Grade 7 Units:
First Six Weeks:
Unit 1: Numerical Understanding: Integers and Positive Rational Numbers
Unit 2: Numerical Operations: Integers and Positive Rational Numbers
Second Six Weeks:
Unit 3: Proportionality: Similar Figures, Representations, and Applications
Unit 4: Geometry: Coordinate Plane, Graphing Transformations, and Perspectives
Third Six Weeks:
Unit 5: Algebraic Expressions and Equations
Unit 6: Algebraic Representations and Applications
Fourth Six Weeks:
*Unit 7: Geometry and Measurement: Two-Dimensional
Unit 8: Measurement: Three-Dimensional
Fifth Six Weeks:
Unit 9: Statistical Representations and Analysis
Unit 10: Probability
Sixth Six Weeks:
Unit 11: Making Connections
Unit 12: Catering Investigation
Grade 8 Units:
First Six Weeks:
Unit 1: Numerical Understanding: Rational Numbers
Unit 2: Numerical Operations: Rational Numbers
Second Six Weeks:
Unit 3: Proportionality: Representations and Applications
Unit 4: Geometry: Transformations in the Coordinate Plane and Perspectives
Third Six Weeks:
Unit 5: Algebraic Representations and Applications
Unit 6: Irrational Numbers and Pythagorean Theorem
Fourth Six Weeks:
*Unit 7: Measurement: Two- and Three-Dimensional
Unit 8: Probability
Fifth Six Weeks:
Unit 9: Statistical Representations and Analysis
Unit 10: Making Connections
Sixth Six Weeks:
Unit 11: Graphing Calculator Investigations
Grade 7, Unit 7:
Concepts:
 Geometry – Angles; Attributes
 Measurement – Angles
 Underlying Processes and Mathematical Tools – Tools to Solve Problems; Communication of
Mathematical Ideas; Validation of Conclusions
Key Understandings:
 Pairs of angles can be classified as complementary or supplementary and validated by the sum of
their measures.
Concepts:
 Geometry – Angles; Attributes; Two- Dimensional Figures
 Measurement – Attributes; Angles; Length
 Underlying Processes and Mathematical Tools – Tools to Solve Problems; Communication of
Mathematical Ideas; Validation of Conclusions
Key Understandings:
 Triangle and quadrilateral classifications are validated by the mathematical properties and
relationships of angle measures and side measures.
Concepts:
 Geometry – Attributes, Two Dimensional Figures; Art and Architecture
 Measurement – Attributes; Angles
 Underlying Process and Mathematical Tools – Mathematics in Everyday Situations; Conjectures;
Validation of Conclusions
Key Understandings:
 Geometric properties of triangles and quadrilaterals may be used to validate conjectures of missing
angle measures of figures in real life-problem situations, such as art and architecture.
Concepts:
 Geometry – Two-Dimensional Figures
 Measurement – Perimeter, Circumference, Area, Length, Units of Measure
 Underlying Processes and Mathematical Tools – Tools to Solve Problems; Communication of
Mathematical Ideas
Key Understandings:
 Linear measurements of a two-dimensional figure may be used to calculate the perimeter,
circumference, or area and communicate the appropriate unit of measure.
Concepts:
 Measurement – Formulas; Area; Perimeter; Circumference,
 Underlying Processes and Mathematical Tools – Mathematics in Everyday Situations; Tools to Solve
Problems
Key Understandings:
 Formulas for perimeter, circumference, and area can be generated and applied to solve real-life
problem situations.
Concepts:
 Measurement – Formulas
 Algebraic Reasoning – Equality; Equivalence
 Underlying Processes and Skills – Problem-Solving Model; Problem-Solving Plan or Strategy; Tools to
Solve Problems; Validation of Conclusions
Key Understandings:
 The process of evaluating a formula that must be rewritten to solve for another variable involves
using a plan or strategy to keep the values on both sides of the formula equally balanced and validating
the solution for reasonableness.
Grade 8, Unit 7:
Concepts:
 Geometry – Attributes; Two-Dimensional Figures; Three-Dimensional Figures
 Measurement – Surface Area; Volume
 Underlying Processes and Mathematical Tools – Mathematics in Everyday Situations; Tools to Solve
Problems; Communication of Mathematical Ideas
Key Understandings:
 Real-life problems may be modeled and measurement application problems may be solved using
three-dimensional models built from two-dimensional models called nets.
Concepts:
 Measurement – Area; Formulas; Surface Area
 Underlying Processes and Tools – Tools to Solve Problems; Communication of Mathematical Ideas
Key Understandings:
 The relationship between the sum of individual areas and the formulas for surface area can be
communicated with mathematical language.
Concepts:
 Geometry – Two-Dimensional Figures
 Measurement – Formulas; Surface Area
 Underlying Processes and Tools – Tools to Solve Problems; Communication of Mathematical Ideas
Key Understandings:
 Concrete models and nets of three-dimensional figures, such as prisms, pyramids, and cylinders,
may be used to communicate the lateral and total surface area of these objects.
Concepts:
 Geometry – Two-Dimensional Figures
 Measurement – Attributes; Formulas; Surface Area; Units of Measure
 Underlying Processes and Mathematical Tools – Tools to Solve Problems; Communication of
Mathematical Ideas
Key Understandings:
 Formulas for lateral and total surface area of prisms, cylinders, and pyramids may be applied to
solve problem situations and communicate the appropriate unit of measure.
Concepts:
 Geometry – Three-Dimensional Figures
 Measurement – Formulas; Volume
 Underlying Processes and Tools – Tools to Solve Problems; Communication of Mathematical Ideas
Key Understandings:
 Concrete models of three-dimensional figures, such as prisms, pyramids, and cylinders, may be
used to communicate the connection between these objects and formulas for volume.
Concepts:
 Geometry – Three-Dimensional Figures
 Measurement – Attributes; Formulas; Volume; Units of Measure
 Underlying Processes and Mathematical Tools – Tools to Solve Problems; Communication of
Mathematical Ideas
Key Understandings:
 Formulas for volume of prisms, cylinders, pyramids, spheres, and cones may be applied to solve
problem situations and communicate the appropriate unit of measure.
Concepts:
 Measurement – Formulas; Surface Area; Volume
 Operations – Estimation
 Underlying Processes and Tools – Mathematics in Everyday Situations; Tools to Solve Problems
Key Understandings:
 Real-life problem situations involving lateral surface area, total surface area, and volume are solved
using estimation and formulas.
Concepts:
 Spatial Reasoning – Similarity
 Measurement – Perimeter; Area; Surface Area; Volume; Dimensional Change
 Underlying Processes and Tools –Problem Solving Plan or Strategy; Tools to Solve Problems;
Communication of Mathematical Ideas
Key Understandings:
 If all dimensions of a figure are changed proportionally, the perimeter ratio is equivalent to the
scale factor, the area ratio is equivalent to the scale factor squared, and the volume ratio is equivalent
to the scale factor cubed. If all dimensions are not changed, the perimeter, area, and volume is affected,
but must be recalculated.
Concepts:
 Measurement – Formulas
 Algebraic Reasoning – Equality; Equivalence
 Underlying Processes and Skills – Problem-Solving Model; Problem-Solving Plan or Strategy; Tools to
Solve Problems
Key Understandings:
 The process of evaluating a formula that must be rewritten to solve for another variable involves
using a plan or strategy to keep the values on both sides of the formula equally balanced.