Weekly Report & Reflection Blog Week #7

Patterning and Algebra
 

Roland O'Daniel. (February 25 2010). Nctm algebra framework. Retrieved from: https://www.flickr.com/photos/rlodan01/4387091999/in/photolist-7FEZBe-9tsKL-4EP91d-73qoa6-fbuYJP-7FEZAr-8Xjfgt-7uPECu-nfpZVZ-aM7YJv-8WXays-67U3in-4JHJ8R-urXvw3-aM7Znz-aM8hhK-nFWe2K-7NzH7j-5G9D3U-nS3oxd-bxBWe8-aM7ZDF-7zqDxi-85Go7w-qn498v-797Gnv-73uj33-3KEu5G-7NvUMc-7FJTz9-aM7ZiZ-aM7VCx-aM81ut-aM81hR-bdWeW2-bmpoit-aM81ba-943Tpe-nHQVZ-7NzNjC-7NvBtg-7NvHUK-7NvQZx-7NvCi4-aM8dmX-aM8d7i-7NvLtp-9mAXgJ-7NzMJQ-7NvTCK

 

This week we discussed Patterning and Algebra. Presentations covered in class dealt with growing relationships, number tricks, and describing relationships and functions. Growing relations was similar to my presentation on describing relationships and functions. Both topics deal with finding algebraic equations that demonstrate how the pattern grows. You can go about this in different ways for different learners. For instance, the first presenter used images to show the growing pattern. This is useful for visual learners because they see an image growing from one step to the next. In my presentation, I used input and output tables to show how each column was growing. Students then had to describe how you get the output number, based on the input number, while finding its algebraic equation. The fact that both our topics were similar because they involved showing relationships through algebraic equations was useful. It was useful because it allows different learners to understand how to solve the problems. For instance, I learned quicker by having the numbers laid out in front of me, but someone else may have learned better by having the graphic images.

 

Roland O'Daniel. (February 25 2010). Jigsaw algebra. Retrieved from: https://www.flickr.com/photos/rlodan01/4387091953/in/photolist-7FEZAr-8Xjfgt-7uPECu-nfpZVZ-aM7YJv-8WXays-67U3in-4JHJ8R-urXvw3-aM7Znz-aM8hhK-nFWe2K-7NzH7j-5G9D3U-nS3oxd-bxBWe8-aM7ZDF-7zqDxi-85Go7w-qn498v-797Gnv-73uj33-3KEu5G-7NvUMc-7FJTz9-aM7ZiZ-aM7VCx-aM81ut-aM81hR-bdWeW2-bmpoit-aM81ba-943Tpe-nHQVZ-7NzNjC-7NvBtg-7NvHUK-7NvQZx-7NvCi4-aM8dmX-aM8d7i-7NvLtp-9mAXgJ-7NzMJQ-7NvTCK-7NvKHk-6j5yG9-6j5xsu-3KEtA3-7NvWoz

I wanted to find a resource that would be useful for students to get a grasp on this topic of patterning and algebra. While performing a simple Google search of “describing relationships algebra” I came across this resource:

Writing Equations to Describe Relationships

This website is useful for students who have a hard time understanding how algebraic equations work. Due to the nature of algebraic equations containing both letters and numbers, students can often become confused on what numbers they need to substitute to replace the letters. I particularly like this link because in the summary, it provides you with an image that serves as a problem solving checklist, which provides students with a list multiple ways of learning and demonstrating relationships in algebra.

 

Can I guess your number?

 

 

Pascal. (July 16 2011). Popular trick. Retrieved from: https://www.flickr.com/photos/pasukaru76/5944308910/in/photolist-a4h8WE-zsdFX-78XnVy-5L2bzA-o6yUkB-h9SNnt-bwDuRY-aAx8RU-79tMEC-49Ck8f-KcgrY-doWMJt-h8XQ7V-3pvgvY-o6yWKB-o4wrKQ-o6yVfn-o6gyrP-5zZnyD-nP5tw4-tafQZX-5y5ShS-8wppQG-9Ac4EN-5Aj7pC-5Aj6Qb-8PH7gd-pmGmXi-66KpGV-8PgrTT-5g4qVj-iebaM4-fEffjD-78U99x-KCeRy-KcoRa-o6gvd4-o6sXEb-4SAqwk-7c2jNb-83wY1k-nYa21M-2hQmh6-bfUSxD-5vofuK-eUZX7N-8zYQmk-aALPDi-4EpPPg-dLor4S/

Furthermore, we also learned about number tricks. This one I found particularly enjoyable. Growing up, my Poppy (for those who don’t know – Poppy means grandpa) used to do a number trick on me and my sisters, and it used to blow our minds that we could not figure out how he was knowing our answers, considering he did not know our starting numbers. It did not matter what number you started with, he always got the answer correct, and it was not always the same answer either (e.g. it could have been 1, 2.5, 4, etc.). I enjoy this type of math fun because it is an engaging way to learn mathematical skills (e.g. multiplication, division, addition, subtraction). I particularly enjoyed the first trick the presenter conducted on the class because the entire class, regardless of the number we started with, ended up with an answer of 5.

