Grade Level Expectations

1.1.1: Understand the concept and symbolic representation of rational numbers.

1.1.1.c: Explain the meaning of square root of a whole number and provide examples.

1.1.2: Understand the relative values of rational numbers.

1.1.2.a: Order rational numbers including integers, whole number powers, and square roots, and explain why one rational number is greater than, equal to, or less than another.

1.1.2.b: Order rational numbers including integers, whole number powers, and square roots based on a picture of a real world model, locations on a number line, or symbolic representation.

Ordering Percents, Fractions and Decimals

Ordering Percents, Fractions and Decimals Greater Than 1

Square Roots

1.1.2.c: Explain why one given rational number including integers, whole-number powers, and square roots is greater than, equal to, or less than another rational number.

1.1.3: Understand and use the distributive property and the properties of addition and multiplication on rational numbers.

1.1.3.b: Use the distributive property to simplify expressions that include integers.

Solving Equations By Graphing Each Side

1.1.3.c: Use the distributive property to factor expressions.

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

1.1.3.e: Use the addition and multiplication properties, including the distributive property, to assist with computations.

1.1.4: Apply the concepts of ratio, percent, and direct proportion.

1.1.4.a: Determine an unknown value for a dimension or a number of events or objects using ratio or proportion.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Geometric Probability - Activity A

Part:Part and Part:Whole Ratios

Perimeters and Areas of Similar Figures

Polling: Neighborhood

Proportions and Common Multipliers

Similar Figures - Activity A

Similar Polygons

1.1.4.b: Determine an unknown value for a dimension or a number of events or objects using percents.

Ordering Percents, Fractions and Decimals

Ordering Percents, Fractions and Decimals Greater Than 1

Percents and Proportions

1.1.4.c: Select and use the most advantageous representation of ratios or percents in a given situation.

Estimating Population Size

Part:Part and Part:Whole Ratios

Polling: Neighborhood

1.1.4.d: Determine a ratio or percent in a given situation.

Estimating Population Size

Part:Part and Part:Whole Ratios

Percents and Proportions

Polling: Neighborhood

1.1.5: Understand the meaning of addition, subtraction, multiplication, division, powers, and square roots on rational numbers.

1.1.5.b: Explain the meaning of taking whole number powers of integers or square roots of whole numbers using words, pictures, or models.

1.1.5.c: Represent a situation involving multiplication or division of integers, whole number powers of integers, or square roots of whole numbers.

1.1.5.d: Explain how the result of dividing a rational number by a fraction between 0 and 1 is different from the result of dividing the same number by a fraction greater than 1.

Dividing Fractions

Dividing Mixed Numbers

1.1.5.e: Translate a given situation, picture, or illustration into a numeric expression or equation involving decimals, fractions, integers, whole number powers, and square roots of whole numbers.

Square Roots

Using Algebraic Equations

Using Algebraic Expressions

1.1.5.f: Select and/or use an appropriate operation to show understanding of whole number powers and square roots.

1.1.5.g: Convert between equivalent forms of rational numbers including whole number powers and square roots of perfect squares.

Improper Fractions and Mixed Numbers

Percents, Fractions and Decimals

Square Roots

1.1.6: Apply strategies or uses computational procedures using order of operations and addition, subtraction, multiplication, division, powers, and square roots on rational numbers.

1.1.6.a: Compute with rational numbers using order of operations.

Dividing Fractions

Dividing Mixed Numbers

Fractions with Unlike Denominators

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Order of Operations

Sums and Differences with Decimals

1.1.6.b: Compute using whole number powers and/or square roots of perfect squares.

Adding Real Numbers

Square Roots

1.1.6.d: Complete multi-step computations using two or more different operations with rational numbers.

Dividing Fractions

Dividing Mixed Numbers

Fractions with Unlike Denominators

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Sums and Differences with Decimals

1.1.7: Apply strategies and uses tools to complete tasks involving computation of rational numbers.

1.1.7.c: Describe strategies for mental computation with integers using powers and square roots.

Adding and Subtracting Integers with Chips

Square Roots

1.1.8: Apply estimation strategies involving computation of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict results or determine reasonableness of answers.

1.1.8.b: Use a variety of estimation strategies to predict results prior to computation.

