Sample Tasks
Common Core-CTE Task Alignment
Note: These tasks have been provided as examples only. It is suggested that you ask participants to bring tasks that are relevant to their content area. Keep in mind that these tasks are works in progress. As you read each sample, consider how they could be improved and aligned.
Extra Tasks 1 [Type text] [Type text] [Type text]
Indirect Measurement Problem
Figure 1 shows a person’s hand held up 2.0 feet in front of his or her eye.
Suppose that the person’s hand is 7.0 inches long and just blocks out a friend who is 6.0 feet tall. Figure 2 shows this.
Figure 2.
1. Name three pairs of triangles that are similar in Figure 2.
2. If the person’s hand is 2.0 feet from his or her face, how far from the person is the friend? Round your answer to the nearest tenth of a foot. (Note: Watch the units.)
3. How much does your answer change if a ¼-inch error is made in the hand measurement and the hand is 7 ¼ inches long?
4. The Washington Monument is 169 meters high. How far do you have to stand from it to block it out with your hand? Assume that your hand is 18.0 centimeters long and you hold it 50.0 centimeters from your eye. (Note: Sketch the situation first.)
Source: Adapted from ResourceMap
Extra Tasks 2 Ramp Problem (architecture/pre-design/ mechanics)
Task Design a wooden ramp that complies with the Americans with Disabilities Act (ADA) requirements for a doorway that is 3 feet above ground level. Calculate the board feet needed for the ramp itself. Calculate the angle at which the ramp boards must be cut to ensure that the bottom edge is tapered to meet the base of the ramp maintaining minimum slope requirements defined by ADA.
Here are the relevant excerpts from Section 4.8 “Ramps” of the ADA Guidelines for Buildings and Facilities:
4.8.1. General. Any part of an accessible route with a slope greater than 1:20 shall be considered a ramp and shall comply with 4.8.
4.8.2. Slope and Rise. The least possible slope shall be used for any ramp. The maximum slope of a ramp in new construction shall be 1:12.
4.8.5. Handrails. If a ramp run has a rise greater than 6 in (150 mm) or a horizontal projection greater than 72 in (1830 mm), then it shall have handrails on both sides.
4.8.6. Cross Slope and Surfaces. The cross slope of ramp surfaces shall be no greater than 1:50.
Special calculations are required for curved ramps because:
a. Inside curve slopes are steeper than outside curve slopes since slopes are a function of rise over run; the shorter distance creating a steeper slope.
b. Curved ramps, when in full compliance with slope and cross slope requirements, are in fact a warped plane. Tighter the radius of a curved ramp, the more warped the surface.
c. Currently, there are no technical recommendations available on minimum curve radii to maintain a reasonably level ramp surface; research may be initiated by the DOJ on this point.
Source: Adapted from Hawai’i American Diploma Project tasks
Extra Tasks 3 [Type text] [Type text] [Type text]
Possible Extensions
1) Student must determine what materials would be necessary to create a ramp designed to the ADA standards. 2) In groups, students design and build an appropriate ramp for a place in need. Students are responsible for all stages of the project from communication to completion. 3) Students determine ADA-compliance of ramps at the school or local businesses.
Extra Tasks 4 Fences (architecture/pre-design)
Task A rectangular swimming pool has been commissioned, and the client wants a fence 4 feet from each pool edge. The client has 120 feet of fencing with which to enclose the pool.
1. If the pool is designed to be 30 feet long, how wide will it be? Explain.
2. Write an expression for the pool’s area in terms of its length (x).
3. The client wants the pool’s area to be as large as possible. What dimensions should the builder make the pool? Explain.
Source: Adapted from ResourceMap
Possible Extensions 1. Student is given options of different fencing (e.g. type of material, size of fence). Based on price, longevity, and stability, student must identify which fencing material is best for the project and defend his/her answer in a mock client presentation.
Extra Tasks 5 [Type text] [Type text] [Type text] 2. The builder needs the section between the pool and the fence to be filled in with concrete. Student must determine how much concrete is needed for the job and determine the total cost.
Floor Plan (architecture/pre-design)
Task Use the plans below to solve the problem. After the chalk lines locating the walls are marked on the subfloor, the next step is to lay out the wall plates. How many linear feet of wall plate material do you need for the walls in red below (add 10% for waste)? Remember the walls are made up of a bottom and two top plates. Don’t reduce the amount for openings or wall finish materials. Note: Interior walls are 4 ½ inches thick; exterior walls are 6 inches thick.
