DRAFT Curriculum Map

Integrated Math 1

Vision for Assessment and InstructionAs a community of learners, we strive to implement a rigorous thinking curriculum that utilizes an inquiry-based formative assessment process in order to provide opportunities for students to develop academic

maturity as disciplinary thinkers.

This document was created to support instructional design and delivery of Integrated Math 1 using the CCSS IP Mathematics I textbook from Walch Education as a resource. © 2015

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Math 1: Year-at-a-GlanceMonth Units/Chapters Content Standards

Sept - Oct

Unit 1: Relationships between QuantitiesIn this unit, students will understand and explain what the terms of an expression or equation mean in terms of a situation that it models, as well as write linear equations, linear inequalities, and exponential equations based on a given context (word problem). Students will also graph linear and exponential equations and understand the constraints of an equation based on the situation it models.

A.SSE.1a,bN-Q.1,2,3

A-CED.1,2,3,4

Nov - Dec

Unit 2: Linear and Exponential RelationshipsA-REI.10, 11, 12

F-IF.1, 2, 3, 4, 5, 6, 7a, 7e, 9

F-LE.1, 2, 3, 5F-BF.1, 2, 3

January

Unit 3: Reasoning with Equations

A-REI.1, 3, 5, 6

Feb – Mar

Unit 4: Descriptive Statistics

In this unit, students will use statistical analysis to summarize, represent, and interpret quantitative data.

S.ID.1, 2, 3, 5, 6, 7, 8, 9

April - May

Unit 5: Congruence, Proof, and Constructions

In this unit, students will understand congruence of geometric figures through rigid motions (rotations, reflections, and translations).

G.CO.1, 2, 3, 4, 5, 6, 7, 8, 12, 13

June

Unit 6: Connecting Algebra and Geometry Through Coordinates

In this unit, students will use algebra to solve and prove simple geometric theorems, like the distance formula and Pythagorean theorem. G.GPE.4, 5, 7

Math 1 Curriculum Map

Overview forUnit 1: Relationships Between Quantities

(Approx. _ days)Content Standards: A.SSE.1a, 1b; A.CED.1,2,3,4; N.Q.1,2,3

chapter OverviewIn this unit, students will understand and explain what the terms of an expression or equation mean in terms of a real-world situation that it models, as well as write linear equations, linear inequalities, and exponential equations based on a given context (word problem). Students will also graph linear and exponential equations and understand the constraints of an equation based on the situation that it models.Essential Questions for Unit 1: For a linear expression that represents a real-world context, what do the coefficient and the constant represent? For an exponential expression that represents a real-world context, what do the coefficient, base, and exponent

represent? How does changing (either) the coefficient/constant/exponent in a given equation affect the other terms? How is writing a linear inequality from a context similar/different to writing a linear equation from a context? How is solving a linear inequality similar and different to solving a linear equation? How do you know if your solution to an equation or inequality makes sense for a given context? What is absolute value? What are some real-life situations that require equations involving absolute value? What is exponential growth? What is exponential decay? What are some real-world situations that provide a context

for either exponential growth or exponential decay? What is a constraint? Give an example of a math word problem that has a constraint. Why might you want to rearrange a given formula to highlight a specific variable or quantity? (For example, consider

the distance equation D = rt. Why might you want to solve for r?)CONTENT Standards

Seeing Structure in Expressions A.SSEInterpret the structure of expressions. (Linear expressions and exponential expressions with integer exponents)1. Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression, such as terms, factors, and coefficients.b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r )n as the product of P and a factor not depending on P.

Creating Equations A.CEDCreate equations that describe numbers or relationships. (Linear and exponential (integer inputs only); for A.CED.3, linear only)1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

Include equations arising from linear and quadratic functions, and simple rational and exponential functions.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate

axes with labels and scales.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret

solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V=IR to highlight resistance R.

Quantities N.QReason quantitatively and use units to solve problems. (Foundation for work with expressions, equations and functions)1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units

consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.2. Define appropriate quantities for the purpose of descriptive modeling.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Math 1 Curriculum Map

Documents to better understand the standards in this unitCA Mathematics Framework Math 1 p. 15 – 22Progressions for the Common Core – High School, AlgebraProgressions for the Common Core – Modeling, HSNorth Carolina Unpacked ContentHigh School CCSS Flip Book

Standards for Mathematical PracticeSMP.1 Make sense of problems and persevere in solving themStudents will not only understand what the terms, variables, coefficients, and constants are in a given expression or equation, they will also make sense of the various parts of an expression or equation in terms of the situation that it models. For example, p+0.05 p can be interpreted as the addition of a 5% tax to a price p, which is why rewriting p+0.05 p as 1.05 p shows that adding a tax is the same as multiplying the price by a constant factor.In this unit, students are expected to estimate solutions before solving, make predictions from a table or graph, and create visual representations for real-world problems involving linear or exponential equations. Students will make sense of linear and exponential equations by making connections between a table of values, a graph, and the equation. Students will understand how constraints limit a given equation and explain what a solution means in terms of the situation it models.

