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TechPaths Grade 8 CMP

VIEWS: 3 PAGES: 39

									Unit Title: Filling and Wrapping

Notes:


         Big Ideas            Contents               Skills           Assessments          Lessons               Anchors


  Surface Area and
Volume of Rectangular
  Prisms, Cylinders,                                                                  INVESTIGATION 1:
 Cones, and Spheres                                                                     Building Boxes
                                             Visualize a net as a
                                             representation of the
                        Nets, Surface Area   surface area of a                      Problem 1.1: Making
                        (Cubes)              cube.                                  Cubic Boxes           M.8.B.2.2;M.8.C.1.1.1

                                             Connect the area of
                        Nets, Surface Area   the net to the surface
                        (Cubes)              area of a cube.                                              M.8.B.2.2;M.8.C.1.1.1

                                             Visualize a net as a
                                             representation of the
                        Nets, Surface Area surface area of a                        Problem 1.2: Making
                        (Rectangular Prisms) rectangular prism.                     Rectangular Boxes     M.8.B.2.2;M.8.C.1.1.1
                                             Connect the area of
                                             the net to the surface
                        Nets, Surface Area area of a rectangular                                          M.8.B.2.2.1;M8.B.2.2.3;
                        (Rectangular Prisms) prism.                                                       M.8.C.1.1.1
                     Visualize a net as a
                     representation of the                         Problem 1.3: Testing
Nets, Surface Area surface area of a                               Nets (Rectangular         M.8.B.2.2.1;M8.B.2.2.3;
(Rectangular Prisms) rectangular prism.                            Prisms)                   M.8.C.1.1.1
                     Use a net for a
                     rectangular prism to
                     develop a strategy
                     for finding the
Nets, Surface Area surface area of the                                                       M.8.B.2.2.1;M8.B.2.2.3;
(Rectangular Prisms) prism.                                                                  M.8.C.1.1.1

                    Find the volume of a
                    rectangular prism by
                    counting the number
Volume (Rectangular of unit cubes it takes
Prisms)             to fill the prism.                                                       M8.B.2.2.2



                    Understand the
                    relationship between
                    the dimensions of a                            Problem 1.4: Flattening
Surface Area        rectangular prism                              a Box (Surface Area of
(Rectangular Prism) and its surface area.                          Rectangular Prisms)       M.8.B.2.2;M.8.C.1.1.1
                    Calculate the srface
Surface Area        area of a rectangular
(Rectangular Prism) prism.                                                                   M.8.B.2.2.1

                     Continue to develop
                     visualization skills
Nets, Surface Area relating rectangular Mathematical Reflection,
(Rectangular Prisms) prisms to their nets. p. 18                                             M.8.C.1.1.1

                                                                   INVESTIGATION 2:
                                                                   Designing Rectangular
                                                                   Boxes
                       Connect the
                       dimensions of a
Volume and Surface     rectangular prism to                              Problem 2.1: Packaging
Area Connections       its volume and                                    Blocks (Finding Surface
(Rectangular Prisms)   surface area.                                     Area)                   M8.B.2.2
                       Understand that
                       rectangular prisms
                       may have the same
Volume and Surface     volume but quite
Area Connections       different surface                                                         M8.B.2.2.1;M8.B.2.2.2;M
(Rectangular Prisms)   areas.                                                                    8.B.2.2.3


                     Predict which
                     rectangular prism of
                     those with a
Volume and Surface common volume will                                    Problem 2.2: Saving
Area Connections     have the smallest                                   Trees (Finding the Least
(Rectangular Prisms) surface area.                                       Surface Area)            M8.B.2.2.1;M8.B.2.2.3
                     Refine a strategy for
                     finding the surface
Surface Area         area of a rectangular
(Rectangular Prism) prism.                                                                       M8.B.2.2.1;M8.D.1.1.3


