Math I

North Carolina Mathematics State Standards

Year Long Math 1 Course at a Glance

(What is the course building on and where is it going?) The purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. This course deepens and extends understanding of linear relationships, in part by contrasting them with exponential and quadratic phenomena, and in part by applying linear models to data that exhibit a linear trend. In addition to studying bivariate data, students also summarize, represent, and interpret data on a single count or measurement variable. The Geometry standards that appear in this course formalize and extend studentsʼ geometric experiences to explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments.

(What should the course focus on as overarching goals?) Instructional time should focus on three critical areas: (1) interpret, build, and model linear, exponential, and quadratic functions; (2) Extend the use of algebra topics such as: seeing structure in expressions, perform arithmetic operations on polynomials, and creating and reasoning with equations and inequalities; and (3) relate data display and summary statistics to single count and two variable measurements. In addition, number sense (properties of exponents) and geometry (distance, midpoint, slopes of parallel and perpendicular lines, and proving geometric theorems algebraically) are also included in the goals.

(Expand on those goals) Students will

1. Focus on comparing properties of linear function to specific non-linear functions and rate of change. They will identify and manipulate key features of linear, exponential, and quadratic functions given multiple representations.

2. Focus on quantities are used to form expressions, equations and inequalities that represent real-world situations and functions describe situations where one quantity determines another and these functions can be used to model real-world situations.

3. Focus on analysis of univariate and bivariate data

• Use of technology to represent, analyze and interpret data

• Shape, center and spread of univariate numerical data

• Scatter plots of bivariate data

• Linear and exponential regression

• Interpreting linear models in context.

The Standards for Mathematical Practice apply throughout each goal and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

North Carolina Math 1 Scope and Units

Unit 1 -

Rational Numbers and Interpreting Expressions

10 days

Students will define rational numbers as any number that can be written as a quotient of two other integers, namely a positive or negative whole number, fraction, or terminating or repeating decimal. Students will be able to order and convert between all forms of rational numbers, and they will be able to perform any operations on rational numbers to solve problems in a mathematical or real-world context. They will define and differentiate between rational and irrational numbers.

6.NS.9,

7.NS.1, 7.NS.2, 7.NS.3, 8.NS.1

Unit 2a- Equations and Inequalities

15 days

Students will build on their understanding of equality to solve single-variable equations and inequalities, both in real-world and mathematical contexts, with variables on one side or both sides involving rational numbers (including fractions, decimals and integers).

6. EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 7.EE.3, 7.EE.4, 8.EE.7

Unit 2b

Solving Equations, Solving Inequalities, and Intro Functions Extended

10 days

Students will understand that quantities are used to form expressions, equations and inequalities that represent real-world situations and functions describe situations where one quantity determines another and these functions can be used to model real-world situations.

A.SSE.1a, A.SSE.1b

A.CED.1, A.CED.4, A.REI.1, A.REI.3, A.REI.12, F.IF.1, F.IF.2, F.IF.3,

F.IF.4, F.IF.5

Unit 3a - Proportional Relationships

10 days

Students will extend their understanding of ratios to include proportional relationships represented in graphs, equations, tables, and written context. They will recognize and analyze unit rates, proportional relationships, and scale factor, and they will use each to solve problems in mathematical and real-world contexts. Students will also extend their understanding of percent to solve problems using the percent as a ratio per 100, including problems with circle graphs.

6.EE.9, 7.RP.1, 7.RP.2, 7.RP.3,

Unit 3b -

Intro to Functions

25 days

Students will extend on their learning of proportional reasoning into linear equations and functions. Students will define functions as numerical relationships in which each input has one output and represent written descriptions of these functions on qualitative graphs. Students will also learn characteristics of these functions represented as tables, graphs, equations, and written contexts and use those to make connections with solving equations/inequalities. Students will also learn characteristics of linear functions, including the slope-intercept form of a linear equation, in real-world and mathematical contexts. They will compare characteristics of functions in various representations.

8.F.1, 8.F.2, 8.F.3, 8.F.4, 8.F.5

Unit 4

Linear Functions

25 days

Students will understand that functions describe situations where one quantity determines another and these functions can be used to model real-world situations.

A.SSE.1, A.CED.2,

A.REI.10, A.REI.11,

F.IF.2, F.IF.3, F.IF.4, F.IF.5, F.IF.6, F.IF.7, F.IF.9, F.BF.1, F.BF.2

F.LE.1, F.LE.5, S.ID.6a, S.ID.6b, S.ID.7, S.ID.8, S.ID.9

Unit 5

Geometry and Systems of Equations and Inequalities

12 days

Students will understand that systems of equations and inequalities can be used to model, analyze and solve real world situations. Students will understand that geometric relationships can be verified using algebraic properties and representations and the coordinate plane.

G-GPE.4, G-GPE.5,

G-GPE.6, A.REI.5, A.REI.6, A.CED.2, A.CED.3, A.REI.10, A.REI.12

Unit - 6 Exponents

10 days

Students will discover and learn rules about the behavior of exponents, both in expressions and equations. With equations, students will realize the inverse properties of exponents and roots, and they will be able to recognize perfect squares and their roots and estimate the values of non-perfect squares. Students will use these concepts as they prove and develop the Pythagorean Theorem and apply it to solve problems. Students will also explore scientific notation as a property of exponents.

8.EE.1, 8.EE.2, 8.EE.3, 8.EE.4, 8.G.6, 8.G.7, 8.G.8

Unit 7 Exponential Functions

14 days

Students will distinguish between exponential growth and decay graphically including rates of change. They will also write, graph, and interpret exponential and linear functions including function notation and sequences. Students will understand how to compare exponential and linear functions and determine exponential and linear regression.

N-RN.2, A-SSE.1a,

A-SSE.1b, A-CED.2, F- LE.1, F- LE.3,

F-BF.1a, F-BF.1b,

F-BF.2, F.IF.2, F.IF.3, F-LE.5, F.IF.4, F.IF.5, F.IF.6, A-REI.11, F.IF.7, F.IF.8, F.IF.8b, F.IF.9, S.ID.6, S.ID.6c

Unit 8

Quadratic Functions

15 days

Students will be able to interpret quadratic expressions and determine the key features of a quadratic function. Students will use graphs and tables to compare linear, exponential and quadratic functions.

A-SSE.1, A-SSE.1a,

A-SSE.1b, A-SSE.3,

A-APR.1, A-APR.3,

A-CED.2, A-REI.1,

A-REI.4, A-REI.11,

F-IF.2, F-IF.4, F.IF.5, F.IF.6, F.IF.7, F.IF.8, F.IF.8a, F.IF.9,

F.BF.1b, F-LE.3

Unit 9

Descriptive Statistics

11 days

Students will explore two-way frequency tables to analyze data and calculate probability. The students will understand that there are various representations to organize, model and analyze data to best fit real world situations based upon its characteristics.

8.SP.4, S.ID.1, S.ID.2, S.ID.3

S.ID.6, S.ID.7, S.ID.8, S.ID.9