**Teacher's Guiding Questions**

- What math is involved in creating a desk?
- How many students will need to fit in the classroom that we are making the desk for?
- How big can the desk be?
- What measurements do we need to make a desk?
- How can we present our design to someone who will create the desk?
- How much will the desk cost?

**ACS (Real world applications; career connections; societal impact)**

Applications – This challenge is directly relevant to the classroom of students in a changing society. They will be creating desks that are more conducive to their learning, which they can immediately relate to.

Career – This challenge relates to careers such as: interior designer, furniture designer, graphic artist, and materials engineer.

Societal – This challenge will allow students to connect with their community when sharing their ideas and creations for their school as well as other schools.

**Engineering Design Process (EDP)**

This will be found in the group project worksheet. Students will need to do research and brainstorm ideas for their group desk design. Then, they will narrow it down to 3 ideas. They will choose one of those designs and create a prototype of this design. They will present the design to others and reflect on the design process.

##### Unit Academic Standard

7.G.6. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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.

##### Unit Activities

__Lesson 1: Volume and Surface Area__

__Activity 1: Designing your desk top__ (all handouts can be found in the activity 1 handout file)

**Day 1:**

a. Students will come in and desks will be crowded with more seats per table (not optimal learning space).

b. Students will complete bell work questions:

i. Find the area of the following figures (draw a square with side length of 3 cm, a triangle with base of 12 in and height 3.5 in., and a rectangle with a length of 10 m and width of 12 m)

ii. What are some ways that your learning space can be improved?

c. Brainstorming session: How can we improve our learning space? (Students come up with essential questions, leading to the essential question: How can we make the perfect desk? Lead students to talk about desks and how we can improve them.

d. Present Challenge: Designing the Perfect Desk

e. Students will be in teams for this project. Assign student teams and have students go to todaysmeet.com (set up a room ahead of time for each class) and have them post guiding questions.

f. Pass out desk challenge packet and rubric while students are posting guiding questions– due at the end of the unit

g. Give pre-assessment on surface area, volume, area, scale, and slicing 3D figures.

**Day 2:**

a. Groups will begin brainstorm their ideas for their desk creation on the challenge handout

b. Students will complete the “Working with Cubes” handout

**Day 3:**

a. The whole class will complete the “Surface Area” handout

b. Groups will complete “Surface Area of a Rectangular Prism Activity”

**Day 4:**

a. Students will work in three stations:

i. Online practice on surface area

ii. Individual student work on “Rectangular Prism Practice Problems” handout

iii. Teacher-Guided Station (problems provided on “Working with Surface Area” handout)

iv. Extension problems are available for students who work ahead in their station

**Day 5:**

a. “Designing Rectangular Boxes: Finding the Volume of Your Desktop” handout together/finish with group

**Day 6:**

a. Students will work in three stations:

i. Online practice on volume

ii. Individual student work on “Surface Area and Volume Practice”

iii. Teacher-Guided Station (problems provided on “Teacher-led Volume Station” handout)

iv. Work on “Desk Challenge Worksheet” to figure out volume and surface area of team desk design

__Activity 2: Designing Your Desk Legs__ (all handouts can be found in the activity 2 handout file)

**Day 7:**

a. Students will complete “Prisms and Cylinders: Designing Your Desk Legs” as a class

**Day 8:**

a. Students will work in three stations:

i. Online practice on volume and surface area

ii. Individual student work on “Prisms Practice” handout

iii. Teacher-Guided Station (problems provided on “Prisms Practice: Teacher-Guided Station”)

__Lesson 2: Scale Drawings__

__Activity 3: Creating a Scale Drawing of your Desk__ (all handouts can be found in the activity handouts file)

**Day 9:**

a. Class notes together on “Making a Scale Drawing” handout and “How to Determine a Scale Factor by Applying Ratios” handout

b. Scale practice on whiteboards together in class

c. Scale Practice handout for homework

**Day 10:**

a. Students will work in 3 stations:

i. Teacher-guided student station

ii. “Scale Drawing Practice” at independent station

iii. Online scale drawing practice

b. Scale drawing extensions available if needed

**Day 11:**

a. “Scale Drawing Activity” in class with objects that students choose

__Activity 4: Designing the Perfect Desk Project and Post-Assessment__ (all handouts can be found in the activity handouts file)

**Day 12:**

a. Student groups will have one day in class to make a prototype of their desk design to scale. They will need to finish this for homework

**Day 13:**

a. Students will take the unit 7 post-assessment in class

##### Where the CBL and EDP appear in the Unit

Challenge Based Learning and the Engineering Design Process occur throughout the entire unit. Students will be working on designing their desk along the way as they learn about volume, surface area, and scale drawings. On the first day, students will come up with the essential and guiding questions. After this, they will begin brainstorming their ideas. As they progress through the unit, they will begin to design their desktop and legs and get student critiques of their team design. At the end of the unit, students will create a prototype of the desk and calculate the costs of making the desk.

##### Misconceptions

- units of measurement for perimeter, area and volume are interchangeable.
- area and perimeter are the same or confuse one for the other.
- the only way to find area of a given shape is length x width.
- volume can be found by determining the area of a single face on a prism and multiply that by the total number of faces.
- area and volume are the result of plugging numbers into a formula. They do not understand the concepts of area and volume.
- Students believe all dimensions have the same similarity ratio.
- Students confuse squaring ratios and using the square root of ratios when converting between linear and area ratios.
- Students confuse cubing ratios and using the cube root of ratios when converting between linear and volume and ratios.

##### Additional Resources

- Lappan, G, Fey, James, Fitzgerald, W, Friel, S, and Phillips, E. Connected Mathematics 2: Filling and Wrapping. Boston: Pearson, 2009. Print.
- Learn Zillion (http://learnzillion.com/)
- CCSS Math (http://ccssmath.org/?page_id=67)

##### Pre-Unit Assessment Instrument

A written pre-assessment will be given to students on the first day of the unit.

##### Post-Unit Assessment Instrument

A summative written post-assessment will be given to students on the last day of the unit.

##### Results: Evidence of Growth in Student Learning

After teaching the Unit, present the evidence below that growth in learning was measured through one of the instruments identified above. Show results of assessment data that prove growth in learning occurred.

Designing the Perfect Desk Pre- and Post-Assessment Scores

##### How to Make This a Hierarchical Unit

Standards that would be used for a high school unit:

**Solve real-life and mathematical problems involving angle measure, ****area, surface area, and volume.**

- Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Activities that might accompany the unit for a higher level are activities involving the formulas for a circle, perhaps for a place on the desk to put a pencil holder. In terms of 3D geometric figures, pyramids would also have to be included, not just prisms.

##### Reflection

This unit was rushed due to snow days, testing, and field trips at the end of the year. Next year, I will have to do some advanced planning to ensure that there is enough time to complete the unit as planned. I felt that the unit overall went well. The students had a real-life application for volume and surface area and they were motivated to design the desks because of the examples and advertisements that I shared with them. I also liked how I got the students to come up with the idea of desk design by just asking them the question, “how can we improve student lives?”

##### How to Make This a Hierarchical Unit

##### Reflection

##### How to Make This a Hierarchical Unit

##### Reflection