                    Understand that
                    prisms can be filled
                    systematically in
                    identical layers, and                                Problem 2.3: Filling
                    that this layering                                   Rectangular Boxes
                    leads to the formula                                 (Finding Volume of a
Volume (Prisms)     for volume.                                          Rectangular Prism)      M8.B.2.2.2;M8.B.2.2.3
                    Develop a formula
                    for finding the
Volume (Rectangular volume of a               Mathematical Reflection,                           M8.B.2.2.2;M8.B.2.2.3;M
Prism)              rectangular prism.        p. 31; Check Up 1                                  8.D.1.1.3
                                            INVESTIGATION 3:
                                            Prisms and Cylinders
                    Develop                 Problem 3.1: Filling
                    understanding of        Fancy Boxes (Finding
Volume, Surface     volume and surface      the Volumes of Other
Area (Prisms)       area of prisms.         Prisms)                  M8.B.2.2.2


                    Develop a strategy
                    for finding the         Problem 3.2: Filling
                    volume of a cylinder    Cylinders (Finding the
Volume (Cylinder)   using its dimensions.   Volume of Cylinders)     M8.B.2.2

                    Connect this strategy
                    to the idea of layers
                    in rectangular and
Volume (Cylinder)   other prisms.                                    M8.B.2.2
                    Begin to develop a
                    strategy for finding
Surface Area        the surface area of a
(Cylinder)          cylinder.                                        M8.B.2.2

                                            Problem 3.3: Making
                    Develop a strategy      Cylinders and Prisms
                    for finding the         from Nets (Finding the
Surface Area        surface area of a       Surface Area of
(Cylinder)          cylinder.               Cylinders and Prisms)    M8.B.2.2


                    Apply understanding     Problem 3.4:Making a
Problem-solving     of volume to solve      New Juice Container
(Volume)            problems.               (Comparing Volumes)      M8.B.2.2.2
                   Understand that a
                   variety of different
                   three-dimensional
                   figures can have the
                   same volume but
Volume and Surface different surface    Mathematical Reflection,
Area Connections   areas.               p. 47; Partner Quiz                                  M8.B.2.2

                                                                   INVESTIGATION 4:
                                                                   Cones, Spheres, and
                                                                   Pyramids
                   Explore a volume
Volume Connections relationship between
(Cylinders and     cylinders and                                   Problem 4.1: Comparing
Spheres)           spheres.                                        Spheres and Cylinders
                   Extend students'
                   understanding of
                   volume as layering to
                   other ways of filling a
                   three-dimensional
Volume             figure.

                   Explore and use a
Volume Connections volume relationship                             Problem 4.2: Cones and
(Cylinders, Cones, between cylinders,                              Cylinders, Pyramids and
and Spheres)       cones and spheres.                              Cubes

                   Explore and use a
                   volume relationship
Volume Connections between prisms and
(Prisms and        pyramids to find the
Pyramids)          volume of a pyramid.
                   Strengthen
                   understanding of the
                   volume relationships                              Problem 4.3: Melting Ice
Volume Connections among cones,                                      Cream (Comparing
(Cones, Spheres,   spheres and                                       Volumes of Spheres,
and Cylinders)     cylinders.                                        Cylinders, and Cones)

                      Use the relationships
                      amond cylinders,
                      cones, and sphers to
                      develop a strategy
                      for finding the
Volume (Cone or       volume of a cone or Mathematical Reflection,
Sphere)               sphere.               p. 61; Check Up 2

                                                                     INVESTIGATION 5:
                                                                     Scaling Boxes
                    Understand how
                    changes in one or
                    more dimensions of                               Problem 5.1: Building a
                    a rectangular prism                              Bigger Box (Doubling the
Volume (Rectangular affect the prism's                               Volume of a Rectangular
Prism)              volume                                           Prism)
                    Design rectangular
Volume (Rectangular prisms with a given
Prism)              volume.


                      Extend students'                               Problem 5.2: Scaling Up
                      understanding of                               the Compost Box
Similarity and Three- similarity to three-                           (Applying Scale Factors
Dimensional Figures dimensional figures.                             to Rectangular Prisms)
                        Understand the
                        effect on surface
                        area of appling a
Similarity and Three-   scale factor to a
Dimensional Figures     rectangular prism.
                        Understand the
                        effect on volume of
                        applying a scale
Similarity and Three-   factor to a
Dimensional Figures     rectangular prism.

