Second Grade: Introduction to Strategic Thinking — NIM

We started a new session of enrichment today.  This time around, all of the students are receiving the same instruction — they are not divided into math and humanities groups.  This means that I see all of the students once each week.  We are working on a strategic thinking unit, and these skills are ones that all of the kids will be able to use.

Today we played NIM.  There are a number of different versions of NIM, but the one we played starts with counters set up like this:

The object of the game is to “stick” your opponent with the last stick.

In this version, the players take turns removing any number of sticks from a single row.

We played on the Smart Board to begin, with the kids taking turns playing against me.  They all quickly figured out “bad” combinations of sticks. For example, you never want to find yourself with three rows of one, or two rows of two.

The students played in pairs for awhile and we stopped frequently for people to explain their strategies.  Many kids thought they had the solution — until they played against me at the Smart Board.  That’s how it was supposed to work — I knew the secret and they didn’t!

I then told the kids the first secret — you can always win if you go second.  If you go first, you can still win, but only if your opponent makes a mistake.  Then I explained the strategy in the simplest way I could.  (I cribbed this explanation from here.  I found it the easiest breakdown to understand.):

The winning strategy is:
You must always take as many matchsticks as possible so that the “Nim sum” of the rows remains ZERO.

What is a “Nim sum”?
Count the matchsticks in each row… And convert them mentally in multiples of 4, 2 and 1. Then, CANCEL pairs of equal multiples, and add what is left. So, when starting, the “Nim sum” of the rows is:

Row1 = 1 = 1 x 1 = 1 = 1
Row2 = 3 = 1 x 2 + 1 x 1 = 2 1
Row3 = 5 = 1 x 4 + 1 x 1 = 4 1
Row4 = 7 = 1 x 4 + 1 x 2 + 1 x 1 = 4 2 1
Total of UNPAIRED multiples = 0 0 0

As you can see, there are currently TWO 4’s, TWO 2’s, and FOUR 1’s (= TWO + TWO + FOUR = 8). You have then an EVEN number of multiples, the remainder after dividing this number (8) by 2 gives 0.

To win at Nim-game, always make a move, whenever possible, that leaves a configuration with a ZERO “Nim sum”, that is with ZERO unpaired multiple(s) of 4, 2 or 1. Otherwise, your opponent has the advantage, and you have to depend on his/her committing an error in order to win.

We played several times on the Smart Board using this strategy.  Some of them got it; some of them didn’t.  They all became much, much better at anticipating what their opponent would do and what would happen after that, and that’s really what I was hoping for.

You can play NIM for free online.  Not that I do that in my free time or anything.  Find one game here.

Kindergarten Reading — Anagrams and Anugrams

Last week, we started class with these words on the Smart Board:

many do

sea duty

sandy weed

yard huts

I explained to the kids what anagrams are, and told them that each of these pairs of words is an anagram for another single word, and the four words all have something in common.

We started by looking for letters common to all the words and discovered that all of the words contain the letters y, d, and a.  We separated those letters and then looked at what we had left.  It didn’t take long before we realized that “many do” is an anagram for “Monday.”  And y, d, and a are all letters in “day.”  It was pretty quick from there:  sea duty = Tuesday, sandy weed = Wednesday, and yard huts = Thursday.

Then we did the next four.  Can you figure out the anagrams and what they have in common:


runs at

teen pun

usa run

The kids did!  Next we did an anagram worksheet.  It was difficult.  Really difficult.  But your kids were champs.  It took them very little time to discover that the words were anagrams for names.  And there were eight sets of them.  And eight kindergarten reading students!  From there, it was a simple hunt for the letters in each child’s name.  I sent the sheet home but it was not homework, the kids just wanted to be able to remember the anagrams for their names.

Homework was a sheet of anugrams.  An anugram is an anagram where the anagram makes a true statement about the original word(s).  For example, twelve plus one is an anugram for eleven plus two.  I provided blanks to fill in the letters for the anugrams and gave punctuation and filled in some letters.  Still, let’s be honest — this is challenging.  Really challenging.  I explained this to the kids and asked them to give it a shot.  I told them to write the original phrase on a separate paper and cross out the letters as they are used so that they don’t cross it out on the original worksheet, make a mistake, and then find themselves without the original phrase.

As I told the kids in class, I am totally okay with blank papers coming back to me.  It may be that your child cannot figure these out.  That is okay!  It may be that s/he loves this kind of stuff and is good at figuring it out.  Fantastic!  Either result is okay.

