Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 8:
Homework

 We said previously that algebra has become very much concerned with operations. So far, the only operations we've used are the ones from arithmetic. Let's take a quick look at another kind of operation that often shows up in algebra. Consider the operation that divides a whole number by 3 and hands you back the remainder. This is usually called the "mod 3" operation. Example: 17 divided by 3 is 5 with a remainder of 2, so we say 17 mod 3 = 2, or 17 = 2 (mod 3). Problem H1 If the input is 5, what is the output?

 Problem H2 If the input is 12, what is the output?

 Problem H3 If the input is 2, what is the output?

Problem H4

Now try some undoing:

 a. Describe all the numbers that produce an output of 1. b. What is the "pullback" of 2? (The pullback of an output is the collection of inputs that produce it.) c. What numbers produce an output of zero? d. How many possible outputs are there for this function? What are they?

 Problem H5 Make an input/output table for this function. What kind of function is it?

 Problem H6 Make a list of all the numbers that leave a remainder of 3 when divided by 5 and a remainder of 1 when divided by 3, then give one rule that would find them all.

 Problem H7 If my age is divided by 3, the remainder is 2. If my age is divided by 5, the remainder is also 2. If my age is divided by 7, the remainder is 5. How old am I?

Problem H8

Here's a table showing the first two outputs for the linear function y = 3x - 2. Come up with at least two other functions that match these outputs, and complete the table using your functions.

 x 3x-2 Your function Your function 1 1 1 1 2 4 4 4 3 4 5