MAT-03 Standards

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Operations – Basic Facts

• MAT-00.AR.OA.01 Automatically add and subtract within 5.
• MAT-01.AR.OA.01 Automatically add and subtract within 10.
• MAT-02.AR.OA.01 Automatically add and subtract within 20.
• MAT-03.AR.OA.01 Using mental strategies, multiply and divide basic facts within 100. Automatically multiply and divide up to 5 x 5 and 10s facts.
• MAT-04.AR.OA.01 Automatically multiply and divide through 10 x 10.
• MAT-05.AR.OA.01 Automatically multiply and divide through 12 x 12.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Solve Problems Using Operations

• MAT-00.AR.OA.04 Solve authentic word problems with addition by putting together or adding to within 10.
• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.
• MAT-02.AR.OA.03 Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.
• MAT-00.AR.OA.05 Solve authentic word problems with subtraction by taking apart or taking from within 10.
• MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.
• MAT-02.AR.OA.04 Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.
• MAT-02.AR.OA.05 Use repeated addition to find the total number of objects arranged in a rectangular array.
• MAT-03.AR.OA.03 Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Solve Problems Using Operations

• MAT-00.AR.OA.04 Solve authentic word problems with addition by putting together or adding to within 10.
• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.
• MAT-02.AR.OA.03 Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.
• MAT-00.AR.OA.05 Solve authentic word problems with subtraction by taking apart or taking from within 10.
• MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.
• MAT-02.AR.OA.04 Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.
• MAT-02.AR.OA.05 Use repeated addition to find the total number of objects arranged in a rectangular array.
• MAT-03.AR.OA.03 Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Solve Problems Using Operations

• MAT-00.AR.OA.04 Solve authentic word problems with addition by putting together or adding to within 10.
• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.
• MAT-02.AR.OA.03 Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.
• MAT-00.AR.OA.05 Solve authentic word problems with subtraction by taking apart or taking from within 10.
• MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.
• MAT-02.AR.OA.04 Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.
• MAT-02.AR.OA.05 Use repeated addition to find the total number of objects arranged in a rectangular array.
• MAT-03.AR.OA.03 Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (D) Data Learners will represent and interpret data.

Proficiency Scale

Progressions

Data Analysis

• MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
• MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
• MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
• MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
• MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
• MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
• MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
• MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
• MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
• MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
• MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
• MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
• MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
• MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
• MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
• MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
• MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• MAT-10.DPS.04 Distinguish between correlation and causation.
• MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
• MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
• MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
• MAT-12.DPS.03 Evaluate reports based on data.
• MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
• MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
• MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
• MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
• MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

3rd Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (G) Geometry Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.

Proficiency Scale

Progressions

Two-Dimensional Shapes

• MAT-00.GM.G.01 Name shapes and identify them as two-dimensional (squares, circles, triangles, rectangles)regardless of their orientations or overall size.
• MAT-00.GM.G.03 Compare and classify two-dimensional shapes to describe their similarities, differences, and attributes (squares, circles, triangles, rectangles).
• MAT-01.GM.G.01 Name shapes and identify them as two-dimensional (trapezoids, rhombuses, pentagons, hexagons, octagons).
• MAT-01.GM.G.03 Determine geometric attributes of two-dimensional and three-dimensional shapes.
• MAT-02.GM.G.01 Identify two-dimensional shapes (parallelograms and quadrilaterals).
• MAT-02.GM.G.03 Compose geometric shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.
• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-03.GM.G.02 Sort quadrilaterals into categories based on attributes.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.G.02 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size.
• MAT-05.GM.G.01 Classify two-dimensional figures in a hierarchy based on properties.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.11 Prove and apply theorems about parallelograms.
• MAT-10.GM.34 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.

Coordinate Plane

• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-05.GM.G.02 Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.
• MAT-5.GM.G.03 Form ordered pairs and graph points in the first quadrant of the coordinate plane to solve authentic word problems.
• MAT-6.GM.GF.01 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.
• MAT-6.GM.GF.02 Draw polygons in the coordinate plane given coordinates for vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.
• MAT-10.GM.27 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.
• MAT-10.GM.28 Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.
• MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segments in a given ratio.
• MAT-12.NO.10 Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.14 Recognize vector quantities as having both magnitude and direction, writing them in polar form.
• MAT-12.NO.15 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
• MAT-12.NO.16 Solve problems involving magnitude and direction that can be represented by vectors.
• MAT-12.NO.17 Add and subtract vectors.
• MAT-12.NO.18 Multiply a vector by a scalar.
• MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
• MAT-12.AR.F.19 Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.

