Review for Final Exam

1. (Ch.9) Proportional reasoning-- create a drawing that helps you visualize the relationship and determine an amount prior to increase/decrease
2. (Ch. 8 & Ch.3) Additive and multiplicative comparison--be able to explain and write problems that model these
3. (Ch.9) Proportional Reasoning--write a problem that models this
4. (Ch.7) Subtraction write problems that model “take away” and “comparison”.
5. (Ch.6) Use benchmark numbers to estimate fractional values
6. (Ch. 5) Estimate operations with percents, decimals, and fractions
7. (Ch. 4) Long division--use and explain the scaffolding method, sometimes called the ‘Big Seven’
8. (Ch 4) Division modeled using ‘Equal Share’ or ‘Repeated Subtraction.’
9. (Ch.2 & Ch.14) Working with Bases other than Ten—operations in other bases
10. (Ch.12 & 13) Be able to model position/time using a qualitative graph

CH 13 Test Review

1. Given a speed and distance determine time; given distance and time determine speed.

2. Create a qualitative speed/time graph and answer questions from information given in a story problem

3. Create a position/time and a total distance/time graphs

CH.9, 10, 12 Test Review

1. Create a drawing and give an explanation to illustrate multiplicative reasoning
2. Create a drawing to represent fractional parts
3. Use proportional reasoning to solve word problems
4. Use open (positive) and closed (negative) dots to model addition, subtraction and multiplication
5. Create a graph on a coordinate system
6. Determine slope of a line
7. Explain rate of change in context
8. Explain important points on the graph

Context for division by negative (If you find other examples, please share them by commenting on this entry.)

(1) My friend gave me 12 tickets and said I can owe her the money. The tickets are 4 for a $1. How much do I owe her for the 12 tickets? This could be solved by dividing 12 tickets by -4 to get -3, which means that I owe her $3.

(2) While scuba diving, it takes me 1/2 second to descend one foot. I was descending for 3 seconds. What is my change in depth? This could be solved by dividing 3 by -1/2 to get -6. Which means I have descended 6 feet.

(3) It is now 4pm. A few hours ago I had a dozen cookies. I have been eating the cookies at a constant rate of 4 cookies/hour. At what time did I start eating? This can be solved by dividing 12 by -4 to get -3. So 3 hours have gone by, which means I started eating the cookies at 1pm.