# Think Through Math CCSS 6th Grade Pathway

```Think Through Math CCSS 6th Grade Pathway
Topic               Objective                               Common Core                       Kentucky
Solving and        Solve word problems,      7.EE.B.4a: Solve real-life and mathematical
Modeling Two-      both algebraically and    problems using numerical and algebraic
Step Problems      arithmetically, leading   expressions and equations. Use variables to
to equations of the       represent quantities in a real-world or
form px + q = r.          mathematical problem, and construct simple
equations and inequalities to solve problems by
reasoning about the quantities. 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?
Solving            Apply the distributive    7.EE.B.4a: Solve real-life and mathematical
Equations with     property when solving     problems using numerical and algebraic
the Distributive   equations.                expressions and equations. Use variables to
Property                                     represent quantities in a real-world or
mathematical problem, and construct simple
equations and inequalities to solve problems by
reasoning about the quantities. 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?```
```Solving            Use the distributive      7.EE.B.4a: Solve real-life and mathematical
Equations with     property to solve         problems using numerical and algebraic
the Distributive   problems.                 expressions and equations. Use variables to
Property in                                  represent quantities in a real-world or
Context                                      mathematical problem, and construct simple
equations and inequalities to solve problems by
reasoning about the quantities. 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?
Interpreting       Identify a unit rate      7.RP.A.2b: Analyze proportional relationships and
Unit Rates on      from a graph,             use them to solve real-world and mathematical
Graphs             especially dealing with   problems. Recognize and represent proportional
ratios of fractions.      relationships between quantities. Identify the
constant of proportionality (unit rate) in tables,
graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
Proportion         Recognize and             7.RP.A.2a: Analyze proportional relationships and
Concepts           represent                 use them to solve real-world and mathematical
proportional              problems. Recognize and represent proportional
relationships in          relationships between quantities. Decide whether
different ways,           two quantities are in a proportional relationship,
including graphs.         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.
7.RP.A.2c: Analyze proportional relationships and
use them to solve real-world and mathematical
problems. Recognize and represent proportional```
```relationships between quantities. 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       Represent                  7.RP.A.2a: Analyze proportional relationships and
Relationships in   proportional               use them to solve real-world and mathematical
Tables and         relationships in tables    problems. Recognize and represent proportional
Equations          and equations.             relationships between quantities. 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.
7.RP.A.2c: Analyze proportional relationships and
use them to solve real-world and mathematical
problems. Recognize and represent proportional
relationships between quantities. 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.
Interpreting       Explain what a point       7.RP.A.2d: Analyze proportional relationships and
Points on          on the graph of a          use them to solve real-world and mathematical
Graphs of          proportional               problems. Recognize and represent proportional
Proportional       relationship means in      relationships between quantities. Explain what a
Relationships      context, especially (0,    point (x, y) on the graph of a proportional
0) and (1, r) where r is   relationship means in terms of the situation, with
the unit rate.             special attention to the points (0, 0) and (1, r)
where r is the unit rate.
7.RP.A.1: Analyze proportional relationships and
use them to solve real-world and mathematical```
```problems. 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.
Using             Analyze proportional     7.G.A.1: Draw, construct, and describe geometrical
Proportions to    relationships and use    figures and describe the relationships between
Solve Problems    them to solve real-      them. Solve problems involving scale drawings of
world, multistep ratio   geometric figures, including computing actual
problems.                lengths and areas from a scale drawing and
reproducing a scale drawing at a different scale.
7.RP.A.3: Analyze proportional relationships and
use them to solve real-world and mathematical
problems. 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.
Proportions in    Solve problems           7.G.A.1: Draw, construct, and describe geometrical
Scale Drawings    involving scale          figures and describe the relationships between
drawings of geometric    them. Solve problems involving scale drawings of
figures, including       geometric figures, including computing actual
computing actual         lengths and areas from a scale drawing and
lengths and areas        reproducing a scale drawing at a different scale.
from a scale drawing     7.RP.A.3: Analyze proportional relationships and
and reproducing a        use them to solve real-world and mathematical
scale drawing at a       problems. Use proportional relationships to solve
different scale.         multistep ratio and percent problems. Examples:
simple interest, tax, markups and markdowns,
gratuities and commissions, fees, percent increase
and decrease, percent error.
