Table Talk math

4/5/2017

Week 30: Games (Christina Tondevold)

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Welcome to Table Talk Math. This week, Christina Tondevold is playing games with her children. Join us!
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Table Talk Newsletter #30


Great news! For the Spanish version of this week's newsletter, click here, thanks to Ed Campos. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/ttm30spanish) with your Spanish-speaking friends.

This week's content is provided by Christina Tondevold, a mother who works with elementary math teachers and her own children to build math fluency in children. Her websites, both of which you need to explore:

www.MathematicallyMinded.com
www.TheRecoveringTraditionalist.com

Check out what Christina has to say:

This weekend, my family did our annual trip with two other families.  One night we were playing a dice game and it was very interesting to see the difference in two of the little boys’ ability to recognize the amounts on the dice.

One of the boys is my 3 year-old son and he can quickly tell you all of the amounts on any side of the die.  The other boy is actually 6 months older than my son and can tell you the amount when it was 1, but nothing else.

What I noticed during the game was these boys’ ability to subitize.  Subitizing is the ability to recognize an amount without having to count.  The interesting thing about subitizing is that you don’t get better at it just because you get older.  Subitizing happens through the experiences you (or your child) has.

So, yes my child could subitize all the amounts on the die but it isn’t because he is ‘smarter’ or has that ‘math gene.’  It’s because he has had LOTS of experiences playing with dice.  The more exposure he has had to the images on the dice, the quicker he is at identifying them and recognizing the amounts.

Games are such a powerful way to not only build subitizing in your children, but so many other math concepts. Our math abilities are developed through our experiences we have with mathematics.  If children experience math through worksheets and tests they see math as boring (let’s be honest, how much fun are worksheets????).  But if children experience math through games and puzzles and real-life problems they see math as interesting.  

I’m a big fan of games because I grew up playing them and have wonderful memories of my family playing games, but also because they are easy for all of us parents to do at home.  Here are my favorite math games:

Make 10 Go Fish

This game is played just like Go Fish but instead of matching cards, you want to make pairs that add up to ten. Deal 5 cards to each player. On each player’s turn they can lay down any “Ten Pairs” they have in their hand, then they ask any player for a number they need (example: I have an Ace so I ask another player if they have a nine). If that player has the nine they give it to the player who asked and the play continues to the next player. If not, the other player says “Go Fish” and the player draws one from the leftover deck of cards. Then it is the next player’s turn. Play ends when one player has gotten rid of all the cards in their hand.

Concentration

Layout 12 to 20 cards face down in rows & columns. This game is played just like Memory or Concentration, where you are trying to find matching cards.  Player 1 flips over two cards, if those two cards match they get to keep those cards.  If not, they turn them back over and play continues to the next person. Once Player 1 flips over two cards, it is the next player’s turn, even if Player 1 made a match. Make sure you are watching the other players so that you can concentrate on where the cards are for your turn.

You can adapt this to have ‘matches’ that total a certain amount.  For example, if you have younger children you can use matches that add to 5. So, you would use all the 1 & 4 and 2 & 3 cards.  If you wanted to make matches that add up to 10, you would need pairs of cards that add to 10.

Yahtzee

This classic game not only builds subitizing, but kids are also working on multiplication and addition and even probability.  All you need are 5 dice and Yahtzee score cards which you can find here.
 

Combat/War

Two people take the entire deck of cards and deal them out face down between the two of them, so that each person has an equal amount in a pile. At the same time, each person flips over their top card. The person with the larger amount on their card gets to take both cards. If you flip over cards with the same amount, you each flip over another card to see who has the larger amount and then that player would take all the cards flipped over. Play continues until one player gets all the cards.

Make Your Own Game

Opportunities can come at anytime to turn something trivial into a powerful math building time, so keep your eyes open.  One day my daughter had the set of Uno cards and she separated the deck and asked me what cards I thought she had showing.  I asked her to give me a hint and she said “They make 11.”  So I started guessing what combinations would make the 11 and eventually found the one she had.  This then became a game we played over and over again and it was especially cool when I had the cards and gave her the hint.  It was fun for me to see her process of how she thought about the combinations possible.

Building your child’s math mind can be done through the use of games.  I love how fun it is for the kids and for me.  They just see it as quality time with family, but I also see the underlying math that is being developed in them.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/4/2017

Week 29: Travel the Country

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Welcome to Table Talk Math. This week, we're traveling across the states
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Table Talk Newsletter #29


Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM29spanish) with your Spanish-speaking friends.

