Kindergarten Enrichment Math: Human Equations

This week in kindergarten enrichment math, we played Human Equations.  First, we reviewed our lesson from the previous week (about reading large numbers).  Some of the students have this down, and some of them definitely still need more practice.

I gave each student a card with a digit from 0 to 7 printed on the front.  Then, I asked them to line themselves up in a way to make the biggest number they could using all of the digits they had.

The kids worked together well.  They quickly decided that they should line up with the biggest digit at the far left and the rest of the digits in descending order.  They arranged themselves in this way to make the number 6,543,210.   Brilliant work!

Then, I asked the students to arrange themselves to make the smallest number they could, while still using all the digits.  They quickly decided to arrange themselves in reverse order.  They then looked at the number, though, and realized that numbers don’t usually start with a 0.  They chatted for a minute, and then they were stumped. They couldn’t figure out where to put the zero.  Most of the kids seemed to decide that it was up to the zero to figure out where he should go, and they gave up trying.  It was frustrating.  Eventually, they made the number 1,023,456, but not without a lot of fits and starts.

We went on from there, creating specific numbers and equations.  It was a fun, challenging, but sometimes frustrating, way to reinforce place value.  There is no homework this week!  I sent home a packet of math puzzles, but it is completely optional.


Second Grade Enrichment Math: Game Factory

We began a new session of second grade enrichment math last week, and with it a new unit.  When the kids arrived, I let them know that I had received a letter requesting their help from a man named Gregory Goodwin.  The letter read as follows:

Dear Second Grade Math Stars in Mrs. Green’s Groups,

My name is Gregory Goodwin, and I need your help!  When my dad, famous game maker Gary Goodwin, died last year, he made a big mistake.  I was really young, so my dad left his share of our business, Goodwin’s Game Factory, to his partner, Cheatum Swindle.  Dad knew that Cheatum was a great businessman, and he was right.  But he also knew that deep down Cheatum hates games and sometimes doesn’t play fair.  Dad worried about this, and he was careful to write his will to give Cheatum control of the company ONLY IF Goodwin’s Game Factory continues to produce FAIR GAMES, where the probable chance of winning is equal for all players. After all, that’s what games are all about!

I think my dad made a huge mistake.  It’s only been a few months, and it looks like Cheatum is making as many games as he can, without paying attention to whether or not the games are fair!  Cheatum just wants to make as much money as he can, as quickly as he can.  But people will get mad if it turns out that the games are unfair and don’t have equal chances for all players to win!  They’ll stop buying our games!  The company my father created could go bankrupt if unfair games are sent to stores and sold to customers.  We can’t let that happen!

I need your help to protect my father’s name and the reputation of the company (after all, it’s not called the GOOD-WIN Game Factory for nothing!).  If I can prove that Cheatum has developed unfair games, I can take over the Goodwin’s Game Factory and run it the way my father would have wanted.

Please help me test the probability behind the games Cheatum created.  Cheatum is out of town on business, so this is our chance!  I can get into the factory design rooms without Cheatum watching.  I will take the games and give them to Mrs. Green, and you and your classmates will test the games to see if they are fair.  If they aren’t, you will need to change the rules to make them fair.  We only have a short time to save Goodwin’s Game Factory before Cheatum returns. Please don’t let me down!

Thank you for your help!

Gregory Goodwin

After reading the letter, the kids agreed that they would like to help.  We talked a bit about probability and what it means.  To prove that they would be good game testers, the kids completed an activity where they predicted the outcome of a series of coin tosses and then performed the coin tosses to find the actual outcome.  They did a great job (but their understanding of probability is definitely not sophisticated at this point).

This week, the students tested their first game, a coin-based game called COIN YOU DO IT?  They reviewed the rules of the game and then made predictions about its fairness.  To play, two players must move the same number of spaces down a path to the finish line.  On each turn, one player tosses two coins.  Player A can only move if s/he tosses two heads or two tails.  Player B can only move if s/he tosses one head and one tail.  After reading the rules, the kids were evenly divided as to whether they thought the game would be fair.