Introduction of   Recognize and apply      7.G.A.1: Draw, construct, and describe geometrical```
```Similar Figures    properties of similar     figures and describe the relationships between
figures.                  them. 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.RP.A.2c: Analyze proportional relationships and
use them to solve real-world and mathematical
problems. Recognize and represent proportional
relationships between quantities. 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.
Use Similar        Use proportional          7.G.A.1: Draw, construct, and describe geometrical
Figures to Solve   reasoning and the         figures and describe the relationships between
Problems           properties of similar     them. Solve problems involving scale drawings of
figures to find the       geometric figures, including computing actual
missing side length in    lengths and areas from a scale drawing and
a figure.                 reproducing a scale drawing at a different scale.
7.RP.A.2c: Analyze proportional relationships and
use them to solve real-world and mathematical
problems. Recognize and represent proportional
relationships between quantities. 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.
Similarity         Generalize the critical   7.G.A.1: Draw, construct, and describe geometrical
attributes of             figures and describe the relationships between
similarity.               them. 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.
Fraction,      Recognize that           7.EE.B.3: Solve real-life and mathematical            MA-6-NPO-S-E1: Students will: estimate and
Decimal, and   fractions, decimals      problems using numerical and algebraic                mentally compute to solve real-world and/or
Percent        (that have a finite or   expressions and equations. Solve multi-step real-     mathematical problems with whole numbers,
Equivalents    repeating decimal        life and mathematical problems posed with             fractions, decimals and percents, checking for
representation), and     positive and negative rational numbers in any         reasonable and appropriate computational
percents are different   form (whole numbers, fractions, and decimals),        results
representations of       using tools strategically. Apply properties of        MA-6-NPO-S-NS1: Students will: continue to
rational numbers.        operations to calculate with numbers in any form;     develop number sense using fractions,
convert between forms as appropriate; and assess      decimals and percents, including percents
the reasonableness of answers using mental            greater than 100% and improper fractions
computation and estimation strategies. For            MA-7-NPO-S-NO2: Students will: extend
example: If a woman making \$25 an hour gets a         concepts and application of operations with
10% raise, she will make an additional 1/10 of her    fractions and decimals to include percents
salary an hour, or \$2.50, for a new salary of         MA-6-NPO-S-NS5: Students will: compare,
\$27.50. If you want to place a towel bar 9 3/4        order and convert between whole numbers,
inches long in the center of a door that is 27 1/2    fractions, decimals and percents using
inches wide, you will need to place the bar about 9   concrete materials, drawings or pictures and
inches from each edge; this estimate can be used      mathematical symbols (e.g., , "greater than or equal to", =, "not
equal to", order on a number line)
MA-5-NPO-S-NS5: Students will: explore,
investigate, compare, relate and apply
relationships among whole numbers,
fractions, decimals and percents
MA-7-NPO-S-E1: Students will: estimate and
mentally compute to solve real-world and/or
mathematical problems with fractions,
decimals, percents and integers, checking for
reasonable and appropriate computational
results
MA-7-NPO-S-NS5: Students will: compare,
order and determine equivalent relationships
among fractions, decimals and percents```
```Percent and       Use proportional         7.RP.A.3: Analyze proportional relationships and
Percent Change    relationships to solve   use them to solve real-world and mathematical
multistep percent and    problems. Use proportional relationships to solve
percent change           multistep ratio and percent problems. Examples:
problems.                simple interest, tax, markups and markdowns,
gratuities and commissions, fees, percent increase
and decrease, percent error.
Percent and       Use proportional         7.RP.A.3: Analyze proportional relationships and
Percent Error     relationships to solve   use them to solve real-world and mathematical
multistep percent        problems. Use proportional relationships to solve
change and percent       multistep ratio and percent problems. Examples:
error problems.          simple interest, tax, markups and markdowns,
gratuities and commissions, fees, percent increase
and decrease, percent error.
Simple Interest   Solve problems using     7.RP.A.3: Analyze proportional relationships and     MA-8-NPO-S-RP1: Students will: use
simple interest          use them to solve real-world and mathematical        percentages and proportions in problem
formulas.                problems. Use proportional relationships to solve    solving, including consumer applications (e.g.,
multistep ratio and percent problems. Examples:      simple interest, percentages of increase and
simple interest, tax, markups and markdowns,         decrease, discounts, unit pricing, sale prices)
gratuities and commissions, fees, percent increase   MA-7-AT-S-VEO2: Students will: substitute
and decrease, percent error.                         values for variables to evaluate algebraic
expressions
MA-8-AT-S-VEO2: Students will: given a
formula, substitute appropriate elements from
a real-world or mathematical situation
MA-7-NPO-S-RP1: Students will: compute
percentages and use percentages in
proportional reasoning
MA-7-AT-S-EI2: Students will: solve problems
involving formulas
Adding and        Construct expressions    7.NS.A.1d: Apply and extend previous
Rational          model real-world         and subtract rational numbers; represent addition
Numbers I         situations.              and subtraction on a horizontal or vertical number```
```line diagram. Apply properties of operations as
strategies to add and subtract rational numbers.
