Final Reflection Week 12

 

Final Reflection

We have now come to an end in our first year mathematics course. I must say, I feel like I have come a far way since the first class back in September. I remember entering day one, and we were instructed to write on the Smartboard one word that describes the way we feel towards math. The word I chose was “challenging”. I started becoming really comfortable with mathematics in grades 11 and 12, though I did not major or minor in the subject for my undergraduate degree. Therefore, I was rather nervous entering the course, not remembering formulas and terms. However, it did not take long to get more comfortable with math again. Although there are still some challenges I face in the activities, like the one during week 11 “co-operative group activities,” where we went around in groups of 3 to solve problems at different stations (such as number charts, blocks and stick figure stations).

In addition, I enjoyed the digital word problems that we had to create. It was a fun way to think about math in your everyday life. I really enjoyed looking at my classmates’ word problems, as I found 3 right away that I could relate to. I was happy to see that Shannon had found my math problem relatable as she had commented saying she had just finished painting her basement. It was nice to see that not only could I relate to what my classmates posted, but that there was at least one classmate who could relate to my world problem. Also, although we were instructed that you couldn’t create a word problem on something that has already been done, I found that everyone was very creative and had a wide range of math topics covered. I was really impressed with what the ones I read had come up with for their problems.

Overall, I am very pleased with this course. Leaving this course, I am not afraid in terms of my capability to teach mathematics. Also, I look forward to the class next year, although the setup will be different as it is said to be six weeks rather than twelve. I wish that we could all be in the same class again next year, to see how we have all grown after we teach math in the New Year. It would be interesting to see how comfortable the entire class felt towards it, and how they feel about math after teaching it. Furthermore, I felt that although we were a fairly quiet bunch in terms of classroom discussion aloud, we were given the instruction needed in order to become more comfortable in this subject before our teaching block begins. The Great Games definitely helped along the way because rather than just reading out of the textbook (which was also very helpful and I will never get rid of that textbook), the games helped to make sure I knew what I was doing for that particular unit of math that we were studying that week.

Weekly Report & Reflection Weekly Blog #11

Formative Assessment

This week we covered Geometric art/shapes, as well as a discussion about assessment. I thought that the Geometric Art by Simon Beck were incredible! I have never seen anything like that, as the closest thing to “snow art” I have seen are snow angels and snowmen. These images led into the discussion about geometric art that our mathematics professor, Patricia M, drew in the snow after seeing these images. After discussing drawing the image of a heart in the snow, we did an activity as a class with seeing how many times we could spell heart, using this pyramid image of the lettering of the word “heart”. The following image demonstrates what the activity looks like, and the answer that we came up with as a class.

 

After this activity, we jumped into another activity after reflecting on prizes that we used to collect at the bottom of our cereal boxes. Typically, the cereal companies will have a series of prizes for you to collect. As kids, growing up you always wanted to have at least one of every prize so that you had the entire collection. However, this was hard to come by, as you would receive multiples often. As a class, we tried to figure out how many boxes you would need to purchase, in order to collect all the prizes in the word problem. In our groups, we conducted trial runs with 1 die to see how many cereal boxes we may need to purchase in order to receive one of every prize. My group was able to conduct 5 trials in the allotted time, and the results can be seen below.

My way of thinking about this problem was that if there are 6 prizes, I thought about it in terms of you have a 1 in 6 chance of getting each prize. Therefore, my original thought was that you might get all 6 prizes if you purchased 36 boxes of cereal. However, there is no guaranteed way of knowing the definite answer to a question like this, as Padraic mentioned – different cities may have different prizes, but not all of them.

In addition, we discussed formative assessment. I found this lesson to be very useful as we are about to enter our two week internship, followed by our five week teaching block placement. I learned a lot about the three forms of assessment, as well as the achievement chart for math and descriptive feedback. I plan on keeping notes in the front of my binder from this lesson in regards to the three forms of assessment, as I feel that this lesson will be very helpful when it comes time for me to begin teaching lessons, and providing feedback on student work. I thought descriptive feedback would be any feedback that can lead to student improvement for learning, though I never thought about only providing positive feedback. I like this idea because if you provide students with positive feedback, it builds their confidence and makes them want to continue to do well.

