Mathematics, Grade 7, 2015


1.) Compute unit rates associated with ratios of
fractions, including ratios of lengths, areas, and other quantities
measured in like or different units. [7RP1]

2.) Recognize and represent proportional relationships between quantities. [7RP2]
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. [7RP2a]
b. Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships. [7RP2b]
c. Represent proportional relationships by equations. [7RP2c]
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. [7RP2d]

3.) Use proportional relationships to solve multistep ratio and percent problems. [7RP3]
Examples: Sample problems may involve simple
interest, tax, markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, and percent error.



4.) 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. [7NS1]
a. Describe situations in which opposite quantities combine to make 0. [7NS1a]
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. [7NS1b]
c. 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. [7NS1c]
d. Apply properties of operations as strategies to add and subtract rational numbers. [7NS1d]

5.) Apply and extend previous understandings of
multiplication and division and of fractions to multiply and divide
rational numbers. [7NS2]
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 by
describing realworld contexts. [7NS2a]
b. 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. [7NS2b]
c. Apply properties of operations as strategies to multiply and divide rational numbers. [7NS2c]
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. [7NS2d]

6.) Solve realworld and mathematical problems
involving the four operations with rational numbers. (Computations with
rational numbers extend the rules for manipulating fractions to complex
fractions.) [7NS3]



7.) Apply properties of operations as strategies to
add, subtract, factor, and expand linear expressions with rational
coefficients. [7EE1]

8.) 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. [7EE2]
Example: a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."



9.) 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. [7EE3]
Examples: 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.

10.) 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.
[7EE4]
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.
[7EE4a]
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. [7EE4b]
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.



11.) 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.
[7G1]

12.) 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. [7G2]

13.) Describe the twodimensional figures that result
from slicing threedimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids. [7G3]



14.) 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.
[7G4]

15.) 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. [7G5]

16.) 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. [7G6]



17.) 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. [7SP1]

18.) 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. [7SP2]
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.



19.) 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. [7SP3]
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.

20.) Use measures of center and measures of
variability for numerical data from random samples to draw informal
comparative inferences about two populations. [7SP4]
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.



21.) 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. [7SP5]

22.) 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. [7SP6]
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.

23.) 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. [7SP7]
a. Develop a uniform probability model by assigning
equal probability to all outcomes, and use the model to determine
probabilities of events. [7SP7a]
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. [7SP7b]
Example: Find the approximate probability that a
spinning penny will land heads up or that a tossed paper cup will land
openend down. Do the outcomes for the spinning penny appear to be
equally likely based on the observed frequencies'

24.) Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
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. [7SP8a]
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.
[7SP8b]
c. Design and use a simulation to generate frequencies for compound events. [7SP8c]
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'
