Second Grade Enrichment Math: Game Testing Pop Go The Sticks

This week, in second grade enrichment math, the students received a new assignment from Gregory Goodwin — they were charged with the responsibility of testing the game Pop Go the Sticks.

The students were each given a game board, a rule card, a paper clip game piece, and three popsicle sticks.  They read the rules of the game to prepare to play. According to the rules, Player A moves two spaces if all the sticks land with their design side up, and one space if all the sticks land with their plain side up, whereas Player B moves two spaces if one stick lands with its design side up and the two other sticks are plain, and one space if the sticks land with one plain side and two design sides up.

I asked the students to explain if they thought the game was fair.  All but one of the students answered that they thought the game was fair and that each player had an equal chance of winning.  Then, they began to play the game.

Normally, my goal is for the students to play each game at least twice, so each student has an opportunity to be Player A and Player B.  On this day, though, we stopped halfway through the first game to check in.  In each class, we had four simultaneous games running.  In all eight games, Player B was winning by a lot. We talked about how likely it would be for this to happen if it were a fair game.

Next, we listed the possible outcomes after tossing the three sticks.  We made a tree diagram and came up with the following possible outcomes:  ppp, ppd, pdp, pdd, ddd, ddp, dpd, dpp (where “d” stands for “design” and “p” stands for “plain”).  Player A can only move if the sticks land ddd or ppp; Player B can move if the sticks land in any of the other configurations.  Once the kids saw the information displayed this way, they were easily able to articulate that Player A had a 2 in 8 chance of being able to move, and Player B had a 6 in 8 chance of being able to move.  I could see their faces change as they came to the realization that the game was far from fair.

The students’ final task was to write a letter to Gregory Goodwin, explaining their conclusion that the game is unfair, and then describing how the rules of the game could be changed to make it fair.  The kids came up with a variety of ways to change the rules.

Each student brought home the game board and popsicle sticks.  Some of them planned to challenge you to play the game with them at home (without letting you know that the game is unfair).  They were quite tickled that they were pretty much guaranteed to win.  Hey, you take a W wherever you can, right?

First Grade Enrichment Math: Charts and Tree Diagrams

Last week in first grade enrichment math, we continued our “Math on the Menu” unit.  We picked up where we left off last week and discussed the Rosada family’s problem of how many tostada combinations can be made with the 5 toppings they plan to offer at their restaurant — beans, cheese, olives, lettuce, and salsa — if each tostada can have 3 of the 5 toppings and no tostada can have a topping repeated twice.

The students presented the conclusions they came to last week.  Most groups agreed that there were ten combinations.  They also agreed that they hadn’t really used a strategy when trying to find the total number of combinations, and that the work would likely be easier if they had a strategy.  (Many of them pointed out that their parent(s) helped them develop a strategy when working on last week’s homework, so they did indeed give you credit!)

I presented two different strategies — using a chart with an organizational system where you exhaust all possible combinations for a particular ingredient before you move on to the next ingredient, and using a tree diagram with the same organizational system.

First, we completed the tostada combinations chart together using the organizational system described above.  The students picked this up quickly and we finished the chart in just a few minutes. We all agreed that it was clear there were only ten combinations.

I then demonstrated this strategy using their homework from last week, which had to do with sandwich combinations.  I also showed the students how to make a tree diagram (my personal favorite).  Most of the students were less than impressed with the tree diagram.  They understood it, they just didn’t love it like I do.  Sigh.


I told the students that for this week’s homework (which has to do with ice cream combinations), they can use a chart, a tree diagram, or whatever method works best for them, so long as they show their work and can explain how they know that they found all of the combinations.

We did not have enrichment math this week because I was out of the building for an all-day PYP training session.

Next week, we’ll perform a cost analysis for the Rosadas, to help them decide how to price their tostadas.   For now, I’m off to find myself a snack — talking about delicious food all day has left my stomach growling!

First Grade Enrichment Reading: What Can’t You Do With a Paper Clip?