Angles/Triangles

• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.M.07 Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.
• MAT-07.GM.GF.01 Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.
• MAT-07.GM.GF.02 Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.04 Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.05 Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.
• MAT-08.GM.GF.06 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.18 Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
• MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.
• MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).
• MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
• MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
• MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-12.AR.F.16 Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.
• MAT-12.AR.F.17 Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.
• MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context

3rd Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Measure Length

• MAT-01.GM.M.01 Measure the length of an object as a whole number of same-size, non-standard units from end to end.
• MAT-02.GM.M.01 Measure the length of an object using two different standard units of measurement. Describe how the two measurements relate to the size of the units chosen.
• MAT-03.GM.M.01 Measure lengths using rulers marked with halves and fourths of an inch.
• MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.

3rd Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Time

• MAT-00.GM.M.02 Tell time as it relates to daily life (today, yesterday, tomorrow, morning, afternoon, night).
• MAT-01.GM.M.03 Tell and write time to the hour and half-hour (including o'clock and half past) using analog and digital clocks.
• MAT-02.GM.M.03 Tell and write time to the nearest five minutes (including quarter after and quarter to) with a.m. and p.m. using analog and digital clocks.
• MAT-03.GM.M.03 Tell and write time to the nearest minute and measure time intervals in minutes.
• MAT-03.GM.M.04 Solve elapsed time authentic word problems on the hour and the half-hour, using a variety of strategies.

3rd Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Perimeter

• MAT-03.GM.M.06 Solve problems involving the perimeters of rectangles given the side lengths or when given the perimeter and unknown side length(s).
• MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.
• MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.
• MAT-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply given formulas to calculate the area and circumference of a circle, including in authentic problems.
• MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.

3rd Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Area/Surface Area

• MAT-03.GM.M.07 Recognize area as an attribute of plane figures and understand concepts of area measurement.
• MAT-03.GM.M.08 Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as found by multiplying the side lengths.
• MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.
• MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.
• MAT-06.GM.AV.01 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals in authentic and mathematical problems by composing and/or decomposing them into rectangles and triangles.
• MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets. Apply these techniques in the context of solving authentic and mathematical problems.
• MAT-07.GM.AV.02 Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including in authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including authentic problems.
• MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.
• MAT-12.GM.04 Derive the formula A=1 ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

3rd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Proficiency Scale

Progressions

Compare Numbers and/or Expressions

• MAT-00.NO.NBT.02 Compare two numbers between 1 and 20 using words greater than, less than, or equal to.
• MAT-01.NO.NBT.02 Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the number of tens and ones.
• MAT-02.NO.NBT.02 Compare two three-digit numbers using symbols >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.
• MAT-03.NO.NBT.01 Compare two four-digit numbers using symbols, >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.
• MAT-04.NO.NBT.02 Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.
• MAT-05.NO.NBT.02 Compare two decimals to thousandths using symbols >, <, and =. Justify comparisons based on the value of the digits.
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.01 Describe the absolute value of a number as its distance from zero on a number line.
• MAT-08.NO.NS.01 Compare and classify real numbers within the real number system.
• MAT-08.NO.NS.02 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line diagram, and estimate the value of irrational expressions involving one operation.
• MAT-08.NO.NS.03 Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.
• MAT-09.AR.06 Solve linear equations and inequalities (to include compound inequalities) in one variable.
• MAT-09.AR.08 Graph the solution set to a two-variable system of linear equations. Create and graph the solution set to a two-variable system of linear inequalities in context.
• MAT-09.AR.09 Solve absolute value equations and inequalities in one or two variables.
• MAT-12.AR.09 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.

3rd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Proficiency Scale

Progressions

Rounding Numbers

• MAT-03.NO.NBT.02 Apply place value understanding to round whole numbers to the nearest 10 or 100.
• MAT-04.NO.NBT.03 Apply place value and/or understanding of numbers to round multi-digit whole numbers to any place.
• MAT-05.NO.NBT.03 Apply place value understanding to round decimals to any place.
• MAT-08.NO.NS.03 Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.

3rd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Proficiency Scale

Progressions

Addition and Subtraction

• MAT-01.NO.NBT.03 Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-01.NO.NBT.05 Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.
• MAT-02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.
• MAT-03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.
• MAT-04.NO.NBT.04 Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.
• MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
• MAT-07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.AR.11 Add, subtract, and multiply polynomials.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.17 Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.
• MAT-12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

3rd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Proficiency Scale

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

3rd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Proficiency Scale

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.