                      Apply students'
                      understanding of
                      scale factor and its
                      relationship to
                      changes in 1-, 2-,      Mathematical Reflection, Problem 5.3: Building
Similarity and Three- and 3-dimensional       p. 75; Unit Test; Unit   Model Ships: Similarity
Dimensional Figures measures.                 Project                  and Scale Factors
DELETE THIS INVESTIGATION?
Unit Title: Thinking With Mathematical Models

Notes:


         Big Ideas          Contents              Skills          Assessments




                                           Make tables and
                                           graphs to represent
                                           data.
                                           Describe
                                           relationships
                                           between variables.

                                           Use data patterns to
                                           make predictions.


                                           Make tables and
                                           graphs to represent
                                           data.
                                           Describe
                                           relationships
                                           between variables.

                                           Use data patterns to
                                           make predictions.

                                           Make tables and
                                           graphs to represent
                                           data.
                                           Describe
                                           relationships
                                           between variables.

                                           Use data patterns to
                                           make predictions.
                                           Compare and
                                           contrast linear and
                                           nonlinear
                                           relationships.
                    Fit a line to data that
                    show a linear trend.
                    Write an equation for
                    a line based on a
                    grpah of the line.
                    Use mathematical
                    models to answer
                    questions about
                    linear relationships.


                    Practice effective
                    strategies for writing
                    linear equations from
                    verbal, numerical, or
                    graphical
                    information.

                    Develop skill in
                    solving linear
                    equations with
                    approximation and
                    exact reasoning
                    methods.
                    Write inequalities to
                    represent "at most"
                    situations.

                    Use equations to
                    represent questions
                    about problem
                    situations and
                    interpret the
                    solutions in the
                    context of the
                    problem.




                    Explore situations
                    that can be modeled
                    by inverse variation
Inverse Variation   relationships.
                    Explore situations
                    that can be modeled
                    by inverse variation
Inverse Variation   relationships.
                    Investigate the
                    nature of inverse
                    variation in familiar
Inverse Variation   contexts.
                    Compare inverse
                    variations with linear
Inverse Variation   relationships.


                    Explore situations
                    that can be modeled
                    by inverse variation
Inverse Variation   relationships.
                    Investigate the
                    nature of inverse
                    variation in familiar
Inverse Variation   contexts.
                    Compare inverse
                    variations with linear
Inverse Variation   relationships.
       Lessons                   Anchors

   INVESTIGATION 1:
     Exploring Data
        Patterns
Problem 1.1: Testing
Bridge Thickness
(Finding Patterns and
Making Predictions)     M8.D.4.1


                        M8.D.4


                        M8.D.1.1

Problem 1.2: Testing
Bridge Lengths (Finding
Patterns and Making
Predictions)            M8.D.4.1


                        M8.D.4


                        M8.D.1.1

Problem 1.3: Custom
Construction Parts
(Extending Patterns)    M8.D.4.1


                        M8.D.4


                        M8.D.1.1



                        ?????
INVESTIGATION 2:
Linear Models and
Equations

Problem 2.1: Linear
Models                    M8.E.4.1.1


                          M8.D.1.1.3



                          M8.D.2.2




Problem 2.2: Equations
for Linear Relationships M8.D.2.2.2




Problem 2.3: Solving
Linear Equations          M8.D.2.1


                          M8.D.2.1




Problem 2.4: Intersecting
Linear Models             M8.D.2

INVESTIGATION 3:
Inverse Variation

Problem 3.1: Rectangles
with Fixed Area
(Relating Length and
Width)                                 Should we eliminate this investigation?
Problem 3.2: Bridging
the Distance (Inverse
Variation Patterns)




Problem 3.3: Average
Cost (Inverse Variation
Patterns)
Unit Title: Looking for Pythagoras

Notes:


         Big Ideas             Contents             Skills           Assessments

  Number Systems;
Pythagorean Theorem


                                            Review the
                        Coordinate System   coordinate system.

