# 7-8th Grade Math Learning Targets

Math, 7-8

ALT 1 - Communication

Communicates clearly and explains reasoning so others can follow how a problem is solved.

**AST.1.1 - Language** : Uses appropriate mathematical language.

**AST.1.2 - Representations** : Uses appropriate forms of mathematical representations to present information correctly.

**AST.1.3 - Transitions** : Moves between different forms of mathematical representations.

**AST.1.4 - Lines of Reason** : Communicates through lines of reasoning that are complete and coherent.

ALT 2 - Modeling

Reasons mathematically to solve problems in real-life contact.

**AST 2.1 - Relevant Elements** : Identifies the relevant elements of the authentic real-life situation.

**AST 2.2 - Strategies** : Selects adequate mathematical strategies to model the authentic real-life situation.

**AST 2.3 - Reaches a Solution** : Applies the selected mathematical strategies to reach a valid solution to the authentic real-life situation.

**AST.2.4 - Degree of Accuracy** : Explains the degree of accuracy of the solution.

**AST 2.5 - Making Sense** : Explains whether the solution makes sense in the context of the authentic real-life situation.

ALT 3 - Patterns

Recognizes patterns and describes them as relationships or general rules.

**AST.3.1 - Pattern ID** : Selects and applies mathematical problem-solving techniques to correctly identify the pattern.

**AST.3.2 - Description** : Pattern is described as relationship or general rule.

**AST 3.3 - Verification** : Verifies the validity of these general rules.

**AST.3.4 - Conclusions** : Conclusions are consistent with the correct findings.

ALT 4 - Expressions and Equations

Uses properties of operations, proportional relationships, and fractions to generate expressions and solve equations.

**AST 4.1 - Addition and Subtraction** : Applies and extends previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

**AST 4.2 - Multiplication and Division** : Applies and extends previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

**AST 4.3 - Applications** : Solves real-world and mathematical problems involving the four operations with rational numbers.

**AST 4.4 - Unit Rates** : Computes unit rate associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

**AST 4.5 - Notice Proportionality** : Recognizes and represents proportional relationships between quantities.

**AST 4.6 - Applications** : Uses proportional relationships to solve multi-step ratio and percent problems.

**AST 4.7 - Algebraic Operations** : Applies properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

**AST 4.8 - Applications of Equivalent Forms** : Understands that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

**AST 4.9 - Modeling with Rational Numbers** : Solves multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Applies properties of operations; converts between forms as appropriate; and assesses the reasonableness of answers.

**AST 4.10 - Algebraic Modeling** : Uses variables to represent quantities in a real-world or mathematical problems, and constructs simple equations and inequalities to solve problems by reasoning about the quantities.

ALT 5 - Geometric Figures and Measurement

Draws, constructs, and describes geometric figures and relationships between them, and solves problems involving angle measure, area, surface area, and volume.

**AST 5.1 - Scale Drawings** : Solves problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

**AST 5.2 - Construction, Constraints and Congruence** : Draws, with a variety of tools, geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

**AST 5.3 - Slicing Solids** : Describes the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms, and right rectangular pyramids.

**AST 7.4 - Circle Area and Circumference** : Knows the formulas for the area and circumference of a circle and uses them to solve problems; gives an informal derivation of the relationship between the circumference and the area of a circle.

**AST 5.5 - Finding Angles** : Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

**AST 5.6 - Volume and Surface Area** : Solves real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

ALT 6 - Exponents

Works with expressions and equations using integer exponents.

**AST 6.1 - Exponent Properties** : Knows and applies the properties of integer exponents to generate equivalent numerical expressions.

**AST 6.2 - Scientific Notation** : Uses numbers expressed in the form of a single digit times an integer power of 10 to estimate very large and very small quantities, and to express how many times as much one is than the other.

**AST 6.3 - Operations with Scientific Notation** : Performs operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

**AST 6.4 - Applications** : Uses scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

**AST 6.5 - Uses Technology** : Interprets scientific notation that has been generated by technology.

ALT 7 - Systems

Analyzes and solves linear equations and systems of linear equations.

**AST 7.1 - One Variable Equations** : Solves linear equations in one variable.

**AST 7.2 - Systems** : Analyzes and solves pairs of simultaneous linear equations.

ALT 8 - Linear Functions and Bivariate Data

Defines, evaluates, compares, and uses linear functions to model relationships between quantities and bivariate data.

**AST 8.1 - Direct Variation** : Graphs proportional relationships, interpreting the unit rate as the slope of the graph. Compares two different proportional relationships represented in different ways.

**AST 8.2 - Writing Linear Equations** : Uses similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis b.

**AST 8.3 - Functions** : Understands that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output (function notation not required).

**AST.8.4 - Compare Properties of Linear Functions** : Compares properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

**AST 8.5 - Slope-Intercept Form (y = mx + b)** : Interprets the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

**AST 8.6 - Derive an Equation of a Line on a Graph** : Constructs a function to model a linear relationship between two quantities. Determines the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interprets the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

**AST 8.7 - Describing Functions** : Describes qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features that has been described verbally.

**AST 8.8 - Scatter Plots** : Constructs and interprets scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describes patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

**AST 8.9 - Lines of Fit** : Knows that straight lines are widely used to model relationships between two quantitative variables.

**AST 8.10 - Using Model Equations** : Uses the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

**AST 8.11 - Categorical Data** : Understands that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

**AST 8.12 - Two-Way Tables** : Constructs and interprets a two-way table summarizing data on two categorical variables collected from the same subjects.

**AST 8.13 - Relative Frequencies** : Uses relative frequencies calculated for rows and columns to describe possible association between the two variables.

ALT 9 - Geometry

Understands congruence and similarity using transformational geometry, triangle-angle relationships, and parallel lines cut by transversals.

**AST 9.1 - Rigid Transformations** : Verifies experimentally the properties of rotations, reflections and translations.

**AST 9.2 - Congruence** : Understands that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; find two congruent figures, describes a sequence that exhibits the congruence between them.

**AST 9.3 - Coordinate Transformations** : Describes the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

**AST 9.4 - Angle Relationships** : Uses informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

ALT 10 - Pythagorean Theorem

Understands and applies the Pythagorean Theorem using rational and irrational numbers.

**AST 10.1 - Identify Irrational Numbers** : Knows that numbers that are not rational are called irrational. Understands informally that every number has a decimal expansion.

**AST 10.2 - Estimate, Compare, Order Irrationals** : Uses rational approximations of irrational numbers to compare the size of irrational numbers, locates them approximately on a number line diagram, and estimates the value of expressions.

**AST 10.3 - Square and Cube Roots** : Uses square and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p where p is a positive rational number. Evaluates square roots of small perfect squares and cube roots of small perfect cubes. Knows that √2 is irrational.

**AST 10.4 - Prove the Pythagorean Theorem** : Explains the proof of the Pythagorean Theorem and its converse.

**AST 10.5 - Find Length in 2D and 3D** : Applies the Pythagorean Theorem to determine unknown side lengths in right triangles in the real world and mathematical problems in two and three dimensions.

**AST 10.6 - Distance and Coordinates** : Applies the Pythagorean Theorem to find the distance between two points in a coordinate system.