Week 3 Activities

Magnetic Math
Math is so much fun anyway, but when you throw a few magnetic marbles into the mix, you’re bound to have a blast - which is exactly what we did with our mental math exercises this week! First of all, I put a predetermined amount of magnetic marbles on the overhead projector. Each child was given a set of number tiles (digits 0-9) and was instructed to use these tiles to make an estimation based on how many marbles they thought were resting on the overhead projector. This estimation was based on a quick flash of the image on the board – It’s important for them to not be able to actually count the marbles since I’m trying to improve their estimation skills. Once everyone had made an initial estimation, I read a list of clues which served as a means for students to refine their estimates. To give you a better idea of the activity, I have included a few sample clues below:
• 2 digit number
• Less than the product of seven and eight
• Sum of the digits is a 2 digit number
• Does not contain the digit in naming the number of days in a week
• Etc…..

By the end of the clues, the majority of the students had refined their original estimate to be the correct answer! But we were not done there! We then explored ways to split the number into groups, which reinforced the concepts of multiplication and division. On top of being exciting, challenging, and fun, this approach is an excellent way to enhance students’ visualization of mathematics, as well as help them to develop number sense through communication with mathematical vocabulary. Just don’t lose your marbles! 

Problem of the Week: Changing Areas
This week we came back to the ideas of area and perimeter. Using 3 to 8 color tiles, the students were posed with the following problem: How many different Color Tile shapes can you make that have the same perimeter? After exploring different shapes, they recorded their findings on grid paper. This activity led the children to understand that the area and perimeter of shapes are not always consistent with each other. It also expanded their understanding of area as the “number of square units that cover an area”, rather than just relying on the formula (length x width). After a day’s worth of exploring these concepts, I took the learning to the next level with an additional challenge (see below)

A zoo needs your help designing a play area for monkeys! Make a design with a perimeter of 36 units of fencing. Use the color tiles to make your design, and then record the design that would give the monkeys the most room to play. (Hint: Don’t record anything on this paper until you have experimented with different designs!) Lastly, on the back of this paper, write a note to the zoo explaining why your design would make a good play area for the monkeys.

First, they analyzed the problem by putting the information into a KWC graphic organizer. Then, they were off to work solving this problem! This stumped a few of them at first, but it allowed us an opportunity to talk about the importance of making mistakes in learning. Trial and error is one of the best problem-solving strategies out there, but far too often, students are deterred from using it because they are afraid to be wrong. I strongly disagree with this stance, so I was delighted to have this conversation with them.


On our last day together, in an attempt to tie everything back together, we used the area from everyone’s monkey pen design to form a stem-and-leaf plot. And what stem-and-leaf plot would be complete without calculating the range, mean, median, and mode? To top it all off, we learned the “Perimeter Song” and of course, set it to moves – complete with our air guitar solo! J I hope this summer learning experience will remain with the students for a long time to come! It certainly has been a pleasure working with these extraordinary young folks!

Thanks for a great time!

Week 2 Activities

Story Problem of the Week - JEB’s License Plate

This week our story problem revolved around Jeb and his license plate. After doing a KWC on the problem, we concluded that our goal was to determine how many different combinations Jeb could come up with for the license plate on his new car. Sound familiar? Well, it should! It has the same underlying premise as Joel’s phone number from week 1. Research has shown that by having children engage in problems with similar formats, yet varying contexts deepens conceptual knowledge. This challenges students to think of even yet more ways that other situations may apply. I definitely saw this to be the case with the Joel & Jeb story problems. Arthur Hyde refers to this as a text-to-text connection in mathematics – relating story problems of similar formats and concepts to one another.

Using the data we collected from week 1’s hand and feet measurements , we explored range, mean, median, and mode. By putting these words to movement and music, we were better able to retain their meanings. Ask your child about Range Dog – a song NOT to be missed!
(Click here to hear an excerpt http://www.songsforteaching.com/math/medianmodemeanrange.htm )
To take learning one step further and to address yet another learning style, the students also made illustrations of each of the terms. As always, I was blown away by their ingenuity and creativity!