7.NS.A.1b: Apply and extend previous
and subtract rational numbers; represent addition
and subtraction on a horizontal or vertical number
line diagram. 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.A.1a: Apply and extend previous
and subtract rational numbers; represent addition
and subtraction on a horizontal or vertical number
line diagram. 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.
Adding and        Construct multiple      7.NS.A.1c: Apply and extend previous
Subtracting       expressions to show a   understandings of addition and subtraction to add
Rational          difference between      and subtract rational numbers; represent addition
Numbers II        two rational numbers.   and subtraction on a horizontal or vertical number
line diagram. 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.
Multiplying and   Learn rules for         7.NS.A.2c: Apply and extend previous
Dividing          multiplying and         understandings of operations with fractions. Apply
Rational          dividing with signed    and extend previous understandings of```
```Numbers   rational numbers. Use   multiplication and division and of fractions to
the distributive        multiply and divide rational numbers. Apply
property to show why    properties of operations as strategies to multiply
the product of a        and divide rational numbers.
positive number and a   7.NS.A.2a: Apply and extend previous
negative number is      understandings of operations with fractions. Apply
negative.               and extend previous understandings of
multiplication and division and of fractions to
multiply and divide rational numbers. 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.A.2d: Apply and extend previous
understandings of operations with fractions. Apply
and extend previous understandings of
multiplication and division and of fractions to
multiply and divide rational numbers. 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.NS.A.2b: Apply and extend previous
understandings of operations with fractions. Apply
and extend previous understandings of
multiplication and division and of fractions to
multiply and divide rational numbers. 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.
Writing and     Interpret signed       7.NS.A.3: Apply and extend previous
Interpreting    rational numbers in    understandings of operations with fractions. Solve
Expressions     context and write      real-world and mathematical problems involving
with Rational   expressions to model   the four operations with rational numbers.
Numbers         situations. Use        7.EE.B.3: Solve real-life and mathematical
multiplication and     problems using numerical and algebraic
division of signed     expressions and equations. Solve multi-step real-
rational numbers in    life and mathematical problems posed with
solving problems.      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.
Operations      Solve real-world and   7.NS.A.3
with Rational   mathematical           Apply and extend previous understandings of
Numbers I       problems involving     operations with fractions. Solve real-world and
the four operations    mathematical problems involving the four
with rational          operations with rational numbers.
numbers.
Operations      Solve real-world and   7.EE.B.3: Solve real-life and mathematical
with Rational   mathematical           problems using numerical and algebraic
Numbers II      problems involving     expressions and equations. Solve multi-step real-```
```the four operations    life and mathematical problems posed with
with rational          positive and negative rational numbers in any
numbers.               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.
Circumference   Find the               7.G.B.4: Solve real-life and mathematical problems    MA-8-M-U-3: Students will understand that:
circumference of a     involving angle measure, area, surface area, and      measurements are determined by using
circle in real-world   volume. Know the formulas for the area and            appropriate techniques, tools, formulas and
and mathematical       circumference of a circle and use them to solve       degree of accuracy needed for the situation.
problems.              problems; give an informal derivation of the          MA-8-M-S-MPA5: Students will: determine the
relationship between the circumference and area       area and circumference of circles
of a circle.                                          MA-7-M-S-MPA6: Students will: explain how
measurements and measurement formulas
are related or different (e.g., perimeter and
area of rectangles)
MA-6-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
MA-6-M-S-MPA1: Students will: find perimeter
of regular and irregular polygons in metric and
U.S. customary units
MA-7-M-S-MPA3: Students will: estimate and```
```find circle measurements in standard units
relationships among them
MA-7-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
Area of Circles   Find the area of a        7.G.B.4: Solve real-life and mathematical problems   MA-8-M-U-3: Students will understand that:
circle, and given the     involving angle measure, area, surface area, and     measurements are determined by using
area, find its diameter   volume. Know the formulas for the area and           appropriate techniques, tools, formulas and
or radius.                circumference of a circle and use them to solve      degree of accuracy needed for the situation.
