Math 201 Prof. Brick
section 2 Fall 02
Math Elem Ed Exam 1
Do the problems in order in your bluebook. Show your work. Give explicit
verbal explanations of your answers.
1. Using a numberline model of arithmetic with cars explain why subtracting a negative
is the same as adding a positive. Do not explain with examples.
2. Explain why we study arithmetic in different bases in this class.
3. Use two models, a partition model and repeated subtractions, describe 18 ÷5
4. Compute 425−245working only in base 5. Explain each of your steps using detailed
drawings of hands.
5. Explain why the distributive law holds using areas of rectangles.
6. Use a Venn diagram to determine if the following is valid:
All males love sports.
Pat loves sports.
Therefore, Pat is male.
7. Use a truth table to determine when the formula (¬p)→qis true and when it is false.
What simpler formula has the same truth values ?
8. List the nonempty subsets of the set B=n∅,{∅}o.
9. Write the contrapositive of the statement “if you love math then you are happy”.
10. Find the cardinality of the set {x|x=i−j, where i, j ∈ {1,2} }
