College and Career Ready Standards
7.RP.1: 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
7.RP.2: Recognize and represent proportional relationships between quantities:
7.RP.2a: Determine whether two quantities are in a proportional relationship, e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers
7.RP.2b: Analyze a table or graph and recognize that, in a proportional relationship, every pair of numbers has the same unit rate (referred to as the “m”).
Dilations
Direct and Inverse Variation
7.RP.2c: 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
7.RP.2d: 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.
7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.
Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
7.NS.1: Represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.1a: Describe situations in which opposite quantities combine to make 0. 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
7.NS.1b: Show 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
Improper Fractions and Mixed Numbers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals
7.NS.1c: Model subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line
Equivalent Algebraic Expressions I
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals
7.NS.1d: Model subtraction as the distance between two rational numbers on the number line where the distance is the absolute value of their difference.
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line
Equivalent Algebraic Expressions I
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals
7.NS.1e: 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
7.NS.2: Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers.
7.NS.2a: Describe how multiplication is extended from positive rational numbers to all rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (?1)(?1) = 1 and the rules for multiplying signed numbers.
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
7.NS.2b: Explain that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. Leading to situations such that if p and q are integers, then ?(??/??) = ???/?? = ??/???.
7.NS.2c: 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
7.NS.2d: Convert a rational number in the form of a fraction to its decimal equivalent using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Percents, Fractions, and Decimals
7.NS.3: Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
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
7.EE.2: Understand 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 ax2+bx+c
Modeling the Factorization of x2+bx+c
7.EE.3: Solve multi-step real-life and mathematical problems with rational numbers. 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 Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)
7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and construct two-step equations and inequalities to solve problems by reasoning about the quantities.
7.EE.4a: 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. Solve equations of these forms fluently (efficiently, accurately, and flexibly). Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
Absolute Value Equations and Inequalities
Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Order of Operations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations
7.EE.4b: 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 and p > 0. 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
7.G.1: Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Dilations
Perimeters and Areas of Similar Figures
Similar Figures
7.G.4: Use the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Circumference and Area of Circles
7.G.5: Investigate the relationship between three-dimensional geometric shapes;
7.G.5a: Generalize the volume formula for prisms and cylinders (V = Bh where B is the base and h is the height).
Prisms and Cylinders
Pyramids and Cones
7.G.5b: Generalize the surface area formula for prisms and cylinders (SA = 2B + Ph where B is the area of the base, P is the perimeter of the base, and h is the height (in the case of a cylinder, perimeter is replaced by circumference)).
Surface and Lateral Areas of Prisms and Cylinders
7.G.6: Solve real-world and mathematical problems involving area of two-dimensional objects and volume and surface area of three-dimensional objects including cylinders and right prisms. (Solutions should not require students to take square roots or cube roots. For example, given the volume of a cylinder and the area of the base, students would identify the height.)
Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
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
Surface and Lateral Areas of Pyramids and Cones
7.SP.1: Use statistics to gain information about a population by examining a sample of the population;
Polling: City
Polling: Neighborhood
Populations and Samples
7.SP.1a: Know that generalizations about a population from a sample are valid only if the sample is representative of that population and generate a valid representative sample of a population.
Polling: City
Polling: Neighborhood
Populations and Samples
7.SP.1b: Identify if a particular random sample would be representative of a population and justify your reasoning.
Polling: City
Polling: Neighborhood
Populations and Samples
7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to informally gauge the variation in estimates or predictions.
Polling: City
Polling: Neighborhood
Populations and Samples
7.SP.3: 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 (requires introduction of mean absolute deviation).
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
7.SP.4: Use measures of center (mean, median and/or mode) and measures of variability (range, interquartile range and/or mean absolute deviation) for numerical data from random samples to draw informal comparative inferences about two populations.
Box-and-Whisker Plots
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
7.SP.5: Express the probability of a chance event as a number between 0 and 1 that represents the likelihood of the event occurring. (Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.)
Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability
7.SP.6: Collect data from a chance process (probability experiment). Approximate the probability by observing its long-run relative frequency. Recognize that as the number of trials increase, the experimental probability approaches the theoretical probability. Conversely, predict the approximate relative frequency given the probability.
Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability
7.SP.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
7.SP.7a: 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
7.SP.7b: 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
7.SP.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
7.SP.8a: Know that, just as with simple events, 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
7.SP.8b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g. “rolling double sixes”), identify the outcomes in the sample space which compose the event.
7.SP.8c: Design and use a simulation to generate frequencies for compound events.
Independent and Dependent Events
Correlation last revised: 9/15/2020