First Grade Enrichment Math: Combination Plates and Joaquin’s Solution

This week in first grade enrichment math, the kids received some alarming news.  While the help they have provided to the Rosadas when it comes to running their restaurant has been well received by the parents, the Rosadas’ son, Joaquin, is not nearly as pleased.  Joaquin would prefer that his parents come to him for help, and he is determined that they should fire our first grade mathies and hire him instead.

This is a perfect transition time for the Rosadas, as they are planning to expand their menu by offering six new entrees.  To encourage customers to try their new items, the Rosadas plan to offer a combination plate deal.  Each combination plate must contain two different entrees, which can be purchased together for a lower price.  The Rosadas need to now how many possible combination plates can be made from the six new entrees.

Joaquin has stepped up and put forth a solution.  He says that, with six new entrees and two entrees in each combination plate, there are clearly twelve combinations.

I presented the students with this information and asked them:  do you agree or disagree with Joaquin?  Use whichever method you prefer (drawing, chart, tree diagram, etc.) to prove that you have found the correct number of combinations.

The students quickly set to work.  Each student had his or her preferred method of solving the problem.  They then wrote a statement saying whether they agreed or disagreed with Joaquin, and explaining why.

Most students (correctly) disagreed with Joaquin.  They identified 15 possible combinations and provided the evidence to back up their claims.

Homework was a sheet of pizza combinations.  The kids are to choose four different pizza toppings and then tell how many possible one-, two-, three-, and four-topping pizza combinations there are.  I’ve seen some papers back already and some of the students are missing some combinations (yes, there is only one four-topping pizza, but students also need to find all of the three-, two-, and one-topping pizzas).

Kindergarten Enrichment Math: Find Your Best Bud (Sums to 10)

In kindergarten enrichment math this week, we started with a five minute addition challenge.  I mention this (although it’s routine and we do this most weeks), because we also had our first kindergarten student complete all 100 addition problems correctly in five minutes.  Congratulations, Rohan!  You did it!

Thereafter, I gave each student a paper with one of the following digits:  1, 2, 3, 4, 6, 7, 8 or 9.  I then told the students their job was to find their “best bud.”  Once they paired off with the student they thought might be their best bud, I would let them know if they really were best buds, and we would keep track.  We played several rounds before someone located a best bud.  In the end, we collected the following information:  Best Buds were 1 & 9, 3 & 7, 4 & 6, and 2 & 8.  Not Best Buds we found (there are more) were 1 & 2, 2 & 3, 4 & 7, 2 & 4, 8 & 1 and 9 & 3.

I asked the kids — what does it take for numbers to be Best Buds?  What do all of these Best Bud combinations have in common?  In both classes, someone answered that both numbers had to be even or both numbers had to be odd.  I conceded that this fit all of the Best Bud examples, except it couldn’t be the answer because it also fit some of the Not Best Bud examples.

The kids were stumped.  It took some coaxing for them to decide they should “do some math” to figure out the answer.  They eventually settled on addition and this led them to the conclusion that all Best Buds, when added together, yield a sum of 10.  Eureka!

We then talked about grouping sums of 10 when adding long columns of numbers.  I showed the students how “finding best buds” can help make this kind of addition faster and easier.

Homework is one sheet of these kind of grouping addition problems (don’t be alarmed when your child is drawing strange lines on the paper to connect “Best Buds;” this is what I asked them to do) and one side of addition practice.

First Grade Enrichment Reading: Disruptus and Solving Problems

Earlier this month in first grade enrichment reading, we played the game Disruptus.   Disruptus is a game that asks players to look at objects and/or ideas and use different approaches to innovate in a variety of ways.  Students roll a die and, based on the outcome of that roll, they then need to CREATE by combining the elements of two objects to make a new object, DISRUPT by taking one object and attempting to achieve its goal in an entirely different way with a new invention, IMPROVE an object by changing one of its elements, or TRANSFORM an object by using it for a completely different purpose.

We had a fantastic time playing this game and the kids were so creative in their solutions to the various problems presented.  I feel like it really set up the kind of thinking we need to be using for our inventions.

