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Integrated Math Year 1

Connecticut Integrated Math Year 1 Curriculum

Video lessons and practice for every Integrated Math Year 1 topic. Aligned to Connecticut Core Standards Math so you stay on track in class.

Connecticut Integrated Math Year 1 Curriculum | StudyPugHelp

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ID

Standard

StudyPug Topic

CC.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context.

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.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.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.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.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.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.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.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Integrated Math Year 1 in Connecticut

Integrated Math Year 1 is the foundation of high school mathematics for Connecticut students. The course weaves together algebra, functions, geometry, and statistics into a unified curriculum aligned to Connecticut Core Standards Math. StudyPug covers every topic in this course with clear video lessons and targeted practice problems.

Algebra and Equations

Students begin by working with algebraic expressions — interpreting them in context, rewriting them using structure, and choosing equivalent forms to reveal properties of quantities. From there, the course moves into creating and solving equations and inequalities in one variable, including those arising from linear, quadratic, rational, and exponential functions. Key topics include:

  • Interpreting and rewriting algebraic expressions
  • Creating equations and inequalities in one and two variables
  • Solving linear equations and inequalities, including those with letter coefficients
  • Rearranging formulas to highlight a quantity of interest
  • Systems of linear equations — solving exactly and approximately
  • Graphing linear inequalities and systems of inequalities in two variables

Functions

A major focus of Integrated Math Year 1 is building a solid understanding of functions. Students learn what a function is, how to use function notation, and how to interpret graphs and tables. Topics include:

  • Definition of a function — domain, range, and function notation
  • Interpreting key features of graphs and tables
  • Average rate of change over an interval
  • Graphing functions and identifying key features by hand and with technology
  • Comparing properties of functions represented in different forms
  • Writing functions to describe relationships between two quantities
  • Arithmetic and geometric sequences — recursive and explicit formulas
  • Transformations of functions: f(x) + k, k·f(x), f(kx), and f(x + k)

Linear and Exponential Models

Students distinguish between situations modeled by linear functions and those modeled by exponential functions. They construct both types from graphs, tables, and verbal descriptions, and interpret parameters in context. This section also explores how exponential growth eventually surpasses polynomial growth — a key insight for data literacy.

Polynomials

Integrated Math Year 1 introduces polynomials as a system closed under addition, subtraction, and multiplication — analogous to the integers. Students add, subtract, and multiply polynomials, identify zeros using factorizations, and use zeros to sketch rough graphs of polynomial functions.

Geometry: Transformations and Congruence

The geometry strand begins with precise definitions of foundational terms — angles, circles, parallel lines, perpendicular lines, and line segments. Students then explore transformations in the plane:

  • Representing transformations as functions on points in the plane
  • Rotations, reflections, and translations — definitions and constructions
  • Drawing transformed figures using graph paper or geometry software
  • Sequences of transformations that carry one figure onto another
  • Congruence defined in terms of rigid motions
  • Triangle congruence criteria: ASA, SAS, and SSS
  • Proving theorems about lines, angles, triangles, and parallelograms
  • Geometric constructions including equilateral triangles, squares, and regular hexagons inscribed in a circle

Coordinate Geometry

Students apply algebra to geometry by using coordinates to prove geometric theorems. Topics include slope criteria for parallel and perpendicular lines, partitioning directed line segments, and computing perimeters and areas using the distance formula.

Statistics and Data Analysis

The statistics strand prepares students to represent, interpret, and analyze data. Topics include:

  • Dot plots, histograms, and box plots on the real number line
  • Comparing center (mean, median) and spread (IQR, standard deviation) across data sets
  • Interpreting shape, outliers, and differences in data distributions
  • Two-way frequency tables and relative frequencies for categorical data
  • Scatter plots and describing relationships between two quantitative variables
  • Interpreting slope and intercept of a linear model in context
  • Computing and interpreting the correlation coefficient
  • Distinguishing between correlation and causation

Quantities and Modeling

Throughout the course, students develop skills in quantitative reasoning — choosing appropriate units, defining quantities for descriptive modeling, and reporting answers with accuracy appropriate to the context. These skills connect mathematics to real-world problem solving across every strand of the curriculum.

How StudyPug Supports Connecticut Integrated Math Year 1 Students

StudyPug provides video lessons and practice problems for every topic in Connecticut's Integrated Math Year 1 course, all aligned to Connecticut Core Standards Math. Whether a student needs help with homework tonight or wants to get ahead before a unit test, StudyPug makes it easy to find the right lesson fast. Lessons are 5–15 minutes, broken into short segments students can pause and replay. Practice problems with step-by-step solutions help reinforce each concept. StudyPug works on computers, tablets, and phones — so students can study wherever they are.