• Seventh Grade Common Core Learning Standards
MATH

Ratios & Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.

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.
2. Recognize and represent proportional relationships between quantities.
a. 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.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships.
c. 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.
d. 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.
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.

The Number System
Apply and extend previous understandings of operations with fractions to add, subtract,
multiply, and divide rational numbers.

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.
a. 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.
b. 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.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).
Show that the between two rational numbers on the number line is the absolute value of their
difference, and this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
2. Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
a. 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 describing real-world contexts.
b. 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.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. 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.
3. Solve real-world and mathematical problems involving the four operations with rational numbers.
.
Expressions & Equations
Use properties of operations to generate equivalent expressions.

1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions
with rational coefficients.
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.”
Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
3. 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.
4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple
equations and to solve problems by reasoning about the quantities.
a. 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?
b. 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.
as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

Geometry
Draw construct, and describe geometrical figures and describe the relationships between them.

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.
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.
3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane
sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical
problems involving angle measure, area, surface area, and volume.
Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
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.
5. 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.
6. 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.

Statistics & Probability
Use random sampling to draw inferences about a population.

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.
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.
Draw informal comparative inferences about two populations.
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.
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 seventh grade science book are generally longer than the words in a chapter of a
Investigate chance processes and develop, use, and evaluate probability models.
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.
6. 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.
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.
a. 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.
b. 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?
8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. 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.
b. 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.
c. 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?

Measurement & Data 2.MD
Measure and estimate lengths in standard units.

1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the
two measurements relate to the size of the unit chosen.
3. Estimate lengths using units of inches, feet, centimeters, and meters.
4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard
length unit.
Relate addition and subtraction to length.
5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by
using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the
numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
Work with time and money.
7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately.
Example: If you have 2 dimes and 3 pennies, how many cents do you have?
Represent and interpret data.
9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated
measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in
whole-number units.
10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve
simple put-together, take-apart, and compare problems1 using information presented in a bar graph.
_________________
1 See Glossary, Table 1.
Geometry 2.G
Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half
of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical
wholes need not have the same shape.
_________________
1 Sizes are compared directly or visually, not compared by measuring.