The following week, I presented the kids with several problem scenarios:

  1. The merry-go-round on a local neighborhood’s playground has been removed. Too many children have been injured while playing on the equipment. Your task is to design a safe merry-go-round to keep children from getting hurt.
  2. I have a long, steep driveway that slants toward the street.  I have to carry the garbage can to the end of the driveway each week for trash pickup. The can is big and heavy and it’s both impossible for me to lift and  difficult for me to drag through the gravel driveway. Your task is to invent something to make this job easier.
  3. One of your chores is to feed your cat.  You don’t like the way the cat food smells or feels, and you especially don’t like washing the spoon when you are finished.  How can you solve this problem?

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Julian illustrates his solution to the merry-go-round problem.

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Gabe illustrates his solution to the trash can problem.

The kids talked about the problems and tried to come up with solutions.  The first problem was the most difficult, though there were many inventive solutions, like trampoline walls and seat belts.  The second problem was the easiest, and in every group someone came up with the idea of adding wheels to the trash can.  The third problem gave rise to lots of creative ideas.  One student remembered the real life solution to the problem because he heard all about it when his older sister did this unit with me two years ago!  (You go, Jack!)  The other students were impressed to learn that the problem was drawn from the real life of Suzanna Goodin, who invented the Edible Pet Food Spoon as a solution when she was in the first grade.

We missed first grade enrichment reading last week because I was home with the flu, and today because the first graders are busy celebrating the 100th day of school.  We will be back on track next week.

Looking ahead, our Invention Convention will be Thursday, March 16th.  All students will need to complete their inventions at home and bring them to school on or before that day.  I will send home a flyer about the Convention soon, but wanted to make sure it is on your radar.

Kindergarten Enrichment Reading: Palindromes and Anagrams

At the beginning of February, we started kindergarten enrichment reading with a rousing game of “My Aunt Birdie Fish.”  My Aunt Birdie Fish has a lot of likes and dislikes.  I told the students that Aunt Birdie Fish likes mom, dad, and racecar, but does not like brother, sister, or subway.  Could the kids use these clues to figure out what Aunt Birdie Fish likes?

We kept adding clues as we discussed.  Aunt Birdie Fish likes pup but not cat, eye but not nose, noon but not midnight, pull up but not push down, Anna but not Anne.  Eventually the kids figured out that all of Aunt Birdie Fish’s likes started and ended with the same letter.  From there, it was a pretty quick road to the realization that the words were the same both forward and backward.  And BAM, we had our introduction to palindromes.

Next, we read Mom and Dad are Palindromes by Mark Shulman and Adam McCauley.

The book is about a boy named Bob who discovers that his life is made up of tons of palindromes.  He finally decides to stop the madness by going by his full name — Robert Trebor.  (Not such a helpful strategy, it turns out).  We talked about how palindromes are words (or phrases or numbers) that read the same forwards and backwards.  We counted the palindromes in the book and came up with some of our own.  WOW, was it fun!  (Favorite palindrome = party boobytrap.  Try to contain your surprise).

Last week, I was out all week with the flu, and we did not have kindergarten reading. Today, we were back to the grindstone and learning about anagrams.  To begin, I shoed the kids 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:

heart

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 ten sets of them.  And ten 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 called “Anagram Adventure” and an optional challenge sheet of anugrams.  An anugram is an anagram that 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 if you decide to skip this part.  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 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!)

Kindergarten Enrichment Math: I Value Xylophones Like Cows Do Milk (**Plus extra bonus discussion on homework in general)

How ’bout that title?  Did your child come home saying that crazy sentence?  (If not, please say it yourself and see how your child reacts!)  Can your kindergarten student tell you what that sentence means/what the letters stand for?

I wrote the sentence on the board at the start of class and read it to the kids.  I wrote each of the capital letters in red ink and the rest of the letters in black.  The kids were easily able to figure out that the red letters were important for some reason, but they were stumped as to why.  I showed them this logo and asked them to explain it to me:

super_bowl_li_logo-svg

The kids knew it was the logo for the Super Bowl, but none of them could explain why the L and I were there.