                                            Explore distances on
                        Coordinate System   a coordinate grid.


                        Properties of       Review properties of
                        Polygons            quadrilaterals.
                                            Connect properties
                        Coordinate System   of figures to
                        and Properties of   coordinate
                        Polygons            representations.
                                            Draw shapes on a
                        Coordinate System   coordinate grid.

                                            Develop strategies
                                            for finding areas of
                                            irregular figures on a
                        Area                grid.



                                            Draw squares on 5
                                            dot-by-5 dot grids
                        Area                and find their areas.

                                           Introduce the
                        Squares and Square concept of square
                        Roots              root.
                                           Understand square
                                           root geometrically,
                                           as the side length of
                        Squares and Square a square with known
                        Roots              area.
                   Use geometric
                   understanding of
                   square roots to find
                   lengths of line
Squares and Square segments on a dot
Roots              grid.




                    Deduce the
                    Pythagorean
Pythagorean         Theorem through
Theorem             explorations.

                    Use the Pythagorean
                    Theorem to find
                    unknown side
Pythagorean         lengths of right
Theorem             triangles.

                    Reason through a
                    geometric proof of
Pythagorean         the Pythagorean
Theorem             Theorem.



                    Use the Pythagorean
                    Theorem to find the
Pythagorean         distance between
Theorem             two points on a grid.

                    Relate areas of
Pythagorean         squares to the
Theorem             lengths of the sides.


                    Determine whether a
                    triangle is a right
Pythagorean         triangle based on its
Theorem             side lengths.

                    Relate areas of
Pythagorean         squares to the
Theorem             lengths of the sides.
                    Learn the meanings
                    of rational number
                    and irrational
Number Systems      number.
                    Estimate the values
Squares and Square of square roots that
Roots; Number       are irrational
Systems; Estimation numbers.

Squares and Square Estimate lengths of
Roots; Number       hypotenuses of right
Systems; Estimation triangles.


Estimation;            Estimate lengths of
Pythagorean            hypotenuses of right
Theorem                triangles.
                       Apply the
                       Pythagorean
Pythagorean            Theorem to a
Theorem                problem situation.


                      Investigate the
Properties of Special special properties of
Triangles             a 30-60-90 triangle.


                      Use the properties of
Properties of Special special right triangles
Triangles             to solve problems.
       Lessons                  Anchors

  INVESTIGATION 1:
   Coordinate Grids
Problem 1.1:Driving
Around Euclid (Locating
Points and Finding
Distances)              M8.C.3.1.1




Problem 1.2: Planning
Parks (Shapes on a
Coordinate Grid)        M6.C.1.1.1



                        M6.C.1.1.1; M8.C.3.1.1

                        M8.C.3.1.1



Problem 1.3: Finding
Areas                   M7.B.2.1; M8.B.2.2

INVESTIGATION 2:
Squaring Off

Problem 2.1: Looking for
Squares                  M7.B.2.1; M8.B.2.2


Problem 2.2: Square
Roots                   M8.A.1.1.2




                        M8.A.1.1.2
Problem 2.3: Using
Squares to Find Lengths M8.B.2.2; M8.C.1


INVESTIGATION 3: The
Pythagorean Theorem


Problem 3.1: The
Pythagorean Theorem       M8.C.1




                          M8.C.1.2.1


Problem 3.2: A Proof of
the Pythagorean
Theorem                   M8.C.1




Problem 3.3: Finding
Distances                 M8.C.1.2.1



                          M8.C.1


Problem 3.4: Measuring
the Egyptian Way
(Lengths that Form a
Right Triangle)        M8.C.1



                          M8.C.1

Investigation 4: Using
the Pythagorean
Theorem
Problem 4.1: Analysing
the Wheel of Theodorus M8.A.1



                         M8.A.1.1.2



                         M8.A.3.2


Problem 4.2: Stopping
Sneaky Sally (Finding
Unknown Side Lengths) M8.A.3.2



                         M8.C.1.2.1



Problem 4.3: Analyzing
Triangles                M8.C.1



Problem 4.4: Finding the
Perimeter                M8.C.a

								
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