Fawn Nguyen’s Olive problem

Last night Fawn Nguyen posted a neat problem for kids:

How would you solve this? There are 75 olives, 40% of which are green. I eat some of the green olives until 10% of the olives that remain are green. How many green olives did I eat?

— Fawn Nguyen (@fawnpnguyen) November 13, 2017

I thought it would be fun to try out the problem with the boys this morning. My younger son went first (while my older son was practicing viola in the background). He described his approach as “guess and check”:

My older son went next. I think we wasn’t super focused at first because Fawn’s problem about 75 olives became a problem about 40 apples, but once he got back on track he found a nice solution. His approach looked at the number of non-green olives since that number stayed constant:

It was fun to see the two different approaches, and also interesting to see that my two kids approach percentages very differently. This was a nice problem to start the day.

Two AMC8 problems that gave the boys a bit of trouble

I had a couple of things going on today and just asked the kids to work through an AMC 8 rather than doing a longer project. Each had one problem that gave them some trouble, so we turned those problems into a short discussion.

Here’s the first problem – this one gave my younger son some trouble – it is #21 from the 1992 AMC 8:

 

Here’s our discussion of the problem:

 

Here’s the 2nd problem – it is problem #24 from the 1999 AMC 8.

There’s some questionable advice from me and also some terrible camera work, but it was a nice discussion!

I like using the AMC problem to help the kids see a wide variety of accessible mathematical ideas. Despite being in a bit of a rush today, this was a fun project.

What a kid learning math can look like – fraction confusion

My younger son is currently in the review section on percents in his algebra book. Last night he chose a fairly standard problem on percents for our movie. The arithmetic with fractions tripped him up a little, though. The first video shows his struggle:

After we finished the problem I decided to propose an alternate solution just to get him a second round of fraction practice. His work here was really good, but the fraction arithmetic at the end still also gave him a tiny bit of trouble:

You never know what’s going to give a kid difficulty and it is interesting to watch them try to work through these unexpected struggles.

What a kid learning math can look like – percents

My son was confused today by a percent problem from Art of Problem Solving’s Algebra book. I liked the problem a lot and thought talking through it would be really helpful for him.

Here’s the introduction to the problem plus some initial steps – he is really confused about how to get going with the problem. His initial thought is to combine equal amounts. That gets us going, but he struggles to see where to go after that:

 

At the end of the last video we were still a little stuck. He knows that we need more than 1 cup of the mixture with more fat and less than one cup of the mixture with less fat. Our first try here is a new split – 1.5 cups and 0.5 cups. This mixture turns out to have too much fat, but it does help us understand the problem a bit better.

 

To finish up the conversation today we summarized what we’d done so far. That gave him the idea to try a split of 1.25 and 0.75. This split got us to the right answer. We’ll revisit this problem again to see how algebra can help us solve it.