Estimating Population Size

Estimating Sums and Differences

1.1.8.c: Use a variety of estimation strategies to verify the reasonableness of calculated results.

Estimating Population Size

Estimating Sums and Differences

1.1.8.d: Compute to check the reasonableness of estimated answers for a given situation.

1.1.8.e: Explain an appropriate adjustment when an estimate and a computation do not agree.

Estimating Sums and Differences

1.1.8.f: Explain or describe a strategy for estimation involving computation with decimals, fractions, and integers, using +, -, x, Ö, powers, and square roots.

Adding and Subtracting Integers with Chips

Square Roots

1.2.1: Understand how a change in one linear dimension affects surface area and volume of rectangular prisms and cylinders and how changes in two linear dimensions affect perimeter and area of rectangles.

1.2.1.a: Determine and/or describe the impact that a change in one dimension has on volume and surface area in right cylinders and rectangular prisms.

Area of Parallelograms - Activity A

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Rectangle: Perimeter and Area

Special Quadrilaterals

Surface and Lateral Area of Prisms and Cylinders

1.2.1.b: Determine and/or describe a change in a linear dimension given a change in volume and/or surface area of rectangular prisms and cylinders.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

1.2.1.c: Determine and/or describe the impact on perimeter and/or area of a rectangle caused by a change in two dimensions.

Area of Parallelograms - Activity A

Circle: Circumference and Area

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Rectangle: Perimeter and Area

Special Quadrilaterals

1.2.2: Understand and use rate, slope, and other derived units of measurement.

1.2.2.a: Explain the concept of a rate or slope in a given situation.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Slope - Activity B

1.2.2.c: Calculate a rate of change or slope in a situation.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Slope - Activity B

1.2.3: Explain why different situations require different levels of precision.

1.2.3.a: Describe or explain why different situations require different levels of precision.

1.2.3.b: Compare situations that require different levels of precision.

1.2.3.c: Select and describe an appropriate unit of measure for the precision needed in a given situation.

1.2.5: Use formulas, including the Pythagorean Theorem, to determine measurements related to triangles, rectangular prisms, and right cylinders.

1.2.5.a: Explain how to use a formula to calculate and label the surface area and volume of a prism or cylinder.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

1.2.5.b: Use the Pythagorean Theorem to determine and label a missing dimension of a right triangle or prism.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Prisms and Cylinders - Activity A

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

1.2.5.c: Determine and label surface areas of right cylinders and right prisms.

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

1.2.5.d: Determine and label dimensions of a triangle, prism, or cylinder based on a given perimeter, circumference, area, and/or volume.

Area of Parallelograms - Activity A

Circle: Circumference and Area

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

1.2.6: Apply strategies to obtain reasonable estimates of surface area and volume of right cylinders and rectangular prisms, and the lengths of sides of right triangles.

1.2.6.b: Use estimation to determine and label volume and surface area for right cylinders and right prisms and explain why an approximation is appropriate.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

1.2.6.c: Use estimation strategies to determine and label the approximate length of the third side of a right triangle given the lengths of two sides.

Classifying Triangles

Triangle Angle Sum - Activity A

1.2.6.d: Use estimation strategies to determine and labels the approximate distance or height in a situation using similar triangles or the Pythagorean Theorem.

Distance Formula - Activity A

Estimating Sums and Differences

Geoboard: The Pythagorean Theorem

Perimeters and Areas of Similar Figures

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Similar Figures - Activity A

Similar Polygons

1.3.1: Understand properties of cylinders, cones, and pyramids.

1.3.1.a: Identify or describe cylinders, cones, or pyramids.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

1.3.1.b: Classify and label cylinders, cones, or pyramids.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

1.3.1.c: Draw nets of cylinders, prisms, and pyramids.

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

1.3.1.d: Identify and label rays, lines, end points, line segments, vertices, and angles in three-dimensional shapes and figures.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

1.3.2: Use the properties of similarity; uses the Pythagorean Theorem to determine if a triangle is a right triangle.

1.3.2.a: Sort, classify, and label similar and congruent figures.

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

1.3.2.b: Use properties of similarity to draw, describe, sort, classify, and/or label two-dimensional figures in illustrations or real life.

Classifying Quadrilaterals - Activity A

Parallelogram Conditions

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

Special Quadrilaterals

1.3.2.c: Draw a shape similar to a given complex shape.

