KentuckyIntegrated Mathematics I
Kentucky Integrated Mathematics I Curriculum
Video lessons and practice for every Integrated Mathematics I topic. Aligned to Kentucky Academic Standards so students can keep up with class or get ahead.
Kentucky Integrated Mathematics I Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
CC.HSA.SSE.A.1 | Interpret expressions that represent a quantity in terms of its context. |
CC.HSA.SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. |
CC.HSA.SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. |
CC.HSA.CED.A.1 | Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. |
CC.HSA.CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. |
CC.HSA.CED.A.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. |
CC.HSA.CED.A.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. |
CC.HSA.REI.A.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. |
CC.HSA.REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
CC.HSA.REI.C.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. |
CC.HSA.REI.C.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. |
CC.HSA.REI.D.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
CC.HSA.REI.D.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. |
CC.HSA.APR.A.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. |
CC.HSA.APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. |
CC.HSF.IF.A.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). |
CC.HSF.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
CC.HSF.IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. |
CC.HSF.IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
CC.HSF.IF.B.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. |
CC.HSF.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. |
CC.HSF.IF.C.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. |
CC.HSF.IF.C.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). |
CC.HSF.BF.A.1 | Write a function that describes a relationship between two quantities. |
CC.HSF.BF.A.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. |
CC.HSF.BF.B.3 | Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. |
CC.HSF.LE.A.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. |
CC.HSF.LE.A.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). |
CC.HSF.LE.A.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. |
CC.HSF.LE.B.5 | Interpret the parameters in a linear or exponential function in terms of a context. |
CC.HSG.CO.A.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. |
CC.HSG.CO.A.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. |
CC.HSG.CO.A.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. |
CC.HSG.CO.B.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. |
CC.HSG.CO.B.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. |
CC.HSG.CO.B.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. |
CC.HSG.CO.C.9 | Prove theorems about lines and angles. |
CC.HSG.CO.C.10 | Prove theorems about triangles. |
CC.HSG.CO.C.11 | Prove theorems about parallelograms. |
CC.HSG.CO.D.12 | Make formal geometric constructions with a variety of tools and methods. |
CC.HSG.CO.D.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. |
CC.HSG.GPE.B.4 | Use coordinates to prove simple geometric theorems algebraically. |
CC.HSG.GPE.B.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. |
CC.HSG.GPE.B.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. |
CC.HSG.GPE.B.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. |
CC.HSS.ID.A.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). |
CC.HSS.ID.A.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. |
CC.HSS.ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
CC.HSS.ID.B.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. |
CC.HSS.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. |
CC.HSS.ID.C.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. |
CC.HSN.Q.A.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. |
CC.HSN.Q.A.2 | Define appropriate quantities for the purpose of descriptive modeling. |
CC.HSN.Q.A.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. |
Integrated Mathematics I in Kentucky
Integrated Mathematics I is a foundational high school math course for Kentucky students. It brings together algebra, functions, geometry, and statistics into one connected course aligned to Kentucky Academic Standards Math. Students who build strong skills here are better prepared for Integrated Mathematics II and beyond.
Algebra and Expressions
Students learn to interpret and rewrite expressions, create equations and inequalities, and rearrange formulas. Topics include solving linear equations and inequalities in one variable, working with systems of equations, and understanding how polynomials behave under addition, subtraction, and multiplication.
- Interpret and rewrite algebraic expressions
- Create and solve equations and inequalities
- Solve systems of linear equations graphically and algebraically
- Add, subtract, and multiply polynomials
Functions
A major focus of Integrated Mathematics I is understanding functions. Students learn function notation, evaluate functions, interpret key features of graphs, and compare linear and exponential functions. Arithmetic and geometric sequences are also introduced as models for real-world situations.
- Understand domain, range, and function notation
- Interpret graphs and tables of functions
- Write and transform linear and exponential functions
- Model situations with arithmetic and geometric sequences
Geometry and Transformations
The geometry strand covers rigid motions, congruence, and coordinate geometry. Students explore rotations, reflections, and translations, then use these ideas to prove triangle congruence and theorems about lines, angles, triangles, and parallelograms.
- Describe and perform rotations, reflections, and translations
- Use rigid motions to define congruence
- Prove theorems about lines, angles, triangles, and parallelograms
- Use coordinates to prove geometric theorems and compute perimeters and areas
Statistics and Data Analysis
Students represent and interpret data using dot plots, histograms, box plots, and scatter plots. They compare data sets using measures of center and spread, interpret linear models, and learn to distinguish between correlation and causation.
- Represent data with dot plots, histograms, and box plots
- Compare center and spread of data sets
- Interpret slope and intercept of a linear model
- Understand correlation vs. causation
How StudyPug Helps Kentucky Students
StudyPug has video lessons and practice problems for every Integrated Mathematics I topic. Whether a student needs help with algebra, functions, or geometry, they can find the exact topic, watch a clear explanation, and practice until they feel confident. All content aligns to Kentucky Academic Standards Math.