Core Curriculum

1.1.2: Understand and explain procedures for multiplying and dividing fractions by using the meanings of fractions, multiplication and division, and the inverse relationship between multiplication and division.

Dividing Fractions

Dividing Mixed Numbers

Function Machines 3 (Functions and Problem Solving)

Modeling and Solving Two-Step Equations

Multiplying Fractions

Multiplying Mixed Numbers

No Alien Left Behind (Division with Remainders)

Solving Two-Step Equations

1.1.3: Understand and explain procedures for multiplying and dividing decimals by using the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number).

Multiplying Decimals (Area Model)

Multiplying with Decimals

1.1.4: Use common procedures to multiply and divide fractions and decimals efficiently and accurately.

Dividing Fractions

Multiplying Decimals (Area Model)

Multiplying Fractions

Multiplying with Decimals

1.1.5: Convert from one unit to another in the metric system of measurement by using understanding of the relationships among the units and by multiplying and dividing decimals.

Multiplying Decimals (Area Model)

Multiplying with Decimals

1.1.6: Convert from one unit to another in the customary system of measurement by using understanding of the relationships among the units and by multiplying and dividing fractions.

Dividing Fractions

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

1.1.7: Multiply and divide fractions and decimals to solve problems, including multi-step problems.

Dividing Fractions

Multiplying Decimals (Area Model)

Multiplying Fractions

Multiplying with Decimals

1.2.1: Understand negative numbers in terms of their position on the number line, their role in the system of all rational numbers, and in everyday situations (e.g., situations of owing money or measuring elevations above and below sea level).

Comparing and Ordering Integers

Real Number Line - Activity A

1.2.2: Understand absolute value in terms of distance on the number line and simplify numerical expressions involving absolute value.

Comparing and Ordering Integers

Order of Operations

Real Number Line - Activity A

1.2.3: By applying properties of arithmetic and considering negative numbers in everyday contexts, explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense.

Adding Real Numbers

Chocomatic (Multiplication, Arrays, and Area)

Multiplying Decimals (Area Model)

Real Number Line - Activity A

1.2.4: Understand positive integer exponents in terms of repeated multiplication and evaluate simple exponential expressions.

Dividing Exponential Expressions

1.2.5: Effectively compute with and solve problems using rational numbers, including negative numbers.

Adding Real Numbers

Dividing Fractions

Dividing Mixed Numbers

Estimating Sums and Differences

Fractions with Unlike Denominators

Multiplying Decimals (Area Model)

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Real Number Line - Activity A

Sums and Differences with Decimals

1.3.4: Understand and determine the square roots of perfect squares.

1.3.5: Understand and estimate square roots of non-perfect-squares, and determine more precise values using a calculator.

1.3.6: Represent, use, and interpret numbers in scientific notation.

1.3.7: Use scientific notation and rational and irrational numbers to model and solve problems.

No Alien Left Behind (Division with Remainders)

1.4.1: Build on understanding of fractions and part-whole relationships to understand ratios (by, for example, analyzing the relative quantities of boys and girls in the classroom or triangles and squares in a drawing).

Beam to Moon (Ratios and Proportions)

Part:Part and Part:Whole Ratios

Polling: Neighborhood

1.4.2: Understand percent as a rate and develop fluency in converting among fractions, decimals, and percents.

Percents and Proportions

Percents, Fractions and Decimals

1.4.3: Understand equivalent ratios as deriving from, and extending, pairs of rows (or columns) in the multiplication table.

Part:Part and Part:Whole Ratios

Polling: Neighborhood

1.4.5: Use a variety of strategies to solve problems involving ratio and rate.

Part:Part and Part:Whole Ratios

Polling: Neighborhood

1.5.1: Understand that a proportion is an equation that states that two ratios are equivalent.

Part:Part and Part:Whole Ratios

Polling: Neighborhood

1.5.2: Understand proportional relationships (y = kx or y/x = k), and distinguish proportional relationships from other relationships, including inverse proportionality (xy = k or y = k/x).

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

1.5.3: Understand that in a proportional relationship of two variables, if one variable doubles or triples, for example, then the other variable also doubles or triples, and if one variable changes additively by a specific amount, a, then the other variable changes additively by the amount ka.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

1.5.4: Graph proportional relationships and identify the constant of proportionality as the slope of the related line.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Elevator Operator (Line Graphs)

Slope - Activity B

1.5.5: Use ratios and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Part:Part and Part:Whole Ratios

Percent of Change

Polling: Neighborhood

Proportions and Common Multipliers

Simple and Compound Interest

2.1.1: Write mathematical expressions, equations, and formulas that correspond to given situations.

