# The Case of the Missing Blink Cards (Age 8)

## The Activities

1. Topic: Measurement. Book: Measuring Penny by Leedy. Lisa gets a homework assignment to measure something in a variety of ways. She decides to measure her dog Penny.
2. Topic: Sorting, Patterns, Charts. We have a card game called Blink, which has cards of six different colors, with six different shapes, and five different numbers (1 – 5). Here are some sample cards.

We calculated that there should be 6 * 6 * 5 = 180 unique cards. However, the Blink deck only contains 60 cards.  I asked the kids to figure out which cards are missing, and if there’s any pattern.

3. Topic: Protractors, Measurement, Triangles. Each kid got a protractor, and  triangle I had drawn before circle. We measured each angle, and then added them up to see what we got.

## How did it go?

We had 4 kids this week. Overall, it was a fun, focused circle.

#### Measuring Penny

We had read this book over a year ago. Some kids remembered it, but 3 out of 4 kids wanted to hear it again. This time I took several different breaks to discuss the book. For example, when they talked about ‘nonstandard units’, I measured one of the kids’ hair in number of “Corey Hands”. We also measured everyone’s ears in centimeter. The kids had a great time with the book, and stayed focused and interested.

We had told the kids about the missing cards several weeks ago, and they all remembered that there are supposed be 180 cards.  We recalculated it again, just to be sure.  Then I asked if we could figure out which cards are missing?  I started them off by sorting through the cards and showing that there were only two cards that had red lightning bolts on them.

The kids took over from there. At first they just randomly picked a color and shape, and looked for the matching cards. Soon this became unmanageable, so one of the kids suggested moving to the floor, and making a separate row for each color, and use columns for the shapes. This resulted in the following chart:

I then asked the kids several questions about the cards, which were easy to answer with this chart. How many of each color are there? 10.  How many of each shape? 10.

How many of each number? This one was trickier because the chart is not sorted by number. One kid wanted to rearrange the chart, but instead we went row by row looking for each number. We found there are 12 of each. We also found that for each color, there are two of each number.  During this time, two kids counted the attributes, and two kids were keeping notes.

One kid’s notes.

Next I asked how many cards are missing from each row? The kids looked at their chart, and said two are missing from each row. We then calculated there must be 12 missing cards total. But that would make only 12 + 60 = 72 cards, not 180, like we calculated.

I should have asked the kids where the other cards were, but instead I just showed them how to update the chart to sort by number too.  So we had a row for each color, and a column for each number/shape combination. Two kids helped me fix the chart:

The new chart.

Then we counted the missing cards in each row. This time we found there are 20 cards missing in each. 20 * 6 = 120 + 60 = 180!

#### Triangles and Protractors

I handed out several big triangles I had drawn with sharpie before circle. The kids used protractors to measure the three angles, and then add them up.

Using the protractor was still challenging for the kids, but they all made progress when I helped them. The kids added angles up to 180 four or five separate times. We also got 182  and 183 a couple times. Weirdly, when I did it myself, I got 188 for a triangle…Not sure why.  But the kids actually noticed that it was near 180 all the time, so we may be almost ready for the proof that they must always be 180.

My daughter measuring a triangle.

# Count on Pascal (Age 8)

## The Activities

1. Topic: Mathematicians, Pascal’s Triangle, Geometry. Book: Mathematicians Are People, Too, by Reimer. Chapter: “Count on Pascal”.
2. Topic: Protractors, Angles, Triangles, Quadrilaterals. We used rulers to each draw triangles. Then we measured each angle, and added them together. Next we tried out quadrilaterals and pentagons.
3. Topic: Pascal’s Triangle. The kids filled in Pascal’s Triangle as far as they could go.

## How did it go?

We had only three kids this week, which is usually very easy to manage. However, this week my daughter was in a very bad mood, and had to be sent out of circle during the story. The other two kids were a bit distracted by her, but did a pretty good job overall.

#### Count on Pascal

This was the first time I’ve read Mathmeticians Are People, Too. David’s read several chapters in past circles. I skipped a couple pages to keep the chapter shorter, but even so, the kids attention drifted. My daughter kept banging on the table and complaining about wanting a different book…she actually had to be sent out during the story which has never happened before.

The content of the chapter was pretty good, it discussed Pascal’s triangle, and his life. Unlike the ancient mathematicians, Pascal was not murdered for learning the dark arts of mathematics. By 1650, the world was a bit more prepared for math.

#### Geometry and Protractors

When Pascal was 12 he worked out a proof that the angles of a triangle add up to 180 degrees. Our first activity this week was to use a ruler to draw triangles, and then measure each angle and add them up.  I’m not sure if any kids had used a protractor before. It was a bit tricky to use because you have to orient the protractor correctly or you’ll get the inverse angle measurement.  With help from me, everyone measured and added their angles. We got between 170 and 185 for the sum.

Next we all drew quadrilaterals and measured and added the angles. This all took awhile because it required precision and help. At this point my daughter was tired of angles but the other two wanted to try pentagons.  So I let them continue and had my daughter work on Pascal’s Triangle.

#### Pascal’s Triangle

My daughter wrote down the first 10 rows of Pascal’s triangle pretty quickly, with no help from me. Eventually one of the other kids also started this activity, but their triangle wasn’t quite correct because they had missed a few of the numbers.