To make anagrams of your own, check out the anagram generator here.  So much fun!

This week, we discussed the Anugram sheet further and completed it in class.  We then worked on parts of speech and completed some mad libs at the online mad lib generator site, which you can find here.  The kids love it and asked me to be sure to mention the site on the blog (you can also, of course, buy an old school book of mad libs!).

Bagpiper Prank Shy!  (that’s an anagram for “happy spring break,” of course!)

Second Grade Math — Number Systems in Other Cultures & Societies

Yes, I know it’s been forever since I blogged about second grade math.  And I know it makes it seem like I prefer humanities.  That really isn’t the case; it’s just that our math unit this session (which I love!) isn’t particularly photo-friendly.  When I don’t take pictures, I tend to be less motivated to post because what I have isn’t pretty to look at.  So apologies for the photo-free post, but here is your update on second grade math.

This session we completed a unit on math in other cultures. We started by talking about primitive math (you may recall when we discussed how long it would take to make a million tally marks — if not, review here).  Next, we moved on to Ancient Egyptian numbers (see here for a reminder).  Then, interspersed with snow days and delays and field trips of various kinds, we learned about ancient Greek numbers, Roman numerals, and the Mayan number system.  The kids marveled at the fact that the Greeks used the same characters for both letters and numbers — so if you saw printed characters, you didn’t know at first if they represented a number or a word.  We reviewed one of my favorite mnemonics — “I Value Xylophones Like Cows Do Milk” — to remember the Roman numerals in order of value.

This week, we learned about the Mayan number system, which used a clam shell for zero, a dot for ones, and a bar for fives.  It was the first number system we’ve discussed (besides ours) where they used place value.  Except the place value was based on 20 (and then 360) and went upstairs  instead of next door.  So if you look at the picture below, you’ll see that 6 and 25 look exactly the same except for the space between the dot and the bar, which tells you that the dot represents 20 and not 1.

See if your child can explain Mayan numbers to you.  It was challenging for a lot of them.  A handful found it completely intuitive, sailing though the Mayan numbers work like it was second nature.

Usually the kids spend the last class comparing the number systems we’ve studied and completing a report card to rate each system.  This session, we simply ran out of time.  We had a lot of fun and learned a ton (and, I think, gained a much greater appreciation for our own number system).  Now we’re moving on to our next session, which will be on strategic thinking — a topic all of the students will cover, instead of being divided into separate math and humanities groups.

Second Grade Humanities: To Dig or Not to Dig? A Simulation

This week and last in second grade humanities, we’ve undertaken a simulation called “To Dig or Not to Dig?” (and yes, many second graders entered the room to see that question on the SmartBoard and loudly followed up with “THAT IS THE QUESTION!”  I’ve never been so proud).

At the beginning of last week’s class, I presented the following scenario to the students:

The city of Falls Church has decided to construct a football stadium on a block of land at the edge of the city, near Poplar Heights Pool.  The City will then acquire Virginia’s first NFL franchise – Falls Church Freedom.  To deal with increased city traffic, the city will also have to build a highway extension to widen the exit of route 66 and an access way from the metro station.  Before they can do any building, though, federal and state law require that the site undergo an archaeological survey to determine if any cultural resources would be impacted during construction.

A group of archaeologists come to excavate the site.  After several weeks of field testing, they report that the site is of tremendous scientific and historical value and could help answer many questions concerning Virginia’s past.  Archaeologists report that they have uncovered an extensive concentration of human remains deposited under the land.  These remains have been identified by a forensic anthropologist as being Native American.

The archaeologists, in compliance with federal and state law, halt further excavation and notify the Native American Tribal Council of Virginia.  Tribal leaders visit the excavation site and immediately identify many of the uncovered artifacts as ancient ceremonial burial objects.  Upon further investigation, tribal leaders inform archaeologists that the proposed stadium construction site is the location of a cemetery of their ancestors, and that it has significant religious and heritage values to Virginia’s Native American population.  Tribal leaders demand that the site be covered again, and left undisturbed with no further archaeological excavation or stadium construction.

This demand sends shock waves through the Falls Church community and the entire state of Virginia, which has long sought to bring an NFL team to the area.  The Governor, the Mayor, and members of the City Council form a task force to make recommendations about what to do.  The task force is composed of the following:

  • The Stadium Building Authority
  • City Archaeologist
  • Owner of the NFL Franchise
  • Tourist Council of Virginia
  • Native American Tribal Council
  • Citizens for the Preservation of Virginia

In addition, the Mayor will serve as the task force chairperson.

