Math

This week we took a break from RightStart Geometry and worked on Challenge Math.

We used Chapter Two of the book, having completed Chapter One several months ago. Chapter 2 is on Problem Solving, and presents several ways to approach various problems: charts and diagrams; think 1; Venn diagrams; patterns, sequences and function machines. Nothing integrates all the various methods -- for example, it's pretty clear that we're studying, say, charts and diagrams, and all problems in this sections are going to be solved using charts and diagrams; and no problems using Venn diagrams will be sneaking in.

We did one section per day. We read through the explanations together. I copied off the page(s) of problems, and Kid1 worked from the copy, using stacks of scrap paper. In the end I stapled all of her scrap paper to the copy of the problems, so we can save it all together as a sort of homemade workbook.

By the way, the answers to all of the problems are in the back of the book, along with a good explanation of how to get the answers.

The first section we tackled was charts and diagrams. This included problems such as: Marilyn had a bag of gold coins. She gave 1/8 of them to her mother and then gave 1/2 of what was left to her brother. She then gave 2/7 of what was left to her dad. If she then had 25 coins left, how many did she have originally?

The method given to solve this is to draw a rectangle representing the original amount of coins, then start divvying it up according to what went where ... so, 1/8 of the rectangle is marked off to show that amount went to her mother, then the rectangular area left is divided into half to show what went to her brother, etc. etc.

Me: "This looks a lot like Singapore math."

Kid1: "Yeah, pretty much."

Next day we took a look at "think 1". This helps with problems such as: a group of 24 college students decided to climb Mt. McKinley. They bought enough food to last 20 days. If 16 additional students join them, how many days will their food last?

To solve this type of problem, you think how long the food will last for 1 student -- which is to say, if only 1 student went, having that amount of food, how many days would the food last? It would last 480 days. So if you have 40 students, that same amount of food should last 12 days.

The problem that we most discussed in this section was about cats: Jay has 8 cats that need to be fed while he is away on a 12 day vacation. If a bag of cat food will feed 3 cats for 15 days, how many bags does he need for his vacation?

Setting aside the image of the litter box situation after a 12 day vacation (is someone coming over to clean them out? and, just how big is Jay's house to hold 8 cats?) we found ourselves remarking that a) there's no way there's going to be an "average" cat in the bunch -- some will be big eaters and some won't eat much, and b) eating patterns vary wildly when the routine is disrupted by vacation -- some will gorge and some will refuse to eat.

But Kid1 starting in on her calculations, and soon discovered that it was going to take a bit more than 2 bags.

"Okay, he needs to buy 3 bags, then."

"Umm, I think they want to to figure out how much more...like two-point-something-or-other."

"Well, that's dumb, because you can't buy partial bags. And anyone leaving for 12 days should leave extra on hand, anyway, in case something happens -- you're not going to measure it out that precisely."

Next section, Venn diagrams. Coincidentally, Poppins posted a link to this site, just chock full of Venn diagrams, the same day we did this section. This was an easy, fun section.

Finally, patterns, sequences and function machines gave us tips on how to solve questions like: in the following sequence, what is the 500th term? 7, 16, 25, 34 .... (the answer is 4498, by the way).

Overall, it's been a fun week of math.