SMP.2 Reason abstractly and quantitatively.Unit 1 focuses heavily on word problems. In all lessons, students are expected to read a word problem, decontextualize the problem in order to write an equation or inequality (and in some instances, create a graph and/or table of values), and solve the equation or inequality. Then, students are expected to interpret their solution (i.e. “recontextualize”) and explain what their solution means in terms of the context of the word problem.SMP.4 Model with MathematicsThis unit’s strong focus on word problems provides a strong foundation for modeling with mathematics. Students will read and understand a context from a word problem, and decide how to represent the context, with either a table of values, an equation (in most cases), and/or a graph. Students will begin to understand the difference between a “linear” context and an “exponential” context, and will continue to build on that understanding in Unit 2.

SMP. 6 Attend to PrecisionEvery lesson in this unit provides opportunities for students to attend to precision. Students are expected to identify appropriate units for a given word problem, to use labels (e.g. on number lines and coordinate plane axes), to determine how a constraint effects a solution, and to identify the appropriateness of a solution for a given context.

SMP 5. Use Appropriate Tools StrategicallyStudents will create and use tables, specifically when creating or solving exponential equations. Students will use a number line to represent solutions to linear inequalities and absolute value equations (in one variable). Students will use the number line to help them understand what the solution means in terms of the context of the problem.In lesson 3, students will use a coordinate plane to plot points and graph lines and curves to represent their solutions.

Differentiation Strategies to Support Unit (EL, SpEd, GATE)Procedural Fluency needed and scaffolding opportunities: Percentages in context, solving equations, proportional thinking for unit conversions (e.g. See Station Activities Set 1:

Ratios and Proportions) Solving inequalities (see Station Activities Set 2: Solving Inequalities) Solving equations (see Station Activities Set 3: Solving Equations)

SEL Competencies Self-awareness Self-management Social awareness Relationship skills Responsible decision making

ELD Standards to Support ChapterPart 1: Interacting in Meaningful WaysA. Collaborative

1. Exchanging information and ideas with others through oral collaborative.2. Interacting with others in written English in various communicative forms.3. Offering and supporting opinions and negotiating with others.

Math 1 Curriculum Map

Sequence of InstructionUnit #1: Extending the Number System

(Approx. 20 days)Content Standards: A.SSE.1a, 1b; A.CED.1,2,3,4; N.Q.1,2,3

Learning OutcomesStudents will be able to…

Strategies for Teaching and Learning Tasks and Resources

Write an expression given a context and identify parts of the expression, such as its terms, factors, coefficients, and constants.

Interpret the meaning of each of the parts (terms, factors, coefficients, and constants) in terms of the context that they represent.

A-SSE.1a

Provide students with a context and also some expressions related to the context, and ask them to identify and interpret what the parts of the expression mean in the context. For example:

Walch 1.1.1Note: For Guided Practice Examples 2 and 3, the PBT, and Practice Problems 6-10, provide the expressions that match the context and ask students to interpret the meaning of the parts of the expression.

Online Tasks (identifying and explaining terms from a context): Mixing Candies The Bank Account

Analyze a linear expression from a given context to determine how the output (independent variable) changes based on the input (dependent variable), in terms of the situation it models.

Analyze an exponential expression from a given context to determine how the output (independent variable) changes based on the input (dependent variable), in terms of the situation it models.

A-SSE.1b

Use a table to input values for a variable and discover what terms/values change and what stays the same.Example: A new car purchased at $25,000 declines in value at an average of $1,800 per year. The expression $25,000−$1,800 t represents the value of the car at t years since the car was purchased. Analyze how a change in t changes each term in the expression and the overall price of the car over time.

Years since

purchase

Expression

$25,000−$1,800 t

What changes and what stays

the same?0

1

2

3

Walch 1.1.2Note: Practice problems 1-3,7, and 9 do not reflect the content of the lesson or target the focus of the standards and can be skipped.

Online Tasks: Kitchen Floor Tiles (Linear

Patterns) Animal Populations

Math 1 Curriculum Map

Context (given): A company uses two different sized trucks to deliver sand. The first truck can transport x cubic yards, and the second y cubic yards. The first truck makes S trips to a job site, while the second makes T trips. What do the following expressions represent in practical terms?Expression (given)

Interpretation of the expression (sample student response)

S+TS+T equals the total number of trips each truck made to a job site.

x+ yx+ yequals the total number of sand (in cubic yards) that both

trucks can transport together in one trip.

xS+ yTxS+ yT equals the total amount of sand (in cubic yards) being delivered to a job site by both trucks.

