. These problems can be utilized as common core learning tasks to ensure application of math in real life situations.
Inside Mathematics Problems of the Month / Resources:
· Textbook Correlation: Investigations 3, 4
· MARS Tasks (www.insidemathematics.org)
· Pedro's Task (revisits factors and multiples)
· Texas Instrument Lesson: Want to Rent a Video Game System Inequalities TI Investigation
Sample Assessment Tasks
Skill-based task
Reuse and Recycle
24 students have pledged to collect 1,200 bottles to raise money for the community service project. During the first week, each student collected 34 bottles. How many more bottles must each student collect? Use an equation and the distributive property to justify your response. / Problem Task
The financial secretary is able to purchase TI-84 calculators for $125.00. He has allotted $12,375.00 of the school’s budget to support this purchase. He is purchasing the same number of $99.00 Nooks for the language arts department. A payment of $9,801 is scheduled for Barnes and Nobles. Use the factoring and distributive property to determine how many items are being purchased.
CORE CONTENT
Cluster 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.
Concepts and Skills to Master:
· Understands how to represent real life situations in the form of an expression, equation or inequality
· Ability to convert fractions, decimals and percents between forms as appropriate.
· Ability to apply properties of operations using mental math and calculators.
· Ability to draw visuals to represent fractions, decimals and percents as evidence that the answers are reasonable.
· Ability to represent rational numbers using a coordinate grids, number lines and realistic visual representations.
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Demonstrates flexibility in fraction, decimal and percent conversions.
· Demonstrates visual understanding of fractions, decimals and percents.
· Interprets real life terminology associated with multiplication, division, addition, subtraction and distribution.
Academic Vocabulary
Linear relationships, linear functions, independent variables, dependent variables, coefficient, constant rate
Suggested Instructional Strategies:
· Prior to plunging further into the unit allow the students an opportunity to reinforce the attributes of equations, inequalities and expressions. Provide students a chance to make their own connections using the Symbols Task. Examples of how to use this task is on the link : Symbols Task Video / Planning
http://www.insidemathematics.org/index.php/classroom-video-visits/public-lesson-equations-inequalities-properties/242-algebraic-equations-inequalities-a-properties-lesson-planning / Resources:
· Textbook Correlation: Investigation 1, 2, 3, 4
· MARS: Odd Numbers (focused on finding patterns)
Odd Numbers
http://insidemathematics.org/index.php/tools-for-teachers/7th-grade-math/mars-tasks-scoring-rubrics-a-analysis (student examples and scoring rubrics)
· MARS: Cat Food (focused on comparing)
Cat Food & Additional MARS Tasks
http://www.noycefdn.org/documents/math/MARS/MARS2009/tft2009gr7.pdf
Texas Instrument Lesson: Table that Sheet http://secondarymath.cmswiki.wikispaces.net/7th+Grade+Equations+and+Inequalities
Sample Assessment Tasks
Skill-based task
Suppose you are a server at a restaurant. Your salary is $24.00 for a four hour shift. The customers you serve leave an average tip of $4.50 each. Write and graph an equation to represent your total earnings. / Problem Task
The manager is impressed with this month’s sales. She has decided to allow you to choose a salary for this year. Which salary is most profitable if your sales average between $1,000 and $2,000 weekly? Use a table, equation and graph to justify your decision.
Salary A: Weekly bonus of $200 and 15% of sales
Salary B: Weekly bonus of $500 and 10% of sales
CORE CONTENT
Cluster Title: Solve real-life mathematical problems using numerical and algebraic expressions and equations.Standard 7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Standard 7.EE.4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers; solve equations of these forms fluently; compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
Concepts and Skills to Master:
· Ability to differentiate between algebraic solution and an arithmetic solution
· Ability to solve double sided equations
· Ability to create three representations to represent linear situations
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Understanding constant rate of change and how to determine slope in real world situations.
· Understanding the connection between different representations of linear situations.
· Ability to solve double sided equations with and without distribution.
· Ability to isolate the variable, when an unknown variable is specified in the formula.
· Ability to construct patterns in a table and graph linear patterns.
· Ability to use words to describe the change in dependent and independent variables.
