Academic Standards

1.1: Proportional reasoning involves comparisons and multiplicative relationships among ratios

1.1.a: Students can: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Estimating Population Size

Geometric Probability

Part-to-part and Part-to-whole Ratios

Proportions and Common Multipliers

1.1.b: Students can: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

Unit Conversions

1.1.c: Students can: Identify and represent proportional relationships between quantities.

1.1.c.i: Determine whether two quantities are in a proportional relationship.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Estimating Population Size

Geometric Probability

Part-to-part and Part-to-whole Ratios

Percents and Proportions

Proportions and Common Multipliers

1.1.c.ii: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Beam to Moon (Ratios and Proportions)

Dilations

Direct and Inverse Variation

1.1.c.iii: Represent proportional relationships by equations.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Geometric Probability

Part-to-part and Part-to-whole Ratios

Proportions and Common Multipliers

1.1.c.iv: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

1.1.d: Students can: Use proportional relationships to solve multistep ratio and percent problems.

1.1.d.i: Estimate and compute unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality.

1.1.d.ii: Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease.

Compound Interest

Percent of Change

Percents and Proportions

Polling: Neighborhood

1.2: Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently

1.2.a: Students can: Apply understandings of addition and subtraction to add and subtract rational numbers including integers.

1.2.a.i: Represent addition and subtraction on a horizontal or vertical number line diagram.

Adding and Subtracting Integers

Adding on the Number Line

Fractions Greater than One (Fraction Tiles)

1.2.a.ii: Describe situations in which opposite quantities combine to make 0.

Adding and Subtracting Integers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

1.2.a.iii: Demonstrate p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.

Adding and Subtracting Integers

Adding on the Number Line

1.2.a.iv: Show that a number and its opposite have a sum of 0 (are additive inverses).

Adding and Subtracting Integers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

Simplifying Algebraic Expressions I

Solving Algebraic Equations I

1.2.a.v: Interpret sums of rational numbers by describing real-world contexts.

Adding on the Number Line

Improper Fractions and Mixed Numbers

Sums and Differences with Decimals

1.2.a.vi: Demonstrate subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).

Adding and Subtracting Integers

Adding on the Number Line

Simplifying Algebraic Expressions I

1.2.a.vii: Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Adding on the Number Line

Sums and Differences with Decimals

1.2.a.viii: Apply properties of operations as strategies to add and subtract rational numbers.

Adding Fractions (Fraction Tiles)

Adding and Subtracting Integers

Adding on the Number Line

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

Sums and Differences with Decimals

1.2.b: Students can: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers including integers.

1.2.b.i: Apply properties of operations to multiplication of rational numbers.

Adding and Subtracting Integers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

1.2.b.ii: Interpret products of rational numbers by describing real-world contexts.

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

1.2.b.iv: Apply properties of operations as strategies to multiply and divide rational numbers.

Adding and Subtracting Integers

Dividing Fractions

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

1.2.b.v: Convert a rational number to a decimal using long division.

Percents, Fractions, and Decimals

1.2.c: Students can: Solve real-world and mathematical problems involving the four operations with rational numbers.

Adding Fractions (Fraction Tiles)

Adding and Subtracting Integers

Adding on the Number Line

Dividing Fractions

Dividing Mixed Numbers

Estimating Population Size

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Sums and Differences with Decimals

2.1: Properties of arithmetic can be used to generate equivalent expressions

2.1.a: Students can: Use properties of operations to generate equivalent expressions.

2.1.a.i: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Solving Algebraic Equations II

2.1.a.ii: Demonstrate 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.

Exponents and Power Rules

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

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

2.2: Equations and expressions model quantitative relationships and phenomena

2.2.a: Students can: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically.

Adding and Subtracting Integers

Rational Numbers, Opposites, and Absolute Values

2.2.b: Students can: Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.

Adding Fractions (Fraction Tiles)

Adding and Subtracting Integers

Adding on the Number Line

Dividing Fractions

Dividing Mixed Numbers

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

Sums and Differences with Decimals

2.2.c: Students can: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

2.2.c.i: Fluently solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

Absolute Value Equations and Inequalities

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

2.2.c.ii: Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Order of Operations

Solving Algebraic Equations II

Solving Equations on the Number Line

2.2.c.iv: Graph the solution set of the inequality and interpret it in the context of the problem.

Absolute Value Equations and Inequalities

Rational Numbers, Opposites, and Absolute Values

Solving Linear Inequalities in One Variable

3.1: Statistics can be used to gain information about populations by examining samples

3.1.a: Students can: Use random sampling to draw inferences about a population.

3.1.a.i: Explain that generalizations about a population from a sample are valid only if the sample is representative of that population.

Polling: City

Polling: Neighborhood

3.1.a.ii: Explain that random sampling tends to produce representative samples and support valid inferences.

Polling: City

Polling: Neighborhood

3.1.a.iii: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Polling: City

Polling: Neighborhood

Populations and Samples

3.1.a.iv: Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

3.1.b: Students can: Draw informal comparative inferences about two populations.

3.1.b.i: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Real-Time Histogram

3.1.b.ii: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Box-and-Whisker Plots

Polling: City

Populations and Samples

3.2: Mathematical models are used to determine probability

3.2.a: Students can: Explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

Geometric Probability

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

3.2.b: Students can: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

3.2.c: Students can: Develop a probability model and use it to find probabilities of events.

3.2.c.i: Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

3.2.c.ii: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

3.2.c.iii: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

3.2.d: Students can: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

3.2.d.i: Explain that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Independent and Dependent Events

Theoretical and Experimental Probability

3.2.d.ii: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

3.2.d.iv: Design and use a simulation to generate frequencies for compound events.

Independent and Dependent Events

4.1: Modeling geometric figures and relationships leads to informal spatial reasoning and proof

4.1.a: Students can: Draw, construct, and describe geometrical figures and describe the relationships between them.

4.1.a.i: Solve 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.

4.1.a.iii: Construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Concurrent Lines, Medians, and Altitudes

Triangle Inequalities

4.2: Linear measure, angle measure, area, and volume are fundamentally different and require different units of measure

4.2.a: Students can: State the formulas for the area and circumference of a circle and use them to solve problems.

Circumference and Area of Circles

4.2.b: Students can: Give an informal derivation of the relationship between the circumference and area of a circle.

Circumference and Area of Circles

4.2.c: Students can: Use properties of supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Investigating Angle Theorems

Triangle Angle Sum

4.2.d: Students can: Solve 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.

Area of Parallelograms

Area of Triangles

Chocomatic (Multiplication, Arrays, and Area)

Fido's Flower Bed (Perimeter and Area)

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Correlation last revised: 1/22/2020

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