Tag Archives: Math

Classical Conversations Week 20 Combinations

Yay! Some thoughts on teaching about CC Cycle 3 Week 20 Combinations
I've posted my lab sheet for this lab on CC Connected (user name lb_oliver). My thoughts here will dovetail with that approach. You can also see my suggestions for ways to expand on this topic in my post here.

Welcome back to week 2 of CC’s statistics-based labs! Here are my thoughts about presenting these topics in class (for what it’s worth!) . . .

Remember to spend a minute or two reviewing last week’s lab and last week’s grammar (probability, outcome). Revisiting those terms and definitions will just help them stick in the kids’ minds. Plus, this week we’re setting aside those topics and picking up a new one, but we’ll be coming back to probability and outcome in future weeks, so it’s to everyone’s benefit to work on getting really comfortable with those terms.

Like last week, let’s begin with the end in mind. What’s the point of this particular lab? In my opinion, for our Classical Conversations Foundations students, it’s twofold:

  1. Grammar: To teach some basic statistics grammar (Combination) and to see that term in action.
  2. Dialectic: To begin teaching children to think about how adding “just one more” option exponentially changes the number of combinations that are possible. In other words, adding ONE additional option does NOT result in just ONE more possible combination. How many more combinations are possible? Well, it would depend on how that new option could be used.

Yay! Some thoughts on teaching about CC Cycle 3 Week 20 CombinationsIn my mind, we’ve got to set a couple of ground rules in this particular lab – We’ll assume that every pizza has to have a crust, sauce (they’ll all have it, so we won’t make it an option), and at least one topping (no plain pizzas here!).

So, if you’re teaching a group of YOUNGER STUDENTS, you’ll want to focus on the grammar and you may need to keep the options more limited. Work up slowly! One crust option and two possible pizza toppings results in how may combinations? Three. Show them how this works, either by drawing it on the board or by using some sort of manipulative – paper, paper plates, or felt. Personally, I like felt and it’s pretty cheap. It’s fun for kids to see and handle something different, and since a parent could easily create something similar at home, I believe this is in keeping with CC’s simple approach.

Once you’ve shown them how it works with two toppings, let them try three. Ask them to think first about how many combinations that would result in. Will one more topping mean only one more possible combination? No. It will mean four additional possible combinations! Wow!

Like last week, I’d suggest that children do this lab in pairs with a parent assigned to each pair to be the record-keeper (if necessary) and auditor (someone to keep up with “have we already recorded that combination?”).

If you’re teaching a group of OLDER STUDENTS, you’ll move through the warm-up quickly, and then you can let them have a turn at one crust and three toppings on their own or in teams of two. Even students of this age will enjoy working in teams usually, and it gives them someone to bounce ideas off of. If they’re still at an age where having a visual will help (or you just want to liven up the lab), you can print out these pizza toppings to match the toppings on my Lab Sheets on CC Connected. You can cut out circles from two different colors of brown construction paper. I bought a pack like this and cut out circles the size of a mason jar lid, but you could just as easily use paper plates. Write “Thick” and “Thin” on them. It doesn’t have to be complicated.

Once they’ve worked through that set of options, they’ll be ready to move to the next step – adding another pizza crust option! What happens then? At this point, they’ll probably be able to guess that it means a lot more than just one more possible combination. But will any of them guess that it actually DOUBLES the possible combinations? (That’s 14 in total) Wow!

And if that is something they can work through, then try adding “just one more” option and going for 4 toppings. What do you end up with? 22 possible combinations, by my calculation! Amazing!

What should you emphasize? For every additional option we add, the combinations grow much larger than “just one more” and that would continue to happen as long as we added more possible options.

For ADULTS/PARENTS– I gave an overview in my post last week of why we do these labs in general. But, why did we do THIS lab? What was the point?

This lab, like all of the others during this 6 weeks is related to the science of origins. One way the math of combinations relates to the science of origins is through DNA. I’m not a scientist nor am I a mathematician, but a scientist would tell you that your DNA contains 23 chromosomes. Scientists are still investigating how many genes make up those chromosomes, but the current ballpark number is 20,000. Based on what I’ve read, the possible combinations of children resulting from a single couple’s DNA is 70,368,744,177,664. This is fascinating and goes a long way toward explaining how all human beings (black-skinned, white-skinned, blue-eyed, brown-eyed, etc.) could have descended from a single original couple created by an amazing (and very creative!) God.

Again, just as I said last week, gathering data, analyzing data and drawing conclusions are very much a part of many explanations of the origins of the universe. Eventually, our children will need to be able to draw their own conclusions from data that is presented to them. These labs are a great introduction to early critical thinking skills.