Using Algebraic Equations

Using Algebraic Expressions

2.1.2: Understand that variables represent numbers whose exact values are not yet specified, use single letters, words, or phrases as variables, and use variables appropriately.

2.1.3: Evaluate expressions (for example, find the value of 3x if x is 7).

2.1.5: Understand that solutions of an equation are the values of the variables that make the equation true.

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

2.1.6: Solve simple one-step equations (i.e., involving a single operation) by using number sense, properties of operation, and the idea of maintaining equality on both sides of an equation.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

2.1.7: Construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and use equations to describe simple relationships shown in a table (such as 3x = y).

Linear Functions

Using Tables, Rules and Graphs

2.1.8: Use expressions, equations, and formulas to solve problems, and justify their solutions.

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

2.2.1: Understand that a proportion is an equation that states that two ratios are equivalent.

2.2.2: Understand proportional relationships (y = kx or y/x = k), and distinguish proportional relationships from other relationships, including inverse proportionality (xy = k or y = k/x).

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

2.2.3: Graph proportional relationships and identify the constant of proportionality as the slope of the related line.

Defining a Line with Two Points

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

Elevator Operator (Line Graphs)

Function Machines 2 (Functions, Tables, and Graphs)

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

2.2.4: Use ratios and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Percent of Change

Polling: Neighborhood

Proportions and Common Multipliers

Simple and Compound Interest

2.3.1: Make strategic choices of procedures to solve linear equations and inequalities in one variable and implement them efficiently.

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

2.3.2: Recognize and generate equivalent forms of linear expressions, by using the associative, commutative, and distributive properties.

Chocomatic (Multiplication, Arrays, and Area)

2.3.3: Understand that when properties of equality are used to transform an equation into a new equivalent equation, solutions obtained for the new equation also solve the original equation.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

2.3.4: Solve more complicated linear equations, including solving for one variable in terms of another.

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Two-Step Equations

2.3.5: Solve linear inequalities and represent the solution on a number line.

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

2.3.6: Formulate linear equations and inequalities in one variable and use them to solve problems, including in applied settings, and justify the solution using multiple representations.

Modeling and Solving Two-Step Equations

Road Trip (Problem Solving)

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

2.4.1: Understand linear functions and slope of lines in terms of constant rate of change.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Elevator Operator (Line Graphs)

Function Machines 2 (Functions, Tables, and Graphs)

Linear Functions

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

2.4.2: Understand that the slope of a line is constant, for example by using similar triangles (e.g., as shown in the rise and run of "slope triangles"), and compute the slope of a line using any two points on the line.

Defining a Line with Two Points

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Elevator Operator (Line Graphs)

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

2.4.3: Build on the concept of proportion, recognizing a proportional relationship (y/x = k, or y = kx) as a special case of a linear function. In this special case, understand that if one variable doubles or triples, for example, then the other variable also doubles or triples; and understand that if the input, or x-coordinate in this case, changes additively by a specific amount, a, then the output, or y-coordinate in this case, changes additively by the amount ka.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

Function Machines 2 (Functions, Tables, and Graphs)

Linear Functions

Using Tables, Rules and Graphs

2.4.4: Understand that the graph of the equation y = mx + b is a line with y-intercept b and slope m.

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

2.4.5: Translate among verbal, tabular, graphical, and algebraic representations of functions, including recursive representations such as NEXT = NOW +3 (recognizing that tabular and graphical representations often only yield approximate solutions), and describe how such aspects of a linear function as slope, constant rate of change, and intercepts appear in different representations.

Arithmetic Sequences

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Elevator Operator (Line Graphs)

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Modeling Linear Systems - Activity A

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Using Algebraic Equations

Using Algebraic Expressions

Using Tables, Rules and Graphs

2.4.6: Use linear functions, and understanding of the slope of a line and constant rate of change, to analyze situations and solve problems.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Elevator Operator (Line Graphs)

Function Machines 2 (Functions, Tables, and Graphs)

Linear Functions

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

2.5.1: Use tables and graphs to analyze and (approximately) solve systems of two linear equations in two variables.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

Using Tables, Rules and Graphs

2.5.2: Relate a system of two linear equations in two variables to a pair of lines in the plane that intersect, are parallel, or are the same.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

3.1.2: Use knowledge of area of simpler shapes to help find area of more complex shapes.

