## Thursday, September 24, 2015

### Talking Math with Your Kids #TMWYK through Chinese Cribbage

Now that summer is officially over I thought I might share a game I like to play when I am at my cottage during the summer months. I enjoy playing this game while I am unwinding from my crazy 10 months that I call a life. I am lucky enough that I have a cottage to hang out at with my family for the summer months. A few pics of what I get to enjoy.

If you are a fan of Talking Math with your Kids from Christopher Danielson or are a fan of the card game cribbage then this post is for you.

I grew up in a house where a deck of cards went a long way. I am the youngest of 4 and we all played cards. We played go fish, solitaire, euchre,  31, BlackJack, Kings in the CornerHearts, Cribbage and the list goes on.

In cribbage you get 4 cards and a starter card will get cut or flipped up.

SCORING
If you have not played cribbage here is how you score points:
• Each combination that adds up to 15 is worth 2 points (no matter how many cards are involved).
• Each pair is worth 2 points.
• The value of a sequence of three, four, or five cards is equal to the number of cards in the run. (Keep in mind that A-K-Q doesn’t count as a run because aces are low.)
So, with 8-9-10-10 your hand is worth 8 points; 3 for one run of 8-9-10; 3 for the run using the other 10; and 2 for the pair of 10s. But for 3-3-4-5 with a 5 as the starter card, you have no less than four different runs, two pairs, and two ways to make 15 points — for a grand total of 20 points!
• If all four cards in your hand are of the same suit, you have a four-card flush worth 4 points. (The rules about a flush are more demanding; four-card flush do not count; see the next point.)
• A five-card flush (five cards in the same suit), using the starter, scores 5 points for either player’s hand. (A five-card flush can also apply to the crib but is quite rare.)
• If you have the jack of the same suit as the starter, it’s worth 1 point

CHINESE CRIBBAGE
When I was younger someone taught me a game called chinese cribbage where you play 5 hands at a time. You add up all your scores for each hand and total the 5 hands. Anything over thirty makes you go up and anything under thirty makes you go down. You play until you get to 31 in your up/down scores. So really solitaire cribbage.

Let me explain in more detail:

To start you lay out your four hands (the down card is your 5th hand which is your missy/kitty). This is actually a terrible start because I have flipped three aces.

Now you start to lay out your second card in each hand. Now you have some choice. The first card I turned over was the 7 which I put with 9 in hopes of a run. Then I turned a 2 which I put with the ace in hopes of a run. Then I turned the Q which I put with the other Heart (ace) in hopes of a flush or pulling a four in the third card. And my last card had to go with the ace of clubs as it was all that was left. Fifth card goes to the missy/kitty. NOTE:EACH HAND MUST HAVE TWO CARDS BEFORE A HAND COULD GET A THIRD CARD

Repeat for third card in each hand. The first card was a 2 of hearts which I put with the ace and queen (flush and run potential). Second card was a 7 which I put with the 9 and 7 because of potential run (need an 8 badly for that hand). Third card was a King which I put with ace and 2. Fourth card was a 4 which had to go in the last hand as it did not have a choice. Fifth card goes in the missy/kitty.

Repeat for fourth card in each hand. The first card was a 3 which I put in the first hand for a run and a fifteen. The second card I pulled was a Queen which I put with the last hand for a fifteen. Third card was a 9 which I put with the third hand for a pair of nine's. And then of course my fourth card was the 8 which I had to put in the second hand (clearly it would of been better in the third hand but I had just filled that-shit). Fifth card goes to the missy/kitty to complete the crib hand. you turn up the next card which becomes the fifth card in all five hands.

Looking at the picture above.
First hand : fifteen 2 (23K), fifteen 4 (5K), run of 3 (A23), makes 7
Second hand : fifteen 2 (258), fifteen 4 (5Q), makes 4
Third hand : pair is 2 (77), pair is 4 (99), makes 4
Fourth hand : fifteen 2 (456), fifteen 4 (A4Q), fifteen 6 (5Q), run of 3 (456), makes 9

Then I look at my fifth hand (missy/kitty/crib)
See below.
Fifth hand : fifteen 2 (69), fifteen 4 (5 10), fifteen 6 (5 other 10), pair is 2 (10 10), makes 8

Here are the hands tallied.

For a score of 32 - 2 over 30. So my scorecard gets +2.

Here is my second full hand scored below

For a score of 26 - 4 below 30. So my scorecard goes down 4 to -2.

And you continue to play until you get to 31.

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Final scorecard.