TSyTxS

TS

yTxS

equals the average amount of sand being transported per trip.

Sequence of InstructionUnit #1: Extending the Number System

(Approx. 20 days)Content Standards: A.SSE.1a, 1b; A.CED.1,2,3,4; N.Q.1,2,3

Learning OutcomesStudents will be able to…

Strategies for Teaching and Learning Tasks and Resources

Describe the appropriate units needed for a given situation/context.

Model a real-world context by writing a linear equation in one variable, and solve the equation for a quantity using appropriate units.

A-CED.1; N-Q.2,3

Strategies to help students make sense of a context when writing an equation:Given a real-world context that represents a linear equation, complete the table below. Have students notice patterns from their picture, table or equation, and make predictions about the solution.

Context (example):Brianna has saved $600 a week to buy a new TV. If the TV she wants costs $1,800 and she saves $20 a week, how many years will it take her to buy the TV?Picture/Visual

What units

will you use?

Record quantities in a table

Write the

equation

Solve the

problem

Walch 1.2.1

Online Tasks: N-Q Giving Raises A-CED Planes and Wheat A-CED Paying the Rent

Model a real-world context by writing a linear inequality in one variable, and solve the inequality for a quantity using appropriate units.

Interpret the solution of an inequality in terms of the context of the problem.

A-CED.1

Strategies to help students make sense of a context when writing an inequality:Given a real-world context that represents a linear inequality, complete the table below. Have students make predictions about their solution or the constraints for the situation.

Context (example):Alexis is saving to buy a laptop that costs $1,100. So far she has saved $400. She makes $12/hour babysitting. What’s the least number of hours she needs to work in order to reach her goal?What are the

known quantities?

What are the unknown

quantities?

Write the inequality

Solve the problem

Interpret the

solution

Walch 1.2.2

Online Task:Math Puzzle (Inequalities)

Teacher Resource:Lesson Plan and Student Worksheet on Solving One-Variable Linear Inequalitiesfrom www.explorelearning.com

Understand the definition of absolute value from:

|x|={−x , x<0x , x≥0 Use the definition of absolute

value to solve one-variable equations and inequalities

Prior Knowledge: Definition of absolute value as the distance from 0 Evaluating expressions involving absolute value

Build on students’ understanding of absolute value and their working definition as the “distance from 0” to help them understand the notation

Not in Walch Text(Do after 1.2.2)Note: Standard A-CED.1 includes creating and solving equations with absolute value which is a CA added standard.

Math 1 Curriculum Map

Sequence of InstructionUnit #1: Extending the Number System

(Approx. 20 days)Content Standards: A.SSE.1a, 1b; A.CED.1,2,3,4; N.Q.1,2,3

Learning OutcomesStudents will be able to…

Strategies for Teaching and Learning Tasks and Resources

involving absolute value. Create one-variable absolute

value equations from a given context (word problem) and interpret parts of the equation in terms of the situation it models.

Solve one-variable absolute value equations from a real-world context, graph the solution to on a number line, and interpret the solution in terms of the context.

A-CED.1(CA),3

|x|={−x , x<0x , x≥0

Students should be able to write and explain this notation in words; i.e. “The absolute value of x is equal to x whenever x is 0 or positive, but the absolute value of x is the opposite of x whenever x is negative”.

Teacher Resource:Understanding Absolute Value Notation

Student Practice Worksheet (intro to absolute value)Absolute Value Equations and Inequalities

Use a given table of values that represents exponential growth/decay to write an exponential equation for the given table in the form y=a ∙bx.

Given a real-world context, write an exponential equation in the formy=a ∙bx and solve it for a quantity using appropriate units.

Interpret the solution of an exponential equation in terms of the context of the problem.

A-CED.1

Prior Knowledge: Evaluating terms with integer exponentsFinding patterns from a table:For students’ first exposure to exponential equations, provide them with a table of values in order to identify a pattern and predict the structure of the equation.For Example:

This is an Introduction to the general form of the equation y=a ∙bx, where a is in the initial value, b is the base (rate of growth/decay), and x is time.

Strategies to help students create an exponential equation:Given a real-world context, students should identify the known and unknown quantities or variables, create a table, write an equation to model the table of values, solve the problem, and interpret the solution in terms

Walch 1.2.3Note: This lesson provides students with the equation y=a ∙bx and asks them to substitute in values. This does not meet the full depth of standard A-CED.1 (“creating” exponential equations from a given context). Students will get more in-depth work with creating and graphing exponential functions in Unit 2.

