Pre-Algebra Extension Menu
Name______
Date______Section ______
Concept and/or Topic: Measurement
Choose a learning activity from one square to complete. If you choose the square, “Write your idea here,” please see the teacher with your idea first.
Circle the number of the learning activity you choose.
Turn in this paper with your work.
1. Carlos thinks that a trianglewith sides 5cm, 6cm, and 9cm forms a right triangle. Apply the Pythagorean Theorem to justify whether or not Carlos is correct.
List all possible Pythagorean Triples where the hypotenuse squared is 100 or less. Analyze any patterns you observe in your list. / 2. Compare two cereal boxes at your house based on surface area and volume. Many products today are designed to be “attractive” to the eye. According to the rule of the “Golden Ratio,” determine which box should be more “attractive” to consumers. Survey at least 10 individuals and ask them which of the two cereal boxes are more attractive. Analyze your results and conclude whether or not the “Golden Ratio” was a contributing factor. / 3. Examine the Farmer Baxter Painting Scenario and apply your knowledge of surface area to determine the most efficient use of paint for him to complete the job.
4. Draw a three-dimensional shape with at least 2 polyhedras. Dilate your figure by a scale factor of 3. Compare the surface areas and volumes of the two figures. Predict what would happen to the surface area and volume if the scale factor were changed to ¼. Explain how your prediction would change if you drew a figure with 3 polyhedras. / 5. Marketing and distribution of products is important in today’s global marketplace. You are to assume the role of “President of Marketing” to explore and develop the most cost effective means of packaging chicken broth. Read A Poultry Proposal and apply your knowledge of mathematics and experience as a consumer to develop your proposal. / 6. Write your idea here.
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Teacher Resource Page
Pre-Algebra Extension Menu
Concept and/or Topic: Measurement
Intended Purpose: Culminating activity for the unit or alternative activity for students who have mastered curricular indicators
Grade 8 Standards:
MA.800.10 KNOWLEDGE of ALGEBRA, PATTERNS and FUNCTIONS
MA.800.20 KNOWLEDGE OF GEOMETRY
MA.800.30 KNOWLEDGE OF MEASUREMENT
MA.800.40 KNOWLEDGE of STATISTICS
MA.800.50 KNOWLEDGE OF PROBABILITY
MA.800.60 KNOWLEDGE OF NUMBER RELATIONSHIPS and COMPUTATION
MA.800.70 PROCESSES OF MATHEMATICS
Indicators Addressed:
Box 1:
MA.800.20.10 Identify and describe the relationship among parts of a right triangle;
use the hypotenuse or the legs of right triangles * (2. A . 1b)
Box 2:
MA.700.30.15 Determine the surface area of geometric solids using rectangular prisms with
whole number dimensions (0-1000) *(3. C. 1b)
MA.800.30.25 Determine the surface area of cylinders, prisms, and pyramids SSL (3. C. 1e)
Box 3:
MA.800.30.25 Determine the surface area of cylinders, prisms, and pyramids SSL (3. C. 1e)
Box 4:
MA.800.30.30 Use proportions, scale drawings (with scales as whole numbers), or rates using
whole numbers or decimals to solve measurement problems (0 to 1000)* (3. C. 2a)
Box 5:
MA.600.30.25 Estimate and determine the volume of rectangular prisms with whole number dimensions (0 – 1,000) *( 3. C. 1b)
MA.700.30.15 Determine the surface area of geometric solids using rectangular prisms with whole number dimensions (0-1000) *(3. C. 1b)
MA.800.30.15 Estimate and determine the volume of a cylinder with whole number dimensions
(0 to 10,000) * (3. C. 1c)
MA.800.30.25 Determine the surface area of cylinders, prisms, and pyramids SSL (3. C. 1e)
Farmer Baxter Painting Scenario
Farmer Baxter must repaint his barn and silo. He will use white paint for walls and red paint for each roof. Calculate the amount of paint necessary to paint each structure. (Do not worry about windows.) One gallon of paint covers approximately 212 square feet. Determine how many one gallon cans of paint Farmer Baxter will need of each color to complete this job. To reduce waste, Farmer Baxter wants the least possible amount of each color of paint leftover. Compare the amount of paint needed for each figure. If he can only paint two of the four composite figures, which should he choose to paint? Justify your answers using words and numbers.
A Poultry Proposal?
Chicken broth comes in a box or can. Determine the volume of each container. Which container has the greater surface area? Evaluate the pros and cons of manufacturing each container. Develop a position as to which container you would choose in order to maximize your profits if you were manufacturing these containers. Explain your position in writing.
Pre-Algebra: Measurement