You will be assigned a role as one of the people or groups on the task force.  You will receive a task card telling you whether you support or oppose building the stadium.  Your job is to prepare remarks to support your position.  You will all then have a chance to speak at our mock task force meeting.

The students then worked together in pairs to prepare their remarks.  They focused on presenting and justifying their positions, and then on putting forward a compromise that might work for all sides.  At one point, a member of the Stadium Building Authority (totally pro-Stadium, of course) passed this note to a member of
The Native American Tribal Council (as anti-Stadium as they come):


Not to overstate the case, but I thought this was the greatest thing ever.  At no point did I tell the kids that they could negotiate with the people on the other side of the issue.  In fact, most groups were very careful to be quiet when speaking around the groups on the opposite side.  But this student felt compelled to reach out and let the Tribal Council know that their needs and desires were understood, and that even though this student’s primary role was to build the stadium, that he and his partner knew there were other concerns that mattered, too.  That’s not something you see everyday.  I can only conclude that my work here is done.  Or, I guess, your work here is done, parents.  Your kids aren’t just making it work academically; they are thinking of the needs of others and making it a part of their calculus without anyone guiding them to do so.  You are winning at this parenting thing and I thank you for it.

We will hold our mock task force meetings today.  Stay tuned!

First Grade Reading — Invention Convention

Yesterday, the first grade reading groups held their Invention Convention.  The students have been working on their inventions for weeks.  We talked about numerous inventions and how they came to be.  The students brainstormed problems and possible solutions and then created their very own inventions at home.  Last week, we discussed alliterative and rhyming names (as well as “scientific” names with a number added at the end — you’ll see this was an attractive concept!).  And now, for your consideration, here are the first graders’ inventions!

Lara confronted the problem of parents having to carry heavy bags of groceries with no help from their children.  Lara’s invention, the Gimme Groceries 3000, aims to solve this problem. The invention is a large stuffed animal that children will want to carry.  (Note that the stuffed animal Lara is holding below is just a prototype).  Grocery bags can be hooked to the bottom of the stuffed animal, so kids will be fooled into carrying the groceries.  I think I need one of these!IMG_7017 Lorien’s problem is that squirrels get into her bird feeder and eat all the birdseed.  So she invented the Squirrel Defeater Feeder.  The bird feeder is covered by a wire mesh cage with openings big enough for birds but too small for squirrels.  Brilliant!IMG_7019 IMG_7022 Mia had a problem where she couldn’t always keep her morning routine straight, and she had to keep asking her mom what to do at what time.  Enter her invention — the No Be Late Schedule Watch.  This handy dandy device doesn’t just tell you the time; it also lists your schedule so that you have it at your fingertips. No more having to ask someone else what to do!IMG_7024 IMG_7026Do you have a toddler who is constantly breaking or wrecking your things?  Then you need JP’s invention, the Toddler TripWire 2000.  Simply set the TTW2000 up around the perimeter and it will alert you to a toddler’s presence with the sound of ringing bells.  Maybe this will also work on my dogs!IMG_7031Does your nose get cold when you are camping?  But a ski mask is too confining and makes your face feel itchy?  Never fear!  You need Hannah’s Nose Cap.  Just hook the velcro tabs around the back of your head and the cotton piece fits right over your nose to keep it safe and toasty.  IMG_7035Do you lose track of your bookmark when you read in the dark?  You won’t if you have Oliver’s Bright Bookmark.  The laminated bookmark is durable and sticks to the back of the booklight with sturdy velcro so you always know where it is.  Gone are the days of searching through your book to find where you left off!IMG_7038 IMG_7041Does your fear of monsters prevent you from falling asleep at night?  If so, you clearly need Isabel’s Good Night Sleep Tight.  This device affixes to the bottom perimeter of your bed to seal off the underside from nocturnal visitors.  It even comes with a customizable sign to warn the bad guys away (I asked if I could make a “no clowns” sign instead of a “no monsters” sign and Isabel assured me that I could).  I feel safer already.IMG_7045 IMG_7047Your sibling is too busy playing the violin to play with you?  Not if you have Corinne’s Jingle Machine 2015!  Simply shake this delightful device to attract your sibling’s attention, and then tell them you won’t stop until they come to play with you.  Warning:  spontaneous dance parties could erupt.IMG_7049Do you find yourself tipping back in your chair, making marks on the wall and endangering your safety?  Not if you have Jahan’s Chair Stopper 3000.  This prototype demonstrates how even Buzz Lightyear can no longer tip back his chair with the Chair Stopper 3000 in place.IMG_7050 IMG_7051Does a family member insist on bothering you when you are trying to have quiet time or do your homework?  Then you need Brooks’ Get Out Now 6000.  When the person crosses over into your space, a loud beeping noise begins and it doesn’t stop until they leave you alone.  I am hooking one of these to my bathroom door as I write this post.IMG_7052Are you in a rush in the mornings when it’s time to feed your fish?  Why not solve that problem with Ezra’s Fish Feeder 2000.  This ingenious device consists of a tube in which you place the fish food when you have the time.  Then, in the morning when you’re rushing to get ready, you just pull the tab on the side of the tube to release the precise, pre-measured serving of food.  Fantastic!IMG_7054 IMG_7055Do you share a bedroom with someone who prefers a different light level than you?  Claire has the solution to your problem — the Just Right Light.  The Just Right Light is affixed to the underside of a box decorated with pictures of the night sky.  You place the box over your pillow, and then you can turn on the light if you need it, and adjust the level with the paper cover.  Read or relax without disturbing your companion!IMG_7058 IMG_7061Does your sleeping bag need an upgrade?  Well, look no further than Nicholas’ Super Sleeping Bag 2000.  The front of the bag contains a storage area for books, there’s a snack bag on one side and a relaxing rainbow light on the other, the sleeping bag has its own built-in comfy pillow, and there’s even a booklight if you would like to read at night!  Camping will never be the same!  (Plus, your nose will be warm because you’ll also be wearing the Nose Cap!).IMG_7066Do you (or your children) have trouble waking up in the morning?  Zoe’s TeleTone 2000 to the rescue!  Zoe designed this device so her dad could speak into it to tell her to “WAKE UP!” and get going in the morning.  IMG_7069Do you need help prioritizing your chores?  Then save your pennies to purchase Eli’s PO3 (Professional Organizer 3000).  This chart lets you decide just how much attention to pay to your different chores by moving a certain number of stickers to the bag dedicated to each chore.  With a quick glance at the chart, you’ll know exactly what to do!IMG_7073I don’t know about you, but I was extremely impressed.  These kids put a lot of thought and effort into their inventions, and it showed!  I could see in their faces how much fun they had and how charmed they were by each other’s ideas.