problems; give an informal derivation of the         MA-8-M-S-MPA9: Students will: explain how
relationship between the circumference and area      measurements and measurement formulas
of a circle.                                         are related or different (perimeter and area;
rate, time and distance; circumference and
area of a circle)
MA-7-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
MA-8-M-S-MPA5: Students will: determine the
area and circumference of circles
MA-7-M-S-MPA3: Students will: estimate and
find circle measurements in standard units
relationships among them
Area of           Find the area of a        7.G.B.6: Solve real-life and mathematical problems   MA-7-M-S-MPA4: Students will: develop and
Complex           figure that is made up    involving angle measure, area, surface area, and     use the formulas for area of a triangle, a
Composite         of more than one          volume. Solve real-world and mathematical            parallelogram and a trapezoid and relate each
Figures           shape.                    problems involving area, volume and surface area     to the formula for the area of a rectangle (b x
of two- and three-dimensional objects composed       h)
of triangles, quadrilaterals, polygons, cubes, and   MA-7-M-S-MPA3: Students will: estimate and
right prisms.                                        find circle measurements in standard units
6.G.A.1: Solve real-world and mathematical           (radius, diameter, circumference, area) and```
```problems involving area, surface area, and           relationships among them
volume. Find the area of right triangles, other      MA-7-M-U-3: Students will understand that:
triangles, special quadrilaterals, and polygons by   measurements are determined by using
composing into rectangles or decomposing into        appropriate techniques, tools, formulas and
triangles and other shapes; apply these techniques   degree of accuracy needed for the situation.
in the context of solving real-world and
mathematical problems.
Surface Area    Find the surface area     7.G.B.6: Solve real-life and mathematical problems   MA-8-G-S-SR3: Students will: compare
and Volume of   of a rectangular prism.   involving angle measure, area, surface area, and     properties of three-dimensional figures
Rectangular     Use the surface area      volume. Solve real-world and mathematical            (spheres, cones, cylinders, prisms, pyramids);
Prisms          of a cube to find one     problems involving area, volume and surface area     apply these properties and figures to solve
of its dimensions.        of two- and three-dimensional objects composed       real-world problems
of triangles, quadrilaterals, polygons, cubes, and   MA-8-M-U-3: Students will understand that:
right prisms.                                        measurements are determined by using
6.G.A.4: Solve real-world and mathematical           appropriate techniques, tools, formulas and
problems involving area, surface area, and           degree of accuracy needed for the situation.
volume. Represent three-dimensional figures          MA-8-AT-S-VEO2: Students will: given a
using nets made up of rectangles and triangles,      formula, substitute appropriate elements from
and use the nets to find the surface area of these   a real-world or mathematical situation
figures. Apply these techniques in the context of    MA-8-M-S-MPA7: Students will: develop and
solving real-world and mathematical problems.        apply formulas for volume and surface area of
6.G.A.2: Solve real-world and mathematical           cubes, cylinders and right rectangular prisms;
problems involving area, surface area, and           investigate relationships between and among
volume. Find the volume of a right rectangular       them
prism with fractional edge lengths by packing it     MA-8-G-U-1: Students will understand that:
with unit cubes of the appropriate unit fraction     characteristics and properties of two-
edge lengths, and show that the volume is the        dimensional figures and three-dimensional
same as would be found by multiplying the edge       objects describe the world and are used to
lengths of the prism. Apply the formulas V = l w h   develop mathematical arguments about
and V = b h to find volumes of right rectangular     geometric relationships and to evaluate the
prisms with fractional edge lengths in the context   arguments of others.
