Final Exam Review

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 ‘Fair Share’ or ‘Repeated Subtraction.’

9. (Ch.2 & Ch.14) Working with Bases other than Ten—operations in other bases and converting to base ten or from base ten using an algebraic model

10. (Ch.12 & 13) Be able to model distance/time using a qualitative graph

CH 14 & 15 Test Review

1. Write an equation that models the information from a story problem
2. Write an equation that models the information from a graph
3. Write a story problem that could be modeled by a graph
4. Create a qualitative time/speed graph and answer questions from information given in a story problem
5. Determine if a situation is better analyzed using a weighted average or regular average, and clearly explain your reasoning
6. Create an equation by examining a pattern (geometric and arithmetic sequences)

CH 12 & 13 Test Review

You should be able to:

1. Create a graph from information given about a situation
2. Determine the slope of a line and its relevance in the context of the problem
3. Interpret a graph in the context of the problem
4. Evaluate a graph for graphing conventions
5. Create qualitative graphs that compare distance from a position vs. time, and total distance traveled vs. time

CH9&10 Test Review

1. Find the portion of a rectangle, use proportions to determine appropriate mixture
2. Compare ratios to determine relative strength
3. Make a drawing and give an explanation to illustrate and answer multiplicative reasoning
4. Modify a drawing to represent fractional parts (percentages).
5. Use proportional reasoning to solve word problems
6. Estimate percentages and explain how you arrived at your estimate
7. Create proportional reasoning questions for given scenarios
8. Use white (positive) and dark (negative) dots to model addition, subtraction and multiplication

Ch.7&8 Review

1. Be able to illustrate multiplication of fractions
2. Be able to illustrate division of fractions
3. Be able to explain additive and multiplicative comparison and be able to write word problems that illustrate this knowledge
4. Be able to illustrate multiplicative relationships (similar to the chocolate bar activity in ch.8) and use that knowledge to solve problems

Division by Fractions

Section 7.3
Dividing by a fraction can be thought about as repeated subtraction or sharing equally.
1/2 divided by 3/4 can be read as:
(a) Repeated subtraction: How much of the three-fourths are in a half? To model this, you would start with the ½ and subtract two-thirds of the ¾.
(b) Equal share: If three-quarters gets a half, how much would a whole get? To model this you would first consider how much of the half is equally distributed in each of the three quarters (each qtr gets 1/6), then using that equal share you can determine how much is in the whole (4/6 = 2/3).

Here are some sample word problems (from 7.3 #15) that use fractions for division.

Repeated subtraction:
15a. If a tortoise is timed traveling an average of 1 2/3 miles per hour, how long would it take the tortoise to travel 6 miles?
15a. The recipe you use to make holiday cookies uses 1 2/3 cups of flour for each batch of cookies. How many batches of cookies can you make with the 6 cups of flour.
15b. How many 2 ¾ feet long strips of ribbon can be cut from a ribbon that is 7 ½ feet long?
15b. If your pea patch is only 7 ½ square yards and the melon plants you want to grow require 2 ¾ square yards each. How many melon plants can you put into your pea patch? Show your work and explain your reasoning.

Sharing Equally:
15b. You have 7 ½ bags of mulch to cover 2 ¾ square yards of garden bed. If you want to distribute the mulch evenly over the garden bed, how many bags will you need to use for each square yard?
15c. If you want to share1 7/8 pizza with 3 people, how much pizza would each person get?

Converting Decimals to Fractions

TERMINATING DECIMALS: Put the decimal’s digits in the numerator. In the denominator, the number of zeros equals the number of digits behind the decimal. Example: (a) 0.079 = 79/1000 (b) 2.13 = 213/100
SIMPLE REPEATING DECIMALS: Put the decimal’s repeating digits in the numerator. In the denominator, the number of nines equals the number of repeating digits. Example: (a) 0.7979797979… = 79/99
COMPLEX REPEATING DECIMALS: Subtract the non-repeating digits from the combination of non-repeating digits and one set of the repeating decimals. Put this number in the numerator. In the denominator, the number of nines equals the number of repeating digits and the number of zeros equals the number of non-repeating decimal digits. Example: (a) 0.12379797979… = (12379 - 123) / 99000 = 12256/99000 (which can then be simplified) (b) 123.797979797... = (12379-123)/99 = 12256/99