Maria's Math News, Vol. 49, January 2011

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Hello again! We're all starting a new year. This time the newsletter a review of a new math facts software, algebra word problems, and some other websites you might try.

1. Review of Math Rider software
2. Fraction of a fraction word problem
3. Two algebra 1 word problems (systems of linear equations)
4. Work & workers word problem
5. Tidbits

1. Review of Math Rider software

If your children like horses, they might fall in love with Math Rider game!

Math Rider is a "math facts" software game; that is, it specifically trains and practices the basic addition, subtraction, multiplication, and division facts.

Some special features include:

Each player has their own "account" in the game, and Math Rider is adaptive in that it trains those facts more that the child misses. I feel this is a great and important feature. More on that below...

I also really liked the statistics. You can see a color-coded chart that shows what facts the child has mastered, what s/he has some trouble with, and what s/he has lots of trouble with. Also, after each ride, the game shows you a bar chart with a bar for each fact in that ride. The taller the bar, the longer the child took to solve the fact.

Here is the home screen.
Continue reading my review

2. Fraction of a fraction word problem

A problem about fraction of a fraction...

The sixth-graders have a fundraiser. They raise enough money to reach 7/8 of their goal. Nikki raises 3/4 of this money. What fraction of the goal does Nikki raise?

The picture below shows first of all 7/8. Nikki raises 3/4 of this goal. We need to find 3/4 of 7/8.

It's not easy to directly see what is 3/4 of 7/8. So to do that, I divide each 1/8 piece into four pieces, and then color three of the four. That way I color 3/4 of each of the seven eighths.

Of course, those tiny pieces are now 1/32 parts. I have colored 3 x 7 = 21 of them. So, the colored part represents the fraction 21/32.

This problem is also simple to solve without a picture, if you understand what is asked. To find 3/4 of 7/8, you simply multiply those two fractions. The word "of" translates into MULTIPLICATION in fraction math!

 3       7      21
---  x  --- =  ----
 4       8      32

3. Two algebra 1 word problems (systems of linear equations)

Here are two problems for you to solve... OR to learn from me when I solve them. Both problems are for algebra 1, and use a system of 2 linear equations.

By the way, the comments have some wonderful ideas for solving these mentally, without using algebra. So please read them too!

Problem: John bought red pens for $4 apiece and blue pens for $2.80 apiece. If John purchased a total of 24 pens for $84, how many red pens did he purchase?

Solution: This is a typical problem that will have two variables and two equations.

Continue reading!

4. Work & workers word problem

Here's another one of those job / workers word problems (inverse or direct variation). Try and see if you can solve it using the "table" method instead of equations:

A certain job can be done by 18 clerks in 26 days. How many clerks are needed to perform the job in 12 days?

Again, we can set up a table and reason this out. Initially set it up like this:

jobs | clerks | days
--------------------------
  1  |  18    |  26
--------------------------
  1  |        |  
--------------------------
  1  |   ?    |  12

Then think of the "days" column. We want to "go" from 26 to 12. You could use a proportion here... or first figure out how many clerks are needed to do this job in 2 days, and then from that go to 12 days.

If 18 clerks do it in 26 days, then how many clerks would do it in 2 days... which is 1/13 the amount of time.... so we need 13 times as many clerks. 13 x 18 = 234 clerks are needed.

jobs | clerks | days
--------------------------
  1  |  18    |  26
--------------------------
  1  |  234  |   2  
--------------------------
  1  |   ?    |  12

Now, if 234 clerks do it in 2 days, how many clerks would do it in 12 days? Now, the time increases 6-fold, so we need only 1/6 as many workers.

234 / 6 = 39.

So 39 clerks are needed.

5. Tidbits

A book on education crisis
I'm just passing on a link that some of you might enjoy (or be sad about). I found it interesting -- a math teacher (Larry Zafran) telling his story of teaching math in an inner city high school in New York in the early 2000s. It appears not much was able to be done but to try to survive and get through the day while presenting the official curriculum topics in class, at least on the board.
EqualApp
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Free tutoring again
David Freeling is again offering promotion beginning January 7th. He will offer free math tutoring online for 4th and 5th graders on www.TutorTalk.org. Classes are open to all students on a first-come first-served basis. He hopes to provide a valuable resource for young learners while also giving users an opportunity to check out his site at no risk or cost.

Till next time,
Maria Miller

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