of solving real-world and mathematical problems.     MA-8-AT-S-EI2: Students will: solve problems
using formulas
MA-7-G-S-SR4: Students will: describe, provide```
```examples of and identify elements (e.g.,
vertices, angles, faces, edges, congruent parts)
of common three-dimensional figures
(spheres, cones, cylinders, prisms and
pyramids)
MA-HS-M-S-MPA3: Students will: determine
the surface area and volume of right
rectangular prisms, pyramids, cylinders, cones
and spheres in realistic problems
MA-HS-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
MA-HS-G-S-SR9: Students will: classify and
apply properties of three-dimensional
geometric figures
MA-7-AT-S-EI2: Students will: solve problems
involving formulas
MA-6-G-S-SR5: Students will: describe, provide
examples of and identify properties (e.g.,
vertices, angles, faces, edges, congruent parts)
of common three-dimensional figures
(spheres, cones, cylinders, prisms and
pyramids)
Surface Area of   Find the surface area   7.G.B.6: Solve real-life and mathematical problems   MA-8-G-S-SR3: Students will: compare
Cylinders         of a cylinder.          involving angle measure, area, surface area, and     properties of three-dimensional figures
volume. Solve real-world and mathematical            (spheres, cones, cylinders, prisms, pyramids);
problems involving area, volume and surface area     apply these properties and figures to solve
of two- and three-dimensional objects composed       real-world problems
of triangles, quadrilaterals, polygons, cubes, and   MA-8-AT-S-VEO2: Students will: given a
right prisms.                                        formula, substitute appropriate elements from
7.G.B.4: Solve real-life and mathematical problems   a real-world or mathematical situation
involving angle measure, area, surface area, and     MA-8-AT-S-EI2: Students will: solve problems
volume. Know the formulas for the area and           using formulas```
```circumference of a circle and use them to solve      MA-7-G-S-SR4: Students will: describe, provide
problems; give an informal derivation of the         examples of and identify elements (e.g.,
relationship between the circumference and area      vertices, angles, faces, edges, congruent parts)
of a circle.                                         of common three-dimensional figures
(spheres, cones, cylinders, prisms and
pyramids)
MA-HS-M-S-MPA3: Students will: determine
the surface area and volume of right
rectangular prisms, pyramids, cylinders, cones
and spheres in realistic problems
MA-HS-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
MA-HS-G-S-SR9: Students will: classify and
apply properties of three-dimensional
geometric figures
MA-7-AT-S-EI2: Students will: solve problems
involving formulas
Surface Area of   Find the surface area    7.G.B.6: Solve real-life and mathematical problems   MA-8-G-S-SR3: Students will: compare
Pyramids          of a pyramid. Use the    involving angle measure, area, surface area, and     properties of three-dimensional figures
pyramid’s base and       volume. Solve real-world and mathematical            (spheres, cones, cylinders, prisms, pyramids);
surface-area             problems involving area, volume and surface area     apply these properties and figures to solve
dimensions to find its   of two- and three-dimensional objects composed       real-world problems
slant height.            of triangles, quadrilaterals, polygons, cubes, and   MA-8-AT-S-VEO2: Students will: given a
right prisms.                                        formula, substitute appropriate elements from
6.G.A.4: Solve real-world and mathematical           a real-world or mathematical situation
problems involving area, surface area, and           MA-8-M-S-MPA7: Students will: develop and
volume. Represent three-dimensional figures          apply formulas for volume and surface area of
using nets made up of rectangles and triangles,      cubes, cylinders and right rectangular prisms;
and use the nets to find the surface area of these   investigate relationships between and among
figures. Apply these techniques in the context of    them
solving real-world and mathematical problems.        MA-8-AT-S-EI2: Students will: solve problems
using formulas```
```MA-7-G-S-SR4: Students will: describe, provide
examples of and identify elements (e.g.,
vertices, angles, faces, edges, congruent parts)
of common three-dimensional figures
(spheres, cones, cylinders, prisms and
pyramids)
MA-HS-M-S-MPA3: Students will: determine
the surface area and volume of right
rectangular prisms, pyramids, cylinders, cones
and spheres in realistic problems
MA-HS-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
MA-HS-G-S-SR9: Students will: classify and
apply properties of three-dimensional
geometric figures
MA-7-AT-S-EI2: Students will: solve problems
involving formulas
Surface Area of   Find the surface area   7.G.B.4: Solve real-life and mathematical problems   MA-8-G-S-SR3: Students will: compare
Cones             of a cone.              involving angle measure, area, surface area, and     properties of three-dimensional figures
volume. Know the formulas for the area and           (spheres, cones, cylinders, prisms, pyramids);
circumference of a circle and use them to solve      apply these properties and figures to solve
problems; give an informal derivation of the         real-world problems
relationship between the circumference and area      MA-8-AT-S-VEO2: Students will: given a
of a circle.                                         formula, substitute appropriate elements from
7.G.B.6: Solve real-life and mathematical problems   a real-world or mathematical situation
involving angle measure, area, surface area, and     MA-8-M-S-MPA7: Students will: develop and
volume. Solve real-world and mathematical            apply formulas for volume and surface area of
problems involving area, volume and surface area     cubes, cylinders and right rectangular prisms;
of two- and three-dimensional objects composed       investigate relationships between and among
of triangles, quadrilaterals, polygons, cubes, and   them
right prisms.                                        MA-8-AT-S-EI2: Students will: solve problems
using formulas```
```MA-7-G-S-SR4: Students will: describe, provide
examples of and identify elements (e.g.,
vertices, angles, faces, edges, congruent parts)
of common three-dimensional figures
(spheres, cones, cylinders, prisms and
pyramids)
MA-HS-M-S-MPA3: Students will: determine
the surface area and volume of right
rectangular prisms, pyramids, cylinders, cones
and spheres in realistic problems
MA-HS-M-U-3: Students will understand that:
measurements are determined by using
appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
MA-HS-G-S-SR9: Students will: classify and
apply properties of three-dimensional
geometric figures
MA-7-AT-S-EI2: Students will: solve problems
involving formulas
Surface Area of   Find the surface area     7.G.B.6: Solve real-life and mathematical problems   MA-8-M-U-3: Students will understand that:
Spheres           of a sphere, and, given   involving angle measure, area, surface area, and     measurements are determined by using
the surface area, find    volume. Solve real-world and mathematical            appropriate techniques, tools, formulas and
its diameter or radius.   problems involving area, volume and surface area     degree of accuracy needed for the situation.
