Tag: Problem solving

Candy-Coded Morse Mondays

These two were so excited about earning their treasure through decoding the Morse Coded Monday Message that they just had to take photos of their discovery; a pile of Hawk Tickets in the vacant locker.

Yesterday was Monday, and among other things, that means Morse Code Morning Work for the Polite Pirates! Each Monday, since I introduced Morse code to the class back in January (Coding Teamwork), I’ve provided dots and dashes for deciphering. The prize for first decoder varies. At times it’s an intrinsic reward. One time, I hid a pile of behavior-plan tickets in the locker of a student who never showed up at the beginning of the year. Many of the codes contain riddles, so they are codes within codes.

The riddle within a riddle on this occasion was the vocabulary word “nonexistent” that described the Polite Pirate who had never shown up.

This was the case yesterday. I made up a word problem involving kids and candy. We have been learning fractions, and I was planning on introducing equivalent fractions first thing. Instead of saying, “Today we are going to learn about equivalent fractions,” I buried the treasure within the Morse coded message.  

Admittedly, not everyone was super into decoding this message. When I am coming up with a message, I try to keep it short. I don’t want the task to seem daunting. Another thing I have to look out for is only including letters. I avoid punctuation, and any numbers need to be spelled out. There is Morse code for letters and punctuation, but the image of the coded alphabet that I provide for the Polite Pirates does not have that code in it. (A fun, albeit challenging, task could be having the Polite Pirates figure out the code for numbers by embedding dash/dot combinations into messages that would only make sense after doing some calculating to figure out the answers to math problems. My students could build their own decoder of numbers through doing math, mixed in with Morse code.)

This is a screenshot of what I put into the Morse code translator website.

I messed up yesterday’s code. I accidentally included a number that wasn’t spelled out. When some students came to the “2” within the text, they knew it was a number. Rather than have them figure out what number it was from the problem, I told them it was an upside down five. (I can’t help myself!) It took them less than a minute to understand it was a two. 

Before stumbling across the number within the code, the Polite Pirates had figured out that it was going to be a word problem. This had some of them annoyed and others intrigued. In order to sweeten the deal, I had hinted that there would be a prize for whoever solved the problem first. Of course my hint was also a riddle: “The first to solve this will literally get the answer.” This worked because some of the first few words include “six candies.” My pirates, polite or otherwise, were going to bite onto this extrinsic motivation! Also, I was able to reteach the vocabulary literal versus figurative while they worked. 

When the word “fraction” was decoded, students knew what they were up against. Mr. Weimann was up to his many tricks. This was going to be “fun learning.” We have been working on fractions. The decoding heated up, and students began working in a frenzy. They were ready for this. 

As the final letters and words were discovered a veil of secrecy seemed to lower over the classroom. In order to earn the answer, you must figure it out. Now, students were back at their desks, hunched over their notebooks. “What is the problem about?” I prompted, half for the students working out the word problem, and half for those who were still decoding the Morse code message. I wanted the first half to understand the message of the problem, and I hoped to light a fire under the ones struggling with dots and dashes. This second goal worked, because one of my students who regularly succeeds in decoding these messages first had come into the classroom late that morning. Her pencil nearly carved the letters into her paper as she frantically discovered each letter of code. 

“Candy!” nearly everyone exclaimed, for the rumor had flown around the room like flu germs in a cramped elevator. 

Approaching the students working out the math, I asked, “What are you asked to find?” This is the second of our four word problem prompts that we use as a mantra when performing problem-solving math. 

  1. What is this problem about?
  2. What are you asked to find?
  3. What is the important information?
  4. What are you going to do? (What operations are necessary?)

I informed the front-runners that there was a riddle within the problem within the code. “Don’t be fooled,” I warned. “Look closely at who is getting candy in the end. It is written in the second person,” I instruct. I was hinting at the fact that, while you are sharing the candies with your friends, you still get to have some! “The problem states, ‘What fraction of the candy would each of you get?’” I quietly read to the students who are working out the math. 

One of the students got it. “There are three people and six candies,” he whispers. 

“Mm hmm,” I encouraged.

“Is this it?” His competition showed me her paper. She has not only written the correct answer, 2/6, but she drew pictures to show her work! I tell her yes, just as the boy shows me his paper. He has the same fraction. I then tell them to see if they can “simplify that fraction. Is there any way to make those numbers smaller, but have it describe the same amount of the candy?” They crunch the numbers simultaneously. 

