Portfolio PBA4

MAE 4310 Fall 2022 – Portfolio Assignment

[Put your name here]

This assignment is designed with the following goal in mind: to demonstrate your understanding of four mathematical content areas: Number and Operations, Algebraic Reasoning, Statistics and Data Analysis, and Geometry and Measurement.

Part One: Number and Opera0ons

This part should be finished already. Just copy and paste PBA (Performance Based Assessment) # 4 Lesson Plan here.

Part Two: Algebraic Thinking

Problem

What is the same as 10?

Supporting Questions:

There is an infinite number of expressions that are the same as 10. Produce a list of 10 expressions that are the same as 10 (for example, 5 + 5 is an expression that is the same as 10). However, there is a catch. I want you to show variety in the expressions that you choose to demonstrate the diverse types of mathematical understanding you possess. For example, 103 / 100 would show your understanding of exponents while 5 + 5 shows your understanding of addition. Below, write each expression and state the mathematical understanding you are displaying. Remember, variety is important. Example solution, 103 / 100 Exponents.

Part Three: Geometry and Measurement

Summarize

1) Typically, in mathematics, the teacher gives students problems where they need to calculate and find the “answer.” For example, 3 + 7 = _____. How is the previous question different from this approach?

2) What can the teacher learn from looking at student’s responses to the problem what is the same as 10?

3) Fill in the blanks. 3 + 8 = ___ + 6 What is the correct answer? Students often answer this question with 11 or 17. Why would these answers make sense to a student? What misconceptions do students who answer 11 or 17 have?

4) How would you as the teacher build on the original problem “what is the same as 10?”, to help address the misconceptions pointed out in question 3.

* You may create the table using pen/paper and insert a photo of your work here instead of typing your answers below

Problem

Use one of each of the following shapes to complete this section: 1 rectangle, 1 triangle, 1 composite shape, and 1 trapezoid. Construct each shape so that it fits one of the following conditions:

1) A shape with a perimeter that is not equal to the area. 2) A shape with the perimeter equal to the area. 3) A shape with a perimeter greater than the area. 4) A shape with an area greater than the perimeter.

In the table below, draw the shape and label its dimensions, calculate the perimeter, and calculate the area.

Notes: Consider using the Pythagorean theorem to find the height or hypotenuse of the triangle or use Pythagorean triples to create the triangle. If any of the above conditions are impossible to meet, explain why.

Draw the shape and label the dimensions

Find the perimeter Find the area

1 A shape with a perimeter that is not equal to the area.

2 A shape with the perimeter equal to the area.

3 A shape with a perimeter greater than the area.

4 A shape with an area greater than the perimeter.

Draw the shape and label the dimensions

Find the perimeter Find the area

Part Four: Sta+s+cs and Data Analysis

Summarize

1) Typically, a teacher will provide the shape and dimensions and ask students to calculate the area and perimeter. What was the difference between these problems? How did this way of asking the questions develop your learning beyond the typical approach? Provide three specific examples of things that you learned (or explored) by completing this problem.

Problem

What does it mean to interpret the mean as a balance point?

Supporting Questions

For each dataset in 1-4 find the meaning. Show or explain how you found the meaning. As you go along try to think about how you could find the mean mentally without simply applying the formula to the complete set.

1) 10, 10, 10, 10, 10

2) 10, 10, 10, 10, 8, 12

3) 8, 12, 9, 11, 10

4) 15, 5, 2, 18

For each question 5-7, construct a dataset that fulfills the given constraints.

5) Create a dataset with 6 values and a meaning of 20. Explain how you selected the numbers.

6) Create a dataset with 6 values, a single mode of 25 and a mean of 20.

7) Create a dataset with 5 values, mean of 20, median of 18.

Summarize

1) Suppose you want to explain to a younger sibling how to create datasets with a given meaning. What would you say?

2) The concept you explored in the problems above is the meaning as a balance point. What do you think this means? Use your experience with these questions to support your answer.