Lastly, we were given time at the end of class to peer-edit the lesson plans that we created in pairs. I found this very useful prior to submitting a final copy. One other pair was able to look over the rough draft of the lesson plan and provide written feedback in the margins to show what could be changed and what needed to be added or expanded on. I found this very helpful as it helps us to improve the lesson plan in a way that a supply would be able to come in and know exactly what is being done that class.

 

Weekly Report & Reflection Weekly Blog #10

Data Management

Mean, Median, Mode, Range

Mean: the average number

Median: the middle number

Mode: the number the occurs most often

Range: the difference between the largest and smallest number 

This week, we covered the data management unit of math. This week our class was in a different environment. We weren't in our normal math classroom where we had access to all our math supplies. This week, math class took place in the computer lab. Our class opened up with stem and leaf plots, based on an estimation of how many oreos fit inside of the jar. Some guesses were repeated (mode), and we were told that our median (based on our guesses) was not accurate to the actual amount of oreos in the jar, which was actually close to one of our outlier guesses. 

 

Evan-Amos. (February 19 2011). Double-Stuf Oreos, by Nabisco. Retrieved from: https://commons.wikimedia.org/wiki/File:Double-Stuf-Oreos.jpg

 

 

In addition, we were told to each select a set of 3 consecutive numbers. From there, we had to determine what our mean was. We repeated the same task for 4, 5, and 6 consecutive numbers. These were my results:

22 + 23 + 24 = 69 / 3 = 23

28 + 29 + 30 + 31 = 118 / 4 = 29.5

22 + 23 + 24 + 25 + 26 = 120 / 5 = 24

28 + 29 + 30 + 31 + 32 + 33 = 183 / 6 = 30.5

Based on my results, I found my mean and median to be the same. I believe that the fact that the numbers were all consecutive is the reason for these results. 

A resource that we learned about this week is Tinkerplots, which is a software made for elementary schools. It allows for us to create statistics with students because it provides us with a lot of the work completed for us. Whether you want to utilize samples or your own findings, you can use this software for both. Some of the resources that this software offers teachers are: 

- instructional movies

- teacher friendly tutorials (teachers can try these out at home before using it as part of their teaching lesson)

- free activities

- free resources

You can utilize this software in the computer lab, and set the students up into sections. If you do not work at an elementary school, you still have access to this software if you purchase it. If you own the software, you can print things to bring into your classroom for your students. The nice thing about this software is that it is a one time fee for life. If you want to access the Website, please visit:

Tinkerplots Software

It is worth noting that you can use this site for other mathematical strands if they deal with patterns. 

Furthermore, one of the math Great Games we were supposed to explore this week was "Probability Games". For anyone who tried to access this game, you too would have been redirected to a different site. If you explore the Website that the link takes you to, you will notice that you can choose games based on what area of math you want to explore, as well as which grade level. If you want to explore this great resource now, or refer back to it for future reference, please visit the following link:

Johnnie's Math Page

 

Lastly, two of the three presentations this week used "Gizmos". I have never used this online resource before but I thoroughly enjoyed it. Thankfully the presenters had everything set up for us so that we didn't have to create an account. This is a resource that I would definitely like to learn how to create lessons on, as a future educator, so that I may utilize this resource in my future math lessons on occasion. 

Weekly Report & Reflection Weekly Blog #9

MEASUREMENT!

Retrieved from: https://pixabay.com/en/inch-tape-tape-measure-measurement-311800/

 

In class this week, we covered the measurement unit. This for me is definitely not my favourite unit in math. We looked at formulas as well as examples provided by our instructor. Our task was to start coming up with lengths and widths in order to find the perimeter and area of these equations. We were to just add them to the table that we had already created based on the teacher’s examples.