Gradually, we made our way to the conclusion that the letters I, V, X, L, C, D, M are Roman numerals.  We then wrote down the letters and their values:

  • I = one
  • V = five
  • X = ten
  • L = fifty
  • C = one hundred
  • D = five hundred
  • M = one thousand

We talked about how to write and read Roman numerals.

This included a discussion of subtractive notation, which isn’t easy for kindergarten students to grasp.  We practiced finding numbers where a lower number was written to the left of a higher one, and reminded ourselves that the numbers need to be read as a pair and the one on the left needs to be subtracted from the one on the right (ex. IV = 4).  This is probably the easiest way to do the homework — group the numbers that require subtractive notation and circle them, then subtract and add as necessary.  This is how we did it in class, so it should look familiar to the kids.

The homework is a single-sided sheet of problems — writing Hindu-Arabic numerals as Roman numerals and vice versa.  It is difficult!  Please help your child work to/through frustration, but if s/he reaches the breaking point (or you do), pause or skip.

I hope you know that I understand that this stuff is not typical kindergarten fare.  From the homework coming back, it seems like you do — the kids are taking their best shot at things and leaving off when they reach frustration level.  That’s what they should be doing.  I don’t expect all of the kids to get these higher-level concepts all of the time.  A lot of it may go over your child’s head.  That’s okay!  Exposure is important, and while they may not remember (or understand) all of what we talk about, they’ll each take away their own pieces of information.

This is probably a good time for me to say a little bit about my philosophy when it comes to homework. I believe that homework is not really appropriate for early elementary students.  Homework can be stressful, the school day is long, and kids need to play outside and have fun when they are home from school.  Despite all this, I still assign homework almost every week, for two primary reasons.

First, I do so because I feel like homework is one of the main lines of communication between you, me, and your child.  I hope most of my students’ parents read this blog, but I know many don’t.  I also know that many children report almost nothing about their day when they arrive home from school.  If your child is the kind where obtaining information is like pulling teeth, the homework helps let you know what we did in class.  Hopefully, it also sparks a memory from your child about what we did, and starts a conversation.

Second, I assign homework because some of the children I see for enrichment absolutely love homework.  They run home, rip open their backpacks, and begin doing the homework before they even take off their coats.  They are so excited about the things we discuss in class that they cannot wait to keep working with these topics at home.

If your kid is not the “I love homework” kind of kid, you probably think I’m making this up, but I promise you I’m not.  These kids exist, there are a lot of them, homework makes them happy, and they are hungry for the kind of challenge it provides.

If your child does not love homework, there’s a simple solution — don’t do the homework.  I’m not being sarcastic (for once).  Once your child reaches the point of frustration where it’s clear that going further is going to be upsetting, take a break.  Write me a note on the homework saying you tried but it was frustrating, and move on with your day.  Not turning in homework will not count against your child or affect his or her membership in an enrichment group.  As I tell the kids in class — while you are doing your homework, at no point should you be crying or wishing that a lake of fire would open up under your chair and swallow you.  If you are feeling these things, stop, put on your shoes and coat, and go play outside.

“But Mrs. Green,” you say, “eventually my child is going to have to learn to power through and do his or her homework even when it is frustrating and hard.”  Yes!  Yes they are.  Not when they’re in kindergarten or first grade, though.  And even later in elementary school (and beyond), homework, when planned and assigned as it’s designed to be, is supposed to be practice for skills that have already been taught and learned at school.  Some of your children haven’t always mastered the concepts I teach in enrichment, and in those cases, homework is a struggle and not practice.  If that is the case, it’s time to move on.  These are advanced concepts, and your child doesn’t need to understand Roman numerals to be a successful kindergarten student.    Your child has plenty of time ahead of him or her to learn to manage homework (and there will be plenty of future homework to use for practice).  I promise.

I’ll step off my soapbox now and get back to valuing my xylophones, but please feel free to reach out if you have questions about any of this.

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!