Future Teachers' Conference

http://www.projectteach.org/Activities%20Programs/FutureTeachersConf.htm

Ch. 9 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

CH. 7 & 8 TEST 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 with 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?

Answer Key Corrections & Course Calendar Adjustment

Please refer to the on-line syllabus, as our course calendar has been adjusted to give us more time in Chapter 7 to work on fraction multiplication and division.

Also, the answer key for 7.3 problem #14 is incorrect. Please refer to my corrections for the answer key.

Fraction Strips

Here is the link to Fraction Strips http://seattlecentral.edu/faculty/alevy/images/fraction_strips.jpg

Chapter 6 Test Review

1. Pictorial representation of fractions: draw a fractional part of a discrete whole and draw a fractional part of a continuous whole.

2. Simplifying fractions: simplify a fraction and explain the process.

3. Equivalent fractions: determine equivalent fractions and use them to convert fractions into decimal numbers (i.e. convert denominators to powers of 10 for terminating decimals and to 9 or 99 or 999 … etc. for repeating decimals.)

4. Convert repeating and terminating decimal numbers to fractional form ( whole#/whole# form)

5. Given two decimal numbers, be able to find others between them

6. Use approximation to find an estimate of an answer with mixed numbers (adding, subtracting, multiplying, & dividing) .

7. Given two fractions be able to use benchmark (neighbor) numbers to find a fraction between them.

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: 0.079 = 79/1000

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: 0.7979797979… = 79/99.

COMPLEX REPEATING DECIMALS: Subtract the non-repeating digits from the digits after the decimal point that includes 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 digits. Example: 0.12379797979… = (12379 - 123) / 99000 = 12256/99000 (which can then be simplified).

Ch4 & 5 Test Review

You should be able to:

• create word problems for each type of model for multiplication and division . . . this means that you understand when they are best applied
• pictorially represent percentage problems and solve them using logic
• state whether your estimate is slightly higher or slightly lower than the actual answer without knowing the actual answer . . .this means that you are able to evaluate what you did to get your estimate
• use number sense to locate the decimal point in an addition, subtraction, multiplication or division problem answer (as opposed to the algorithm)
• when given a division problem, estimate the percent it represents
• convert very small and very large numbers into scientific notation, and use scientific notation to solve problems
• set up a problem so that it results in appropriate units (i.e. change seconds to hours or miles per hour to number of hours).

Powers of Ten Video

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html

Math and Music/Motion

This is a great place to ask questions of your group members about identifying EALR's and Standards, sharing sources for materials.

Math and Art

This is a great place to ask questions of your group members about identifying EALR's and Standards, sharing sources for materials.

Mathematizing Literature/Math & Culture

This is a great place to ask questions of your group members about identifying EALR's and Standards, sharing sources for materials.

Service Opportunitites

Please check out the webpage http://seattlecentral.edu/faculty/alevy/service.htm to find Schools and After-School Programs. New on the list, and for whom the contact persons are students in the Math for Teachers courses this quarter: Meany Middle School and Bailey Gatzert Elementary.

Dozenal Counting

This webpage was recommended by Sidney Deering. http://www.polar.sunynassau.edu/~dozenal/intro.pdf
Check it out as they use symbols to represent the digits ten and eleven.

Base 16

This fellow devised a very creative numeral system for base 16. http://www.artima.com/artimaicon.html

Mathematician as Elementary School Teacher

In an interesting article by a mathematician (Ron Ahroni), who took time off to teach in an elementary school, he tells about what he learned from this experience.
http://www.aft.org/pubs-reports/american_educator/issues/fall2005/aharoni.htm

Why we teach for conceptual understanding

http://www.youtube.com/watch?v=zs_z1M2yrLg