L.F. of wall plate = ______
Amount for waste = ______
Total L.F. of wall plate = ______
Source: Adapted from Hawai’i American Diploma Project Work
Possible Extension 1. Student must design the other side of the house to include: a kitchen, dining room, bathroom, and den. Student must then determine new wall plate needs based on new design.
Extra Tasks 6 False Positives (health sciences)
Suppose a cancer test is 92% accurate: if one has the disease, the test comes back "yes" 92% of the time (and "no" 8% of the time), and if one does not have the disease, the test comes back "no" 92% of the time (and "yes" 8% of the time). In a town of 48,730 people, 0.5% of people actually have the disease. In your solutions, round up to the nearest person.
1. How many people in the town have cancer? (How many do not?)
2. Of the people that do have cancer, how many will test positive on the test?
3. Of those that do not have cancer, how many will test positive on the test?
4. If a person tests positive, what is the probability that the person has cancer? What is the percent?
5. If a person tests negative, what is the probability that the person has cancer? What is the percent?
Source: Adapted from http://www.j-bradford-delong.net/movable_type/archives/001394.html
Extra Tasks 7 [Type text] [Type text] [Type text]
Task: Spread of Disease (health sciences)
Disease can spread quickly in enclosed spaces, such as on an airplane. The spread of the flu is modeled by the equation where P (t) is the total number of passengers infected after t days of a trip on an airplane.
1. Estimate the initial number of people infected with the flu.
2. Haw fast is the flu spreading after 3 days?
3. When will the flu spread at its maximum rate? What is the maximum rate?
Source: Adapted from http://yale.edu/ynhti/curriculum/units/2009/5/09.05.08.x.html
Extra Tasks 8 Grain Silo (agribusiness)
Farmer John stores grain for the small town of Bakersville in a large silo located at the edge of his farm. The cylinder-shaped silo has one flat, rectangular face that rests against the side of his barn. The barn is 5 feet from the center of the silo. The height of the silo is 30 feet and the face resting against the barn is 10 feet wide. This silo holds the exact amount of grain Bakersville requires for the year.
1. Determine the capacity of Farmer John’s silo in cubic feet of grain.
2. The Bakersville agriculture committee has predicted a 23% increase in grain consumption for the next year. What is the new amount of grain required in cubic feet?
3. Farmer John will now need to build a new silo. Design a new grain storage facility for the town of Bakersville. Source: Adapted from Algebra.com.
Task – Rabbit Food (Food Products & Processing Systems)
In order to ensure optimal health rabbits must be fed a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein and should be fed no more than five ounces of food a day. Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. Taking into account cost, what is the optimal blend? Extra Tasks 9 [Type text] [Type text] [Type text]
Source: Adapted from Purplemath.com.
Bluegrass Shipping Company (business management)
Extra Tasks 10 Your small furniture building company makes unfinished tables and chairs. Each table uses 40 board feet of wood. Each chair uses 20 board feet of wood. It takes 6 hours of labor to make a table and 8 hours of labor to make a chair. There are 2000 board feet of wood available in the shop and 15 employees who are each scheduled to work 40 hours for the next week.
1. Let T represent the number of tables your employees can produce in the next week and C the number of chairs. Write inequalities that relate T and C to the total available amount of wood, and to the total available hours for labor.
2. Draw a graph that represents this situation. Label the axes and ALL boundary lines, identify any intersection points, and shade the region of the graph that includes all feasible numbers of tables and chairs (feasible region).
3. Can your company produce 30 tables and 35 chairs in the next week? Can you produce 50 tables and 10 chairs in the next week? Explain your answers, identifying shortages when necessary.
4. If the company wants to sell the tables and chairs in sets of 1 table to 4 chairs, what is the maximum number of sets your employees can build in the next week? Explain how you know your answer is correct.
5. After building the maximum possible number of sets of tables and chairs from question 4 there is likely to be some labor and wood remaining. How many man-hours and board feet are remaining after the sets are completed? Show how you found your answer.
6. Each employee will need to be paid for their full 40 hours and as much of the wood as possible should be used. How will you most efficiently use the remaining man-hours and materials to the best advantage for your company? Explain your reasoning.
Source: Adapted from ResourceMap
Extra Tasks 11