**SMTE Key Ideas**

** KSB 1: SURFACE AREA AND VOLUME CALCULATIONS**

** Students will know that: **

Volume is a measure of filling an object and surface area is a measure of wrapping an object.

*To demonstrate their understanding, students will: *

- Given representations of three dimensional (3D) shapes, students will compare and contrast volume and surface area.
- Given the outside dimensions and the mathematical formulas for the volume of each shape, correctly calculate the volume of four geometric shapes: a cube, a sphere, a square-based pyramid, and a cylindrical prism.
- Given the outside dimensions and the mathematical formulas for surface area for each shape, correctly calculate the surface area of four geometric shapes: a cube, a hemisphere, a square-based pyramid, and a cylindrical prism.
- Given two dimensional nets reflecting a variety of geometric shapes, convert the nets to three dimensional models.

**KSB 2: CONDUCTIVE HEAT FLOW**

** KSB 2A: Students will know that: **

Heat (q) flows from hot (T_{h}) to cold (T_{c}) through a material by conduction.

*To demonstrate their understanding, students will: *

Given an object with a temperature difference from one side to the other, students will describe that as the temperature difference (ΔT) increases, the conductive heat flow (q) increases.

** **

**KSB 2B: Students will know that: **

Since heat is transferred from a hot temperature (T_{h}) to a cold temperature (T_{c}) through a flat surface, reducing the amount of surface area reduces heat transfer.

*To demonstrate their understanding, students will: *

Given objects with different surface areas (everything else being equal) the student will analyze how surface area affects conductive heat flow.

** **

**KSB 2C: Students will know that: **

Different materials conduct heat at different rates depending upon their thermal conductivity. Thermal conductivity is symbolized by the letter (*k*).

*To demonstrate their understanding, students will: *

- Given a list of materials with different k values, students will differentiate those that are good insulation materials from those that are not.
- Given a heat source and two objects of the same dimensions made from different materials, students will be able to evaluate how different materials affect conductive heat flow.

**KSB 2D: Students will know that: **

As the thickness of a material increases, the heat flow through it decreases.

*To demonstrate their understanding, students will: *

Given different thicknesses of the same material (everything else being equal) students will analyze how thickness affects conductive heat flow.

** KSB 2E: Students will know that: **

The formula that relates heat flow (q) to its determining factors is q = kA (T_{h} -T_{c})/L

*To demonstrate their understanding, students will: *

Given the heat flow formula and a standard calculator, students will correctly formulate an outcome based upon manipulation of the variables in the formula.

** **

**KSB 3: ****RELATIONSHIP BETWEEN K VALUE AND R VALUE**

**KSB 3: Students will know that: **

- k value and R value are both measures of a material's resistance to heat flow. k value relates only to the type of material where R value also takes into account the material's thickness (L).
- Since R value takes thickness (L) into account, yet is related to k value,
**R, L, and k can be expressed in a relationship**. The R value of a material equals its thickness / its k value (**R=L/k).** - The total R value (R
_{t}) of a system of materials is the sum of each of the individual R values (R_{t}= R_{1}+ R_{2}+ R_{3 }+R....).

*To demonstrate their understanding, students will: *

- Given information about k value and R value, students will describe the similarities and differences between them.
- Given information about the relationship between k value, R value, and thickness of a material, students will analyze a variety of materials to determine differences in k and R value.
- Given k values and thicknesses for several different materials, students will calculate the R value of each material using the formula R = L/k.
- Solve for heat loss using the formula
**Q = A (ΔT) / R**given surface area, R value, and ΔT. - Given individual R values of several materials, students will determine the total R value of a system made from layers of those materials by summing the individual R values.

**KSB 4: STRUCTURAL DESIGN**

**KSB 4A: Students will know that: **

Dead loads, live loads, and wind loads are among those that have to be taken into consideration when designing a structure.

*To demonstrate their understanding, students will: *

- Given information about dead and live loads, students will define dead load as a load of constant magnitude (such as the weights of the materials of construction) and live load as a load that changes in magnitude and/or location (such as people in a building, or cars on a bridge).
- Given a representation of wind blowing against a tower on a foundation that supports a platform with a filled water tank upon it, students will correctly label dead loads and live loads.
- After engaging in an activity that shows the effect of wind on a structure (such as playing a game that illustrates how wind affects a structural shape, or seeing a video of “Galloping Gertie,” the Tacoma Narrows Bridge Collapse), students will recognize that wind loads have to be considered in designing a structure in addition to “dead loads” and “live loads.”

** **

**KSB 4B: Students will know that: **

Structural integrity refers to the ability of individual structural members that comprise the structure (and their connections) to perform their functions under loads.

*To demonstrate their understanding, students will: *

Given a representation of a structure that supports a load, students will recognize that a lack of structural integrity would affect the structure’s ability to stand up under load.

**KSB 4C: Students will know that: **

Selecting materials involves making tradeoffs between qualities.

*To demonstrate their understanding, students will: *

After explaining that structural integrity depends upon the ability of individual structural members that comprise the structure to perform their functions under loads, students will explain how selecting materials for a structural project involves making tradeoffs between competing qualities such as its strength, cost, availability, and the ease of working with the material.

**KSB 4D: Students will know that: **

The overall stability of a structure refers to its ability to resist overturning and lateral movement under load.

*To demonstrate their understanding, students will: *

- Given the challenge to improve the structural stability of a structure students will select improvements that will help the structure resist overturning and lateral movement under load.
- After investigating the shape of 3 D structures, students will evaluate the wind load effect on these shapes.

**KSB 4E: Students will know that: **

Structural design is influenced by climate and location, function, appearance, and cost.

*To demonstrate their understanding, students will: *

After reviewing images or models of a variety of structures built for different purposes in different geographic areas (deserts, mountains, icy climates) students will describe how structural design is influenced by function, appearance, cost, and climate/location.

**Team-based Design Challenge Learning Objectives **

**Prerequisite**

Learns must individually complete knowledge and skill builder singleplayer levels that are focused on surface area and volume of geometric shapes; conductive heat flow; k and R value; and structural design.

**Purpose**

8^{th} Grade Technology Education (or ETE) learners will:

- Develop an appreciation for the use of STEM skills applied in a “real-life” context.
- Apply individual KSB skills situated in a complex design problem scenario.
- Develop an appreciation for team work in solving a complex design problem.
- Develop an understanding of the Informed Design Process.

**Learning Objectives**

Working in teams of four on an emergency shelter design challenge problem, the learner will:

- Consider more than one shelter design before making their final choice of shape and size.
- Determine and defend the choice of shape of the shelter design.
- Demonstrate that their shelter meets design specifications.
- Calculate the surface area and volume of the shelter.
- Calculate the minimum R value of the shelter exterior
- From a variety available, select the most appropriate materials for the shelter exterior to that will provide the necessary insulation.
- Determine and defend the choice of framing for their shelter design that will provide the necessary structural integrity.
- From a variety available, select the most appropriate materials for the shelter framing that will provide the necessary structural strength.
- Determine, through use of mathematical modeling, if their shelter design will limit heat loss (in BTU/hour) to less than the heat generated by the body heat of the shelter inhabitants
- Communicate their achievements to an interested audience