 

 

GotCredit. (March 16 2015). Learn. Retrieved from: https://www.flickr.com/photos/jakerust/16846023595/in/photolist-rECgUF-aoMmRf-iZuD4v-egmGV3-55fbhg-cJHGxJ-9iYGTz-5nNSSG-61HzUd-qex9y4-72n24g-a6rwJ7-rbkMWB-d27mBb-4Qou3Y-dZu4aS-66kvP2-p3ErN7-qY13Fs-crGWio-8W35Xo-raCSPN-cEJya3-9mBT1m-6oKrRd-4BErB7-niKRjD-fjyxkZ-4m5ojv-c5hdHC-ihNtgp-bpRSVN-88PM4K-9LXkW-aZhtG4-omuR6Y-dGNUyL-eaVyv6-9Md5QC-gStxEe-qPvbC2-cHF3VJ-eqxQSg-c5hcwm-dSfPUP-jr1bQZ-7J1gDR-9rjHzK-8vHsBS-7FSYt1/

In addition, there were two activities that we did as a class. I really enjoyed the first activity where we were given five slips of paper for each table. The task was to tell the class what you are (i.e. area – where we started at in the task) and then state a definition for a mathematical term, which then would be answered by whoever had the name of the term. The task continued in this manner until everyone had a term to speak, bringing us back to the definition of area by the end of the task. This activity might not be the greatest activity if someone is not an auditory learner. However, it is an engaging way to make sure students are listening to the speaker, while testing their knowledge on definitions and terms.

The second activity we were all told to grab a card at random. Once everyone had a card, and it came time to the activity, we had to find one person in the class who had a card with the same number on it. This task involves inquiry learning. We were to work through the questions on the handout, and try to get as many questions finished in the amount of time we were given. Furthermore, this activity is great for visual learners because we had tools (string, scissors, stamp pad, 2 toilet paper rolls, and measuring tape) in order to help us solve for surface area.

 

 

Dvortygirl. (December 28 2006). Miniature marshmallows, close up. Retrieved from: https://commons.wikimedia.org/wiki/File:Mini_marshmallows_in_bowl.JPG

We then moved on to student presentations. One that stood out for me was the activity that involved marshmallows. This activity was beneficial for me because it allowed me to learn things that I forgot. For instance, we were given two sheets of paper that were the same size. However, we were supposed to make cylinders out of them, by folding them differently (one was short and large, while the other was tall and thin). When determining volume, I assumed they would both hold the same, due to the dimensions of the flattened sheet of paper being equal. However, I quickly learned that the taller and thinner an object is, the less room it has inside to hold something, therefore, the shorter larger one held more marshmallows. I was glad that I got to participate in this activity because that is something I had completely forgotten when dealing with volume, and therefore, this activity served as a great refresher.

 

 

 

Lastly, this week I explored 2 tools on Great Games. The first tool was “Illumination Cube”. This game allows students to look at the flattened image (faces) that make up a cube. Students then can put the cube together to see what it would look like assembled. The task is to find the volume and the surface area of each cube that the tool provides you with.

Illumination Cube

 The second tool was “Shodor’s Interactive Shape Explore”. In comparison to the first tool, I found this tool much simpler to use. I preferred to use this tool to find perimeter and area. I think this is a great tool for students to see a shape, and find the area and perimeter for the shape on the grid. The grid squares are nice and big so that students can physically count the squares to double-check their answers. Give it a try if you haven't already!

Shodor’s Interactive Shape Explore

Weekly Report & Reflection Weekly Blog #8

Geometry and Spatial Sense

This week we covered Geometry and Spatial Sense. What I enjoy about this unit of mathematics is trying to figure out what shapes can come together to build new shapes. We got to work with 7 geometric shapes and we were to try to build other shapes using any or all of the shapes. The challenge was to find up to 7 different ways to build these shapes, which was a fun way to challenge the class, due to the nature of the activity being a challenge.

 

Retrieved from: https://pixabay.com/p-155306/?no_redirect

NCTM Isometric Drawing Tool is one of the Great Games that we were to explore this week. The tool allows you to build 2-D and 3-D shapes. It provides you with tools that allow you to draw figures using cubes, faces and edges. This would be a great resource for younger grades that are being introduced to geometry. The link provides you with clear instructions on what to do on the grid, and which tools can be used for different purposes. If you go to the “Exploration” tab, there are 3 different images you can create using faces or edges. Personally, I preferred using edges when trying to create these shapes. Overall, this is a great beginners resource for students to learn how to create and draw different shapes. You can explore this tool as well by clicking on the following link:

Isometric Drawing Tool

Retrieved from: https://pixabay.com/en/cubes-impossible-geometry-161964/

One of the presenters came up with a Bus Route activity, where students had to find different bus routes to their destination point, as well as spot the parallel and perpendicular lines using the math provided on the handout. This activity serves as a double lesson. While teaching students about parallel and perpendicular lines using real life streets, you are also teaching students how to take different bus routes for those students who may rely on the bus for transportation. The following image is not from the activity, though it resembles part of what we were looking for in terms of parallel and perpendicular lines.