Recently, I saw a post on XKCD that tackled the question,

"How fast could you visit all 50 states?"

Keep in mind that this is for the United States of America, so feel free to interchange it with wherever you and your family lives. For me and my family, this was an outstanding conversation using a globe and a little bit of creativity.

We talked about driving, which is what we normally do, and the amount of time it would take to travel all that distance. How far is it from our house to Florida? What about to Washington? Oh, how about ALASKA?! And we aren't even going to talk about Hawaii and how we would drive there...

So then we talked about flying, and how expensive it would be. After all, that's a flight for every single state, and that would get ridiculous in a hurry.

Because my kids are younger, we stopped with a lot of noticing and wondering and a little bit of counting and addition. I'm interested to hear where you might take this with your kids, so let me know!

XKCD took this question a step further and thought about how few straight lines it would take to touch all 50 states, assuming Alaska is Northwest of Washington and Hawaii is West-Southwest of California.

Use any of these as your reference maps and have at it:
United States
Mexico
Canada
Europe

How few of lines can you create? Any reason or logic behind it? Share with me by replying to this email or Tweeting me at @tabletalkmath.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/4/2017

Week 28: Clothesline Math pt. 1

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Welcome to Table Talk Math. This week, we're talking about clotheslines.
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Table Talk Newsletter #28


Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM27spanish) with your Spanish-speaking friends.

All you need for this week is:
  • string or clothesline
  • sheets of paper
  • a marker
  • two chairs
"Hey kids, I need your help putting these numbers in order. Do you think you could do it for me?"

On the table next to me is a stack of sheets of paper folded in half with a number on it, ready to be put onto the clothesline that is strung up between two dining room chairs. 
Yes, this is a twist on the traditional number line activity and can be accessed by young children. 

Yes, this is an elementary lesson.

Yes, this can be a quick conversation.

However, over at clotheslinemath.com, there are ideas aplenty for children of all ages, including high school students.Chris Shore has built a variety of clothesline ideas for middle and upper grade levels, so please take a look!

My boys spent around 5 minutes noticing, wondering, and exploring the number line by sliding sheets of paper across a string, spacing them out accordingly as more information became available. Because it was happening so fast, I wanted to throw a minor wrench in the system and did so with the 4 1/2. Even though he hadn't been introduced to fractions, it didn't take long to figure out that the 4 1/2 fell neatly between the 4 and the 5.

Next up, we are going to do sums:
  • 1+5
  • 3+6
  • 2+4
  • ...and so on
When they get older, we will head over to the clothesline math website and find more ideas and information to support both boys, but a clothesline will certainly be a part of our discussion for years to come.

If you want to see my boys go through the progression,it's here.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/4/2017

Week 27: Geometry in Motion

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Welcome to Table Talk Math. This week, we're bringing in Geometry Dad to talk about animations.
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Table Talk Newsletter #27


Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM27spanish) with your Spanish-speaking friends.

This week's content is provided by Geometry Dad:

Children interact with shape from a very early age and, to build on this, I encouraged my son (when he was about 2) to make patterns on the fridge from magnetic pattern blocks. As we continued experimenting together, we moved on to Polydron and, along the way, I became interested in using simple geometric animations to further engage my son, Dexter, (and then also my daughter, Cleo) in conversations about shapes and patterns in an attempt to engender an appreciation of the beauty of geometry. Often, at bedtime, my children would ask to see these ‘aminations’ as they sometimes called them when they were younger.

Many of the animations lend themselves to questions about how many shapes there are or the path taken by one particular shape, line or point. Some animations lead to more obvious questions. The one below, for example, simply morphs through a looping sequence of common polygons.

For example, by clicking on the image below, you'll see that the animation simply morphs through a looping sequence of common polygons.

It's a triangle, square, pentagon, hexagon, octagon, decagon & dodecagon #animation. Your children can say each shape! #GeoGebra #Geometry pic.twitter.com/CQmWvpZ7MD

— Geometry Dad (@GeometryDad) January 12, 2017
The aim here is to encourage the identification of shapes while entertaining them with the way each shape morphs into the next. Can your child name each shape? What other questions can you ask about the animation?

Animations can also be a source of more complex questions. Click on the image below to see an example:

If the triangle takes 3s to rotate, the square 4s & the pentagon 5s, how long is it between alignments? Why? #animation #GeoGebra #Geometry pic.twitter.com/X4ceFsfnOF

— Geometry Dad (@GeometryDad) February 8, 2017
The answer to this question uses the concept of the lowest common multiple (or modulo arithmetic). However, there is a small sting in the tail. Did you get the right answer? There are also many other questions that we can ask:
  • How often do the triangle and square align? Why
  • How often do any two shapes align and why?
  • How does the answer change if a hexagon (with a dividing line) is added that takes 6s to rotate?
You can even encourage an empirical approach to the answer(s) and use a stopwatch!