I was so impressed with their work that I took pictures to project on the board.

“One-third!” they exclaim in unison. If I don’t say that they are correct verbally, my face assures them of victory. And, the action of getting a big bag of candy out of a cabinet is more proof of triumph than the class can handle. Everyone’s attention is on the Monday Morse code math masters who have earned the prize; literally the answer to the problem; six candies each to share between themselves and two of their friends. 

Before giving them the candies, I had them explain their work. They took turns writing and drawing on the board, talking their Polite Pirate peers through what they had done. The student who had drawn pictures in her notebook, not only drew them on the board but wrote complete sentences describing the whole procedure. I was so impressed that I was tempted to give her additional candies, but no, I am a pirate captain, if nothing else, and I be stingy with me treasure! (Really, I like to keep my word, strictly, when I can, because I stretch my meanings all of the time!!)

Who to share their treasure with, these two could not decide. I suggested that they witness who goes back to their desk the quietest and does the best job copying what is on the board into their spiral notebooks. The Polite Pirate pair nodded and the race was on… again. This time, every pirate but two were scrambling to get to their seats, sit up straight, and quickly copy everything the first two had explained. The candy captains walked around inspecting the work of their peers. Candy was dispersed, but you couldn’t tell because everyone was feverishly writing. 

And, this is how we began discussing equivalent fractions. As kids crunched on candy, I used the idea of candy to suggest each piece being cut in half or thirds. Halves would produce 4 pieces out of a total of 12 going to each student. Thirds would make it so that 6 pieces out of 18 would be had by each friend. We went backward, too. “How many sixes are in 18?” I asked. I had a worksheet for students to try out, and I circulated my ship… I mean classroom, and checked for understanding. 

One last thing about Morse Code. Some students complained and grumbled about the work of decoding the message. When the dust settled, I told my Polite Pirates that my intention is for them to know the code so well that they do not need to keep referencing the alphabet decoder. I had them try it out. I told them to close their eyes. “What letter is four dots?” I asked the group.

“H!” they called out in unison. 

“And, what letter is only one dot?”

“S,” the class provided. I did this with several more letters that we have seen over and over, and they had used to decipher the message still in front of them on the Monday Morning Board. They were amazed at their memory. I told them that this is how you memorize something. You have to work at it, practice it, use it. I’m planning on helping them memorize the code and see if they can decipher something without me providing the alphabet. 

Building Bridges: A Hands-On Math Lesson

This blog serves two purposes: First, I just shared a lesson with the Polite Pirates (my class) that went so well that I want to share it with everyone. And, second, due to its complexity, several students need additional clarification. I am hoping that by writing this down, I can make clear how the business of bridge-building works.

Yesterday morning I dug out the colorful, connectable, plastic blocks I’d stored away in a bin under the counter. I told my students that they would be building bridges. Cheers rang out. They were to work as a team to construct a way for a car to travel from one pile of dictionaries to another. The Polite Pirates cheered with joy.

“There’s a catch, however. You have to buy the blocks!” I exclaimed. The class groaned. “Each one costs ¼ of a dollar. (I’ve been teaching fractions and mixed numbers.)”

“How much is that?!” a few students grumbled.

“You know how much a quarter of a dollar is,” I accused. 

“Twenty-five cents?” a student clarified.

“Yes. You will work as a team of engineers. Use your Spiral Notebooks to keep track of the number of blocks. You’ll need to figure out the total cost of your bridge.

“Oh, one more thing: Your bridge is going to make you money. That’s right! Sure, it will cost you to build it, but once it is done, you can charge a toll for cars to use it. For every foot of bridge you are allowed to charge one dollar. 

Making money got their attention;)

This is the slightly confusing part (one of them, anyway): If about twenty vehicles travel across your bridge per hour, how long will it take to make (dramatic pause) one thousand dollars? 

Before setting them loose, I showed them that this problem was doable. (The looks on their faces were incredulous.) “Let’s say you build a 10 foot bridge. How much money can you charge to cross it?”

“Ten dollars.”

“Right, but that is $10 per car. If twenty cars travel across your bridge in one hour, how much money do you earn?”

Thinking… “Two hundred dollars,” a student offers. 

“Good; You are correct. Where did that number come from?” I prompt. I want the class to know how to do these calculations.