Oran Viriyincy. (October 4 2010). Metro Route 75 Semi-Circle. Retrieved from: https://www.flickr.com/photos/viriyincy/5049887867/in/photolist-8GeZJc-86gLCy-9tXA9R-cA3kB1-f2kaE8-7Gcyum-7xyzQK-aFfVij-qvMwdg-9W23sZ-ahPRR6-diCWTP-diCUdL-diCUmG-48Mr8z-4qobYE-sCgcR-oQwphU-ahPKQR-bnANpX-bs3os6-ahSvfq-ahNPXV-ahQP66-pRaF7A-wiPky-dFUxaG-9yeMNs-dFP8VP-4KevGv-cA3LNS-cA3jkm-8J7tc6-dFUzJG-as8mv6-ahSCyC-5oh8sR-ahPMdk-ahPNPi-yEYhU-sjTw-9yeMJS-9ybNMF-9yeMpJ-9yeMaQ-9ybP2r-9ybPj4-9ybP4D-cPkQj9-cA1uw3

Another activity we worked on at our seats was a Mario Mirrors Handout. I really enjoyed this activity, particularly because I enjoy drawing. However, I completely forgot about the math tool, miras. We had these tools in my elementary school for this unit. It was refreshing seeing different math tools being used as the presentations continue. I thought that this was a fun way to get the audience engaged. We all had to complete Part A which was finding the line of symmetry in the shapes provided. Once that was complete, we could move on to Part B which had 9 Mario images. We were to draw the half of the image that was missing, whether freehand or with the miras. If you got through both sections in a timely fashion, there was a bonus section where you could draw the other half of Mario himself. I like how the presenter acknowledged the fact that some people are right-handed, while others are left-handed, therefore creating handouts that suited both writers. Once the class was finished with their worksheets, the teacher presenter called for volunteers to approach the whiteboard, where they were to complete the mirror image of the incomplete images. The way the presenter set up the whiteboard was as if it was a level in a Mario game. I thought this was engaging for students because many students at the elementary age seem to enjoy playing video games. Therefore, this activity demonstrates how you can make this unit of math fun for students, and have them engaged in the activity.

 

JD Hancock. (July 21 2012). Super Blast Mario. Retrieved from: https://www.flickr.com/photos/jdhancock/7629235266/in/photolist-cCaPR5-et81BA-tcP96D-q9SZza-4FcEsG-4FcEkQ-5S5u7E-dXEcWi-5S5u9Q-7SvZ3M-aVmZ2r-4Hwo86-9RvFkK-qFAsAA-4FcEM5-a4iHmx-5nWUNx-9gztNU-6oTkEy-qNetYS-qLnQNH-pSrhGC-g5GSa-8ZQ4Bz-9j17xH-4HABEj-abh4j6-et81dA-5xviQr-nKP7Jo-a1U5hT-4QWaEQ-5bypdv-pM2Syx-a8K4cL-a2u2Wa-4StQAb-frwyY3-8axuPD-9MNEAs-4dMyLv-c3xpD-33yijA-qHqRCH-4W1UWj-8HaM65-ztKpB-mg5MR6-cPKZyd-ogUi5g

 

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.

Weekly Report & Reflection Blog Week #4

In my exploration of decimals, I learned that I have been reading/speaking decimals incorrectly. One of the points that the text makes is that when reading a decimal such as 0.34, we are to read it as thirty-four hundredths. However, I have always read it as zero decimal (or point) three four. According to the text, this is the improper way to read decimals. By reading it the way I do, I am slipping away from the understanding of decimals being an equivalent of a fraction. As I reflect on how I read decimals, I think about the example the text gives about reading money. Now, I am left to wonder if this is where I began reading decimals incorrectly. Hopefully now that I am conscious of this error, I will be able to correctly discuss decimal values.