Teacher Resource:Lesson Plan and Video - Create Equations to Model Geometric Change (from LearnZillion.com)

Math 1 Curriculum Map

Context: A colony of mice starts with 100 mice, and doubles every month.

What patterns do you notice from the table?What is the initial value?

How is the colony increasing?

Could you write an equation represent the relationship between x and y?

Month (x) Mice (y) 0 1001 2002 4003 8004 16005 3200

Sequence of InstructionUnit #1: Extending the Number System

(Approx. 20 days)Content Standards: A.SSE.1a, 1b; A.CED.1,2,3,4; N.Q.1,2,3

Learning OutcomesStudents will be able to…

Strategies for Teaching and Learning Tasks and Resources

of the context of the problem. For example

Graph a linear equation in two variables (from the form y=mx+b) on a coordinate plane.

Create and graph a linear equation in two variables from a given context.

A-CED.2, N-Q.1

Pre-Requisite knowledge: Plotting points on a coordinate plane Understanding of slope and y-intercept

Build on students understanding of creating an equation in one variable (lesson 1.2.1) to now create an equation in two variables, and graph the equation.

Guiding questions and strategies to assist students in writing and graphing a linear equation from a context: What are the known and unknown quantities? What units will you use? Create a table of values to represent the situation Write an equation for the situation (see lesson 1.2.1

for assistance) Identify the slope and the y-intercept from your

equation Set up a coordinate plane, label the axes based on

the units that were identified Graph the equation (students may start by plotting

points from their table, or using the slope and y-intercept from the equation)

Walch 1.3.1Note: Guided Practice Example 1 has students substitute the “m” and “b” values into the slope-intercept formula, which does not meet the full depth of standard A-CED.2. Students will continue to get more in-depth work with linear functions in this Unit, as well as Units 2 & 3.

Online Task:Escalator

Graph an exponential equation in two variables on a coordinate plane.

Create and graph an exponential equation in two variables from a given context.

See “Strategies for Teaching and Learning” above for lesson 1.2.3Provide contexts for students that involve exponential growth (e.g. population) and exponential decay (e.g. half-life).Have students identify first whether the given word problem is exponential growth or decay, before writing

Walch 1.3.2

Online Task:Exponential Decay (Half-Life)

Math 1 Curriculum Map

Context: A population of mice quadruples every six months. If a mouse nest started with 2 mice, how many mice would there be after 2 years?

What are the known and unknown quantities?

Write an equation to model the situation.

Solve the problem.

What does the solution mean?

Month (x) Mice (y)

Sequence of InstructionUnit #1: Extending the Number System

(Approx. 20 days)Content Standards: A.SSE.1a, 1b; A.CED.1,2,3,4; N.Q.1,2,3

Learning OutcomesStudents will be able to…

Strategies for Teaching and Learning Tasks and Resources

A-CED.2, N-Q.1 the equation or drawing a graph.At this point, students can graph exponential equations by making a table of values, plotting points, and drawing a curve. They will continue to build their understanding of graphing exponential functions in Unit 2.

Identify constraints of a linear equation or inequality, within the context of a given situation.

Decide if solution(s) make sense within the context of a given situation.

A-CED.3

A constraint, in mathematics, is a limitation usually imposed upon on either the domain of a function (the input) or the range of the function (the output).To introduce constraints, first provide a context that has a simple equation. Then provide follow-up information that puts a limitation on the domain or the range, and ask how it restricts or limits the solution(s).For example,

Context: A rental car company charges a flat rate of $40 plus $2 for every mile driven.

Write an equation for this situation

You only have $200 to spend on a rental car.What are your

limitations?Rewrite this situation as

an inequality

What does your solution mean?

Walch 1.4.1Note: Guided Practice Examples 3 and 4 ask students to write a system of inequalities, as a way to understand constraints. Writing, solving, and understanding systems of equations and inequalities will be taught in Units 2 and 3, and should only be used here to understand “constraints” from a given context.

Online Tasks: Writing Constraints Growing Coffee Fishing Adventures

Rearrange a given formula in order to solve for a specific variable or quantity of interest.

A-CED.4

Build on students’ understanding of solving linear equations to assist them in solving for a specific variable or quantity of interest. For example:

Solve for x;15 x−5=25

Solve for x;15 x−5 y=25

How are you solutions similar?How are your solutions different?

Include real-world examples and common formulas for students to highlight a specific quantity. For example:Given the formula for distance, d=rt, where d is distance, r is rate, and t is time, solve the formula for time, t .

Walch 1.5.1Note: The Problem-Based Task has students substitute and solve, and does not have students rearrange the given formula. Provide students the opportunity to rearrange the formula first, and then give values to substitute.

Online Task:Rewriting Equations

Math 1 Curriculum Map