ExploreLearning.com

Maryland: Voluntary State Curriculum - Grade 8

This content correlation lists the recommended Gizmos for the above state curriculum standard.

Click any of the Gizmo names below to see the corresponding Gizmo Details page. If you are currently logged in to ExploreLearning.com as a teacher, you will be able to add the Gizmos to your classes from their Gizmo Details pages.

Content correlation last revised: 3/3/2004

1.0. Knowledge of Algebra, Patterns, or Functions: Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

A. Patterns and Functions

1. Identify, describe, extend, and create patterns, functions and sequences

a. Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph. Assessment Limit: Provide the nth term no more than 10 terms beyond the last given term using common differences no more than 10 with integers (-100 - 5000)

Arithmetic Sequences

b. Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph. Assessment Limit: Provide the nth term no more than 5 terms beyond the last given term using the recursive relationship of geometric sequences with a common ratio of whole numbers no more than 5 (0 - 10,000)

Geometric Sequences

c. Determine whether functions are linear or nonlinear when represented in words, in a table, symbolically, or in a graph. Assessment Limit: Use a graph to determine if a function is linear or nonlinear

Linear Functions

d. Determine whether functions are linear or nonlinear when represented symbolically

Linear Functions

B. Expressions, Equations, and Inequalities

1. Write, simplify, and evaluate expressions

a. Write an algebraic expression to represent unknown quantities. Assessment Limit: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)

Using Algebraic Expressions

b. Evaluate an algebraic expression. Assessment Limit: Use one or two unknowns and up to three operations and rational numbers (-100 to 100)

Solving Equations with Decimals

c. Evaluate numeric expressions using the order of operations. Assessment Limit: Use no more than 5 operations including exponents of no more than 3 and 2 sets of parentheses, brackets, a division bar, or absolute value with rational numbers (-100 to 100)

Order of Operations

2. Identify, write, solve, and apply equations and inequalities

b. Solve for the unknown in a linear equation. Assessment Limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and integers (-2000 to 2000)

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

c. Solve for the unknown in an inequality. Assessment Limit: Use a one- or two-operation inequality with one variable on one side no more than 3 times whose result after combining coefficients is a positive whole number coefficient with integers (-100 to 100)

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

d. Identify or graph solutions of inequalities on a number line. Assessment Limit: Use one variable once with a positive whole number coefficient and integers (-100 to 100)

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

f. Apply given formulas to a problem-solving situation. Assessment Limit: Use no more than four variables and up to three operations with rational numbers (-500 to 500)

Solving Formulas for any Variable

C. Numeric and Graphic Representations of Relationships

1. Locate points on a number line and in a coordinate graph

a. Graph linear equations in a coordinate plane. Assessment Limit: Use two unknowns having integer coefficients (-9 to 9) and integer constants (-20 to 20)

Points in the Coordinate Plane - Activity A

Slope-Intercept Form of a Line - Activity A

2. Analyze linear relationships

a. Determine the slope of a graph in a linear relationship. Assessment Limit: Use an equation with integer coefficients (-9 to 9) and integer constants (-20 to 20)

Slope - Activity A

b. Determine the slope of a linear relationship represented numerically or algebraically

Slope-Intercept Form of a Line - Activity A

2.0. Knowledge of Geometry: Students will apply the properties of one-, two, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects.

A. Plane Geometric Figures

1. Analyze the properties of plane geometric figures

a. Identify and describe relationships between angles formed when parallel lines are cut by a transversal.. Assessment Limit: Use alternate interior, alternate exterior, or corresponding angles

Parallelogram Conditions

b. Identify and describe the relationship among the parts of a right triangle. Assessment Limit: Use the hypotenuse or the legs of right triangles

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

2. Analyze geometric relationships

a. Determine the measures of angles formed by parallel lines cut by a transversal. Assessment Limit: Use alternate interior, alternate exterior, and corresponding angles

Parallelogram Conditions

b. Apply right angle concepts to solve real-world problems. Assessment Limit: Use the Pythagorean Theorem

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Sine and Cosine Ratios - Activity A

