# SMTE 1350

## Final Exam Study Guide – SMTE 1350

The final exam study guide includes instructions and 20 practice problems related to numbers, operations, fractions, etc. The problems are designed to prepare future elementary teachers to demonstrate they understand the content of SMTE 1350 with Joe Champion during Spring 2012.

# Instructions for the Final Exam

1. This exam counts for 20% of your grade in the class.
2. The exam has 14 exercises for 100 points and must be completed during the scheduled time:The T/R at 9:30 final is Thurs, May 3rd, 8 am – 10:30 amThe T/R at 11 final is Tues, May 8th, 11 am – 1:30 pm.
3. To earn full credit on any problem, justify your solutions, make your reasoning clear, and always indicate your methods.
4. You may use a calculator with factory-shipped programs, 1 side of a 8.5 by 11 inch page written in your own handwriting, and a writing utensil, but nothing else.
5. This is a guide, which means exercises are sampled from among the ideas on the exam, but are obviously different from actual exam questions.
6. The exam is comprehensive, but focuses primarily on in-class content and assignments after 2/14/12 on the course calendar.

## Creative Review Activity

In order to remind ourselves about the most important things in the class, we worked as a class to create posters like “In SMTE 1350… WE DO…” wall panels (like the pictured example).

## Rules

• Stay Positive
• Tell the Truth
• Each line of text has equal width
• Use ALL CAPS
• Break the rules

## The 2-Color Counter Game

This is a two-person game designed to get students thinking about probability, negative numbers, and the concept of 0 pairs. I wouldn’t call it “fun”, but it’s interesting.

## Find the Common Value

Some applications of the number theory ideas LCM and GCD. Each involves finding a common value.

1. Shane has 72 inches of copper wire and 42 inches of steel wire.
1. What are the largest pieces he can cut these wires into so that each piece is the same length?  Explain how you determined your answer.
2. How many pieces of wire will he have?  Explain how you determined your answer.
2.  A school principal plans to form teams from 126 third-graders, 180 fourth-graders, and 198 fifth-graders.  Each team will be composed of students from the same grade, and all of the teams need to have the same number of students.  If all students participate, what is the largest possible size of the teams and how many teams will there be?  Explain how you determined your answer.
3. A scientist starts two experiments at the same instant.  In the first experiment, a measurement has to be made every 168 seconds, while in the second, a measurement has to be made very 108 seconds.  After how many seconds will the scientist have to make two measurements at the same instant?  Explain how you determined your answer.
4. Find the smallest whole number that is a multiple of both 72 and 378.  Explain how you determined your answer.

## Waffle Makers

This activity introduces students to the idea of GCD through the simple task of dissecting a rectangle into maximal squares.

## The Set-up

The Silver kids, Sydney, Scout, Sean, and Shay, love when Mom and Dad make them waffles for breakfast. Ever since an unfortunate accident with a rolling waffle (don’t worry, everyone’s okay), however, Mom and Dad have decided the kids will only get square waffles.

The Silvers have a big rectangular waffle maker (45 x 35 squares), so they just cut the largest possible squares from whatever rectangular waffle they make inside of the waffle maker. If there is a leftover rectangle, the Silvers simply cut the largest possible squares from the leftover portion and so on. The parents don’t worry about passing out the waffles because the kids know how to share so that everyone gets enough for breakfast.