of two- and three-dimensional objects composed       MA-8-AT-S-VEO2: Students will: given a
of triangles, quadrilaterals, polygons, cubes, and   formula, substitute appropriate elements from
right prisms.                                        a real-world or mathematical situation
MA-8-AT-S-EI2: Students will: solve problems
using formulas
MA-HS-M-S-MPA3: Students will: determine
the surface area and volume of right
rectangular prisms, pyramids, cylinders, cones
and spheres in realistic problems
MA-HS-M-U-3: Students will understand that:
measurements are determined by using```
```appropriate techniques, tools, formulas and
degree of accuracy needed for the situation.
Surface Area of   Find the surface area    7.G.B.4: Solve real-life and mathematical problems   MA-8-AT-S-VEO2: Students will: given a
Composite         of a shape that is       involving angle measure, area, surface area, and     formula, substitute appropriate elements from
Solids            made up of two or        volume. Know the formulas for the area and           a real-world or mathematical situation
more three-              circumference of a circle and use them to solve      MA-8-M-S-MPA7: Students will: develop and
dimensional shapes.      problems; give an informal derivation of the         apply formulas for volume and surface area of
relationship between the circumference and area      cubes, cylinders and right rectangular prisms;
of a circle.                                         investigate relationships between and among
7.G.B.6: Solve real-life and mathematical problems   them
involving angle measure, area, surface area, and     MA-HS-M-S-MPA3: Students will: determine
volume. Solve real-world and mathematical            the surface area and volume of right
problems involving area, volume and surface area     rectangular prisms, pyramids, cylinders, cones
of two- and three-dimensional objects composed       and spheres in realistic problems
of triangles, quadrilaterals, polygons, cubes, and
right prisms.
Angle Pairs       Find the measures of     7.G.B.5: Solve real-life and mathematical problems   MA-HS-G-S-SR3: Students will: analyze and
complementary,           involving angle measure, area, surface area, and     apply angle relationships (e.g., linear pairs,
supplementary,           volume. Use facts about supplementary,               vertical, complementary, supplementary,
vertical, and adjacent   complementary, vertical, and adjacent angles in a    corresponding and alternate interior angles) in
angles.                  multi-step problem to write and solve simple         real-world or mathematical situations
equations for an unknown angle in a figure.          MA-7-G-S-SR2: Students will: identify
vertical, corresponding, interior, exterior)
Angles in a       Find the measure of      7.G.B.5: Solve real-life and mathematical problems   MA-HS-G-S-SR3: Students will: analyze and
Polygon           an angle, and find the   involving angle measure, area, surface area, and     apply angle relationships (e.g., linear pairs,
sum of interior angles   volume. Use facts about supplementary,               vertical, complementary, supplementary,
in polygons.             complementary, vertical, and adjacent angles in a    corresponding and alternate interior angles) in
multi-step problem to write and solve simple         real-world or mathematical situations
equations for an unknown angle in a figure.          MA-HS-G-S-SR1: Students will: identify and
8.G.A.5: Understand congruence and similarity        apply the definitions, properties and theorems
using physical models, transparencies, or            about line segments, rays and angles and use
geometry software. Use informal arguments to         them to prove theorems in Euclidean
establish facts about the angle sum and exterior     geometry, solve problems and perform basic```
```angle of triangles, about the angles created when        geometric constructions using a straight edge
parallel lines are cut by a transversal, and the         and a compass
angle-angle criterion for similarity of triangles. For   MA-8-G-S-SR2: Students will: identify and
example, arrange three copies of the same                compare properties of two-dimensional