Distance Formula - Activity A

c. Determine whether three given side lengths form a right triangle

Classifying Triangles

B. Representation of Geometric Figures

1. Represent plane geometric figures

a. Draw quadrilaterals. Assessment Limit: Provide their whole number dimensions in inches or centimeters or angle measurements

Polygon Angle Sum - Activity A

b. Construct perpendicular line segments. Assessment Limit: Provide a given point on a given line segment

Construct Parallel and Perpendicular Lines

c. Construct triangles. Assessment Limit: Construct a congruent triangle to a given triangle

Proving Triangles Congruent

Constructing Congruent Segments and Angles

C. Congruence

1. Apply the properties of similar polygons

a. Determine similar parts of polygons. Assessment Limit: Use the length of corresponding sides or the measure of corresponding angles and rational numbers with no more than 2 decimal places (0 - 1000)

Similar Figures - Activity B

D. Transformations

1. Analyze a transformation on a coordinate plane

a. Identify, describe, and plot the results of multiple transformations on a coordinate plane. Assessment Limit: Identify and plot the result of two transformations using translations (horizontal or vertical), reflections (horizontal or vertical), or rotations (90° or 180°) about a given point

Rotations, Reflections and Translations

3.0. Knowledge of Measurement: Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements.

A. Applications in Measurement

1. Estimate and apply measurement formulas

a. Estimate and determine the circumference or area of a circle. Assessment Limit: Include circles with rational numbers with no more than 2 decimal places (0 - 10,000)

Circle: Perimeter, Circumference and Area

c. Estimate and determine the volume of a cylinder. Assessment Limit: Include cylinders with whole number dimensions (0 - 10,000)

Prisms and Cylinders - Activity A

d. Determine the volume of cones, pyramids, and spheres

Pyramids and Cones - Activity A

e. Determine the surface area of cylinders, prisms, and pyramids

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

2. Analyze measurement relationships

a. Use proportional reasoning to solve measurement problems. Assessment Limit: Use proportions, scale drawings, or rates and whole numbers or decimals (0 - 1000)

Beam to Moon (Ratios and Proportions)

Perimeters and Areas of Similar Figures

4.0. Knowledge of Statistics: Students will collect, organize, display, analyze, or interpret data to make decisions or predictions.

A. Data Displays

1. Organize and display data

b. Organize and display data to make box/whisker plots. Assessment Limit: Use no more than 12 pieces of data and whole numbers (0 - 1000)

Constructing Box-and-Whisker Plots

c. Organize and display data to make a scatter plot. Assessment Limit: Use no more than 10 points and whole numbers (0 - 1000)

Scatter Plots - Activity A

B. Data Analysis

1. Analyze data

a. Interpret tables. Assessment Limit: Use no more than 5 categories having no more than 2 quantities per category and whole numbers or decimals with no more than 2 decimal places (0 - 100)

Line Plots

b. Interpret box/whisker plots. Assessment Limit: Use minimum, first (lower) quartile, median (middle/second quartile), third (upper) quartile, or maximum and whole numbers (0 - 100)

Constructing Box-and-Whisker Plots

c. Interpret scatter plots. Assessment Limit: Use no more than 10 points using whole numbers or decimals with no more than 2 decimal places (0 - 100)

Scatter Plots - Activity A

Scatter Plots - Activity B

e. Analyze multiple box/whisker plots using the same scale

Constructing Box-and-Whisker Plots

5.0. Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation.

A. Sample Space

1. Identify a sample space

a. Describe the difference between independent and dependent events

Compound Independent and Dependent Events

b. Determine the number of outcomes. Assessment Limit: Use no more than 5 dependent events with no more than 10 outcomes in the first event

Compound Independent and Dependent Events

B. Theoretical Probability

1. Determine the probability of an event comprised of no more than 2 independent events

a. Express the probability of an event as a fraction, a decimal, or a percent. Assessment Limit: Use a sample space of 36 to 60 outcomes

Compound Independent Events

Part:Part and Part:Whole Ratios

Theoretical and Experimental Probability

2. Determine the probability of a second event that is dependent on a first event of equally likely outcomes

C. Experimental Probability

6.0. Knowledge of Number Relationships or Computation: Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology.

A. Knowledge of Number and Place Value

1. Apply knowledge of rational numbers and place value

a. Read, write, and represent rational numbers. Assessment Limit: Use exponential notation or scientific notation from (-10,000 to 1,000,000,000)