Of course, I do not typically write all that down. Did it to help explain. Below is what my scoresheet actually looks like. You are seeing 4 full games. first, second and third games all took 7 hands and my second game took 4 hands.

TALKING MATH WITH YOUR KIDS #TMWYK

I taught my oldest son who is 8 how to play cribbage. He has seen me play chinese cribbage and asked me about it. I like this. Lots of math. Here is his scorecard from the summer.

Here is a video of him playing it. I encourage you to watch this.

My youngest son watched us play for quite a while. He invented his own game called Big Hands.
A ton of beauty in both these videos. Here is my youngest explaining Big Hands. All I can say about this game is that I have watched him play it on multiple occasions and he plays it exactly the same way every time.

If you have young kids I encourage you to get them playing cards.

## Sunday, April 26, 2015

### Shirts

Day 1

Thought a good title might be "Shi?ts" and might make you "notice and wonder".  Students walked into my class on a Monday morning to this pile of shirts on my desk.

I immediately asked them to write down what they noticed and what they wondered. I did this with two classes for the record.
Here are their noticings:

And here are their wonderings:

After we got through all the noticings and wonderings we focused in on this question.
How many shirts are in that pile?
Asked students to - Guess too low, guess too high, best guess.
Students were randomly put in groups of three. I let them know I would give them a sample of 10 shirts.

Here are some samples of groups work on vertical surfaces.

Group 1
Group figured out the volume of all the shirts and then the volume of their ten shirts as a sphere and as a cone. Got 771 shirts using sphere and 258 shirts using the cone.

Group 2
Group figured out the volume of all the shirts and then the volume of their ten shirts as a cone. Got 304 shirts.

Group 3
Group figured out the volume of all the shirts and then the volume of one folded shirt (rectangular box). Got 146 shirts.

Day 2
At the start of class I modelled a solution to find out the number of shirts. It looked like this. Two solutions one for each class.

And the reveal.
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The rest of the second day was spent figuring out how many shirts each student could fold per second. Class decided to include time to get shirt from pile, lay it out, fold it and pile it on their chair.
Students kept a table of values of time and number of shirts folded. We did it for 0, 20, 40, 60, 80, 100 and 120 seconds. Students plotted data, did line of best fit, and calculated slope to find their rate.

Here are some photos of one students data, scatterplot, equation, and graph.

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Here are the final rates for both classes:

 NAME RATE in Shirts per Second A 0.042 C 0.080 M 0.080 H 0.077 E 0.051 C 0.090 W 0.007 E 0.040 D 0.090 Z 0.117 W 0.083 K 0.046 M 0.067 L 0.081 A 0.046 E 0.041 E 0.082 F 0.092 L 0.033 K 0.039 D 0.047

 NAME RATE in Shirts per Second S 0.063 R 0.044 T 0.080 L 0.036 R 0.047 J 0.084 A 0.068 L 0.046 A 0.053 S 0.044 A 0.067 H 0.058 L 0.067 L 0.038 B 0.046 O 0.054 E 0.027 M 0.032 T 0.046

And a photo of the madness.

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Day 3

Today's question to focus on."How long would it take the class to fold all 282 shirts?" Asked students to - guess too low, guess too high, give best guess. Students were asked to devise and write out a strategy individually on how they might figure it out. Students were then put into random groups and asked to share their strategies. Once they talked it over they were to execute the group strategy on vertical white boards. Many groups wanted the data from the day before - I provided that. Some groups asked how many students were in the class - I provided that (23 for one class and 24 for the other). Some groups asked about attendance - how many students were in class on average. I told them to make their best guess based on a usual day. Groups were given the entire period to work on this.

Here are some samples of group work on vertical surfaces:

Day 4
﻿Today's question to focus on, "What area could we cover with all those shirts?" Asked students to - guess too low, guess too high, give a best guess. Students were asked to devise and write out a strategy individually on how they might figure it out. Students were then put into the same groups as yesterday and asked to share their strategies. Once they talked it over they were to execute the group strategy on vertical white boards. I gave groups about 30 minutes to get through this problem.

A few photos of students doing some measuring.

And some of the groups solutions on vertical surfaces.

Time to do answer "How much area could we cover?" we went out in the hallway and got to work.

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After some measurements with both classes, here is what we got.

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I hustled students back into the class with all the shirts. We tossed them back into the pile and set up the room for folding. I posted the predicted times from the group work on day 3.
And then it was time to fold.﻿

Actual time to fold them all for each class.

Final Reflection:
This was great. Based on the number of selfies that were taken during the area layout of all the shirts I would say this was a success. I bet you all have questions?

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