These tools will be useful in my educational activities because it has to do with self-reflection. Prior to reading these chapters, I would not have realized that I was reading decimals incorrectly. Therefore, I can use decimals and fractions combined in educational activities to teach students how the two relate. This may help students learn one concept more quickly once they grasp the other, as well as teach students the proper way to read decimals.

The uses of fractions and decimals are to describe something that is being divided into parts. There is help available online for students to learn how the two relate. My investigation involved exploring Great Games, which is an online gaming site that helps students solve mathematical equations for different units. I explored “Puppy Chase” which involves the computer showing you a fraction, and you would have a multiple choice question where you have to determine what the decimal value for the fraction is. I envision using the tool as a math refresher to contribute to my work in building my mathematical knowledge.

Furthermore, I explored further into Great Games after attempting a game that another student found online. This game is called “Meteor Multiplication”. The game deals with meteors that have multiplication questions written on them. The missile that blows up the meteors has an answer written on it. For each answer, you have to blow up the meteor that has the multiplication equation on it. This is a useful tool that you can use in an educational activity because it teaches students how to use mental math. Due to the nature of the game, you only have a limited amount of time to blow up the meteor equation. This does not leave time to use a calculator or use pencil-and-paper method, therefore forcing game players to utilize their mental math skills. Therefore, this game can develop a student’s mental math abilities, making this skill set stronger.

Lastly, the text reveals different principles and algorithms for both units. This is beneficial to learn and reflect on as a future teacher because it teaches you that there are multiple ways to solve mathematical problems. Some of your students will solve mathematical problems differently than others, and the text reveals the different ways of problem solving. In addition, understanding the differing principles and algorithms demonstrates a gain in your mathematical knowledge because it shows an understanding of whatever unit you are working on.

Resources:

Puppy Chase

Meteor Multiplication

Weekly Report & Reflection Blog Week #2

Retrieved from : https://pixabay.com/en/mathematics-pay-colorful-chaos-80449/

I feel as though there is a negative opinion of mathematics for many students. Some students have the experience of getting an answer wrong, and being called out for it, which discourages the student from enjoying the subject. Many of us feel this need to always have the correct answer, but if we always have the correct answer, we have nowhere to improve.

Personally, I felt confident with math until grade nine came along. Grade nine academic math, I did not do too well in. However, I left the course feeling like I could do better next year. However, when grade ten academic math came around, I had a very discouraging teacher. I was sitting at a 62 in the course, and I so badly wanted to achieve an 80 in the course. During a parent teacher interview, she told me and my dad that I would never achieve an 80 in math, and that some students just don’t understand math. I felt so discouraged by her comment that I basically was at a standstill with my grade that year. Again, I was determined to do better, but this time not just for myself. I wanted to prove her wrong. I wanted to prove that students could succeed in math, no matter what previous grades show. I was in a grade eleven University/College math course that next year, and I passed the course with an 87. I was thrilled, and it made me realize that I actually enjoy doing math when I had an encouraging teacher working with me.

That being said, a good mathematics student is one who believes in themselves, regardless of what educators tell you that you are capable of. Therefore, an excellent mathematics teacher would be one who encourages the student to succeed, rather than bring that student down. This relates to this idea of a fixed mindset and a growth mindset. An excellent mathematics teacher will always have a growth mindset for their students because they know that all students have the ability to do well in math, some just might need more assistance than others.

Lastly, I would like to discuss what I learned in class. I learned how to make the classroom more fun for students, when it comes to different ways kids can learn how to add. Some kids (or all) would enjoy the blocks because it’s hands-on, as opposed to paper and pencil adding. It reminded me of when I was in elementary school, and we used to use these blocks. I thought it was interesting when the 1000 block came out. I knew the block would have to be solid full in order to equal 1000, however, when the teacher mentioned how students ask if it’s full, I thought that was smart on their part, because if the cube of 1000 wasn’t full, it wouldn’t equal 1000, but rather 600. I didn’t have an “ah ha” moment though I was worried about the problem solving activity that we have to do by October 1^st because I realized how easy it is to forget simple math skills when you have been out of practice for years. It will be interesting to see how the students solve these problems, because I feel like I could learn different problem solving methods from them, as opposed to the ones I used.