Comparing and Ordering Rational Numbers

b. Compare, order, and describe rational numbers with and without relational symbols (<, >, =). Assessment Limit: Use no more than 4 integers or positive rational numbers using equivalent forms or absolute value (-100 to 100)

Comparing and Ordering Rational Numbers

B. Number Computation

1. Analyze number relations and compute

a. Add, subtract, multiply and divide integers. Assessment Limit: Use one operation (-1000 to 1000)

Adding and Subtracting Integers

b. Calculate powers of integers and square roots of perfect square whole numbers. Assessment Limit: Use powers with bases no more than 12 and exponents no more than 3, or square roots of perfect squares no more than 144

Ordering and Approximating Square Roots

c. Identify and use the laws of exponents to simplify expressions. Assessment Limit: Use the rules of power times power or power divided by power with the same integer as a base (-20 to 20) and positive single digit exponents

Exponents and Power Rules

2. Estimation

a. Estimate the square roots of whole numbers. Assessment Limit: Use whole numbers (0 - 100)

Ordering and Approximating Square Roots

3. Analyze ratios, proportions, or percents

a. Determine and use unit rates. Assessment Limit: Use positive rational numbers (0 - 100)

Multiplying with Decimals

b. Solve problems using percents, rates of increase and decrease, discount, commission, sales, and simple interest in the context of a problem. Assessment Limit: Use positive rational numbers (0 - 10,000)

Percent of Change

c. Solve problems using proportional reasoning. Assessment Limit: Use positive rational numbers (0 - 1000)

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Correlation by State

Maryland: Voluntary State Curriculum - Grade 8

1.0. Knowledge of Algebra, Patterns, or Functions: Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

A. Patterns and Functions

1. Identify, describe, extend, and create patterns, functions and sequences

a. Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph. Assessment Limit: Provide the nth term no more than 10 terms beyond the last given term using common differences no more than 10 with integers (-100 - 5000)

c. Determine whether functions are linear or nonlinear when represented in words, in a table, symbolically, or in a graph. Assessment Limit: Use a graph to determine if a function is linear or nonlinear

d. Determine whether functions are linear or nonlinear when represented symbolically

B. Expressions, Equations, and Inequalities

1. Write, simplify, and evaluate expressions

a. Write an algebraic expression to represent unknown quantities. Assessment Limit: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)

b. Evaluate an algebraic expression. Assessment Limit: Use one or two unknowns and up to three operations and rational numbers (-100 to 100)

c. Evaluate numeric expressions using the order of operations. Assessment Limit: Use no more than 5 operations including exponents of no more than 3 and 2 sets of parentheses, brackets, a division bar, or absolute value with rational numbers (-100 to 100)

2. Identify, write, solve, and apply equations and inequalities

b. Solve for the unknown in a linear equation. Assessment Limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and integers (-2000 to 2000)

c. Solve for the unknown in an inequality. Assessment Limit: Use a one- or two-operation inequality with one variable on one side no more than 3 times whose result after combining coefficients is a positive whole number coefficient with integers (-100 to 100)

d. Identify or graph solutions of inequalities on a number line. Assessment Limit: Use one variable once with a positive whole number coefficient and integers (-100 to 100)

f. Apply given formulas to a problem-solving situation. Assessment Limit: Use no more than four variables and up to three operations with rational numbers (-500 to 500)

C. Numeric and Graphic Representations of Relationships

1. Locate points on a number line and in a coordinate graph

a. Graph linear equations in a coordinate plane. Assessment Limit: Use two unknowns having integer coefficients (-9 to 9) and integer constants (-20 to 20)

2. Analyze linear relationships

a. Determine the slope of a graph in a linear relationship. Assessment Limit: Use an equation with integer coefficients (-9 to 9) and integer constants (-20 to 20)

b. Determine the slope of a linear relationship represented numerically or algebraically

2.0. Knowledge of Geometry: Students will apply the properties of one-, two, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects.