Academic Vocabulary
Slope, rise, run, y-intercept, horizontal change, vertical change, x-intercept, intersecting lines, scale
Suggested Instructional Strategies:
· Model multiple representations of the solutions. Prior to expecting students to respond to performance based tasks model problem solving using all three representations to determine solutions. Use the DVD Task as a preliminary task
Videos, Student Samples, Rubrics
http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-comparing-linear-functions/274-comparing-linear-functions-faculty-debrief / Resources:
· Textbook Correlation: Investigations 1, 2, 4
· MARS: Toy Trains (Grade 7 link has student examples with rubrics)
Toy Trains page 3
http://www.noycefdn.org/mars2009.php
· Texas Instrument Lesson: Writing an Equation http://secondarymath.cmswiki.wikispaces.net/7th+Grade+Equations+and+Inequalities
Sample Assessment Tasks
Skill-based task
Your parents are willing t spend $300.00 to purchase movie passes and dinner for each friend that attends your birthday party. The movie tickets are $7.50 for all ages and the dinner will cost $14.50 for each guest. If both parents and the birthday person attends what is the maximum number of guests that are allowed to attend. Write an inequality or equation to represent the situation. / Problem Task
Environmental Connection: Did you know that every drop of water that runs down the drain ends up flowing into the sewage system? Sending clean water down the drain fills up the sewer and allows dirty water and waste overflow into the streams and oceans. Polluted water can harm, and even kill, animals that drink it and live in the water. What can you do? www.futurefriendly.com
Water Saving Tip - Turn off water when brushing your teeth. The average bathroom faucet runs at 2 gallons per minute. Turning it off when you brush your teeth is one of the easiest ways to save water. Use the number of members your household to write and equation and construct a linear representation of how much water could be saved in two weeks. Explain your linear representation and describe the variables used to support your explanation.
CORE CONTENT
Cluster Title: Solve real-life mathematical problems using numerical and algebraic expressions and equations.Standard 7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Standard 7.EE.4b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers; graph the solution set of the inequality and interpret it in the context of the problem.
Concepts and Skills to Master:
· Ability to develop correct usage of all four inequality symbols and related terminology (at least, more than, etc.)
· Ability to solve inequalities to determine the solution set
SUPPORTS FOR TEACHERS
Critical Background KnowledgeConceptual
· Understands of language and related terminology used to represent inequalities
· Understands the similarities and differences between the attributes of equations, expressions and inequalities
Procedural
· Ability to solve and graph equations and inequalities
Academic Vocabulary
Inequality, represent, describe, relate, solve, at least, greater than, minimum, maximum, no more than, less than, infer
Suggested Instructional Strategies:
· Inequalities are represented indirectly in the textbook, therefore you must introduce the concept when you are teaching properties. Use real life situations which represent inequalities.
· Success on performance based tasks requires several opportunities for the students to create multiple representations. Use the Carnival Ticket Plan as a preliminary task and video clips for new ideas.
Differentiate 6th and 8th Related Task
http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-comparing-linear-functions/274-comparing-linear-functions-faculty-debrief / Resources:
· Textbook Correlation: Investigations 2, 3, 4
· MARS Task: ( Student Responses and Rubrics) Buses http://www.noycefdn.org/mars2009.php
· Texas Instrument Task: Table That Equation
Sample Assessment Tasks
Skill-based task
The PTSA is purchasing season passes for the students that received the President’s Award. If each pass is $85.99 and they have $1,000 in the awards account, write an inequality to represent the maximum number of students that will receive the award. Include a table to represent the information represent the information represented in your inequality. / Problem Task
Andy wants to buy a very special yo-yo. He is hoping to be able to save enough money to buy it in time to take a class in which he would learn how to do many fancy tricks. The 5-ounce aluminum yo-yo costs $89.99 plus 6% sales tax. Andy has already saved $17.25, and he is earning $7.20 a week by doing odd jobs and chores. How many weeks will it take him to save enough money for the yo-yo?
CORE CONTENT
Cluster Title: Define, evaluate, and compare functions.Standard 8.F.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Concepts and Skills to Master
· Understand that functions describe relationships where one variable determines a unique value of the other.
· Recognize a graph of a function as the set of ordered pairs consisting of an input and corresponding output.
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Graph ordered pairs on the coordinate plane.
· Evaluate expressions for a given value.
Academic Vocabulary
function, input, output, dependent, independent
Suggested Instructional Strategies
· Explore functions that arise from real-life relationships where one variable determines a unique value of another.
· Use a variety of representations to have students identify functions and relations that are not functions. / Resources
· No Textbook Correlation
· Function Investigation
· Function Machine: Interactive Practice
· NCTM 9-12 Activity: Function Matching
§ Texas Instrument 8.F.1 Lessons
Sample Formative Assessment Tasks
Skill-based Task
· Could the set of ordered pairs, (2,5), (3,5), (4,6), (2,8), (6,7) describe the number of seconds since you left home and the number of meters you’ve walked? Is this a function? Justify your answers.
· Does the set of students in the classroom and their birthdays represent a function? Justify your answer. / Problem Task
Find three examples of relationships in the real world that can be represented by functions and three relationships that are not functions.
CORE CONTENT