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 threedimensional 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
Code 
Standard 
Lessons 
Worksheets 
Games 
7.RP.A.1 
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. 

7.RP.A.2 
Recognize and represent proportional relationships between quantities. 
See Below 

7.RP.A.2a 
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. 
Analyzing and identifying proportional
relationships 

7.RP.A.2b 
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 

7.RP.A.2c 
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. 
Proportional Relationships Word Problems 

7.RP.A.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.A.3 
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. 
MultiStep Word Problems 
Code 
Standard 
Lessons 
Worksheets 
Games 
7.NS.A.1 
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. 


7.NS.A.1a 
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. 
Understanding addition and subtraction with negative numbers 

7.NS.A.1b 
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 realworld contexts. 
Add
Rational Numbers 
Add
negative numbers 

7.NS.A.1c 
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 realworld contexts. 

7.NS.A.1d 
Apply properties of operations as strategies to add and subtract rational numbers. 

7.NS.A.2 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 
See Below 

7.NS.A.2a 
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 realworld contexts. 

7.NS.A.2b 
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero 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 realworld contexts. 

7.NS.A.2c 
Apply properties of operations as strategies to multiply and divide rational numbers. 

7.NS.A.2d 
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 

7.NS.A.3 
Solve realworld and mathematical problems involving the four operations with rational numbers. 
Operations with rational numbers 
Code 
Standard 
Lessons 
Worksheets 
Games 
7.EE.A.1 
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 
Combine like terms 

7.EE.A.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. For example, a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05. 

7.EE.B.3 
Solve multistep reallife 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. 
Average word problems 

7.EE.B.4 
Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 
See Below 


7.EE.B.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. 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? 
Algebra Worksheets 

7.EE.B.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. 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. 
Solving & graphing linear
inequalities 
Code 
Standard 
Lessons 
Worksheets 
Games 
7.G.A.1 
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. 

7.G.A.2 
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. 
Constructing triangles 

7.G.A.3 
Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 

7.G.B.4 
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 & Circumference of Circles 

7.G.B.5 
Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. 
Find
Angles 
Complementary & supplementary angles 

7.G.B.6 
Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 
Area,
Volume & Surface Area 
Code 
Standard 
Lessons 
Worksheets 
Games 
7.SP.A.1 
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. 

7.SP.A.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 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. 

7.SP.B.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. 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. 

7.SP.B.4 
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 seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book. 

7.SP.C.5 
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. 

7.SP.C.6 
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun 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. 

7.SP.C.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. 
See Below 

7.SP.C.7a 
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. 

7.SP.C.8 
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 
See Below 

7.SP.C.8a 
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. 

7.SP.C.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.C.8c 
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? 