While we’re on the topic of inventions, I’ve heard that this Camp Invention is a fantastic summer camp program (thanks, Liz!).  I don’t have personal experience with the program, but the description on the website looks fantastic.  For example, the description of the “I Can Invent” program says “Engages children in product-based, entrepreneurial thinking through video game design while considering user-friendliness, game-play operation, aesthetic appeal and functionality. Increases understanding of the value of Intellectual Property and the roles that patents, trademarks and copyrights play in the landscape of invention and innovation.”  Wow! I’m kind of hoping I can disguise myself as a sixth grader and attend.  The next-best scenario is that some of you send your children and tell me all about it.  You can check it out and register here.  (I’m not receiving any kickbacks from this program; I just think it looks really fun and interesting!).

First Grade Reading — Inventions, Logos, and the Power of Branding

This week in first grade reading, we continued our inventions unit by talking about brand recognition, focusing on logos.  We talked about what a logo is (a symbol of some kind to represent a business, team or product) and then I showed the kids some logos and we discussed them.  First we talked about pictures embedded or hidden in logos.  For example, you probably recognize the Washington Capitals logo:

Have you noticed the outline of the U.S. Capitol building that is “hidden” at the bottom of the eagle.  If you haven’t, you sure will now.  It’s one of those things you can’t un-see!

How about the arrow in the FedEx logo?

Or the arrow in the logo, signifying both that they have everything from A to Z and that their products will make you smile (or, if you’re like me, that the ability to obtain virtually anything in two days via Amazon prime will make you smile)?

To illustrate the power of brand recognition, I then showed the kids just small slices of a series of logos (a technique I cribbed from intellectual property attorney and Falls Church City parent Erik Pelton, who was kind enough to give a presentation on this subject to my students two years ago).

With only a tiny sliver, the kids were immediately able to identify the logos for McDonald’s, Starbucks, Star Wars, Lego, XBox, Minecraft, American Girl and Nike.  It was scarily impressive.

We ended class by talking about next week’s Invention Convention.  We discussed names for products and inventions and talked about the power of alliterative and rhyming names.  Remember, inventions are due next Wednesday!  Students should come to class with their inventions.  Inventions should have catchy names, and the students should be prepared to present their inventions to the class at the Invention Convention.