Each team played the game at least twice.  We then analyzed our data to decide if the game is fair.  Last week, many of the kids favored more of a gut feeling approach to probability than a math-based approach.  (For example, even after acknowledging that there are two possible outcomes when you toss a coin, and that there is one head and one tail, several students still maintained that it was more likely to toss heads or tails “because that’s what happens to me ALL THE TIME!”).  Let’s hope that changes over the course of this unit.


Have a wonderful long weekend, play fair, and be wary of anyone with the name Cheatum Swindle.

Second Grade Enrichment Humanities: Fairy Tale Mock Trial

Last Tuesday, second grade enrichment humanities groups met for the first time this session.  We introduced our unit for this session with a discussion about the law.  The students listed some laws they knew, and then we talked about why we have laws.  We talked about trials, when we have trials, and some of the people who are present during a trial.  We discussed the roles of different parties in the trial process.  We wrapped up our session with a discussion of crimes committed by fictional characters, particularly in fairy tales.  The students identified the crimes committed by characters like Goldilocks and the Big Bad Wolf (perhaps a life of crime was inevitable with a moniker like that?!).

This Tuesday, I placed the students in pairs and assigned each pair a fairy tale character.  Their job was to think about their fairy tale story and identify which parts of the story their character would be responsible for telling on the witness stand.  Each pair then needed to write four questions to help the assigned witness tell his or her part of the story.

Next week, I’ll introduce the second graders to the facts of the case we’ll be dealing with this session.  They’ll find out if their group will serve as the prosecution or the defense, and our mock trial unit will be off and running.


Kindergarten Enrichment Reading: Anagrams and Anugrams

Today in kindergarten enrichment reading, we started class with these words on the Smart Board:

many do

sea duty

sandy weed

yard huts

I asked the kids if they knew what anagrams are.  None of them did.

We read Word Wizard by Cathryn Falwell to help us figure out the answer.  Anna’s adventures with anagrams helped them kids figure out that anagrams are words made out of the same letters as another word, just with the letters in a different order.

I told the kids that each of the pairs of words on the Smart Board was an anagram for another single word, and the four words all had 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 moved them around — hey, these letters spell day!  It didn’t take long before we realized that “many do” is an anagram for “Monday.”  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 moved on to a super tough anagram challenge.  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 six sets of them… and six 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 is not homework, the kids just wanted to be able to remember the anagrams for their names.

Homework is 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 demands to keep at it until a solution is found.  Fantastic!  Either result is fine.

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

Ravaged hay eat!  (That’s an anagram for “Have a great day!” of course!)


First Grade Enrichment Math: Cooperative Logic Problems (with Bears!)

New first grade enrichment math groups met this past Friday.  We are working on solving logic problems in cooperative groups.  We began with eleven “Bear Line-Up” problems.  The kids worked in groups of three or four.  Each group received a set of cards, with each card containing a clue.  The kids read the clues in turn and then attempted to arrange the bears according to the parameters given on the cards.

For example:

  1. Three green bears are at the front of one line
  2. In one line, there are 3 blue bears and 4 yellow bears.  Each blue bear is just behind a yellow bear.
  3. There are 2 lines of bears.  There are 7 bears in each line.
  4. Four red bears are at the back of one line.

All of the clues were necessary to complete each task.  The students had to listen to each other read the clues and then agree on the appropriate course of action.  This isn’t always easy.  Some years, this activity results in a great deal of frustration.  This was not one of those years!  The children were polite and cooperative from the moment we began until the moment we finished.  They took turns, pointing out when someone had been skipped over (and not just when they were that someone!).

We finished the Bear Line-Up problems through task nine or ten (depending on the group), and next week we will move on to a series of problems called Bear Street.  These are similar problems, but they involve placing the bears on a map.  We’ll work on these logic activities for the next few weeks.