“I multiplied ten by twenty.”

“Right. If your bridge makes $200 every hour, how long will it take to get to a thousand dollars?” Their minds were working, now! 

“Five!” several students shouted in unison. 

“Don’t forget that you need to use some of that money to pay for the building blocks that you used to construct the bridge,” I remind them. And, they’re off! 

The Polite Pirates had a blast working together. I was impressed that they almost instantly formed the idea of making supports to hold up longer sections of bridge. In this way they could earn more toll money. Of course, they had to count the blocks that they used to hold up their bridge when tallying up the cost of building materials. I didn’t let them use anything other than the building blocks for construction. 

Once the bridges got to be several feet long, every single student on the team was needed to hold the bridge in place as more supports and lengths were added. I overheard one third grader explaining to his partners that even though it would cost more to use extra blocks, they would make more money from tolls, because they could make their bridge longer. I reinforced this idea by sharing, “Sometimes you have to spend money to make money, folks!”

After a timer I had set went off, I had everyone stop building and count up the number of blocks that they had used. One team split up the task by divvying up the sections to be counted. They then added all the numbers together. Next, it was time to calculate the cost of all of those blocks. One team had used 355 blocks! How could they figure out 25￠ per block? 

I reminded them that they already knew what a quarter of 100 was. “Separate the 300 from the 55,” I told them. “Each 100 would be how much?”

“Twenty-five dollars,” someone answered. 

“That’s right. Now, how many twenty-fives do you have? We’re talking about 300 blocks.” I wrote 100÷4=25 on the board. When someone suggested that they needed 3 twenty-fives, I put X3 under the 25. “These might seem like really big numbers, but you already know what ‘three-quarters of a dollar is,” I prompt.

“Seventy-five cents!” a few blurt out. 

“Not cents, though…” I can see the gears turning behind my students’ eyes. It feels like I can hear the steam coming from their ears. They even gasp with understanding. 

“Seventy-five dollars.”

“Now, for the 55 other blocks. Is there a number close to 55 that is divisible by four,” sounded like Greek to them. I reworded my question in a more leading way. “Can 48 be evenly divided by 4?” This connected with their math facts. A student raised his hand.

After deciding that 48 blocks would cost $12, we tackled the leftovers. “What’s left?” I asked the Polite Pirates who were sitting so patiently on the carpet in the front of my classroom. Counting up from 48 to 55, we discovered there were seven blocks left. “How can we figure out the cost of these?”  

When this question was met with blank stares, I quickly drew seven (very ugly) squares on the dry erase board. I drew a hasty circle around the first four. “Each of these cost 25￠. How much money is four quarters?” Lights blinked on in every students’ eyes. 

“One dollar…!”

 “And…” I prompted for the cost of the remaining three unaccounted for blocks. 

“A dollar and 75￠,” a student finished the thought.  

“So, these seven cost $1.75, the 48 blocks cost $12, and the 300 blocks cost $25 X 3,” I summed up our calculations thus far. “What will this team need to do next? Tell the person next to you.” Then I sent everyone back to their seats to work out the costs of their bridges. I told them to figure out the prices independently. Then compare your work with your teammates. In this way you can double-check your math accuracy. 

I walked around the room, helping students with their division facts. There was a wonderful hum of productive struggle. Some individuals figured out that they would have to add more than one additional hour on to their original answer in order to account for the cost of the bridge. Most found that only one hour would do the trick. 

Now that all of the math was done, it was time to write about it. I had posted a question in the Polite Pirates’ Google classroom: “How long will it take for your engineering firm to make one thousand dollars?”

They could work with partners and discuss their writing with their team, but each student was responsible for producing their own explanation of what they did. I left the math that I’d shown them on the board, so they could copy it into their notes, or just write about what we figured out together. 

One of the things I like most about using Google classroom on iPads is how easy it is to use the “Speak to Text” feature. It’s true, you have to teach and practice rereading and editing your text, in order for students to use this effectively, but it speeds up typing entire paragraphs. It also helps facilitate a more “Discourse” -style text. When my students purely type, they are less likely to include opening statements, and they will leave out key details. Through the process of “Telling” their iPads what they did, you get a more structured description. And, because it is easy and fast to do, students don’t have a problem including more details. 

Here are just a few samples of the amazing answers that the Polite Pirates typed into their Google classroom assignment.