Classifying Quadrilaterals - Activity A

3.1.3: Understand and apply formulas to find area of triangles and quadrilaterals.

Area of Parallelograms - Activity A

Rectangle: Perimeter and Area

3.2.1: Understand that two objects are similar if they have the same shape (i.e., corresponding angles are congruent) but not necessarily the same size.

Investigating Angle Theorems - Activity A

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

3.2.2: Understand similarity in terms of a scale factor between corresponding lengths in similar objects (i.e., similar objects are related by transformations of magnifying or shrinking).

Dilations

Parabolas - Activity A

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

3.2.3: Understand that relationships of lengths within similar objects are preserved (i.e., ratios of corresponding sides in similar objects are equal).

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

3.2.4: Understand that congruent figures are similar with a scale factor of 1.

Congruence in Right Triangles

Dilations

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

3.2.5: Use understanding of similarity to solve problems in a variety of contexts.

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

3.3.1: Find the area of more complex two-dimensional shapes, such as pentagons, hexagons, or irregular shaped regions, by decomposing the complex shapes into simpler shapes, such as triangles.

Area of Parallelograms - Activity A

Fido's Flower Bed (Perimeter and Area)

3.3.2: Understand that the ratio of the circumference to the diameter of a circle is constant and equal to pi, and use this fact to develop a formula for the circumference of a circle.

Circle: Circumference and Area

Measuring Trees

3.3.3: Understand that the formula for the area of a circle is plausible by decomposing a circle into a number of wedges and rearranging them into a shape that approximates a parallelogram.

Circle: Circumference and Area

Parallelogram Conditions

Perimeter, Circumference, and Area - Activity B

3.3.4: Develop and justify strategies for determining the surface area of prisms and cylinders by determining the areas of shapes that comprise the surface.

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

3.3.5: By decomposing prisms and cylinders by slicing them, develop and understand formulas for their volumes (Volume = Area of base x Height).

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

3.3.6: Select appropriate two-and three-dimensional shapes to model real-world situations and solve a variety of problems (including multi-step problems) involving surface area, area and circumference of circles, and volume of prisms and cylinders.

Balancing Blocks (Volume)

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Road Trip (Problem Solving)

Surface and Lateral Area of Prisms and Cylinders

3.4.1: Explore and explain the relationships among angles when a transversal cuts parallel lines.

Investigating Angle Theorems - Activity A

3.4.2: Use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and apply this fact about triangles to find unknown measures of angles.

Investigating Angle Theorems - Activity A

Triangle Angle Sum - Activity A

3.4.3: Understand and explain how particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines (e.g., "slope triangles").

Investigating Angle Theorems - Activity A

Similar Polygons

Triangle Angle Sum - Activity A

3.4.4: Use reasoning about similar triangles to solve a variety of problems, including those that involve determining heights and distances.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Perimeters and Areas of Similar Figures

Prisms and Cylinders - Activity A

Pythagorean Theorem - Activity A

Similar Figures - Activity A

Similar Polygons

3.4.5: Explain why the Pythagorean Theorem is valid by using a variety of methods ? for example, by decomposing a square in different ways.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

3.4.6: Apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane and to measure lengths and analyze polygons.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

3.4.7: Understand and apply transformations ? reflection, translation, rotation, and dilation, and understand similarity, congruence, and symmetry in terms of transformations.

Dilations

Holiday Snowflake Designer

Perimeters and Areas of Similar Figures

Quilting Bee (Symmetry)

Reflections

Rock Art (Transformations)

Rotations, Reflections and Translations

Similar Figures - Activity A

Similar Polygons

Translations

3.5.1: Recognize and draw two-dimensional representations of three-dimensional figures, including nets, front-side-top views, and perspective drawings.

3D and Orthographic Views - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

3.5.2: Identify and describe three-dimensional shapes, including prisms, pyramids, cylinders, and spheres.

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

3.5.3: Examine, build, compose, and decompose three-dimensional objects, using a variety of tools, including paper-and-pencil, geometric models, and dynamic geometry software.