There are around 100 animations on the Geometry Dad Twitter feed at the moment. In contrast, the Geometry Dad Facebook page generally contains photos of Dexter and Cleo’s constructions. These days, they mostly use Magnetic Polydron since it allows them to explore 2D and 3D space quickly and see their ideas come to life without being distracted by how the polygons attach to each other.

This is a great journey for me and my children. Feel free to join us!

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/3/2017

Week 26: Valentine Math

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Welcome to Table Talk Math. This week, we're overhauling the idea of Valentine's Day Grams.
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Table Talk Newsletter #25


Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM26spanish) with your Spanish-speaking friends.

This week, my wife came home with a box of cards for our son to fill out and distribute to his first grade classmates. They're super cheesy and lack sincerity, but I guess that's what we've come down to.

As the kids get older, the distribution of cards becomes less and less until, at some point, they disappear altogether. 

Well, thanks to Desmos, the free online graphing calculator that you really need to know about, you can now give out Math-O-Grams! Sure, you can use one of the pre-created templates and email it to a friend, but you can also create your own.

To create your own, head over to desmos.com/calculator and start designing. It would certainly help if your child is in high school, but it isn't necessary; here's one you can play with.

What can you create with mathematical functions that express your affection for a friend or loved one? I'd love to see what you come up with! Share your work by emailing them back to me, posting them onto Twitter, or sharing them on the Table Talk Math Facebook page.
 

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

A number of people mentioned that a Spanish version of the newsletter would benefit them or parents that they knew, so Ed has joined the team for that support. If you have any requests, please feel free to let me know.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/3/2017

Week 25: Daily Overview

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Welcome to Table Talk Math. This week, we're taking an overhead view of Earth. Seriously!
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Table Talk Newsletter #25


Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/ttm25spanish) with your Spanish-speaking friends.

How many airplanes do you see in the image above?
How many terminals do you see?
How many people do you think this airport can serve in a day?
How much would all those airplanes cost?
Why did they design the airport terminals like this?

Sometimes, the best thing we can do to understand a problem is taking a step back and looking at it from a different approach. In The Daily Overview, you get a stunning satellite image of a new place around the world, all for free. In the image above, you are looking at Chicago O'Haire International Airport, an incredibly busy and large hub for travel, both domestic and international. Even better than asking these questions, find out what questions your child(ren) have after taking a minute or two to analyze it. 

For more images like this, head over to www.dailyoverview.com/fiftyseven and explore the site. Maybe it isn't a math conversation that starts up, and that's completely fine. If we can give our children a different perspective, they might just begin taking a large-scale approach to other problems that they face as well.

So here's a way to report back: what questions did you and your family come up with? Did you find out any solutions to those questions? Share them by emailing them back to me, posting them onto Twitter, or sharing them on the Table Talk Math Facebook page.
 

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

A number of people mentioned that a Spanish version of the newsletter would benefit them or parents that they knew, so Ed has joined the team for that support. If you have any requests, please feel free to let me know.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/3/2017

Week 24: Four Fours

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Welcome to Table Talk Math. This week, we're talking about a classic puzzle using only a single number: Four Fours.
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Table Talk Newsletter #24


Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/ttm24spanish) with your Spanish-speaking friends.

Here's the challenge:

How many numbers can you generate using only four fours and the operations below?
  • addition
  • subtraction
  • multiplication
  • division
  • parenthesis
  • exponents
  • factorials (optional)
Here's how it works:

4*4 - 4*4 = 0
(4 + 4) / (4 + 4) = 1

... and so on. I don't want to give you a solution for each, but how high can you and your child(ren) go?

For the younger crowd, it's OK to bounce around. For example, using addition and subtraction will only get you so far, and won't get all number between 0 and 10, but that's alright. Playing around with numbers and seeing what can happen is a big part of the puzzle.

For the older crew, write down the values 1 through 20 and talk about how each total can be achieved. As solutions pop up, fill them into the table (or onto the sheet of paper). Once you get the first twenty, there are solutions up to 100 and beyond, so get wild and make it a family challenge!

So here's a way to report back: what numbers are you having trouble creating? What is your most creative set of four fours? Share them by emailing them back to me, posting them onto Twitter, or sharing them on the Table Talk Math Facebook page.
 

