Download Mathematics Grade 7

Teacher:
CORE Math Grade 7
Year: 2014-15
Month: All
Months
Course: Math Grade 7
Ratios and Rates ~
7th Grade - Topic 1
Standards
Essential Questions
7.RP.1-Compute unit rates
associated with ratios of
fractions, including ratios of
lengths, areas and other
quantities measured in like or
different units.
What does it mean if two different Teacher created
ratios describe the same situation? quizzes 9/30/2014
How can being able to describe the Teacher created
situation in multiple ways help you totests 9/30/2014
solve problems?
Midterm Exam
How can you identify a rate? How 9/30/2014
can unit rates help you to solve
Pennsylvania State
problems?
Standardized
How can you write a ratio if at least Assessment
one term is a fraction? How is this 9/30/2014
different from writing a ratio in which Final Exam
both terms are whole numbers?
9/30/2014
How can you write a unit rate if at
least one term is a fraction? How is
this different from writing a unit rate
when both terms are whole
numbers?
Proportional Relationships ~
Standards
Assessments Skills
write equivalent ratios (1-1)
compute unit rates and determine best buy (1-2)
write equivalent ratios with fractions (1-3)
Content
Lessons
ratio
terms of a ratio
equivalent ratio
rate
unit rate
unit price
Resources
Approved Digits
Content
supplemental
resources
manipulatives
Scientific
calculators
compute unit rates with fractions (1-4)
7th Grade - Topic 2
Essential Questions
Assessments Skills
7.RP.2-Recognize and
What does it mean for two quantities Teacher created
represent proportional
to have a proportional relationship? quizzes 9/30/2014
relationships between quantities. How can you
Teacher created
7.RP.2a-Decide whether two
tell if a table shows a proportional tests 9/30/2014
quantities are in a proportional relationship between two quantities? Midterm Exam
relationship, e.g., by testing for How can you tell if a graph shows a 9/30/2014
equivalent ratios in a table or
proportional relationship between
Pennsylvania State
graphing on a coordinate plane two quantities?
Standardized
and observing whether the
What is a constant of
Assessment
graph is a straight line through proportionality? What does the
9/30/2014
the origin.
constant of proportionality tell you? Final Exam
7.RP.2b-Identify the constant of How can you tell if an equation
9/30/2014
proportionality (unit rate) in
shows a proportional relationship
tables, graphs, equations,
between two quantities? How can
diagrams, and verbal
you identify the constant of
descriptions of proportional
proportionality in an equation that
relationships.
represents a proportional
7.RP.2c-Represent proportional relationship?
relationships by equations.
How can you use proportional
7.RP.2d-Explain what a point (x, relationships to solve problems that
y) on the graph of a proportional involve maps and scale drawings?
relationship means in terms of
the situation, with special
attention to the points (0, 0) and
(1, r) where r is the unit rate.
determine if a relationship is proportional (2-1)
Content
proportional
relationship
Decide whether two quantities are in a proportional proportion
relationship by graphing on a coordinate plane and
scale
observing whether the graph is a straight line through scale drawing
the origin.(2-2)
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. (2-2 and 2-3)
Identify the constant of proportionality (unit rate) in
tables, graphs, equations, diagrams and verbal
descriptions of proportional relationships. (2-3 and 24)
write equations representing proportional
relationships and use them to answer questions. (2-4)
write and use a proportion to answer questions. (2-4)
use scaled maps and drawings to solve problems (25)
determine the scale on a map or drawing (2-5)
Lessons
Resources
Approved Digits
Content
supplemental
resources
manipulatives
Scientific
calculators
Percents ~
7th Grade - Topic 3
Standards
Essential
Assessments Skills
Questions
7.RP.3-Use proportional relationships to
solve multistep ratio and percent problems.
7.RP.2c-Represent proportional
relationships by equations.
7.RP.2-Recognize and represent
proportional relationships between
quantities.
7.RP.2b-Identify the constant of
proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal
descriptions of proportional relationships.
Adding and Subtracting Rational Numbers ~
Teacher created
quizzes 10/31/2014
Teacher Created Test
10/31/2014
PSSA 10/31/2014
Content
determine each part (part, percent, whole) of a percent
equation (3-1)
determine if a statement involving percents is true or
false (3-1)
solve percent equations (3-1)
solve real world percent problems, including discount,
tax, tip, and commission (3-1 and 3-2)
identify the principal, interest rate, time, and interest of
a simple interest problem (3-3)
solve simple interest problems (3-3)
Lessons
Resources
percent equation
simple interest
percent increase and
decrease
7th Grade - Topic 4
Standards
7.NS.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.1a-Describe situations in which opposite quantities
combine to make 0.
7.NS.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 real-world contexts.
7.NS.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
real-world contexts.
7.NS.1d-Apply properties of operations as strategies to add
and subtract rational numbers.