Classical Conversations Cycle 3 Week 19: Probability

Classical Conversations Cycle 3 Week 19 Probability
I've posted my lab sheet for this lab on CC Connected (user name lb_oliver). My thoughts here will dovetail with that approach. You can also see my suggestions for ways to expand on this topic in my post here.

First, if you’ve got a better handle on these labs than me, stop reading now and move on.

I’m not claiming to be an expert on the subject.

But, if you don’t, or you’re just looking for someone else’s perspective, here are my 2¢.

Let’s begin with the end in mind. What’s the point of this particular lab? In my opinion, for our Classical Conversations Foundations students, it’s twofold:

  1. Helpful approach to tutoring CC Cycle 3 Week 19's Science lab!Grammar: To teach some basic statistics grammar (Probability, Outcome) and to see those terms applied.
  2. Dialectic: To begin teaching children to think about the “probability” that something (anything) could occur.

So, if you’re teaching a group of YOUNGER STUDENTS, you’ll want to focus on the grammar and getting children to use it and understand it. Set your objectives (and your bar for feeling successful) accordingly. Focus on the terms. Use them clearly during your lesson. Move through the “warm-up” slowly. Help them to really think about what you’re asking. You can use the term “probability” and “chances” (or other synonyms – likelihood, expectation, etc.) interchangeably, while you’re talking. Just be keep coming back to the term “probability” so they begin to understand what that term means. In addition, for some young students, this will be the first time that they hear the term “tally marks” and see them used. For them, that’s good stuff! Take the time to explain them and show them quickly how they work. I also suggest for younger children that they do this lab in pairs of two with a parent assigned to each pair to help with counting and making tally marks.

If you’re teaching a group of OLDER STUDENTS, you can probably move through the warm up more quickly as they catch on to what you’re asking and how it relates to the chips in your hand. You might need to quickly review tally marks before allowing them to start performing and recording their results. These students can work individually or in teams. Once they’ve completed the lab, you can add up the results of the class to see how they might have differed from individual results. Explain to them that while their individual results might have varied, that 20 is really not very many draws. Over time, with even more draws, the results of the experiment would be 1/2. Then, use the lab to begin to expand their ability to use logic. What would they need to start with in order to GUARANTEE they could get the results they wanted to? They’d have to start with chips that were all the same color. Even if there was only one chip of a different color in the mix, at some point, with enough draws, you’d pull that color out. So, the only way to be sure you can get the results you want, if you only want to draw a white chip, for example, is to start with all white chips. This seems totally logical to many of us as adults, but we take for granted that children have the same ability to be logical that we do. Their minds are all at different points in beginning to make those leaps, so this is a great exercise for them, and you will likely discover that you have some children who understand it immediately and others who are slower to grasp it (or are silent as they work through it in their heads).

For ADULTS/PARENTS– Why do we care? Why are we doing these labs? What is the point of this with children this age?

The science of origins is the effort of scientists to explain how the universe began.  The science grammar that we’ll learn in these 6 weeks is the basic definition of different ways used to explain how life began and developed. As always, YOU are the teacher. You decide how (or if) you want to elaborate on this at home. Tutors will drill the sentences/definitions. You decide what you want to teach your child. The science labs involve an introduction to basic statistics (probability, odds, combinations, etc.). Probability relates to the science of Origins because data is collected and analyzed and different and opposing conclusions are often drawn from the same data! Learning how to collect, record and analyze data is a skill that all scientists use. Gathering data, analyzing data and drawing conclusions are very much a part of many explanations of the origins of the universe. Eventually, our children will need to be able to draw their own conclusions from data that is presented to them. These labs are a great introduction to early critical thinking skills.

 

Photo credit: Flickr

Classical Conversations Statistics Labs from Cycle 3

Elementary Statistics Labs

We are entering Weeks 19-24 of Classical Conversations Cycle 3. ThAwesome ideas for teaching kids about statistics!is is the second time I’ve been through this cycle, and I have a better appreciation for the Statistics Labs. For the youngest, the abecedarians, this will probably be their first exposure to tally marks and making charts. I realized, having experienced with my own daughter, how much easier this made some of our math lessons a year after we were actually done with this cycle. Many of the concepts taught in these labs are challenging to our Foundations-age students (and their mothers!), but if we’ll slow down, try not to get intimidated, and take the time to try and understand them, these labs are great exposure to the grammar of basic statistics.

This time around, I’m more determined than I was last time to make them meaningful for my students at CC and for my kiddos at home. I thought I’d share with you some of the resources that I’ve found for expanding on the labs that we’ll be doing during our CC Community days.

For those of you on CC Connected who might find them helpful, I’ll be uploading the lab sheets that I’ve created for these weeks in the next few days.

