# Building Benches

 Author: Katie Doyle Unit Title: Building Benches Grade: 7th/8th Subject: Mathematics Estimated Duration: 10 bells Unit Activities: Activity 1: Introduction Activity 2: Design It, Scale It, Sketch It Activity 3: Ordering Materials Background Knowledge:  Students will come with varied knowledge.  All students will have some understanding because of their work on unit 4. Some of the concepts that proportional reasoning is built upon are: understanding of rational numbers, multiplicative reasoning, relative thinking, understanding quantities and change, spatial reasoning, measuring, linear models, area and volume, unitizing, comparing quantities and change, scaling up and down and partitioning. Date: July 2014
##### The Big Idea (including global relevance)

The big idea for this unit is furniture. Students will explore how furniture has changed and why furniture is made the size that it is.

##### The Essential Question

How do we design benches that will be the correct size for our bodies?

##### Justification for Selection of Content

In this unit, students will explore proportionality. Proportional reasoning is a concept that is essential for students to continue further in their study of mathematics. This is the overarching concept that students should have mastered by the end of their middle school years.

##### The Challenge

Student teams will build a bench that is a given height in under \$30 using 2 X 6 boards, 2 X 4 boards, 4 X 4 boards, a hammer and nails.

##### The Hook

The teacher will read Goldilocks and the Three Bears to the students. The teacher will ask questions about what makes Baby Bear’s items “just right”.

##### Teacher's Guiding Questions

Activity 1

1-What are the steps in the EDP?

2-How has the size of furniture changed over time?

3-What challenge could we design to show our understanding of this?

4-What are guiding questions that you will need answered to solve this challenge?

Activity 2

1-What height should our benches be?

2-How many students should each bench fit?

3-What is the best design to use?

4-How will we use Google Sketchup to build a model of our bench?

##### Activity 3

1-How do we know what type and how much of each material we need?

2-How do we access and navigate the websites?

3-How do I make an organized spreadsheet so that materials can be properly ordered?

##### Activity 4

1-How do we build our bench to the design we created?

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

Real World Applications: All of us use furniture every day. The size of the furniture matters. Students will determine what materials they need, make a plan for their design, order the correct materials and build a bench.

Career Connections: There are many engineering careers that focus on building. They could be Materials, Manufacturing, Construction or Building Engineers. In addition, careers involved in carpentry are connected to this unit.

##### Engineering Design Process (EDP)

The Engineering Design Process is evident in this unit during each activity. In activity one, students will define the challenge and complete necessary research. In activity two, students will be brainstorming possible solutions and will determine one solution and create a prototype of it on Google SketchUp. In activity 3, students will order their materials referencing back to their constraint of no more than \$30. Students will also redesign at this stage if needed. During activity 4, students will build the actual bench they have designed.

RP 2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

G1: 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.

G2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.

G6: 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.

G1:Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines

G2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

G3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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

Activity 1: Identify the Problem, Identify Criteria and Constraints

Activity 2: Brainstorm Possible Solutions, Generate Ideas, Explore Possibilities, Select an Approach, Build Model

Activity 3: Redesign if model does not meet constraints

Activity 4: Build actual design

##### Misconceptions

Students will often use additive reasoning instead of multiplicative. Students will not understand the difference between proportional and non-proportional situations. Students will not confuse fractions, rations and proportions.

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

Proportional reasoning should be taught during the Middle School years. However, being able to reason proportionally will help students understand concepts in high school. In high school, students can determine whether a linear relationship is proportional or not. They could also study interest rates. They could explore the effects of doubling the rate of interest earned. They could look at differences in simple and compound interest. They might look at relationships when a diagonal of a square is doubled and what effect that has on the perimeter and area. Students could look at relationships of solid figures when height, length or width is doubled. Students could look at triangles and explore angle sizes with side lengths. Most of these topics could be explored designing a bench at the high school level, simply using different criteria and constraints.