Essential
Assessments Skills
Questions
Content
categorize numbers (whole, integers, rational numbers, opposites
rational numbers) (4-1)
and absolute value
order numbers (4-1)
adding integers
represent a situation using positive and adding rational numbers
negative numbers (4-1)
subtracting integers
state the opposite of a number (4-1) subtracting rational numbers
describe an addition problem as
calculating distance on a
movement on a number line to
number line
determine the answer (4-2)
determine if the value of an expression
is "less than, equal to, or greater than
0" (4-2 and 4-5)
write and simplify an addition
expression using integer tokens (4-2)
identify properties of addition
(commutative, associative, inverse,
identity, zero) (4-3)
add rational numbers (4-2 and 4-3)
write and simplify an expression to
model a situation (4-3 to 4-5)
write equivalent subtraction and
addition expressions for a number line
model (4-4 and 4-5)
rewrite a subtraction expression into
an equivalent addition expression and
simplify (4-4)
Lessons Resources
Multiplying and Dividing Rational Numbers ~
7th Grade - Topic 5
Essential
Assessments Skills
Questions
Standards
7.NS.2-Apply and extend previous understandings of
multiplication and division and of fractions to multiply and divide
rational numbers.
7.NS.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 real-world contexts.
7.NS.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 real-world contexts.
7.NS.2c-Apply properties of operations as strategies to multiply
and divide rational numbers.
Decimals and Percents ~
identify if a product is positive or
negative (5-2)
multiply rational numbers (5-2)
solve real world problems (5-2 to 5-4)
determine if quotients are positive or
negative (5-3)
divide integers (5-3)
identify the reciprocal of a number (54)
rewrite a problem involving division of
fractions as multiplication of fractions
(5-4)
Lessons Resources
multiplying integers
multiplying rational numbers
dividing integers
dividing rational numbers
operations with rational
numbers
7th Grade - Topic 6
Essential
Assessments Skills
Questions
Standards
7.NS.3-Solve real-world and mathematical problems
involving the four operations with rational numbers.
7.NS.2b-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.
7.NS.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.
7.RP.3-Use proportional relationships to solve multistep ratio
and percent problems.
Equivalent Expressions ~
multiply integers (5-1)
identify equivalent products (5-1)
Content
Content
Lessons Resources
convert mixed numbers, fractions,
repeating decimals
percents, and decimals (3-1, 3-2, and 3- terminating decimals
5)
percents greater than
identify decimals as repeating or
100
terminating (3-1 and 3-2)
percents less than 1
determine if a fraction can be written as afractions, decimals and
terminating decimal (3-2)
percents
calculate using percents, including real
world problems (3-3 to 3-5)
calculate the percent error (3-6)
7th Grade - Topic 7
Standards
7.EE.1-Apply properties of operations as strategies to add,
subtract, factor, and expand linear expressions with rational
coefficients.
7.EE.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.
Essential
Assessments Skills
Questions
determine if an expression can be
written in expanded form (10-1)
write an expression in expanded
form (10-1)
write an expression in factored form
(10-2)
simplify expressions by combining
like terms (10-2 to 10-4)
Content
Lessons Resources
Equations ~
7th Grade- Topic 8
Essential
Assessments Skills
Questions
Standards
7.EE.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.
7.EE.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.
7.EE.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.
Inequalities ~
Lessons Resources
solve one-step equations (8-1)
translate a situation into a mathematical
equation using a variable for the unknown
(8-2 to 8-4)
solve two step equations (8-3)
solve equations using the distributive
property (8-4)
7th Grade- Topic 9
Standards
7.G.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.
Angles ~
Content
Essential
Assessments Skills
Questions
Content
Lessons Resources
Content
Lessons Resources
represent a statement with an inequality symbol (13-1)
write, solve, and graph an inequality (13-1 to 13-4)
7th Grade- Topic 10
Standards
7.EE.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.
7.EE.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.
7.G.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.
7.G.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.
Essential
Assessments Skills
Questions
measure angles using a protractor (10-1)
classify angles (10-1)
calculate angle measures using algebra (10-1)
name adjacent angles (10-2)
calculate angle measures (10-2)
calculate the complement of a given angle (10-3)
name complementary angles (10-3)
calculate the angle measures of complementary angles
using algebra (10-3)
name supplementary angles (10-4)
calculate angle measures of supplementary angles (10-4)
name vertical angles (10-5)
calculate angle measures of vertical angles (10-5)
name alternate interior, alternate exterior, and
corresponding angles
calculate angle measures when parallel lines are cut by a
transversal.
Probability Concepts ~
Accelerated 7th Digits- Topic 17
Standards
Essential
Assessments Skills
Questions
7.SP.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.
7.SP.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.
7.SP.8-Find probabilities of compound events using
organized lists, tables, tree diagrams, and
simulation.