 

Younger Students

Wonderful book for teaching young children about probability!I’ve found some awesome books for making statistics concepts approachable for even the youngest of our students! My favorite is “probably” It’s Probably Penny. The first few pages do an EXCELLENT job of teaching the concepts of the Week 23 lab in a way that works well for elementary age students.

These three books are also fun books for elaborating on the concepts of probability (although I will warn you that the last of these, A Very Improbable Story uses the terms probability and odds interchangeably, as do many of us, while mathematically that is incorrect. I had to work pretty hard to get these two term and their use straight in my head in preparation for these labs, so I did stumble on that in this otherwise entertaining and educational book):

Great elementary age book about probability!  Entertaining book about probability for elementary-aged kids!  An entertaining way to learn about odds and probability for children

This video covers Mean, Median, and Mode. Honestly, I found it a little annoying, but the aspects that annoyed me may very well be what help it stick in a child’s head.

If you prefer something musical (and who doesn’t?), there are multiple versions of this little diddy out there, but this is one of the more creative recordings. It teaches the concept of “Range,” which isn’t covered in our CC labs, but it’s still a very handy way of remembering the basic definitions of these terms. Here’s the poem:

Hey Diddle Diddle,

the Median’s the middle.

You add, then divide for the Mean.

The Mode is the one

that you see the most,

and the Range is the difference between.

 

Older Students

If your kids would like a fun rap song to help them with understanding Mean, Median and Mode, this one absolutely fits that bill!

If your child is ready to expand on their knowledge of statistics (or you are), but still wants it to be fun, both of these books contain some great information about statistics, but present it in fun ways. I’ll bet a few of you out there have a child who will read anything as long as it involves a comic-book/graphic-novel approach (I do!). Start with the first one – The Cartoon Introduction to Statistics, and if that isn’t meaty enough, or your child is ready for even more, try The Cartoon Guide to Statistics (which is like a college course, but with cartoons).

A fun book for older elementary kids to learn about statistics!  Cartoons make learning about statistics fun!

The following video (see link below) is a little too complex for all but the oldest (or most mathematically-oriented) of our Foundations-level students, but it is basically a class on probability done in a very conversational and approachable way. The kids in the video are pretty adept at mental math, which might even inspire a few students to embrace math with more gusto.

https://www.teachingchannel.org/videos/teaching-probability-odds

There are also some good courses available at Khan Academy for learning about probability and statistics.

 

I know this isn’t the end of the good resources for these subjects out there, so please share in the comments if you have other suggestions! I’d love to hear them!

Classical Conversations Cycle 2 Week 12

Classical Conversations Cycle 2 Week 12

Our Classical Conversations group took a field trip this week to the Dyer Observatory. If you live in or around Nashville, I would HIGHLY recommend it. It was an exceptionally good field trip and dovetailed BEAUTIFULLY with our recent CC Cycle 2 Science Grammar and Science Projects. The astronomer in charge re-visited the relative size of the planets and stars, took us on a planet walk to show us the relative position of the planets, educated us about the different planets as we walked, then did an activity to illustrate the phases of the moon and showed us the telescope they use at the observatory and how the roof moves to allow it access. It was very cool!

Our field trip yesterday is one of the reasons I’m a day later than usual getting this post up! We were gone half the day for that and then we also had to deal with a neighborhood dog attacking one of our chickens! We thought she was a goner when we left for our field trip, but my husband (now known as the “Chicken Whisperer”) did not give up on her and, while she is terribly beaten up, she’s definitely hanging in there. We’re now referring to her as “Timex” since she can “take a licking and keep on ticking!”  What a crazy day!

Classical Conversations Week 9 Skip Counting 15Math

For this week’s math, I love to do hand motions. The hand motions have helped ME to remember the conversion of teaspoons, tablespoons, and fluid ounces, so hopefully they’re helpful to the kids, as well! I’ve done these same hand motions for a couple of years, so I don’t know if I saw someone else suggest these, or if I stumbled upon doing them myself!

Skip-Counting-Squares-Image

For 3 teaspoons = 1 tablespoon, we make a teacup with our hands using our thumb and first three fingers. We stick out our pinky to drink our tea “fancy-schmancy-style” and as a result when you tilt up your 3-fingered TEA cup, you end up with 1 pinky sticking up in the air to remind you that 3 teaspoons=1 tablespoon.

Then, we pretend to be holding a glass using our thumb and first two fingers and we set it down on the table to remember that 2 tablespoons=1 fluid (the liquid we pretend is in the cup) ounce.