First Grade Enrichment Reading: Inventions

This week, we started a new unit in first grade enrichment reading.  This session, the first grade readers will be working on a unit about inventions.  To begin, I divided the kids into two groups and gave each group a different object — one group received a cup and one received scissors.  I asked the groups to talk to each other about the following four questions:

*What is your invention?

*What problem was your invention created to solve?

*How has your invention helped people?

*What are five alternate uses for your invention?

We discussed the students’ thoughts.  Everyone had an easy time answering the first two questions.  Some groups struggled to explain how their invention helped people.  It rapidly became clear that some students were particularly talented at devising alternate uses.  I told the students that they had to ignore the part of their brain that was shouting at them “But I know the RIGHT answer!  They’re scissors!  They cut paper!” and listen to the part of their brain that can see things differently.

I then asked the kids if they thought the items were technology.   They all looked at me like I was crazy.  We went around the room, and every student in the class argued that no, of course these items are not technology.  We talked about the definition of technology — the students decided that to be technology, something must have an outside power source.  The kids specifically mentioned electricity, batteries and solar power.  They came up with these on their own.  I then read them the wikipedia definition of technology:

Technology is the making, modification, usage, and knowledge of tools, machines, techniques, crafts, systems, methods of organization, in order to solve a problem, improve a preexisting solution to a problem, achieve a goal or perform a specific function. It can also refer to the collection of such tools, machinery, modifications, arrangements and procedures. Technologies significantly affect human as well as other animal species’ ability to control and adapt to their natural environments.

Based on this definition, what do you think?  Are a cup and scissors technology?  The kids decided that indeed they are.   I assigned the kids secret homework that had to do with this concept.  This homework was just something they were supposed to say to you at the dinner table.  If you don’t think you heard it, ask your child!  I also sent home a “thingamajig” worksheet with a picture of an odd-looking device.  The students were supposed to list possible uses for the thingamajig.  I told them I wouldn’t give them a suggested number of possible uses, but that they should come up with somewhere between 5 and 675.

As our unit progresses, we’ll examine a number of enduring inventions that were actually “accidents.”  I love the idea of leading the students to the realization that  “mistakes” are not just okay, sometimes they’re actually more valuable than if things had gone the way we expected.  Students will also come up with their own inventions, and we will share them at our Invention Convention at the end of the unit.  Many, many more details about this project will follow.


Update — Kindergarten, First and Second Grade Happenings

Normally, I publish a separate post for each group, but this week we’re trying something new!  There is so much to catch up on, I thought it might be best to have it all in one place.

Kindergarten enrichment math students have been working with patterns. This week, we played Target Addition. The game uses a five-row, five-column board where the top row is all 5’s, the next row is all 4’s, then 3’s, 2’s and 1’s.  Before beginning play, each pair chooses a target between 25 and 55.  Players then take turns placing a marker on one of the numbers on the board.  Each time a player places his or her marker, s/he announces the total of the covered numbers.  For example if the first player covered a 4, the second a 3, and then the first a 2, the sum would be 4 + 3 + 2 = 9.  The first player to reach the target number exactly wins.  If a player goes over the target number, s/he is out.

This game is great to strengthen mental math skills.  The kids are really good at addition, but working on accuracy and speed is always helpful.  Keeping track of the total in Target Addition can be a challenge, but since the board is always in front of you, it’s no problem to start from zero and add up all of the covered numbers, if necessary.  The game also encourages the kids to think a few steps ahead.  Once you near your target, you need to start thinking about what your opponent will do if you cover a certain number, and how you can avoid setting your opponent up to win.  The students brought a board home with them so that they can teach someone else how to play. This is the only homework this week!

In first grade enrichment math, we continue to work on different kinds of puzzles. This week, we worked on using clues to locate a “secret number” on a hundreds chart.  I gave the kids four clues for each number.  As they received the clues, they used dry erase markers to eliminate numbers on the chart that could not be the secret number.  For example, if the clue was “the number is odd,” then the kids crossed off all of the even numbers.  This is a bit more confusing than perhaps it sounds, because one has to be careful to be sure to mark off the inverse of the clue (if it says that the number is even, for example, then you need to mark off the odds).  Some of the kids got the idea quickly; many of them did not.  Of course, then the clues got harder (“if you add the digits, the sum is 12,” for example).  They worked hard and with great enthusiasm (for some of them, finding the number in question was quite difficult, but it was almost equally difficult not to shout out the number as soon as they found it).