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

1.3.2.e: Use the Pythagorean Theorem to determine if a triangle is a right triangle.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

1.3.3: Describe the relative position of points on a coordinate grid.

1.3.3.a: Locate a missing vertex given the coordinates of the vertices of a polygon.

Points in the Coordinate Plane - Activity A

1.3.3.b: Explain a method for finding the missing side of a triangle in a real-world setting.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

1.3.4: Apply a combination of translations, reflections, and/or rotations to 2-dimensional figures.

1.3.4.a: Use any combination of rotations, reflections, and/or translations to draw or locate congruent figures on a grid.

Reflections

Rotations, Reflections and Translations

Translations

1.3.4.b: Use ordered pairs or labels to describe the location of a picture or an object transformed by any combination of translations, reflections, and/or rotations on a coordinate grid.

Points in the Coordinate Plane - Activity A

Reflections

Rotations, Reflections and Translations

Translations

1.4.1: Understand the concept of compound events.

1.4.1.a: Determine and explain when events are compound.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

1.4.1.b: Describe the difference between compound events involving "and" or "or".

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

1.4.1.c: Describe or represent compound events.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

1.4.2: Use procedures to determine the probability of compound events.

1.4.2.a: Determine the sample space for simple experiments involving independent or compound events.

Compound Independent and Dependent Events

Independent and Dependent Events

1.4.2.b: Calculate the probability of two independent events occurring simultaneously using various methods including organized lists, tree diagrams, counting procedures, and area models.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Permutations

Permutations and Combinations

1.4.2.c: Explain the relationship between theoretical and empirical probability of compound events.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

Polling: City

Probability Simulations

Theoretical and Experimental Probability

1.4.2.d: Predict the probability of outcomes of experiments and relates the predictions to empirical results.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

1.4.2.e: Design a situation that would produce a given probability.

Geometric Probability - Activity A

1.4.2.f: Design a game using compound probabilities with equal chances of winning for all players.

Compound Independent and Dependent Events

Independent and Dependent Events

1.4.3: Describe how different samples of a population may affect the data collected.

1.4.3.a: Describe bias in population samples and explains a procedure for selecting an unbiased representative sample.

1.4.3.c: Determine whether claims made about results are based on biased data due to sampling.

1.4.4: Identify clusters and outliers in data and determine effects on the measures of central tendency.

1.4.4.a: Identify clusters and outliers and determine how they may affect measures of central tendency.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

1.4.4.b: Modify a set of data so that the median is a more reasonable measure of central tendency than the mean.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

1.4.4.c: Examine variations in data, including clusters and outliers, to select the most appropriate measure of central tendency to describe a given set of data.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

1.4.4.d: Determine and/or use the mean, median, mode, and/or range for a set of data.

Box-and-Whisker Plots

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

1.4.5: Read and interpret data presented in diagrams, tables of ordered pairs, and scatter plots and makes predictions based on the data.

1.4.5.a: Describe trends or patterns in data presented in a table of ordered pairs or a scatter plot.

Arithmetic and Geometric Sequences

Correlation

Finding Patterns

Geometric Sequences

Scatter Plots - Activity A

Solving Using Trend Lines

1.4.5.b: Read and interpret the data in Venn Diagrams, tables of ordered pairs, and/or scatter plots.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

1.4.5.d: Draw trend lines with or without technology and makes predictions about real-world situations.

1.4.5.e: Explain whether stem-and-leaf plot, box-and-whisker plot, or scatter plot is more appropriate for a given set of data, a particular situation, or purpose, or answers a question most effectively.

Box-and-Whisker Plots

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

Stem-and-Leaf Plots

1.4.5.f: Determine whether claims made about results are based on biased representations of data.

Box-and-Whisker Plots

Histograms

Line Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

1.4.5.g: Predict an outcome given a linear relationship involving non-negative rational numbers.

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

1.5.1: Apply knowledge of linear and non-linear relationships to recognize, extend, and create patterns and sequences in tables and graphs.