I hope you enjoyed hearing/reading about this lesson that my students experienced this week. If you have ideas on ways to improve or modify it, let me know in the comments. Thanks, and take care.

“How to Teach Cribbage to Kids, AND Why They Need to Learn”

(Part 1 of obviously more than 1, but not sure how many just yet;)

With the winter holidays approaching, I wanted to prepare The Polite Pirates (my students) for being stuck in the house with “nothing to do.” While I’m not against video games, I think it’s wise to have some alternatives. 

Hands-on games that promote thinking and problem solving are my favorite to teach and play. Chess and Dominoes are begun early on in the year. Now, it’s time to break out the Cribbage board. 

The fact that there are tiny pieces that could easily get lost makes the unpackaging mysterious and exciting. The board looks interesting, and young students can’t wait to get their little fingers on those tiny pegs! This affords a concrete reward for paying close attention and practicing the game well. 

Teaching Cribbage to children requires a scaffolding approach. There are many rules and ways to acquire points. They must learn all of these before earning the privilege of placing pegs on the board. This motivation helps keep them interested and focused. 

Analyzing combinations to find potential points.

After showing and modeling the board just enough to wet their appetite, I explain that the first part of the game is all about analyzing your cards. You must decide which cards to keep and which ones to discard (They go in what is called a “Crib,” but we don’t worry about that at first). First, I model, looking closely at 6 cards. Leaving out the idea of runs, I explain that we are looking for pairs and combinations that make 15. With only these 2 criteria, we work on adding up card values and counting potential points.

Cribbage for Homework!

[A couple of things to keep in mind: Aces are always valued at 1 in Cribbage, and face cards are all 10. Also, and this is fun for teaching the point system/using combinations, three-of-a-kind is 3 separate pairs, totaling 6 points (2 points per pair).]

Shuffling between rounds makes it feel more like a card game than math practice.

After modeling making wise decisions regarding which card combinations make the most points, I have students try. In groups of 3, I give kids 6 cards to puzzle over. I always shuffle the deck between every “round.” This makes it feel more like a card game and less like math practice.

If interest wanes at all, you could move the pegs on the board. That will get kids into looking for as many points as possible. Also, you could suggest that if one team sees points in another team’s cards that were not discovered and therefore not counted, the team that discovered the missing points gets them! 

In other words, you have Team A and Team B. Each team gets 6 cards. If Team A only found ways to earn 4 points, but when they show their combinations, a player from Team B notices an additional way to make a combination of 15 that Team A failed to see or mention, the sly individual from Team B who uncovered the extra points gets them for their team (B, not A). This keeps everyone on the alert. 

Listen to the amazing thinking going on.

Notice that the students have to use “math discourse” to share what their cards provide. They do this to prove that they deserve the points they are claiming. It allows every player to perform backup mental math. 

This exercise of looking for combinations of 15 will continue in this way for a week or two. Once students have grasped all of the ins and outs, you can introduce “The Starter.” This card is pulled from the middle of the deck after the cards have been dealt. It is placed face up on top of the pile of leftover cards. Students now have one more card to consider when choosing the 4 cards that they will keep. The Starter is static, staying on top of the deck and being used by all teams. 

If you are interested in enriching the decision making process, tell the students that one team will actually get the cards that you discard. The two cards that each team gets rid of go into a “Crib” that the dealer uses to make points at the end of each round. This means that, in addition to trying to figure out what combinations of cards will afford you the most points, you want to keep points out of the hands of others. Don’t gift the dealer with good combinations. Or, if you are the dealer, you can feel comfortable placing a pair or good combination into the Crib. 

Students practice skip counting by twos.

A way to differentiate for your students who are continuing to make progress but could use some help is providing a chart of addends that form 15. You could also have manipulatives or base-ten boards/charts for students to make 15. Make a lesson of looking for tens and fives in number combinations. 

Just as I would have The Polite Pirates practice for a while before introducing further ideas, I will end this blog right here. Playing with numbers, considering the value of combinations, analyzing which cards should stay and which ones should go, students will enjoy the randomness of shuffled hands. “Cribbage affords players both the anticipation of the luck of the deal as well as ample opportunity to exercise their skills in discarding and play” (Bicycle blog).

https://thecaptainofclass.com/2019/12/02/card-games-can-be-controversially-classy/
Previous blog about Cribbage
Cribbage