7.SP.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.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.8c-Design and use a simulation to generate
frequencies for compound events.
Circles ~
Content
Lessons Resources
determine if a situation is impossible, unlikely, as likely as
not, likely, and certain (17-1)
write a probability as a fraction and percent (17-1)
use probability to make calculations (17-1)
determine the number of outcomes in a sample space
(17-2)
determine the number in the event (17-2)
determine the action, sample space, and the event (17-2)
calculate the relative frequency for an event (17-3)
write the experimental probability as a fraction, decimal,
and percent (17-3)
calculate the theoretical probability (17-4)
determine if a situation represents experimental or
theoretical probability (17-4)
complete a probability model for a given situation (17-5)
7th Grade - Topic 11
Standards
7.EE.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.
7.EE.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.
7.G.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.
7.G.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.
Essential
Questions
Assessments Skills
identify radii, diameter, and center of a
circle (11-1)
calculate the length of the radius or
diameter of a circle, including problems
that require algebra (11-2)
calculate the circumference of a circle
(11-2)
calculate the area of a circle (11-3)
Content
Lessons Resources
2- and 3-Dimensional Shapes ~
7th Grade - Topic 12
Essential
Questions
Standards
7.G.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.
7.G.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.
7.G.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.
Surface Area and Volume ~
Content
Lessons Resources
draw geometric shapes with given
conditions (21-1 to 21-3)
determine if their drawing is unique, not
unique, or not possible when given
conditions (21-2 and 21-3)
draw or state the dimensions of a cross
section of a right rectangular prism (21-4)
describe the shape, state the dimensions,
or compare the area of a cross section of
a right rectangular pyramid (21-5)
7th Grade -Topic 13
Essential
Questions
Standards
7.G.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.
Sampling ~
Assessments Skills
Assessments Skills
Content
Lessons Resources
Content
Lessons Resources
calculate the surface area of right prisms (221)
calculate the volume of right prisms (22-2)
calculate the surface area of right pyramids
(22-3)
calculate the volume of right pyramids (22-4)
7th Grade - Topic 14
Standards
7.SP.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.3-Informally assess the degree of visual overlap
of two numerical data distributions with similar
variability, measuring the difference between the
centers by expressing it as a multiple of a measure of
variability.
7.SP.4-Use measures of center and measures of
variability for numerical data from random samples to
draw informal comparative inferences about two
populations.
Essential
Questions
Assessments Skills
determine the sample of a given situation
(15-1)
determine if a sample is likely to contain a
bias (15-1)
estimate a population in a given situation (152, 15-4, 15-5)
determine if a sampling is a convenience,
representative, systematic , or simple
random sample (15-3 to 15-6)
Comparing Two Populations ~
7th Grade - Topic 15
Essential
Assessments Skills
Questions
Standards
7.SP.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.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.
7.SP.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.
7.SP.7a-Develop a uniform probability model by assigning equal probability to
all outcomes, and use the model to determine probabilities of events.
7.SP.7b-Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process.
Probability Concepts ~
Content Lessons Resources
calculate the mean, median, range,
and interquartile range of a data set
(16-1, 16-3, 16-4)
determine if a situation applies to a
single population or a multiple
population (16-2)
determine if an inference is valid (16-2)
calculate the mean average deviation
(16-5)
7th Grade - Topic 16
Standards
7.SP.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.
7.SP.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.
7.SP.8-Find probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
7.SP.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.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.8c-Design and use a simulation to generate frequencies for compound
events.
Essential
Assessments Skills
Questions
determine if a situation is impossible,
unlikely, as likely as not, likely, and
certain (17-1)
write a probability as a fraction and
percent (17-1)
use probability to make calculations
(17-1)
determine the number of outcomes in
a sample space (17-2)
determine the number in the event (172)
determine the action, sample space,
and the event (17-2)
calculate the relative frequency for an
event (17-3)
write the experimental probability as a
fraction, decimal, and percent (17-3)
calculate the theoretical probability
(17-4)
determine if a situation represents
experimental or theoretical probability
(17-4)
complete a probability model for a
given situation (17-5)
Content Lessons Resources
Compound Events ~
7th Grade - Topic 17
Standards
7.SP.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.
7.SP.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.
7.SP.8-Find probabilities of compound events using organized
lists, tables, tree diagrams, and simulation.
7.SP.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.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.8c-Design and use a simulation to generate frequencies for
compound events.
Essential
Questions
Assessments Skills
determine the number of steps or choices
of an action (18-1 and 18-3)
determine if an event is dependent or
independent (18-1)
determine the number of possible
combinations of a given situation,
including the use of a tree diagram (18-2)
display all the possible outcomes of a
situation using a table (18-3)
calculate the probability of compound
events (18-4)
calculate the probability using simulations
(18-5 and 18-6)
Content Lessons
Resources