1.5.1.a: Extend, represent, or create linear and non-linear patterns and sequences using tables and graphs.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Finding Patterns

Geometric Sequences

Linear Functions

Using Tables, Rules and Graphs

1.5.1.c: Use technology to generate graphic representations of linear and non-linear relationships.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Cubic Function Activity

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Linear Functions

Point-Slope Form of a Line - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

1.5.1.d: Extend a pattern by supplying missing terms in the beginning, middle, or end of a linear or non-linear pattern.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

Linear Functions

1.5.2: Determine a rule for linear and non-linear functions represented in tables, graphs, patterns or situations.

1.5.2.a: Determine a rule, developed from a table, graph, or situation, using words or algebraic symbols.

Cubic Function Activity

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Introduction to Functions

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

1.5.2.b: Develop a rule that describes a recursive pattern in terms of current and previous values such as the Fibonacci sequence.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

1.5.2.c: Describe a rule and/or construct a table to represent a pattern.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

Linear Functions

Using Tables, Rules and Graphs

1.5.2.d: Use technology to develop a table or graph from a given rule.

Cubic Function Activity

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Introduction to Functions

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

1.5.3: Express relationships between quantities using equality and inequality symbols.

1.5.3.a: Express relationships between quantities including whole number exponents and square roots using =, "not equal to", <, >, "less than or equal to" and "greater than or equal to".

1.5.3.b: Describe a situation represented by an equation or inequality involving whole number exponents and/or square roots.

Square Roots

Using Algebraic Equations

1.5.3.c: Use equality and inequality symbols to express relationships between rational numbers using square roots and powers in a given situation.

Simplifying Radicals - Activity A

Square Roots

1.5.4: Use variables to write expressions, linear equations, and inequalities that represent situations involving relationships with rational numbers.

1.5.4.a: Use variables to write an expression, equation, or inequality to represent a given situation.

Using Algebraic Equations

Using Algebraic Expressions

1.5.4.b: Describe a situation that corresponds to a given expression, equation or inequality.

1.5.4.c: Describe a situation involving a linear relationship that matches a given graph.

Arithmetic Sequences

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

1.5.4.d: Translate among different representations of linear equations, using symbols, graphs, tables, diagrams, or written descriptions.

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Linear Functions

Point-Slope Form of a Line - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

1.5.4.e: Explain the meaning of a variable in a formula, expression, equation, or inequality.

Using Algebraic Equations

Using Algebraic Expressions

1.5.6: Apply a variety of properties to solve multi-step equations and one-step inequalities with one variable.

1.5.6.a: Solve multi-step single-variable equations involving parentheses, like terms, or variables on both sides of the equal sign.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

1.5.6.b: Write and solve multi-step single variable equations involving parentheses, like terms, or variables on both sides of the equal sign.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

Using Algebraic Equations

1.5.6.c: Solve, or write and solve, one-step inequalities.

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Using Algebraic Equations

1.5.6.d: Explain or show the meaning of the solution to an equation.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

3.1.1: Analyze numerical, measurement, geometric, probability, statistical, and/or algebraic information from a variety of sources.

3.1.1.a: Analyze mathematical information or results.

Biconditional Statement

Conditional Statement

3.1.1.b: Compare mathematical information represented in tables, charts, graphs, text, diagrams, figures, or pictures.

Biconditional Statement

Conditional Statement

Populations and Samples

3.1.1.d: Differentiate between valid and invalid analysis of mathematical information or results.

Biconditional Statement

Conditional Statement

3.3.1: Justify results using evidence.

3.3.1.a: Justify results using evidence and information from the problem situation and/or known facts, patterns, and relationships.

3.3.2: Evaluate reasonableness of results.

3.3.2.b: Verify that the solution to a real-world problem makes sense in relation to the situation.

Biconditional Statement

Conditional Statement

4.1.2: Extract numerical, measurement, geometric, probability, statistical, and/or algebraic information from multiple sources.

4.1.2.a: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, diagrams, models, and graphs including scatter plots, stem-and-leaf plots, and box-and-whisker plots for a purpose.

Box-and-Whisker Plots

Scatter Plots - Activity A

Solving Using Trend Lines

Stem-and-Leaf Plots

4.2.2: Represent numerical, measurement, geometric, probability, statistical, and/or algebraic information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using tables, charts, scatter plots, stem-and-leaf plots, box-and-whisker plots, pictures, models, drawings, or other appropriate forms including title, labels, appropriate and consistent scales, and accurate display of data.

Box-and-Whisker Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.