Classical Conversations Week 10 Skip Counting 15

I got some feedback that the Skip Counting 14’s booklet was helpful for some children to review, and I think some of you who tutor used it in class. I’m OVER THE MOON (seriously, you have no idea!) to hear that something I created was actually HELPFUL! So, I went ahead and made booklets for the 15’s, the Squares and the Cubes. You can click on the images to the right, or you can find them on the printables page.

Geography

I can’t tell you how much I appreciate the person that put together these geography review games out at Purpose Driven Games! My children love them, and I plan to use them OFTEN over the break to review! You can click on the image below to go to all three of their Cycle 2 review games, or you can click on the individual links below the image.

Classical Conversations Geography Review Games

Cycle 2, Weeks 2-6 review game.

Cycle 2, Weeks 7-13 review game.

 

Classical Conversations Waterloo Napoleon Bonaparte

Lion’s Mound Waterloo Memorial
Photo Source: fatboyke

History

The video at the link below does not specifically talk about the Battle of Waterloo, but it’s well done and a good biography of Napoleon. You’ll need to be around to read the captioning for any non-readers. There are a handful of other videos on this website about Napoleon and the French Revolution, so it’s just an all around handy place to visit to expand on Week 11 and Week 12’s history sentences!

http://www.history.com/videos/napoleon#napoleon

Once you’ve watched the little overview, above, this 5 minute video concentrates on the Battle of Waterloo itself.

http://www.youtube.com/watch?v=5Go5nlOCqi4#t=40

I’m not in love with the game at the following link because I think it’s probably not the right combination of education and fun for my two kiddos, but hey, just finding a video game about Waterloo is pretty cool, so I wanted to pass it along!

http://www.bbc.co.uk/history/british/empire_seapower/launch_gms_battle_waterloo.shtml

Again this week, some of the best books are no longer in print. Bummer! So, check your library, or pick them up used from Amazon. For example, we have this great Usborne book on our bookshelf to read this week:

This one is still in print, and the Kindle version is only $0.99:

For the tweens and up (this one is actually still in print!):

Science

One thing that I would LOVE to do with my kids during this break period is put together a paper mache solar system model like this CC mom is working on! I think the kids would love for us to do a project like that and I’ll bet we’d learn a lot!

The Right Stuff is a full-length movie and rated PG, so I wouldn’t normally recommend it here (Common Sense Media recommends is for 10 and up). BUT, I really enjoyed this movie several years ago, and this week’s science just makes me want to watch it again! It’s about the 7 astronauts of the Mercury space program, the early days of NASA and the Space Race and it’s a very well made movie! So, for you parents, or children for whom you think it appropriate, settle back and enjoy a great movie about a really cool period in our country’s history! It reminds you of how incredibly brave and adventurous astronauts really are!

Product DetailsSigh . . . and now that I’ve started recommending regular movies (this makes me feel very guilty for some reason!), I’ll go ahead and throw in a plug for Apollo 13 (recommended for 12 and up by Common Sense Media). Another great movie about the Space program that really makes you think about all that goes into successfully getting into space . . . and getting back home again.

I’m going to try not to feel too guilty about recommending those movies! It’s time to take a break, after all, so so take a break and curl up with something that will make you appreciate that CC Science sentence even more!

Product DetailsThere is also a documentary series by BBC Earth available on Amazon (free streaming for Amazon Prime Members! We love our Amazon Prime, and I think you can try it free for 30 days if you want to stream this video for free.) called “The Planets.” I’ve just discovered it, so I can’t say whether it’s a winner or not, but the fourth episode is about the Moon and the process of getting there.  Some of the other episodes also look like they’d be good fits for the last few weeks of CC Science Grammar.

And here’s another video series, this one is on the history of NASA, that looks great for this week and is also has free streaming for Amazon Prime Members!

One last (REALLY!) video recommendation . . . and it’s one I mentioned in an earlier post, but it fits even better with this week’s Science grammar:  A Tour of the International Space Station on YouTube. If you read the CC Science Snippets (available on CC Connected), this week’s talks about how the Shuttle program was responsible for building the International Space Station, so it’s a good time to take a tour and see what living in space is all about!

There are SO many great books on Space and the Space program available, that I won’t recommend a ton. You can hit your local library and walk out with a stack, I feel sure. Here are just a couple to whet your appetite:

This one is available on Kindle for only $2.99:

We read this one a few years ago, and will read it again in the next week. It’s really neat to read a children’s book written by Buzz Aldrin himself.

Product Details

 

 

And with that, we head off into the sunset for a break for a few weeks! On one hand, I’m ready for a break and on the other hand I’ve got lots and lots of ideas related to this upcoming 12 weeks that I’m ready to get going on! I’ll be back on the blog during the break with some thoughts and plans that just can’t stay in a holding pattern until January! See you then!

This post is linked to:
Half-a-Hundred Acre Wood