This week in First Grade Enrichment Reading, we revisited the humble paper clip.  Last week, I used the paper clip as my example when explaining how to come up with alternate uses for common objects.  We spent some time discussing a number of unconventional things a person could do with a paper clip.  This week, we turned that activity on its head.

I divided the kids into two teams and we played “What Can’t You Do With a Paper Clip?”  To begin, I gave the students five minutes to list as many things as they could think of that can’t be done with a paper clip.  I encouraged them to strive for quantity over quality, telling them that they could narrow down their ideas to the best ones once we were finished with our lists.  The teams then had two minutes to discuss their ideas with their group.

Then the game began in earnest.  One person from each team would announce something that can’t be done with a paper clip.  For example, one student said “You can’t turn it into electricity!”  The opposing team then had ten seconds either to concede that that thing can’t be done or to challenge and respond “YES YOU CAN!”  If the team decided to challenge, they had twenty seconds to explain how exactly one could use a paper clip for that purpose.

Any unchallenged claim earned the claim-making team a point.  A successfully challenged claim earned the challenging team a point.

In the case of the electricity claim, the other team challenged, and a student pointed out that you could attach a paper clip to a kite and go out in a thunderstorm a la Ben Franklin and make some electricity.  This earned the challenging team a point.

The kids came up with so many creative ideas and seemed energized by the competitive nature of the game.  (Shouting YES YOU CAN! is kinda fun, even if you don’t have a plan for what to say next).

For homework, I asked the students to start a “Problem Journal.”  We talked about how inventions are really just solutions to problems, and so to come up with an idea for an invention, we need to identify a problem that needs a solution.  In previous years, I’ve had many students claim that they don’t have any problems!  I always tell them that I hope that’s true but I kinda doubt it, and in any event it doesn’t matter because they just need a problem, it doesn’t have to be theirs.  I’m hoping the Problem Journal helps the kids notice just how many problems are out there waiting to be solved.  All the students need to do is pay attention to when someone is grumbling and then write down what that person is grumbling about.  If your house is like mine, they could knock this out in no time.  (But your house might be like Lucas Z.’s, whose parents are “always cheerful,” in which case please invite me over for dinner some time.).

Have a wonderful long weekend and know that, even if something goes wrong, at least it will be fodder for your student’s Problem Journal!

Second Grade Enrichment Language Arts: State v. Jack Jones

Last week in second grade enrichment language arts, we started a new session and a new unit to go with it.  To begin, we talked about laws and why we have them.  Then we discussed some fairy tales and the crimes that may or may not have been committed by the fairy tale characters.  When the kids came in to class this week, I gave them a packet of documents marked CONFIDENTIAL. Each group was then assigned to a team — one class is the defense and one is the prosecution.  We talked about how there can’t be any information sharing between the teams.

I then introduced the case, which is State v. Jack Jones.  The following short facts are undisputed by all parties and were presented to both teams:

Short Facts

On March 31, 2015, Jack Jones attended a local market with his cow, at the request of his mother, Mrs. Nora Jones.  Jack Jones apparently swapped the cow for a bag of beans and returned home.  His mother, unhappy with his dealings at the market, threw him out of the house and did not see him until the following day.

Jones then planted the bean seeds and went to sleep in the field near his home.  Upon waking the next morning, April 1, 2015, Jones discovered a giant beanstalk had grown from the beans.  He climbed the beanstalk and arrived at the home of A. Giant and his wife, M. Giant, situated upon a cloud at the top of the beanstalk.  Jones entered the Giants’ home via a catflap hidden within the premises.  While inside the premises, he saw a goose owned by the Giants apparently laying a golden egg.

While Mr. Giant was sleeping, Jones took the goose and the egg and ran from the premises.  The noise made by the stolen goose woke Mr. Giant, who chased Jones down the beanstalk.  Upon reaching the ground, Jones obtained an axe and cut down the beanstalk, causing Mr. Giant to fall approximately 500 meters.  Mr. Giant subsequently died from head injuries sustained in that fall.

Shortly thereafter, Jones was arrested and charged with the offenses before the court.

