Finals Review

1. (Ch9) Proportional Reasoning: Create a drawing that helps you visualize the relationship and determine an amount prior to the increase or decrease
2. (Ch3, Ch8 & Ch9) Additive and multiplicative comparison and proportional reasoning: Be able to compare and contrast and write word problems that model them
3. (Ch3) Subtraction: Write problems that model "take away" and "missing addend"
4. (Ch6) Use benchmark numbers and number sense to estimate fractional values and find a number between fractions
5. (Ch5& Ch6) Estimate operations with percents, decimals, and fractions and explain your reasoning
6. (Ch4) Long Division: Use the scaffolding method which is sometimes called the "Big Seven" and compare it to the standard method of division
7. (Ch4) Division modeled using "Equal Share" or "Repeated Subtraction"
8. (Ch2 & Ch14) Working with bases other than ten: operations in other bases
9. (Ch12 & Ch13) Be able to model position/time using a qualitative graph
10. (Ch.7) Dividing by a Fraction: Write a word problem and model the solution process with a picture.

12.1, 12.2, ch14, 15.3-15.6 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 speed/time graph and answer questions from information given in a story problem (i.e.,over-and-back problem)

5. Create a distance/time and a total distance/time graphs (i.e., Wiley Coyote)

6. Solve a weighted average problem.

Ch.9, 10, 12.5, 13.1, & 13.2 Test

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

CH 6, 7, 8 Review

You should be able to:

1. Provide a pictorial representation of fractions, whether using a discrete whole or a continuous whole.

2. Write a decimal number as a fraction in simplified form: i.e 2.25 = 225/100 = 9/4, or .32525252525... = 322/990 = 161/495

3. Demonstrate your understanding of decimal numbers by finding numbers that would be between consecutive decimal numbers. i.e. what decimal numbers are between 0.2 and 0.3

4. Find a fraction between fractions with unlike denominators without converting to decimal numbers or using common denominators. This means understanding how “neighbor numbers” work.

5. Illustrate multiplication and division of fractions

6. Explain additive and multiplicative comparison and be able to write word problems that illustrate this knowledge

7. Illustrate multiplicative relationships (similar to the chocolate bar activity in ch.8) and use that knowledge to solve problems

Dividing by a Fraction

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 superimpose ¾ over it, then determine how much of the 3/4 is in the half.

(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). (Multiplicative reasoning covered in chapter 8)

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:
15a. It took you 6 hours to cover 1 2/3 chapters of the book. How much time did you spend per chapter?

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 share 1 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 decimal 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 to 1532/12375 (b) 123.797979797... = (12379-123)/99 = 12256/99

6.1 #20 Comparing Fractions

How do we know that: 1/4 < 2/7 < 1/3

If we have 7 pieces, 1/4 of 7 is (1 3/4), so: 1/4 = (1 3/4)/7 < 2/7

If we have 7 pieces, 1/3 of 7 is (2 1/3), so: 1/3 = (2 1/3)/7 > 2/7