Walters-Concept Based Unit

Unit Title:  Stretching and Shrinking (title from CMP3 curriculum)

Conceptual Lens:  Relationships and Change

Unit Strands:  Perimeter and Scale Factor, Area and Scale Factor

Web out Unit’s topics and concepts:

Generalizations:

• The scale factor of a polygon has a relationship towards how the perimeter and area of the new figure changes.
• Scale factor is how much larger or smaller a figure is getting in all dimensions.
• The perimeter change will be the scale factor
• The area change will be the scale factor squared
• The changes of perimeter and area only apply if the 2 figures are similar.

Develop the guiding questions

• How do you find the area of a polygon? (F)
• How do you find the perimeter of a polygon? (F)
• How do you find scale factor? (C)
• How do you see the perimeter is affected by a scale factor? (C)
• How do you see the area is affected by the scale factor? (C)
• What would happen if you are looking at volume changes with a scale factor? (D)

Identify the Critical Content

• Perimeter is the outside distance around a figure
• Area is the inside space of a figure
• Scale factor affects all dimensions of a figure and is the number I multiplied each of the sides of the original figure to get to my new figure
• Similar shapes have a scale factor, same angles and same shape.

Identify the Key Skills

• How to calculate area and perimeter
• How to build a figure based on a certain scale factor
• Using multiplication and division skills to find a pattern
• Be familiar with and be able to calculate problems involving an exponent of 2

Standards:

7.RP.2:  Recognize and represent proportional relationships between quantities.

7.RP.3:  Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

  7.G.1:  Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.G.2:  Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Day 1:  

• Students will watch this you tube video to refresh their thinking on scale factor before we begin our activity:

https://www.youtube.com/watch?v=8HNsG6qhl60

• Students are given centimeter cubes in their groups and a piece of white paper.  They are to create a rectangle of any number of cubes long (from 4-20) and any number of cubes wide (from 4-20).

• Using a ruler, they draw their created rectangle and remove the cubes.
• Each group is given a die and they will roll to see what scale factor they will have to draw of their figure (excluding 1).  
• Using the centimeter cubes, they will create their new rectangle based on the scale factor. Then, they will draw the new rectangle on their paper.
• They will find the area and perimeter of each rectangle and write down those answers on a new piece of paper
• All the student groups will then hang up their work around the classroom and we will do a gallery walk where they have to go look at 3 other groups work.  As they are walking around they need to write down their original area and perimeters, the scale factor, and the new areas and perimeters while trying to come up with a pattern.
• At the end of the day, students will write down their predictions after day 1 as to how scale factor affects area and perimeter changes.  It could be helpful to ask the question, “How could I get from the original perimeter to the new perimeter?”

Day 2

• The day will begin with students bringing out their observations from yesterday and looking over them to see what their predictions are so far with scale factor relationships.
• Students today will be using a program on phet.colorado.edu to compare perimeter and area of similar shapes.

• They will begin by starting with a non-traditional shape (no squares, rectangles, etc.) and the computer will calculate the area and perimeter for them. I tell students to think about Tetris pieces if they are stuck with what shape to make. 

• Then, they will have to recreate their original picture with a scale factor of 2.  
• They will do the same for scale factor of 3.  Without the program they will try to do the same activity on paper for a scale factor of 4.  
• At the end of this lesson, students will again write down their observations and predictions for what they see happening.  As a teacher I would ask the question, how do you see the scale factor changing the perimeter?  the area?

Day 3

• Students will get into their groups and each will share their predictions from the past two days of how scale factor relates to area and perimeter.
• They will then use the MTV strategy of headlines and create a headline for what they believe is happening.
• We will discuss the headlines as a class, making observations and establish as a group what is happening.
• I would then have us get out white boards and practice this concept as well as doing some practice at our seat to get them ready for the assessment day tomorrow

Day 4:  Assessment Day

Assessment and scoring guide/rubric

What:  Investigate the relationship with scale factor affecting changes in area and perimeter

Why: In order to understand that the scale factor times perimeter will give me my new perimeter among similar figures and the scale factor squared times area will give my new area among similar figures.

How:  In our textbook that we use, we introduce the “Wump Family” to teach the students about similar figures.  This is not in our textbook but I bring the Wump Family back through the sad new of a murder.  I have the classroom marked up like a crime scene and tape a “dead” Wump cartoon character on the floor.  Students are given a scale drawing of the murdered Wump.  

They are then given a list of clues of who killed him.  Clues

It is their job as detectives to draw to scale the murderer based on the clues.  All of the clues deal with scale factors of the “dead” wump.  Some questions are phrased as changes in perimeter and some are asking about changes in area.  When they are completed with their drawing, they will turn it in for me to grade.  Here is the grading rubric that their grade will be based on:

Correct Body ___/3

Correct Hat ___/3

Correct Legs ___/3

Correct Arms ___/3

Correct Face ___/3

TOTAL ___/15

Unit overview

What happens to the perimeter when a similar figure is double in size? What happens to the area when the similar figure is scaled down?  Who killed Mug Wump?  All of these questions will be answered and more as we jump into our new unit of Stretching and Shrinking. Through this unit, we will be looking at the relationship scale factor has on both area and perimeter of a similar figure.  So get ready to explore and become detectives on this great mystery we are about ready to embark on.