# 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.

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.

# First Grade Enrichment Math: Crack Pack, Inkies, and Salamanders

Has your first grade enrichment math student gone down the Inky rabbit hole?  I introduced the students to Inkies last week, and some of them are completely obsessed.  I can’t tell you how happy this makes me!

We’ve been working on math puzzles in class, using some from the Math Salamanders website, and also practicing CodeBreaker puzzles and now Inkies.

Some students are taking the CodeBreaker Challenge and trying to join the Crack Pack.  On Friday, I taught the secret Crack Pack handshake to my first two members.  To join the Pack, the students need to complete CodeBreaker Challenge packets. The packets are available in my office.  Once a student completes a packet, s/he can return it to me at any time during the week and I will correct it as soon as possible.  If there are no errors, I’ll pass along the next Challenge packet.

At the same time, some students are working to join the Inky Club.  Here is a picture of our first member, proudly displaying his Inky Club Badge:

I’m thinking he’s a tiny bit excited about his accomplishment.  Wouldn’t you agree?

# First Grade Enrichment Reading: Mystery Solving, Crime Scene Analysis and Crime Lab Results

When I picked up the first graders two weeks ago for reading group, I let them know that my office contained a crime scene. I told them that their job was to be the detectives, observe the crime scene, and record everything they observed so that we could figure out the solution to the mystery.  I reminded them that it’s important to record everything because it’s impossible to tell at first glance which things might be clues.

I gave very little details about the mystery. When we met the following week, we went into much greater depth about what exactly happened.

The kids diligently began to make maps of the crime scene.

The next week, we talked about the circumstances leading up to the crime.  During class, I told the kids the facts of the case.  We met our main characters (and suspects) — five friends named Sam, Brandon, Tessa, Julia and Alex.  These friends formed the Stuffed Animal Adventure Club (DUN DUN DUN!) (<—- ask your child about this).  The friends got together for a playdate and to build a clubhouse.  After awhile, they wanted to do something else but could not agree on what.  They decided to take a nap, and when they awoke, they found that someone had played with Danny the stuffed hippo while they slept, leaving him soaking wet.

After we discussed the facts, I gave the kids a fact sheet and a graphic organizer that we will use throughout the unit.  They spent some of our class time filling out their Clue Board.

This week, we turned my office into a crime lab and set out to do some tests to help determine exactly what happened to Danny, the pilfered hippopotamus.  The office was divided into five stations, and the kids rotated among the stations to perform the tests.

The first station was the Juice Test station.  The juice found at the scene seemed a little suspicious.  Had something been added to it?  The children used Ph paper to test the acidity of the juice.  They dipped a strip of paper in the juice, knowing that if the paper turned green, it meant that some kind of powder had been put in the juice, but if it stayed yellow, nothing had been added to the juice.

The next station was the pen or dye station.  A paper towel with a mystery brown stain was left at the scene of the crime.  Was the stain made by pen or by dye?  The kids dipped a piece of the stained paper towel into water and watched the water spread up through the stain.  If it stayed brown (just a lighter shade), it was made by a brown pen.  If it separated out into its component colors (red and green), it was made by brown dye.

At the Fingerprints station, the kids looked at a picture of the cup found at the scene.  Three fingerprints were found on the cup.  The kids matched the fingerprints to their owners, using a chart of the fingerprints of the five club members.

At the next station, we examined three types of thread — cotton thread, wool thread, and the mystery threads found at the scene of the crime.  Were the mystery threads smoother and tighter, like the cotton threads?  Or were they wiry and loose, like the wool thread?  Who was wearing cotton and who was wearing wool?

Finally, there was the Smells station.  When Danny was found at the scene of the crime, he had a distinctive smell.  Brandon and Julia had both just washed their hair.  Did Danny smell like their shampoo?  And if so, which one?  The kids endeavored to find out.

First, the students smelled Danny.  Then, they smelled Brandon’s shampoo, and then Julia’s shampoo.  The kids decided which smell they thought matched Danny, and they recorded this information on their data sheets.

Ask your child about the results!  Do the clues point to a particular club member as the culprit?  Or does it seem like more than one person looks guilty?  After we finished the five stations, the kids met to discuss their results, and then this week’s homework is to write a paragraph explaining the conclusions.

During this unit, the kids are working on logical and sequential thinking, making inferences, using evidence to support an argument, and not jumping to conclusions unsupported by the text.  They don’t really know they’re working on these things, of course.  They just think they’re sleuthing out a solution to a mystery.  I won’t tell them if you don’t!

# Second Grade Enrichment Language Arts: Creating and Using a Grid and Playing Artifact Battleship

The past few weeks in second grade enrichment language arts, we talked about gridding. We discussed how an archaeological dig destroys a site, and how keeping records during a dig is so important.  I showed the kids a sample site grid and we talked about how grids help archaeologists remember exactly where items were found.  The kids remembered that context is super important, and that knowing which items were found together makes a huge difference.

The students created their own grid over a drawing of artifacts at a site and then recorded the coordinates for items they “dug up.”

The next week, to practice working with a grid, we played Artifact Battleship.  Each student “buried” a spear, pottery, jewels, coins, and bones.  They then played against a partner to try to excavate their opponent’s items, calling out coordinates to find out if that spot was a “hit” or a “miss.”

If you’re interested in playing at home (hey, it could happen!), you can find the board here:  Artifact Battleship.

# Welcome to Kindergarten Enrichment Math!

I met with kindergarten math groups for the first time last Friday. To begin, I explained that they would be coming to see me once each week for enrichment math. I told the kids that the math they do with me is supposed to be challenging, and that if they don’t get it right away, that’s okay.

We then took our first Five Minute Challenge — trying to correctly complete 100 addition problems in five minutes. No one completed all 100, nor did I expect them to, but several students came close. We noted the starting scores and the kids will try to beat their scores in the coming weeks.

We then spent some time talking about even and odd numbers. We talked about how even numbers end in 0, 2, 4, 6, or 8, and odd numbers end in 1, 3, 5, 7 or 9. I told the kids that even numbers have best friends and can be divided into pairs so that everyone has a “BFF.” Odd numbers don’t all have best friends and there is always one left without a BFF. Or, as a kindergarten student explained, there’s always “an odd man out.”

Homework for the week was an even and odd worksheet. Homework is always due one week after it is assigned. Your child can give the homework to his or her classroom teacher and it will find its way to me.