I Have….
Mental math is an important skill for students to continually practice. Exercises in mental math can utilize the language and vocabulary of mathematics, as well as refine computation skills and develop number sense. I Have is a great way of “playing” with mental math. Children are dealt a card that contains a statement and a question. One student begins the game by reading his/her statement (ex: I have 49.) Then the same student reads his/her question (ex: Who has an even number between 52 and 77?) The other students listen, think, evaluate their answer, and respond by reading their solution when it satisfies the question asked. This means that students have to pay close attention to the clues that are given, while simultaneously staying focused on the information contained on their card. Whew! It’s quite the mental workout!

Week 1 Activities

Here is the story problem we "played with" this week: Joel's Mystery Phone Number. First, I covered each sentence of the story with strips of construction paper. Then we removed the paper strips to read the story sentence-by-sentence, transferring pertinent information into a KWC graphic organizer. A KWC is divided into three columns asking the folliwng questions: K - What do you know for sure? W - What are you trying to find out? C - Are there any special conditions: (Special rules? Tricks to watch out for? Things to remember? Then after our thorough analysis of the problem, we summarzied what we knew and paraphrased the question. At this point, we started brainstorming ideas on how to solve the problem in our cooperative groups. What I quickly realized was that students had the right idea (of substituting in the odd numbers) but there was not rhyme nor reason to what they were doing. They needed help in organization - a very typical trait of this aged learner! :) So I stopped the cooperative groups, and we had a whole-group brainstorming session on how we could effectively organize this information. Eventally, they came up with the idea of having an organized list, which I took a step further and put into a table format. After much thought and discussion, some of the students concluded that if they could find all of the possible combinations for "1" as the first odd digit, then they would know ALL of the possible numbers because each subsequent odd digit would have the same number of possible combinations! At that point, many of them used the number sentence, 12 x 5 = 60 to solve the problem - 12 being the number of possible combinations per digit and 5 being the number of odd digits (1, 3, 5, 7, 9).

This was very rich story problem which spurred a lot of mathematical discourse among the kids. The key to the success of this exercise was to not rush it! We took the time up front to make sure we really understood the problem (also know by some as "front-loading"). Then we organized the information into three categories as demonstrated on the KWC. This thorough understanding allowed them to strategically formulate a plan, thereby leading them to the correct solution.



At the conclusion of the week, we wrote reflectively about the problem answering these three questions: How did you solve this problem? Why did you solve it this way? Why do you think your solution is correct and makes sense? This challenged them to explore their ideas further and to internalize their thinking on a deeper level.

On top of our "story problem" focus, we also worked with the concept of measurement this week. I asked the kids to consider the surface of their hands (the area). Then I posed them with this question: How could we measure the surface of our hands? They all had some really creative ideas, mostly involving non-standard units of measurement. Then I took the question a step further: How could we measure the surface of our hands so that we could accurately compare our measurements? This question led into a really great discussion about non-standard vs. standard units of measurement. After much thought and debate, one student came up with a brilliant idea! "We could use that grid paper to trace our hands!" So that's exactly what we did! To integrate data collection and interpretation into this activity, we also took area measurements of our feet, and recorded all of our data on a large chart. Prior to making these measurements, I had the students predict (or estimate) what they thought their measurements would be. Also, I had them predict whether they thought their foot or hand would be larger. But the learning doesn't stop there! Next week, we will taking all of this a step further by comparing our data, as well as finding the range, mean, median, and mode.

Skills are also important, so we spent some time working specifically on these as well. Students played games focusing on mulitplication facts and place value. They also spent time in the computer lab practicing their individual targeted areas for growth. This week, I used a wonderful website that you can also use at home: http://www.rainforestmaths.com/ And don't forget about the music and movement! We learned a Mrs. V "original", The Last Ten and we played Mulitplication Ball Toss! Ask your child about these activities.....