While browsing on Google, I was able to find a number trick that was scary. I was unable to find one that allows for reuse due to copyright laws, however I will share with you the link to Google images that I found the image. If you click on the following link below, you too will be able to give this number trick a try. Don't forget your calculator!

Phone Number Trick

 

Dave Dugdale. (October 20 2010). Simple calculator. Retrieved from: https://www.flickr.com/photos/davedugdale/5100067174/in/photolist-8LFbhE-bnZQ8Z-9VCot1-Bq74-2WdaSy-9Ajs9g-7ASToy-bgfKPz-biaBRX-6Y3eoz-9biQY6-bgfFKc-98yw4q-9VBTZs-7wKLgq-peP4yt-7vBn9x-beBtDe-biaY1B-5XFw6m-9vhaAV-dDqzhQ-oXA73Y-oXA6Sh-oXALBj-oXALeA-pd3YsL-oXANk9-f42KUw-qgskU-6DtkQL-9VA6L5-9VzuXL-pszSbf-zuvpv-oXAKfF-HXgs4-oXAM8E-pf5Wr4-oXA7rJ-8BYA4a-9kMUyb-9fHDJG-hT9yw7-ceqmcw-ceqm8d-5B8z4Q-ehE2Rm-9kVa1n-dQ3mXG

Also, if you are interested in learning other number tricks to perform on people you know, or in your practicum classes, you can visit the following link which provides you with 10 different math tricks to choose from!

Number Tricks

 

 

Weekly Report & Reflection Blog Week #6

Today in class, we discussed ratios. We recall that a ratio is the same as a fraction, just put in a different format. An example from class was to choose “two equivalent fractions” that “have denominators that are 10 apart”. The example someone wanted to figure out was the equivalent of 7/11.  Therefore, we needed to figure out what the numerator is, when our denominator is 21. In order to solve this problem, I turned the first fraction into a decimal. My answer was 0.6363636363636364. From here, I rounded to 0.64. Now, I still need to figure out my numerator. Therefore, I multiplied my approximate number of 0.64 by my denominator 21. This gave me a numerator of 13.44. Therefore, 7/11 is equivalent to 13.44. We have now shown a simple fraction being equivalent to a complex fraction. I had to explain my work to the class to show how I got my numerator to the question. This is an example I would enjoy assigning my students, perhaps at the grade 8 level. I could use any simple fraction, but the purpose would be to see how they would solve the problem.

I explored all three Great Games this week. The first one I explored was “Ratio Stadium”. The game involves racing dirt bikes. In order to get your bike moving through the race, you must choose the corresponding ratio that is equivalent to the one that is provided for you. In comparison to most games we have explored thus far, the game provides you with four answers, though only one is the correct answer. Personally, this was the first game where I felt I was paying attention to where I was in the race, more than finding the correct answer every time. Due to this reason, I probably would not use this game in my classroom.

Ratio Stadium

The second game I explored was “Dirt Bike Proportions”. This game also involves racing dirt bikes, though it is set up differently than the first game. Dirt Bike Proportions provides you with one complete fraction and one incomplete fraction. The incomplete fraction only shows the denominator. Your task is to find the numerator so that the incomplete fraction becomes equivalent to the complete fraction. You are given four possible answers to choose from. I would utilize this game in my classroom when teaching my future students mathematics because it is more of a challenge than the first game I explored this week. The main difference I like between the two is how you have to solve the answers in this game. Although I feel both games are beneficial for teaching elementary school kids ratios, I feel that this game presents the students with deeper thought, due to having to solve the missing numerator, as opposed to simply comparing two sets of ratios.

Dirt Bike Proportions

The last game I explored was “Ratio Martian”. Your task in the game is to complete the ratio so that the Martian can eat. These ratios are the Martians only source of food. You have one minute to complete the game. It is important that you read the text that enters the strike zone. Personally, I found this game to be very slow paced. I assumed that I would feel rushed completing this game, due to the 1 minute time restriction. However, although you can hit the spacebar quickly to feed the Martian, the ratios and non-ratios move slowly across the board into the strike zone. An improvement to the game would be to create a button that can dispose of the non-ratios as soon as you see them. This way, after you feed the Martian, you do not have to wait for the non-ratio to pass through. However, I suppose this would be an appropriate speed for a student who is just learning ratios, but not a student who has already studied them. Overall, aside from time restriction and speed, this game is an engaging way to reveal how well students understand ratios.