We then went through the charges.  We talked about murder and burglary, and the elements of each crime (in the fictional State of Fable) that the prosecution would need to prove beyond a reasonable doubt.  Some kids protested — “But Jack had to do it!  He had no choice!” — and this led nicely into our discussion of Self Defense.  Someone else said that it was Mr. Giant’s fault, and then we discussed Provocation.

The members of the prosecution received the statements of Mrs. Martha Giant and Inspector Morse.  The members of the defense received the statements of Jack Jones and his mother, Nora Jones.  The kids were riveted.  They eagerly pointed out relevant facts and expressed alarm when they discovered things that were damaging to their case.  They couldn’t wait to put together their arguments and strategy.  Our 40 minutes together flew by so quickly that I had to set an alarm to let me know class was ending so that I could clear the room in time for the next group.

I won’t see the kids next week because of the Friday holiday, so they will have awhile to chew on the facts of the case.  Most of them had very strong feelings about Jack’s guilt or innocence.  We talked a bit about how our judicial system is designed to make it difficult to find defendants guilty.  I asked the students why they think this is — don’t we want to punish people who do bad things?  And if we do want to punish them, why do we make it so hard?  Something else must be more important to us than punishing the guilty.  It didn’t take the kids long to come to the conclusion that our society cares deeply about protecting the innocent, and we want to have a high level of confidence in someone’s guilt before we punish them.

The Friday after next, the kids will begin crafting their arguments and drafting questions for direct and cross examination.  Wish Jack luck (or not, I guess, depending on what you think about his guilt!).

Second grade enrichment math: The 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 once, but we ran out of time.  Next week, they’ll play the game at least twice more and then analyze their data to decide if they think the game is fair.  At this point, the kids still seem to favor more of a gut feeling approach then 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.


As a side note, we had a discussion the other day about why one side of a coin is called tails.  We understand that tails is “kind of the opposite” of heads.  But the heads on coins are heads of people, and people don’t have tails.  Shouldn’t it be heads and feet?  If you would like to join the fight to rectify this wrong, please contact Ella.

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


Kindergarten enrichment reading: homonyms, homophones, homographs

This week in kindergarten enrichment reading, we learned about homonyms, homophones, and homographs.  I don’t really expect the kids to grasp the difference (or at least I don’t expect them to remember it), but I think it’s important to know that there are different categories.  (Homonyms are words that sound alike but have different meanings; homophones sound alike, and have different meanings but different spellings; homographs are spelled and sound the same but have different meanings).

The kids were excited to name pairs of words they knew that fell into each category.  Some of the kids were still a bit confused (mentioning examples of words in different contexts instead of words with different meanings), but most of them caught on quickly.  This week’s first grade musical included some homonym jokes and the kindergarten students had just seen the show so we talked about these in class (the show is about a lost bear and a group of characters discuss where she could be [“did she bear left or bear right?”] and how sad it is that she’s missing [they “can’t bear it!”]).

As part of the lesson, we went over there/their/they’re, to/two/too, and your/you’re.  They may not have it down right now, but if we start emphasizing the difference in kindergarten, you’re child’s future Facebook friends will thank us.

Homework was a one-page sheet writing sentences using homonyms/homophones.  Enjoy the long weekend — eat a pair of pears, perhaps?

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 (Connor, I’m looking at you!), and some of them definitely still need more practice.

I gave each student a card with a digit from 0 to 6 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 photos below show them discussing where each person should stand to make the number.


The kids worked together so 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 (pictured below).  (Also pictured below: the tip of my finger.  Trying to fit 7 kindergarten students in a cloffice is difficult enough; fitting them all in a picture taken within the cloffice walls adds an extra level of challenge!).



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 just 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 decided to have the 0 and the 1 switch places, making the number 1,023,456.

We went on from there, creating specific numbers and equations.  It was such a fun way to reinforce place value — at least I thought it was!  The kids seemed to enjoy themselves (while sharing knowledge and learning new things) as well.

Homework this week is a one-page worksheet about writing bigger numbers.  Enjoy the long weekend!