Homework is to create a set of four clues that lead to one and only one secret number.  All of the clues should be necessary to find the number, and they should lead to only one number.  I sent home a hundreds chart to help.  Please do not cut out the clue cards — keep them as a whole sheet, turn them in and let me check them, and then we will use them in class the next time we play “Secret Number.”  I told the kids they need to practice to be sure that their clues actually lead to one (and only one) number.  It might be a good idea to make copies of the hundreds chart, in case they need to practice more than once.

This activity was “confusing, and hard, and SO FUN” according to one of the first graders. I would say this is a pretty accurate summation of how most of the kids felt.  Your child may need some help creating his/her clues and practicing to make sure they only lead to one number.

You can find the packet at this link (Secret Number), if you need another hundreds chart or more cards.

In first grade enrichment reading, we completed our second day of Crime Lab testing, and the students wrote paragraphs synthesizing their results.  Their paragraphs were impressive — super detailed and full of factual support for their hypotheses.  In the end, most kids correctly identified the two guilty parties:  Brandon and Julia.

We knew Brandon looked guilty because he brought the brown dye, he brought pie, he didn’t drink from the cup, his footprints (well, footprint!) were at the scene of the crime, he wanted to swim in the ocean, and he was wearing a purple cotton sweater.  We knew Julia looked guilty because she didn’t drink from the cup, her footprints were at the scene of the crime, Danny smelled like her shampoo, she brought pie, and she has a dog, whose hair was found on Danny and whose footprints were found at the scene of the crime.

In case you were wondering (we were!), the mystery powder in the ice cubes (and then the juice) was indeed sleeping powder.  Ask your kids how the powder wound up in the juice!

Next week, we’ll be working on cracking some codes!

In second grade enrichment math, we spent this week’s class time working with Babylonian numbers.  Like Ancient Egyptian numbers, Babylonian numbers are additive.  Babylonian numbers do, however, have place value.  The students were thrilled!  Place value!  Something we understand!  They were overjoyed to tell me that the place to the left of the ones place must be the tens place.  They were correct!  It was glorious.

Then they couldn’t wait to let me know that the next place had to be the hundreds place.  But nope, it didn’t have to be that at all.  In the Babylonian number system, the next place is the sixties.  A base 60 number system?  Say it isn’t so!

Here is a sample of some Babylonian numbers:


Some of the kids made (with my encouragement) “cheat sheets” listing multiples of 60.  This made translating Babylonian numerals considerably easier.  We spent the remainder of class working with Babylonian numerals and translating back and forth.  Next week, we’ll be comparing Egyptian, Greek, Mayan, and Babylonian numerals.

In second grade enrichment language arts, we embarked upon a simulation called “To Dig or Not to Dig?” 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.  This week, we held our task force meeting, and the students took turns explaining their positions.  Most of them also presented compromises they had developed that might help bridge the gap between the two sides.

During one task force meeting, a student representing the Tourist Council spoke rather stridently about how “bones don’t matter! Who cares about bones?” and argued that “the stadium will bring in money, lots of money.”  I know this wasn’t a real meeting, but I’m going to be totally honest and say that I felt uncomfortable.  I’m quite certain that the student was trying to be funny, but it didn’t come across that way at the table, and the students representing the Native American Tribal Council looked alarmed.

After everyone had their chance to speak, I asked if anyone had any follow up remarks.  One of the students raised his hand and said “I just want to say that it’s not always about money, and money isn’t the only thing that matters.  There are other things that really matter and those things are important to people, too, and we should pay attention to them.”

Sometimes, the state of the world can look pretty bleak.  Then I spend time with five-, six-, and seven-year-olds, and I know that everything is going to be okay.