Pre-Algebra Culminating Unit

Unit Driving Question

How can mathematical patterns be used to expand our understanding?

Essential Questions

1. What influences temperature?

2. Which polygons can be tessellated?

Big Ideas

1. Patterns can be used to make predictions about data.
2. Patterns and polygons can be used to create tessellations.

Big Ideas for Development Lessons

2-3 Weeks (approximately 1 week per big idea)

Big Idea 1: Patterns can be used to make predictions about data.

Collaborative Engagement 

• What Influences Temperature? (OpenUp Resources): In this optional exploration in applied mathematics, students develop and use a mathematical model to predict temperature given the latitude of a location. The activities in this lesson provide students a chance to go more deeply and apply mathematics to a real-world context. Students get a chance to engage in many aspects of mathematical modeling. The activities in this lesson build on each other, so should be done in order. Doing all of the activities would take more than a single class period—possibly as many as four. It is up to the teacher how much time to spend on this topic. It is not necessary to do the entire set of problems to get some benefit from the activities in this lesson, although more connections are made the farther one gets.

Interim Assessment: 

• Best Buy Performance Assessment (covers PA.D.1.3, PA.A.2.2, PA.A.2.3, PA.A.2.4, and PA.A.2.5): For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.  

Evidence of Understanding 

•  Understand difference between functions modeling input/output pairs and using statistics to analyze bivariate data

• Make assumptions to set up a mathematical model

• Use a mathematical model

• Make predictions

• Understand limitations of a mathematical model 

Big Idea 2: Patterns and polygons can be used to create Tessellations.

Collaborative Engagement

• Tessellations of the Plane (OpenUp Resources): In this optional exploration in pure mathematics, students are introduced to tessellations of the plane. The activities in this lesson provide students a chance to go more deeply and apply geometry concepts from multiple grades to a mathematical context. The activities in this lesson build on each other, so should be done in order. Doing all of the activities would take more than a single class period—possibly as many as four. It is up to the teacher how much time to spend on this topic. It is not necessary to do the entire set of problems to get some benefit from the activities in this lesson, although more connections are made the farther one gets.

Evidence of Understanding 

•  Examine patterns of polygons that fill the plane

• Build and study patterns with specific polygons

• Understand the concept of a regular tessellation

• See that triangles, squares, and hexagons can be used to make a regular tessellation

• Understand that no other regular polygon can be used to make a regular tessellation

• Tessellate the plane with special polygons (triangles, quadrilaterals, and one pentagon)