6th Grade Unit 6: Area

Unit Driving Question

Why is finding area important?

Essential Questions

1. How can we use rectangles to help to find the area of other quadrilaterals?

2. How can finding the area of other shapes help to find the area of a triangle?

3. How can we find area without a formula for that shape?

Big Ideas

1. The area of a square and a parallelogram is related to the area of a rectangle.
2. The area of a triangle is half the area of a rectangle or parallelogram.
3. The area of composite figures can be found by decomposing the polygon into rectangles and triangles.   

Useful Websites 

The following apps, websites, and smartboard lessons can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards.  They are also useful for students who may need reinforcement, remediation, or differentiation.

1. Virtual Nerd: Virtual Nerd provides video tutorials as a supplemental resource for both students and teachers.

2. Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard so that students may study at their own pace both in and outside of the classroom.

3. Mr.Naussbaum.com: MrNussbaum.com offers interactive games specifically designed to pinpoint one or several essential concepts to make the learning process more interactive and enjoyable.

4. Interactive Sites for Education: These interactive activities work great on your interactive whiteboard, computer, laptop, or Chromebook for whole group or small group instruction or use in the computer lab or at home for individual learning. Most of these activities are Flash-based.  This means that they will NOT work on iPads unless you are running an app that allows Flash to play such as Puffin.  

5. Kahoot: Kahoots are fun, learning games best played in a group setting.  Players answer questions on individual devices (Ex: Chromebook, iPads) while games are displayed on a shared screen (Ex: Smartboard or TV).  Choose a Kahoot to match your desired skill or create your own.

6. Zapzapmath: Zapzapmath has over 150 math lessons designed to incorporate higher order thinking skills in the fields of creation, evaluation, and analysis. This is combined into a game-based system of fun math learning.

7. Mr.Anker Tests: Interactive activities and games for dozens of math skills.  Most of these activities run on Flash.

Launch Task

1 Lesson

• Introducing Area (Open Up): This initial task has students thinking about area in terms of decomposing pieces to make different shapes with the same area.  Students will work with tangram manipulatives (Printed pieces from the Blackline Master are included or there is an optional digital version link) to decompose and rearrange pieces with the same area.   

Big Ideas for Development Lessons

5-6 Weeks (approximately 1 week per big idea)

Big Idea 1: The area of a square and a parallelogram is related to the area of a rectangle.

Key Resources

1. Area of a Rectangle (Open Middle): These Open Middle activities are a great way to get students reasoning about the area of a rectangle.  Activity 1 asks students to use a specific perimeter to find the greatest area that can be made.  Activity 2 also asks students to find the greatest area of a rectangle but instead asks students to find the dimensions of the rectangle.

2. Parallelograms (Open Up):  These activities ask students to first understand the characteristics of a parallelogram.  Then, students will begin reasoning about finding the area of a parallelogram, including comparing strategies like decomposition.

3. Area of Parallelograms (Open Up): These activities more towards using the formula for finding the area of a parallelogram.  Students must be able to reason and explain how to find the area of parallelograms of different shapes and sizes.

4. Area of Parallelograms (GeoGebra):  This applet helps students visualize how a parallelogram can be dissected to show that the parallelogram’s area is equivalent to the area of the rectangle with the same base and height as the given parallelogram.
   

    

Big Idea Probe

• Area of a Square, Rectangle, Parallelogram Probe

Evidence of Understanding 

• Investigate area using grid paper or cutting methods to discover ways of finding area of a rectangle.

• Use knowledge of rectangle area to continue exploring with squares and parallelograms to find area of each shape.

Apply the formulas for finding the area of a rectangle, square, and a parallelogram.

Use formulas to write equations for finding area and/or missing sides of shapes.

• Apply knowledge of solving equations to find area or solve for the measurement of a missing side length.

Accurately choose and label units. 

Big Idea 2: The area of a triangle is half the area of a rectangle or parallelogram.

Key Resources

1. From Parallelograms to Triangles (Open Up):  This lesson prepares students to apply what they know about the area of parallelograms to reason about the area of triangles.  Highlighting the relationship between triangles and parallelograms is a key goal of this lesson. The activities make use of both the idea of decomposition (of a quadrilateral into triangles) and composition (of two triangles into a quadrilateral). 

2. Areas of Right Triangles (Illustrative Mathematics): This task is intended to help build understanding as students work toward deriving a general formula for the area of any triangle.

3. Formula for the Area of Triangles (Open Up): Students will begin with recognizing base and height measurements of a triangle.  Then, they will find area until they can arrive at an expression (formula) for finding the area of any triangle. Students will also practice using this formula while finding the correct base and height measurements of each triangle.

4. Families of Triangles (Illustrative Mathematics):  In this task, students should have already developed and become comfortable with a formula for the area of a triangle. The focus of this task should be on noticing the relationship between height and area.

     

Big Idea Probe

• Area of a Triangle Probe

Evidence of Understanding

Recognize area formula for triangles can be developed by the figures’ connection to rectangles or parallelograms.

• Investigate rectangles and parallelograms using grid paper or cutting methods to discover their connection to triangles.  

Apply the formulas for finding the area of a triangle.

Use formulas to write equations for finding area and/or missing sides of shapes.

• Apply knowledge of solving equations to find area or solve for the measurement of a missing side length.

Accurately choose and label units.

Big Idea 3: The area of composite figures can be found by decomposing the polygon into rectangles and triangles.

Key Resources

1. Reasoning to Find Area (Open Up):  This lesson helps students begin identifying strategies for finding area and applying them to various figures. Students will have opportunities to find areas of regions using a variety of strategies while working both on and off a grid.  A discussion should center around how different strategies—decomposing, rearranging, subtracting, and enclosing—are used to find area.

2. Finding Area of Polygons (Georgia):  This activity introduces students to thinking about different ways to find the area of polygons.  Students look at three different figures on a grid and are asked to find the area of each.  They are also asked to compare different ways of finding area among the three shapes.  

3. Wallpaper Decomposition:  The purpose of this task is for students to experiment with composition and decomposition of polygons to examine shapes in a real-world context.

    

Big Idea Probe

• Area of Composite Figures Probe

Evidence of Understanding

Analyze and discuss strategies for finding the area of irregular figures.

• Decompose polygons into shapes such as triangles, squares, and rectangles.

• Understand that area is additive and consists of the sum of non-overlapping regions of the composite figure.

• Use correct formulas to write and solve equations for each individual shape.  

Accurately choose and label units.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment) 

• 24 Unit Squares:  This activity helps students think about the concept of area in multiple shapes. This activity requires students to understand the meaning of area by drawing shapes with specified areas.  For differentiation, students could do this activity both on and off grid paper.  Drawings produced by students can offer many opportunities for classroom discussion and for students to explain their reasoning.