triangle so that the sum of the three angles             figures (circles; triangles: acute, right, obtuse,
appears to form a line, and give an argument in          scalene, isosceles, equilateral; quadrilaterals:
terms of transversals why this is so.                    square, rectangle, rhombus, parallelogram,
trapezoid; regular/irregular polygons); apply
these properties and figures to solve real-
world problems
MA-6-G-S-SR4: Students will: identify, describe
and provide examples and properties of two-
dimensional figures (circles, triangles [acute,
right, obtuse, scalene, isosceles, equilateral],
properties and figures to solve real-world
problems
MA-7-M-S-MPA2: Students will: estimate and
find angle measures and segment measures
MA-6-G-S-SR1: Students will: formulate and
use the rules for the sum of angle measures in
a triangle (180°) and in a quadrilateral (360°)
MA-7-G-S-SR2: Students will: identify
vertical, corresponding, interior, exterior)
Sampling   Use data from random   HSS-ID.A.2: Summarize, represent, and interpret
samples to make        data on a single count or measurement variable.
inferences about       Use statistics appropriate to the shape of the data
populations and to     distribution to compare center (median, mean)
compare key            and spread (interquartile range, standard
characteristics        deviation) of two or more different data sets.
between two            7.SP.A.2: Use random sampling to draw inferences
populations.           about a population. 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.4: Draw informal comparative inferences
about two populations. Use measures of center
and measures of variability for numerical data
from random samples to draw informal
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
Comparing     Use data displays to      7.SP.B.3: Draw informal comparative inferences
Data          compare the measure       about two populations. Informally assess the
of both center and        degree of visual overlap of two numerical data
spread of populations.    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.
Simple        Find the probability of   7.SP.C.5: Investigate chance processes and            MA-8-DAP-S-CD2: Students will: make
Probability   simple events.            develop, use, and evaluate probability models.        predictions, draw conclusions and verify
Understand that the probability of a chance event     results from statistical data and probability
is a number between 0 and 1 that expresses the        experiments, making use of technology as```
```likelihood of the event occurring. Larger numbers     appropriate
indicate greater likelihood. A probability near 0     MA-8-DAP-S-P7: Students will: determine
indicates an unlikely event, a probability around     theoretical (mathematical) probabilities (e.g.,
1/2 indicates an event that is neither unlikely nor   express probability as a ratio, decimal,
likely, and a probability near 1 indicates a likely   percent, area model as appropriate for a given
event.                                                situation)
7.SP.C.7b: Investigate chance processes and           MA-6-DAP-S-P3: Students will: make
develop, use, and evaluate probability models.        predictions, draw conclusions and verify
Develop a probability model and use it to find        results from statistical data and probability
probabilities of events. Compare probabilities        experiments
from a model to observed frequencies; if the          MA-5-DAP-U-6: Students will understand that:
agreement is not good, explain possible sources of    probability can be used to make decisions or
the discrepancy. Develop a probability model          predictions, or to draw conclusions.
(which may not be uniform) by observing               MA-8-DAP-U-6: Students will understand that:
frequencies in data generated from a chance           probability can be used to make decisions or
process. For example, find the approximate            predictions or to draw conclusions.
probability that a spinning penny will land heads     MA-6-DAP-U-6: Students will understand that:
up or that a tossed paper cup will land open-end      probability can be used to make decisions or
down. Do the outcomes for the spinning penny          predictions or to draw conclusions.