A. Plane Geometric Figures

1. Analyze the properties of plane geometric figures

a. Identify and describe relationships between angles formed when parallel lines are cut by a transversal.. Assessment Limit: Use alternate interior, alternate exterior, or corresponding angles

b. Identify and describe the relationship among the parts of a right triangle. Assessment Limit: Use the hypotenuse or the legs of right triangles

2. Analyze geometric relationships

a. Determine the measures of angles formed by parallel lines cut by a transversal. Assessment Limit: Use alternate interior, alternate exterior, and corresponding angles

b. Apply right angle concepts to solve real-world problems. Assessment Limit: Use the Pythagorean Theorem

c. Determine whether three given side lengths form a right triangle

B. Representation of Geometric Figures

1. Represent plane geometric figures

a. Draw quadrilaterals. Assessment Limit: Provide their whole number dimensions in inches or centimeters or angle measurements

b. Construct perpendicular line segments. Assessment Limit: Provide a given point on a given line segment

c. Construct triangles. Assessment Limit: Construct a congruent triangle to a given triangle

C. Congruence

1. Apply the properties of similar polygons

a. Determine similar parts of polygons. Assessment Limit: Use the length of corresponding sides or the measure of corresponding angles and rational numbers with no more than 2 decimal places (0 - 1000)

D. Transformations

1. Analyze a transformation on a coordinate plane

a. Identify, describe, and plot the results of multiple transformations on a coordinate plane. Assessment Limit: Identify and plot the result of two transformations using translations (horizontal or vertical), reflections (horizontal or vertical), or rotations (90° or 180°) about a given point

3.0. Knowledge of Measurement: Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements.

A. Applications in Measurement

1. Estimate and apply measurement formulas

a. Estimate and determine the circumference or area of a circle. Assessment Limit: Include circles with rational numbers with no more than 2 decimal places (0 - 10,000)

c. Estimate and determine the volume of a cylinder. Assessment Limit: Include cylinders with whole number dimensions (0 - 10,000)

d. Determine the volume of cones, pyramids, and spheres

e. Determine the surface area of cylinders, prisms, and pyramids

2. Analyze measurement relationships

a. Use proportional reasoning to solve measurement problems. Assessment Limit: Use proportions, scale drawings, or rates and whole numbers or decimals (0 - 1000)

4.0. Knowledge of Statistics: Students will collect, organize, display, analyze, or interpret data to make decisions or predictions.

A. Data Displays

1. Organize and display data

b. Organize and display data to make box/whisker plots. Assessment Limit: Use no more than 12 pieces of data and whole numbers (0 - 1000)

c. Organize and display data to make a scatter plot. Assessment Limit: Use no more than 10 points and whole numbers (0 - 1000)

B. Data Analysis

1. Analyze data

a. Interpret tables. Assessment Limit: Use no more than 5 categories having no more than 2 quantities per category and whole numbers or decimals with no more than 2 decimal places (0 - 100)

b. Interpret box/whisker plots. Assessment Limit: Use minimum, first (lower) quartile, median (middle/second quartile), third (upper) quartile, or maximum and whole numbers (0 - 100)

c. Interpret scatter plots. Assessment Limit: Use no more than 10 points using whole numbers or decimals with no more than 2 decimal places (0 - 100)

e. Analyze multiple box/whisker plots using the same scale

5.0. Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation.

A. Sample Space

1. Identify a sample space

a. Describe the difference between independent and dependent events

b. Determine the number of outcomes. Assessment Limit: Use no more than 5 dependent events with no more than 10 outcomes in the first event

B. Theoretical Probability

1. Determine the probability of an event comprised of no more than 2 independent events

a. Express the probability of an event as a fraction, a decimal, or a percent. Assessment Limit: Use a sample space of 36 to 60 outcomes

2. Determine the probability of a second event that is dependent on a first event of equally likely outcomes

C. Experimental Probability

1. Analyze the results of a survey or simulation

2. Conduct a probability experiment

3. Compare results of theoretical probability and experimental probability

4. Describe the difference between theoretical and experimental probability

6.0. Knowledge of Number Relationships or Computation: Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology.

A. Knowledge of Number and Place Value