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

A number of people mentioned that a Spanish version of the newsletter would benefit them or parents that they knew, so Ed is coming onto the team for that support. If you have any requests, please feel free to let me know.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/3/2017

Week 23: SolveMe Mobiles

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Welcome to Table Talk Math. This week, we're talking about mobiles and puzzles at the table.
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Table Talk Newsletter #23


This week, I'll get straight to the point: you need to check out Solve Me Mobiles with your child!

The Education Development Center, or EDC, has built this site to provide challenges and puzzles to kids of all ages (that's right, even you!). For example, take a look at this one:
My four year-old and I can look at this mobile, talk about it for a bit, and come to the conclusion that the diamond and the heart weigh the same, so they should be... equal. With that, what's the value of the diamond? SEVEN!

For my older son, we can try something like this:
OK, so five plus five is ten, plus five is fifteen. We already have twelve on the right, so how much more until we have an even side?

These questions are setting a foundation for balancing equations and, in the bigger pictures, solving equations with multiple variables. While these two are fairly basic, the types of mobiles on the site can get pretty wild:
Are your palms sweating yet? Eh, don't worry about it! If you have a high schooler in the house, these might be some fun challenges to tackle, but don't stress too much about it. 

Here's my solution for the one on the right:

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

ALSO, BIG UPDATE. There is a good chance that I will be working with someone to translate these newsletters into Spanish. If that would benefit you--or someone you know--please let me know. I'd hate to do this if it isn't helpful, but will be more than happy to if it will!

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/2/2017

Week 22: Water Fountains

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Welcome to Table Talk Math. This week, we're talking big numbers and open questions.
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Table Talk Newsletter #22


As we made our way around the Phoenix airport during a layover, it was a good time to fill up our water bottles. In airports around the country are these filling stations that come with a "helped eliminate waste from ___ disposable plastic bottles" and it just makes you feel good to fill up!

My six year-old son thought it was cool, but he was very perplexed by the numbers in the top right. The first fill-up station saved 23,260 bottles and the second saved 362,253 bottles.

"Wow, daddy, three six two two five three?! That is wayyyy bigger than the first one we saw!"

"It sure is, buddy. So what questions do you have?"

"Why is this one so much more?"
"How do you say this number?"
"Are plastic bottles really that bad for us?"


All of these are worth diving into. All of these are worth exploring. And, because we had the time, all of these got answered. He's only six, but we talked about place value because it mattered in this context. I asked him why he thought one was more than the other, leading him to a possible solution that the picture on the left was right next to the bathroom.

"Oh, so when people are done going potty, they can just fill up their water bottle!"

You're onto something, kid.

I would love to hear from you! What picture (or situation) can you put in front of your child to elicit questions? Remember to avoid giving an answer; instead, ask a question that might start a conversation. 

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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4/2/2017

Week 21: Earth's Population

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Welcome to Table Talk Math. This week, we're taking a small look at a big question.
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Table Talk Newsletter #21


"Daddy, how many people are on Earth?"

Quick, think of something! I dunno, uh, a trillion? Seven billion? A whole bunch?

"Well, buddy, I don't know if I can count that high."

Whew. Did I pass? Is it over? Did he notice that I don't really know?

"So, then there's infinity people?"

Dang. No! That's not what I wanted!

On a recent walk with my six year-old son, we had this conversation. At first, I was upset because I didn't have a good enough answer for him. After thinking about it, though, I was thrilled that he brought up infinity, so we talked about it and what it meant in terms of people on Earth. We talked about how infinity is a number that keeps going, but that there is actually a finite (or certain) number of people who exist on Earth, even though that number is constantly changing.

Yes, I could have easily searched for the answer online and found a solution, but there is something about the "Google-able" question that still creates an abundance of good conversation. I won't share the solution with you on here, but you can click through to find it. 

The value didn't come from the solution—we never got to a solution—but from the questions that arose. We talked about how many people are in the United States, Europe, and beyond, and how we could add them all together. If he was older, we could have talked about the Census and how it can help us keep track of people. We could have discussed population density and why people live in certain areas compared to others.

But in that moment, on that walk, we used it to talk about infinity. 

Here's a challenge for you: Ask your child the same question, or find a way to have them ask it to you.

What are the questions you reply with?
What information would you provide or seek out?
How long before you get to "the right answer" of it all?
If that question didn't come up, which ones did?

I would love to hear from you!

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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    John Stevens is working to give parents ideas on how to have mathematics-based discussion at home. 

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