appear to be equally likely based on the observed     MA-5-DAP-S-P1: Students will: determine the
frequencies?                                          possible outcomes of simple probability
experiments that are conducted by using
manipulatives
MA-6-DAP-S-CD1: Students will: make
predictions, draw conclusions and verify
results from statistical data and probability
experiments
MA-6-DAP-S-P4: Students will: determine
simple probabilities based on the results of an
experiment and make inferences based on the
data
MA-5-DAP-S-P2: Students will: determine the
likelihood of an event and represent that
likelihood in numerical terms```
```MA-5-DAP-S-P3: Students will: examine events
and describe their probability as likely or
unlikely
Compound      Find the probability of   7.SP.C.5: Investigate chance processes and              MA-HS-DAP-S-P13: Students will: determine
Probability   compound events.          develop, use, and evaluate probability models.          probabilities involving replacement and non-
Understand that the probability of a chance event       replacement
is a number between 0 and 1 that expresses the          MA-HS-DAP-S-P6: Students will: compute the
likelihood of the event occurring. Larger numbers       probability of a compound event
indicate greater likelihood. A probability near 0       MA-HS-DAP-S-P5: Students will: apply the
indicates an unlikely event, a probability around       concepts of conditional probability and
1/2 indicates an event that is neither unlikely nor     independent events and be able to compute
likely, and a probability near 1 indicates a likely     those probabilities
event.
7.SP.C.7a: Investigate chance processes and
develop, use, and evaluate probability models.
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. 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.8a: Investigate chance processes and
develop, use, and evaluate probability models.
Find probabilities of compound events using
organized lists, tables, tree diagrams, and
simulation. 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: Investigate chance processes and
develop, use, and evaluate probability models.
Find probabilities of compound events using
organized lists, tables, tree diagrams, and
simulation. 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.
Making        Use probability to   7.SP.C.6: Investigate chance processes and            MA-8-DAP-S-CD2: Students will: make
Predictions   make predictions.    develop, use, and evaluate probability models.        predictions, draw conclusions and verify
Approximate the probability of a chance event by      results from statistical data and probability
collecting data on the chance process that            experiments, making use of technology as
produces it and observing its long-run relative       appropriate
frequency, and predict the approximate relative       MA-8-DAP-S-P1: Students will: make
frequency given the probability. For example,         predictions, draw conclusions and verify
when rolling a number cube 600 times, predict         results from probability experiments or
that a 3 or 6 would be rolled roughly 200 times,      simulations, making use of technology as
but probably not exactly 200 times.                   appropriate
MA-8-DAP-S-P2: Students will: analyze
situations, such as games of chance, board
games or grading scales and make predictions
using knowledge of probability
MA-HS-DAP-U-6: Students will understand
that: probability can be used to make
decisions or predictions or to draw
conclusions.
MA-8-DAP-U-4: Students will understand that:
inferences and predictions from data are used
to make critical and informed decisions.
MA-8-DAP-U-6: Students will understand that:
probability can be used to make decisions or
predictions or to draw conclusions.```
```MA-HS-DAP-U-5: Students will understand
that: inferences and predictions from data are
used to make critical and informed decisions.
MA-HS-DAP-S-P10: Students will: determine
and compare theoretical and experimental
probabilities
MA-HS-DAP-S-P12: Students will: make
predictions and draw inferences from
probabilities. and apply probability concepts
to practical situations to make informed
decisions
Simulations of   Identify and use       7.SP.C.8c: Investigate chance processes and
Simple and       simulations to         develop, use, and evaluate probability models.
Compound         represent simple and   Find probabilities of compound events using
Events           compound events.       organized lists, tables, tree diagrams, and
simulation. 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?
Solving Word     Rewrite expressions to 7.EE.A.2: Use properties of operations to generate
Problems with    help identify how      equivalent expressions. Understand that rewriting
Algebra          quantities in a        an expression in different forms in a problem
problem situation are context can shed light on the problem and how
related.               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.”
Common           Apply properties of    7.EE.A.1                                               MA-HS-AT-S-VEO8: Students will: factor
Factors in       operations as          Use properties of operations to generate               polynomials by removing the greatest
Polynomials      strategies to add,     equivalent expressions. Apply properties of            common factor
subtract, factor, and  operations as strategies to add, subtract, factor,     MA-HS-AT-S-VEO6: Students will: add,
expand expressions     and expand linear expressions with rational            subtract and multiply polynomials```
```with rational          coefficients.                                         MA-HS-AT-S-VEO11: Students will: add,
coefficients.                                                                subtract, multiply, divide and simplify rational
expressions
MA-HS-AT-S-VEO9: Students will: factor
Concept of        Write and graph        7.EE.B.4b: Solve real-life and mathematical
Inequalities II   complex inequalities   problems using numerical and algebraic
and interpret the      expressions and equations. Use variables to
solution set in the    represent quantities in a real-world or
context of a real-     mathematical problem, and construct simple
world problem.         equations and inequalities to solve problems by
reasoning about the quantities. 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.``` 