Apartment Proportions 7.G.A.1

Apartment Proportions

Problem:

Congratulations! You just got your first apartment. It’s located right in the heart of downtown Ellensburg. You just realized you do not have anything to put in your new living room which is 14’ by 12.5’.

Sadly, the store you want to get your furniture from only has a few options but they come in multiple proportions. Make sure you have at least one item from each of the categories. If an item is too large or small, use ratios to change the proportions. You are only allowed to have ten of the following items in your living room!

Hint: Do some of the sizes seem odd? You should probably use ratios to change the size.

Show your work!

Below are the furniture you can select from with the measurements.

Seating                                                            Misc

Couch 8’x4’                                                    Lamp 4’x4’

Chair 2’x3’                                                     Fan 4’x2’

Bean bag square 3’x3’                                  Bookshelf 3’x2’

 

Table                                                              Entertainment

Coffee Table 16’x9’                                       TV with stand 12’x10

Side Table .5’x.5’                                           TV 10’x2’

                                                                           Gaming Consoles 4’x6’

Rug

Fuzzy Rug 15’x8’

Rug 14’x6’

 

This picture was found at Clipart-Library. This lesson will focus on the CCSS.Math.Content.7.G.A.1 which is 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.

I would teach this culturally by understanding that all students come from different cultures and different cultures have different housing expectations.

Other standard:

CCSS.ELA-Literacy.W.7.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

Shape Sorter 6.SP.B

By Rachel Van Kopp, Kimberly Younger, Tracy Van Lone, Natasha Smith, and Naomi Johnson

CCSS.MATH.CONTENT.7.G.A.3In the NCTM shape sorter activity, students use aVenn diagram to understand concepts of sorting geometric shapes by categories. For this activity our group of pre-service teachers sorted figures based on these parameters: 1. the figure has rotational symmetry and 2. the figure has at least one line of symmetry. Our group came up with two rules that we found to be true:

  1. All regular polygons have at least one line of symmetry
  2. All parallelograms  have rotational symmetry, but not a line of symmetry with the exception of the rectangle.

The following images are examples of attempts our group has made with the given categories.

 

Common misconceptions: Some common misconceptions with the categories has one line of symmetry and has rotational symmetry is that parallelograms have a line of symmetry. This is actually not true because no matter where the line is drawn on every parallelogram, except a regular trapezoid and rectangles, the angles will be off-set. Another misconception is that all figures with rotational symmetry have a line of symmetry. This is also untrue because parallelograms have rotational symmetry, but no line of symmetry.

To bring this activity in the classroom, we created a lesson warm-up and the worksheet pictured below, which can be download here. The warm-up (which is available via the link but not pictured) focuses students on relevant geometric vocabulary, and the worksheet serves as an activity tracker, helping students make connections between geometric concepts and sets and logic learning via their activity on the NCTM Shape-Sorter app.