Classifying Quadrilaterals - Activity A

3.5.4: Use visualization and three-dimensional shapes to solve problems, especially in real-world settings.

3D and Orthographic Views - Activity A

Prisms and Cylinders - Activity A

4.1.1: Extend prior work with mode, median, and mean as measures of center.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

4.1.2: Compute the mean for small data sets and explore its meaning as a balance point for a data set.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Movie Reviewer (Mean and Median)

Reaction Time 2 (Graphs and Statistics)

4.1.3: Extend prior work with bar graphs, line graphs, line plots, histograms, circle graphs, and stem and leaf plots as graphical representations of data to include box-and-whisker plots and scatterplots.

Box-and-Whisker Plots

Correlation

Describing Data Using Statistics

Elevator Operator (Line Graphs)

Graphing Skills

Histograms

Line Plots

Mascot Election (Pictographs and Bar Graphs)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Scatter Plots - Activity A

Solving Using Trend Lines

Stem-and-Leaf Plots

4.1.4: Create and interpret box-and-whisker plots and scatterplots.

Box-and-Whisker Plots

Correlation

Line Plots

Mascot Election (Pictographs and Bar Graphs)

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Scatter Plots - Activity A

Solving Using Trend Lines

4.2.1: Select, determine, explain, and interpret appropriate measures of center for given data sets (mean, median, mode).

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Movie Reviewer (Mean and Median)

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

4.2.2: Select, create, explain, and interpret appropriate graphical representations for given data sets (bar graphs, circle graphs, line graphs, histograms, line plots, stem and leaf plots, box-and-whisker plots, scatterplots).

Box-and-Whisker Plots

Correlation

Describing Data Using Statistics

Elevator Operator (Line Graphs)

Graphing Skills

Histograms

Line Plots

Mascot Election (Pictographs and Bar Graphs)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Scatter Plots - Activity A

Solving Using Trend Lines

Stem-and-Leaf Plots

4.2.3: Summarize and compare data sets using appropriate numerical statistics and graphical representations.

Box-and-Whisker Plots

Describing Data Using Statistics

Histograms

Line Plots

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Scatter Plots - Activity A

Stem-and-Leaf Plots

4.2.4: Compare the information provided by the mean and the median and investigate the different effects that changes in the data values have on these measures of center.

Describing Data Using Statistics

Distance-Time Graphs

Elevator Operator (Line Graphs)

Line Plots

Mean, Median and Mode

Movie Reviewer (Mean and Median)

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

4.2.5: Understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center, and thus consider and describe the variability of the data (e.g., range and interquartile range).

Box-and-Whisker Plots

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

4.2.6: Informally determine a line of best fit for a scatterplot to make predictions and estimates.

Lines of Best Fit Using Least Squares - Activity A

4.2.7: Formulate questions, gather data relevant to the questions, organize and analyze the data to help answer the questions, including informal analysis of randomness and bias.

Determining a Spring Constant

Mascot Election (Pictographs and Bar Graphs)

Movie Reviewer (Mean and Median)

Polling: Neighborhood

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

4.3.1: Use proportions to make estimates relating to a population on the basis of a sample.

Polling: City

Polling: Neighborhood

4.3.2: Apply percentages to make and interpret histograms and circle graphs.

Graphing Skills

Histograms

Mascot Election (Pictographs and Bar Graphs)

Populations and Samples

4.3.3: Explore situations in which all outcomes of an experiment are equally likely, and thus the theoretical probability of an event is the number of outcomes corresponding to the event divided by total number of possible outcomes.

Geometric Probability - Activity A

Polling: City

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

4.3.4: Use theoretical probability and proportions to make approximate predictions.

Probability Simulations

Theoretical and Experimental Probability

4.4.1: Represent the probability of events that are impossible, unlikely, likely, and certain using rational numbers from 0 to 1.

Spin the Big Wheel! (Probability)

4.4.2: List all possible outcomes of a given experiment or event.

4.5.2: Compute probabilities for compound events, using such methods as organized lists, tree diagrams (counting trees), area models, and counting principles.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Histograms

Permutations

Permutations and Combinations

4.5.3: Estimate the probability of simple and compound events through experimentation and simulation.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

4.5.4: Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the effect of sample size on this relationship.

Geometric Probability - Activity A

Polling: City

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

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.