Thursday, February 12, 2009

Math problems of the week: 6th grade Connected Math vs. Singapore Math

1. The final word problems on percent in Connected Math's "More about Percents," Bits and Pieces II: Using Rational Numbers, p. 26:

In a survey of 100 dog owners about their pets' habits, 39% said that their dogs eat bugs. How many dog owners surveyed said this?

When 300 tarantula owners were surveyed, 26% said they let their spiders crawl on them. How many tarantula owners surveyed said this?

In a survey of 80 students, 40% said they had a savings account of their own. How many students surveyed said this?

During a survey of 80 students artists, about 6% said they had sold at least one of their works of art. About how many students surveyed said this?

2. The final word problems on percent in Singapore Math's "Percentage," Primary Mathematics 6A, p. 64:

A dress was sold for $42 after a 30% discounts. What was the usual price of the dress?

The price of a television set was increased by 10% to $2420. What was the price before the increase?

In a school choir, the number of boys was increased by 20% to 60 and the number of girls was increased by 20% to 60. Find the overall increase or decrease in membership of the choir.

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3. Extra Credit:

Estimate the percentage increase in mathematical understanding effected by bug and spider humor vs. problems that require higher level mathematical thinking.

4 comments:

lgm said...

Our m.s. now does percents as rote proportions...it avoids the problem of teaching decimal multiplication or actually understanding the problem and solution.

So, need 20% of 38?

Simply memorize this formula and set up your proportion:

% IS
-- = ---
100 OF

20/100=x/38

Cross multiply (38X20) and divide by 100.

It can all be seen here:
http://www.algebasics.com/3way3.html

mathercize said...

On the choir problem... should one of the 'increases' read as 'decreases'?

Kim said...

I can understand why teaching the percentage as a ratio would seem the easy way out. It is easy to calculate the percentages that way. It's also correct. A percentage, in my mind, is another way of saying "some portion" where the whole is normalized to 100. It is, of course, important for the students to understand the 40% is the same as .4 (which is 40/100). It is also very important for the kids to be able to read the problem to discover which part they are looking for. This set up is a great way to prepare for solving any of the missing pieces. What is the percentage of 10 out of 25? When you have 25% of 30, how many do you have? You have 12, which is 56% of what? Just because it's set up well and is easy to use doesn't make it invalid or a cheat.

lgm said...

Kim,
I have no problem with using the proportion method. I do have a problem with the rote aspect and the lack of visualization to go along with the verbage. IMHO it is unfair to students not to develop an understanding what a percent is, or why cross multiplying is done. The end result is that students cannot mentally figure tax or tip. They can however, pass the state exam without having to understand the problem.