Ratio Martian

Weekly Report & Reflection Blog Week #3

Amirki. (October 11 2008). Addition Shapes. Retrieved from: https://en.wikipedia.org/wiki/Addition#/media/File:AdditionShapes.svg

 

This week we explored “Whole Number Operations”.  This deals with whole numbers that are multiplied and/or divided amongst one another. Whole number operations are a unit that students study as soon as they start math. It is probably without saying, one of the, if not the, easiest unit of math. The numbers are easy to work with and make for simpler equations, as opposed to trying to multiply or divide decimals for instance.  

One of the in-class presentations dealt with a horse race. The task that each table had was to see how close your horse was to the finish line, after solving a set of mathematical equations. Each table had a different set of numbers; though the horse gradually moved up by 10 each time you got a new answer. Therefore, the presenter used a pattern to demonstrate whole number operations.

 

Resources:

Canoe Penguins Race

Demolition Division

The first game I explored in Great Games was “Canoe Penguins Race”. It shows that you have a partner in the game, though you are solving the math problems alone. This game involves a multiplication question followed by four possible answers. You job is to chose the correct answer for the corresponding question. If you answer correctly, your canoe moves forward in the race. However, if you answer incorrectly, you stay put until you answer another question correctly. You are racing against four other canoes in the race. You have one 2-digit number to multiply with a single digit number. This causes you to think more about your answer because it is not a simple answer that will always equal less than 100. At least half of the answers involved numbers greater than 100, which takes more time to complete.

The next game I explored was “Demolition Division”. This came involves tanks moving towards your blaster. Your blaster is where the answer is given. The object of the game is to shoot the blaster at the tank that reveals the equation to your answer. It is a one player game to get students practicing their division facts of 12. Although it is not a racing style game, the tanks move closer the longer you take to blast them. This game is opposite of “Canoe Penguins Race” for two reasons; (1) it is division rather than multiplication, and (2) you are given the answer and have to find the equation. I found this game to be easier to play because the math was at a lower grade level than the first game.

These games would be useful in an elementary school math class. It is a fun way for students to practice their multiplication and division skills, while being provided with the correct answers at the end of the game, in the event that they got answers wrong. Rather than teaching math the way I was taught, textbook and blackboard, I can use these resources to my advantage. Students will be more eager to learn math if they get to play a competitive game (seeing as these games all involve racing). Great Games is an excellent resource for engaging students in course content. Due to the competitive nature of the games, students will be more likely to want to answer questions correctly rather than guessing, in order to advance further in the race. I cannot wait to introduce this educational resource to my future students, in hopes of changing the negative opinion of math that so many students carry with them.

Weekly Report & Reflection Blog Week #5

Kismalac. (June 21 2012). Illustration of 3 - 4 with a number line. Retrieved from: http://commons.wikimedia.org/wiki/File:AdditionIntegers.svg

 

In my exploration of integers, I learned that I may need to brush up on my skills. I got through the reading just fine, so I thought. I felt confident enough in my ability to understand integers until it came to the in-class presentations. For the most part, I understood how to do the work. However, I had problems solving the one worksheet. I walked away from the class still puzzled on how to solve the problem. However, luckily, that is just one problem I had a difficult time understanding.

It was nice working in groups at our tables because you realize you’re not alone when it comes to not understanding some of the problems. I enjoyed helping a student understand one problem because it was a simple mistake that was easy to solve. I felt a personal achievement being able to help someone else understand a problem. I personally like the fact that me helping them will allow them to solve similar problems like the one we solved together. This just reassured me that I can teach math (maybe not all units as of right now, but I am getting one step closer each week).

In addition to the course reading and in-class presentations, I explored the links we were given to explore within Great Games. You can also explore these games by clicking the following links that I have provided below for you.

 

 

Resources
Orbit Integer

Spider Match

Orbit Integer is a great game because it gives you a mathematical question along with four answers to chose from. The only setback to this game is that it is a race. Players might be more concerned about where they stand in the race, as opposed to getting the answers correct. I wanted to see what would happen if a player got an answer wrong, so I played the game for a second time and purposely chose the wrong answer to a question. The game provides you with a bolded answer so that students know what the correct answer should be. I think this is important because that way even if students are more focused on how far they are in the race, they are forced to stop to see what the right answer is, which could actually slow you down even further in the race.

Spider Match is another racing game. This one was different from Orbit Integer as it only gives you the answer, and you have to come up with the equation. This game causes you to think more than the previous game. Therefore, this game is more challenging because it forces you to slow down in the race to think about which two numbers will give you the answer in the center of the web. The answer does not change, so you have to come up with multiple equations to give you that answer. However, you are playing against 3 other players who are using the same numbers that are caught in the web to solve your problem. Therefore, this is the racing aspect of the game because they can take those numbers for their equation before you get the change to do so.

Lastly, walking away from these games, I realized integers are not something that you should fear in math. Integers can be quite easy to solve, if you pay attention to the positives and negatives that come before the number. I think this may be the biggest downfall for some students, that they perhaps are just reading the equations incorrectly.