| Date |
Sections |
Topics |
Prerequisite Skills |
Student learning outcomes
|
| Weeks 1-2 |
Module 1 |
Definition of Polygons |
|
- Understand the development of geometric (mathematical) definitions through examples and non-examples
- Build definitions for the terms: closed, simple, polygon, convex, and regular
|
| Weeks 1-2 |
Module 1 |
Properties of Polygons (Sides, Angles and Diagonals) |
|
- Build, express, and justify a pattern for the diagonals of an n-gon by using geometric reasoning
- Use geometric reasoning to build and express the formula for the sum of interior angles of a polygon
- Use geometric reasoning to build and express the formula for the internal angles of a regular polygon
|
| Week 3 |
Module 1 |
Lines & Angles |
|
- Develop and use visual reasoning skills to decompose and identify angle measures based on a given a reference angle on a grid
|
| Week 3 |
Module 1 |
Transversal lines |
|
- Explore relationships between angles formed between parallel lines and transversals and solve problems using these relationships
|
| Week 4 |
Module 1 |
Classifying Triangles |
|
- Classify triangles by angles/sides and articulate relationships between classes
- Create and use an ordered list to enumerate combinations of characteristics
|
| Week 4 |
Module 1 |
Triangle Inequality |
|
- Informally justify and be able to use the triangle inequality
|
| Week 5 |
Module 1 |
Triangle Congruence |
|
- Informally justify triangle congruence theorems by construction
|
| Week 5 |
Module 1 |
Theorem of Right Triangles |
|
- Understand when and how to apply the Theorem of Right Triangles to calculate lengths
- Use different models to informally justify the Theorem of Right Triangles
|
| Week 6 |
Module 1 |
Definitions and Hierarchy of Quadrilaterals |
|
- Explore relationships between and the consequences of given definitions of classes of quadrilaterals
- Build and integrate visual representations with thinking about logical statements
- Understand relationships between classes of quadrilaterals
|
| Week 7 |
Module 2 |
Measurement (LINEAR) |
Definition of multiplication (# groups x group size = total) |
- Describe measurement as an iteration of a constant unit
- Develop an understanding of the Inverse relationship between size of unit and number of units needed to measure something
|
| Week 7 |
Module 2 |
Measurement (LINEAR) – CONVERSION |
|
- Convert between different units of length measurement
|
| Week 8 |
Module 2 |
Measurement (AREA) |
|
- Calculate areas on a grid using additive and subtractive approaches
|
| Week 8 |
Module 2 |
Measurement (AREA) – CONVERSION |
|
- Convert between different units of area measurement
|
| Week 9 |
Module 2 |
Area of Polygons - Formulas |
|
- Develop, relate, and justify area formulas for parallelograms, triangles, and trapezoids
|
| Week 9 |
Module 2 |
Perimeter Area |
|
- Calculate perimeters of non-standard objects with right angles by reasoning about missing lengths
- Calculate perimeters of objects on a grid using the Pythagorean theorem
- Understand the relation and distinguish between Perimeter and Area
|
| Week 10 |
Module 3 |
Rigid Transformations |
|
- Define the three basic rigid motions and given the result of a transformation, identify a correct sequence of rigid motions that maps the pre-image to the image
- Define congruence as a result of properties of rigid motions
|
| Week 10 |
Module 3 |
Symmetry |
|
- Identify rotation and reflection symmetry and use rigid motions to create figures with different types of symmetry
|
| Weeks 11-12 |
Module 3 |
Similarity |
|
- Determine whether two figures are similar and justify this determination by referring to angles and scale factor
- If two figures are similar, determine/describe the correspondence between the two
- Use proportionality and scale factors (instead of additive thinking) to determine measurement of similar figures
|
| Week 13 |
Module 4 |
Mathematical & Statistical Reasoning |
|
- Identify statistical and non-statistical questions
|
| Week 13 |
Module 4 |
Display of Categorical Data |
|
- Given data, select a variety of appropriate displays
- Identify and justify appropriate displays for a given type of data
|
| Week 14 |
Module 4 |
Display of Numerical Data |
|
- select appropriate graphical and numerical methods and use those methods to analyze data
- use appropriate tools for exploring (represent/ summarize/interpret) distributions including bar graphs, dot plots, stem & leaf plots, box-whisker plots, and measures of center
- use sophisticated tools such as histograms, the IQR (interquartile range), mean absolute deviation, 5-number summaries, and boxplots for describing distributions, summarizing and comparing distributions, and for making inferences
|
| Week 15 |
Module 4 |
Probability |
|
- Compare displays of empirical data with theoretical probabilities
- Create and use an ordered list to enumerate combinations of characteristics
- Identify equally probable outcomes and combine them to find the probability of events
- Use probability to evaluate the fairness of games
|
