A: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems.

A.1: Students express or interpret numbers using scientific notation from real-life contexts.

A.1.b: Convert between standard and scientific notation forms and compare the relative size of numbers including the interpretation of numbers as displayed on calculators and computers.

Circumference and Area of Circles
Simplifying Radical Expressions

A.1.c: Use square roots. Be able to estimate the value of the square roots of whole numbers and place them on the number line.

Square Roots

B: Students make measurements and collect, display, evaluate, analyze, and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students: understand that most measurements are approximations and that taking repeated measurements reveals this variability; understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement; understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.

B.3: Students use the mean, median, mode, range, and quartiles to solve problems involving raw data and information from data displays.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)

B.4: Students understand and apply concepts of probability.

B.4.c: Compute probabilities for compound events, using such methods as organized lists, tree diagrams, and area models.

Independent and Dependent Events

C: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct two-dimensional and three-dimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures students use estimation to check the reasonableness of results.

C.1: Students know and use properties of polygons.

C.1.a: Apply the triangle inequality.

Triangle Inequalities

C.1.b: Find the sum of the measures of the interior angles of a polygon.

Polygon Angle Sum
Triangle Angle Sum

C.1.c: Apply the property that the sum of the measures of the exterior angles of a polygon is 360 degrees.

Polygon Angle Sum
Triangle Angle Sum

C.2: Students know and use angle properties of parallel lines to solve problems and determine geometric relationships.

C.2.a: Know and use properties of angles created when parallel lines are cut by a transversal.

Triangle Angle Sum

C.2.c: Know and use properties of angles created by parallel lines and transversals to determine the angle properties of trapezoids and parallelograms, and apply these properties in problem situations.

Parallelogram Conditions
Special Parallelograms

C.3: Students know and use the Pythagorean Theorem.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

C.4: Students find the volume and surface area of prisms, pyramids, cylinders, and other figures composed of these solids.

C.4.a: Apply the understanding that the volume of prisms and cylinders can be found by multiplying the area of a base by the height of the solid.

Prisms and Cylinders
Pyramids and Cones

C.4.b: Apply the understanding that the volume of pyramids can be found by multiplying the area of a base by 1/3 the height of the solid.

Pyramids and Cones

C.4.c: Apply the understanding that the surface area of a figure is the sum of the areas of its faces and find the surface areas of cylinders.

Surface and Lateral Areas of Prisms and Cylinders

D: Students use symbols to represent or model quantities, patterns, and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs, and verbal rules choosing the most effective representation and converting among representations.

D.1: Students create, evaluate, and manipulate expressions.

D.1.a: Create and evaluate expressions using real numbers.

Order of Operations

D.1.c: Apply the properties of the real number system, including distributive and associative laws, to create equivalent expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

D.2: Students understand and solve problems involving linear equations.

D.2.a: Solve any linear equation including linear equations of the form ax + b = cx + d.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

D.2.b: Recognize that, in general, linear equations have just one solution-but know also that some linear equations can have no solution and those linear equations that are identities have every value of x as a solution.

Linear Inequalities in Two Variables

D.3: Students understand and solve linear inequalities in one unknown.

D.3.a: Represent problem situations as inequalities.

Comparing and Ordering Decimals
Linear Inequalities in Two Variables

D.3.b: Solve linear inequalities.

Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

D.4: Students understand and use the basic properties of linear relationships, y = kx + b.

D.4.a: Understand that linear relationships are characterized by a constant rate of change, k.

Compound Interest
Direct and Inverse Variation
Slope-Intercept Form of a Line

D.4.b: Understand that the graph of a linear relationship y = kx + b is a line where the slope is k and b is the y-coordinate of the point where the graph crosses the y-axis (i.e., value of y when x = 0).

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line