Do Sessions and Weeks Build Upon One Another? Will My Child Be Behind If We Miss Days?

If you think about the snowman analogy I gave earlier, than you probably know the answer. However, I also realize that this is summer, after all, and that there are many other activities and opportunities for your child to learn and grow – including VACATIONS! (Something that cannot be underestimated!) Therefore, I make a conscious effort to make sure all activities can be entered each day with minimal reliance on the previous day’s activities. However, the more days your child can attend in a row, the better. If I were focusing solely on “skills” rather than “concepts”, this would be much easier. However, knowledge of skills without conceptual understanding is very limiting, and for your child to further his/her mathematical abilities, he/she must have first built that solid conceptual foundation.

So How Do Reading and Writing Fit Into All of This?

Another great question! At CCS, we strive to integrate all subject areas in as many ways as possible. Like I mentioned earlier, learning is all about having experiences and making connections, so the more integrated their experiences are, the more connections they’re likely to make. Problem-solving is LOADED with opportunities to integrate language arts. First of all, reading skills are essential for the first part of the problem-solving process – reading and understanding the problem. I’ve been teaching for quite some time, and I would argue that for many students, this first step is often the hardest – and most important. Without understanding what is being asked, how on earth can we expect kids to arrive at a reasonable solution? So I’ve found it very helpful to teach kids how to use the same reading strategies they utilize in language arts (making connections, inferring, predicting, questioning the author, determining importance, synthesizing, etc...). Once again, why compartmentalize their learning when their brains are physiologically and neurologically longing to make those connections?
Since reading and writing are reciprocal process and therefore inseparable, writing becomes an essential tool for students to make meaning. I use graphic organizers (see the KWC example) to organize information, and then I have students both explain their solutions and reflect on the problem-solving process in writing. Keep in mind that ALL of this is done in a cooperative setting. Kids need lots of opportunities to talk out their ideas, and the more they talk and listen to one another, the more ideas they generate, thereby enhancing the overall quality of their thinking and writing.

Doing Math Through Problem-Solving

What exactly does that mean? Doing math? Well to consider this question, we first need to ask ourselves, what is math? Most of our initial thoughts or responses would more than likely have something to do with numbers and computation. Right? And while it is true that numbers play a significant role, math is actually much more encompassing. More recently, definitions of math look something like this: the science of patterns and order. By thinking of math in this way, everyday real-life applications of math come to life right before our very eyes.
So back to our original question. What does it mean to “do” math. Many of us grew up doing arithmetic, not math. If the definition for mathematics above holds true, I’m sad to say that as a child, I did very little math consciously. I believe that we all “do” math every day (both children and adults), but once one is made aware of the world of pattern and order, the level of consciousness of this type of thinking heightens. Therefore, part of my job is helping children discover this order through patterns and helping them make sense of it all through the process of discovery.
I believe that we all are creators of our own knowledge. We encounter information, formulate ideas, and then connect these things to one another in our brains. The more connections we make, the better and more thoroughly we understand a concept. Some people think of understanding as a light switch – at some point, the person “understands” and the light comes on with the flick of a switch in an all-or-nothing fashion. Others think understanding is more of a process happening over time by accumulating multiple and various experiences and connecting them to one another. I prefer Arthur Hyde’s metaphor for understanding:

“I like to think of it as building a snowman. First, you find some good snow for making a snowman – not too wet and slushy, not too dry and powdery. You make a snowball with your hands and roll it in some good snow. The ball gains size as more snow sticks to it. You do this to make a big sturdy ball of snow for the foundation. You repeat this process for other parts of the snowman. But you must continue to roll it in the right kind of snow; the wrong snow, or worse, rolling it on grass, will not accumulate more snow.?”
from Comprehending Math by Arthur Hyde.

So I know it’s summer, and you probably don’t want to even think about snow, but this is such a powerful comparison. This is my goal for your child this summer – to roll them around in the right kind of snow to help build that indispensable foundation of deep, conceptual understanding.