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## CO.7.1.Number Sense, Properties, and Operations

Number Sense, Properties, and Operations
7.1.1. Proportional reasoning involves comparisons and multiplicative relationships among ratios. Students can:
7.1.1.a. Analyze proportional relationships and use them to solve real-world and mathematical problems. (CCSS: 7.RP)
Flip Charts Applying Percents
Flip Charts Box It Up
Flip Charts Triangle Tricks
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Proportions/Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Proportions

7.1.1.b. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (CCSS: 7.RP.1)
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

7.1.1.c. Identify and represent proportional relationships between quantities. (CCSS: 7.RP.2)
7.1.1.c.i. Determine whether two quantities are in a proportional relationship. (CCSS: 7.RP.2a)
Flip Charts Applying Percents
Flip Charts Box It Up
Flip Charts Triangle Tricks
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Proportions/Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Proportions

7.1.1.c.ii. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (CCSS: 7.RP.2b)
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

7.1.1.d. Use proportional relationships to solve multistep ratio and percent problems. (CCSS: 7.RP.3)
7.1.1.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 (PFL).
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

7.1.1.d.ii. Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease (PFL).
Flip Charts Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Percent, Rate, Base
Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

7.1.2. Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently. Students can:
7.1.2.a. Apply understandings of addition and subtraction to add and subtract rational numbers including integers. (CCSS: 7.NS.1)
7.1.2.a.ii. Describe situations in which opposite quantities combine to make 0. (CCSS: 7.NS.1a)
Flip Charts The Real Numbers

7.1.2.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. (CCSS: 7.NS.1b)
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

7.1.2.a.iv. Show that a number and its opposite have a sum of 0 (are additive inverses). (CCSS: 7.NS.1b)
Flip Charts The Real Numbers

7.1.2.a.vi. Demonstrate subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). (CCSS: 7.NS.1c)
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

7.1.2.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. (CCSS: 7.NS.1c)
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

7.1.2.a.viii. Apply properties of operations as strategies to add and subtract rational numbers. (CCSS: 7.NS.1d)
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

7.1.2.b. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers including integers. (CCSS: 7.NS.2)
7.1.2.b.i. Apply properties of operations to multiplication of rational numbers. (CCSS: 7.NS.2a)
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

7.1.2.b.ii. Interpret products of rational numbers by describing real-world contexts. (CCSS: 7.NS.2a)
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

7.1.2.b.iii. Apply properties of operations to divide integers. (CCSS: 7.NS.2b)
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

7.1.2.b.iv. Apply properties of operations as strategies to multiply and divide rational numbers. (CCSS: 7.NS.2c)
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

7.1.2.b.v. Convert a rational number to a decimal using long division. (CCSS: 7.NS.2d)
Flip Charts Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiple Representation of Rational Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers

7.1.2.b.vi. Show that the decimal form of a rational number terminates in 0s or eventually repeats. (CCSS: 7.NS.2d)
Flip Charts The Real Numbers

7.1.2.c. Solve real-world and mathematical problems involving the four operations with rational numbers. (CCSS: 7.NS.3)
Flip Charts Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Percent, Rate, Base
Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

## CO.7.2.Patterns, Functions, and Algebraic Structures

Patterns, Functions, and Algebraic Structures
7.2.1. Properties of arithmetic can be used to generate equivalent expressions. Students can:
7.2.1.a. Use properties of operations to generate equivalent expressions. (CCSS: 7.EE)
7.2.1.a.i. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (CCSS: 7.EE.1)
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

7.2.1.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. (CCSS: 7.EE.2)
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations

7.2.2. Equations and expressions model quantitative relationships and phenomena. Students can:
7.2.2.b. 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. (CCSS: 7.EE.3)
Flip Charts Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Mixed Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiple Representation of Rational Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Simplify Fractions

7.2.2.c. 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. (CCSS: 7.EE.4)
7.2.2.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. (CCSS: 7.EE.4a)
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Algebra

7.2.2.c.iii. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. (CCSS: 7.EE.4b)
Flip Charts Inequalities
Flip Charts Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

7.2.2.c.iv. Graph the solution set of the inequality and interpret it in the context of the problem. (CCSS: 7.EE.4b)
Flip Charts Inequalities
Flip Charts Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities

## CO.7.3.Data Analysis, Statistics, and Probability

Data Analysis, Statistics, and Probability
7.3.1. Statistics can be used to gain information about populations by examining samples. Students can:
7.3.1.a. Use random sampling to draw inferences about a population. (CCSS: 7.SP)
7.3.1.a.ii. Explain that random sampling tends to produce representative samples and support valid inferences. (CCSS: 7.SP.1)
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

7.3.2. Mathematical models are used to determine probability. Students can:
7.3.2.a. Explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. (CCSS: 7.SP.5)
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Probability

7.3.2.b. 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. (CCSS: 7.SP.6)
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability

7.3.2.c. Develop a probability model and use it to find probabilities of events. (CCSS: 7.SP.7)
7.3.2.c.i. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (CCSS: 7.SP.7)
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability

7.3.2.c.ii. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (CCSS: 7.SP.7a)
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

7.3.2.d. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (CCSS: 7.SP.8)
7.3.2.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. (CCSS: 7.SP.8a)
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Probability

7.3.2.d.ii. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. (CCSS: 7.SP.8b)
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Probability

## CO.7.4.Shape, Dimension, and Geometric Relationships

Shape, Dimension, and Geometric Relationships
7.4.1. Modeling geometric figures and relationships leads to informal spatial reasoning and proof. Students can:
7.4.1.a. Draw construct, and describe geometrical figures and describe the relationships between them. (CCSS: 7.G)
7.4.1.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. (CCSS: 7.G.1)
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

7.4.2. Linear measure, angle measure, area, and volume are fundamentally different and require different units of measure. Students can:
7.4.2.a. State the formulas for the area and circumference of a circle and use them to solve problems. (CCSS: 7.G.4)
Flip Charts Dot to Dot
Flip Charts Perimeter & Area
Flip Charts Shape Up
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Circumference of Circles
Quiz, Flash Cards, Worksheet, Game & Study Guide Diameter of Circle
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

7.4.2.b. Give an informal derivation of the relationship between the circumference and area of a circle. (CCSS: 7.G.4)
Flip Charts Dot to Dot
Flip Charts Perimeter & Area
Flip Charts Shape Up
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Circumference of Circles
Quiz, Flash Cards, Worksheet, Game & Study Guide Diameter of Circle
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

7.4.2.c. 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. (CCSS: 7.G.5)