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
Subtracting       and equations to         understandings of addition and subtraction to add
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
                                          understandings of addition and subtraction to add
                                          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
                                          understandings of addition and subtraction to add
                                          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
                                                                                                 (radius, diameter, circumference, area) and
                                                                                                 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
                                                                                                 (radius, diameter, circumference, area) and
                                                                                                 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
                                                                                                characteristics of angles (e.g., adjacent,
                                                                                                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],
                                                                                           quadrilaterals, regular polygons); apply these
                                                                                           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
                                                                                           characteristics of angles (e.g., adjacent,
                                                                                           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
                                        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.
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
                                                                                               quadratic polynomials
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.
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