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Common Core Mapping for Grade 7

In Grade 7, instructional time should focus on four critical areas
(1) developing understanding of and applying proportional relationships
(2) developing understanding of operations with rational numbers and working with expressions and linear equations
(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume
(4) drawing inferences about populations based on samples.

Related Topics:
Common Core Lesson Plans and Worksheets for Grade 7
Common Core for Mathematics

Ratios and Proportional Relationships





Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Unit Rates

Ratio of Fractions

Rate Problems

Rate problems

Ratio Games


Recognize and represent proportional relationships between quantities.

See Below



Decide 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.

Proportional Relationship

Rates and Proportions

Analyzing and identifying proportional relationships

Proportional Relationships

Ratio Games


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

Constant of Proportionality

Unit Rate

Rate problems

Constant of Proportionality

Ratio Games


Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Equations of Proportional Relationships


Proportional Relationships Word Problems

Constructing and comparing proportional relationships

Ratio Games


Explain what a point (xy) 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.

Graphs of Proportional Relationships


Graphs of Proportional Relationships

Ratio Games


Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Ratio & Percent Problems

Multi-Step Ratio Problems

MultiStep Word Problems

Percent Error & Percent Increase

Commissions, Fees & Tax

Simple Interest

Constructing proportions


Writing proportions

Ratio Games

The Number System





Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Adding Integers using the Number Lines


Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Opposite Quantities

Opposite Quantities

Understanding addition and subtraction with negative numbers


Understand 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. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Add Rational Numbers

Add Integers

Subtract Rational Numbers

Distance between Rational Numbers

Add negative numbers

Add & subtract negative numbers

Add & subtract fractions

Integer Worksheets


Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (- q). 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.

Subtract Rational Numbers

Add and Subtract Rational Numbers

Subtract Integers

Add & Subtract Integers


Apply properties of operations as strategies to add and subtract rational numbers.

Add & Subtract Rational Numbers

Add & Subtract Integers


Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

See Below


Understand that multiplication is extended from fractions to 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. Interpret products of rational numbers by describing real-world contexts.

Multiply Rational Numbers

Multiply Integers

Multiplying fractions


Understand 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. If p and q are integers, then -(p/q) = (- p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

Divide Rational Numbers

Divide Integers

Dividing positive and negative fractions


Apply properties of operations as strategies to multiply and divide rational numbers.

Multiply Divide Rational Numbers

Integers (Mixed Operations)


Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Rational Numbers and Decimals

Convert a rational number to a decimal

Convert fractions to decimals

Convert decimals to fractions


Solve real-world and mathematical problems involving the four operations with rational numbers.

Rational Number Word Problems

Operations with rational numbers

Rational number word problems

Expressions and Equations





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

Linear Expressions

Combine like terms

Combine like terms with distribution

Manipulate linear expressions with rational coefficients

Algebra Games


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. For example, a + 0.05a = 1.05a means that ԩncrease by 5%ԍ is the same as ԭultiply by 1.05.Լ/em>

Rewrite Expressions

Interpreting linear expressions

Algebra Games


Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. 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. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

MultiStep Word Problems

Average word problems

Discount, tax, and tip word problems

Markup and commission word problems

Multistep equations without variables

Word Problems

Algebra Games


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.

See Below


Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where pq, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Equation Word Problems

Algebra Worksheets

2-step equations

Linear equation word problems

Algebra Games


Solve word problems leading to inequalities of the form px + q > r or px + q < r, where pq, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Inequality Word Problems

Solving & graphing linear inequalities

One step inequalities

Linear equation and inequality word problems

Algebra Games






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.

Scale Drawings

Scale Drawings, Ratios and Rates

Constructing scale drawings

Interpreting scale drawings

Similarity Games


Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Construct Shapes

Constructing triangles

Geometric Shapes with given conditions


Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Slicing 3D Shapes

Understand 3-D Figures

Slicing 3D figures


Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Area & Circumference of Circles

Area of Circle

Area & Circumference Problems

Area & Circumference of Circles

Area of a circle

Circumference of a Circle


Circle Games


Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Find Angles

Find Unknown Angles

Solve for Unknown Angles using Equations

Complementary & supplementary angles

Quadrilateral angles

Solving for unknown angles

Vertical angles

Angle Games


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, Volume & Surface Area

Composite Shapes

Real World Area Problems

Real-World Volume Problems

Area, volume & surface area

Word Problems

Solid Geometry

Geometry Games

Statistics and Probability





Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Random Sampling

Valid claims

Understand Random Sampling

Statistics Games


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 gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Make Inferences from Data

Variation in Samples

Make Inferences from Data

Statistics Games


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. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Measures of Variability

Assessing Overlapping Data Sets

Comparing populations


Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Measures of Central Tendency & Variability

Measures of Center & Variability

Comparing populations


Understand that the probability of a chance event is a number between 0 and 1 that expresses 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.

Probability of an Event

Chance Experiments

Understanding probability

Probability of an Event

Probability Games


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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Probability & Frequency

Approximating Probabilities

Finding probability

Probability of Chance Events

Probability Games


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.

See Below


Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Probability Models

Chance Experiments - Equally Likely


Probability models

Creating Probability Models

Probability Games


Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

See Below


Understand 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.

Compound Probability

Compound events

Dependent probability

Probability Games


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., polling double sixes, identify the outcomes in the sample space which compose the event.

Probability (Sample Space)

Probability space

Sample spaces for compound events


Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Probability (Counting Principle)

Probability of Compound Events

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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