> y <bjbj 7{{4LLLLL````t`$@$d!\LLLcccRLLcccc 3M12c0$cr!cr!ccr!Lcc$r!: Grade 7How will we assess this?Related textbook pages Related additional resources and activitiesRatios and Proportional Relationships (7.RP)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 (7.NS) 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 real-world
contexts.
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 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 by
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 and Equations (7.EE) 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 inequalities 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.Geometry (7.G)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.
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 and Probability (7.SP)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 ina 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 fourth-grade science book.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?
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