Math Technology in the Classroom Week 11

Hi Everyone,

Katic (2015)©. Burlington Festival of Lights.

It's that time of year when I am really getting into the holiday spirit! I seriously can't seem to get enough hot chocolate by the fire, baking holiday treats or attending as many hockey games as possible (being a student and all). More than anything though, I absolutely love snow, and what makes for a better study break then getting outside to enjoy the lights and snow? If you're looking to get into the holiday spirit too, I would highly recommend the Burlington Festival of Lights, it's a great way to spread the holiday joy of this season and spend time with family and friends! The photo to the right is one I had to include from the Festival of Lights, and while the snowflakes didn't really show up in the photo, it really puts me in the holiday spirit!

Bugs and Bunnies, App.

Anyways, before I go on a tangent about the holidays - because believe me I definitely can - I will discuss the topic for this final math blog post. The topic that was discussed this week in class is technology in the classroom. For this week, there is not a specific chapter in the Small textbook that discusses the importance of incorporating math technology in the classroom, however, technology is something that can be included into every single math unit, it just depends how it is used. For example, the app called Bugs and Bunnies is a unique collection of activities and games that are educational and fun. The user can explore a variety of games that focus on a multitude of mathematical learning strategies, including fine motors skills, memory, classification, counting, tracking and geometry.

Jacqui (2015). ProdigyGame.com

Going off of this concept, one of my classmates Katie Morgan did a great presentation on the Prodigy Math Game. This game is amazing, because unlike other math games, there are over 900 Ontario-aligned skills for the Primary, Junior and Intermediate grades. This game ensures that each student is successful at their own pace, it is free for teachers to use and they get online reporting of what their students are performing correctly and which areas they need to have further instruction on. The format of the game is really eye-catching, and the students are so focused on the competition and winning, they forget they're learning new math material. As students are playing Prodigy, depending on their answers, the difficulty of the questions is increased or decreased, and there are manipulatives offered for many lessons if the student is progressing with difficulty. Setting up an account is really straight-forward, and potentially the best feature of this game is that the teacher doesn't have to be an expert on the game, there are very straight forward instructions and helpful tips throughout. The only downfall of the game is that it prompts the players to upgrade to the Premium version, so this is something that will need to be addressed to the students to not go through with, as there is no educational impact on the Premium versus free versions of the game. For me, as an emerging educator, there are so many benefits for using Prodigy in the classroom, and I hope that after exploring this great resource, other emerging educators will feel the same way!

So there is is, eleven weeks of informative, self-reflexive blog posts that have hopefully helped other emerging educators with the ideas, games and concepts I have written about. This Part 1 Mathematics J/I course has been an interesting experience, and after learning so many strategies, I can only hope that everyone else is as excited as I am to start their Block this January. See everyone in the New Year, and have a safe and happy holiday season.

Kreative Eye Blog (2014). Happy Holidays.

References 
Burlington (2015). Burlington Festival of Lights. Retrieved http://burlingtonfestivaloflights.com/ 
Kreative Eye Blog (2014). Happy Holidays. Retrieved http://www.kreativeeyedesign.com/happy-holidays/
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Prodigy (2015). Prodigy Math Game. Retrieved https://www.prodigygame.com/ 
Jacqui (2015). Website Review: ProdigyGame.com. Retrieved http://askatechteacher.com/2015/02/16/website-review-prodigy-game/
Small, M. (2013). Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 

Data Management and Probability Week 10

Hello Everyone,

Katic, K. 2015©. Fall Nature Walk with Grade 8s.

Let me begin by saying that this will be the second last blog post on my math blog for this semester, it is quickly coming to a close and I am very excited to begin my practicum placement in a few weeks! My Grade 8 classes have been amazing so far and I am really looking forward to teaching them multiple units and subjects! To the left I have included a photo from a nature walk that my associate teacher, students and I went on a few days ago, and like I have said before, sometimes there is nothing better then getting into nature and becoming inspired.

With that being said, I'm going to go right into what we have discussed in math class this week; Data Display and Analysis, Collecting and Describing Data, and Probability. From my own personal experience, I am a huge fan of probability, mostly due to the perceived randomness and the outcome of chance. The Small textbook it does an absolutely fantastic job with layout these chapters with great teaching strategies. For example, I am a huge fan with all of the probability games that teachers can show their students to explore the outcome of chance, such as spinners and card games (Small, 2013: 589). In regards to the Ontario Curriculum, students become introduced and begin to explore these topics in Grade 4, however as with anything in math, it is something they learn to explore from a very early age. When I am applying this to my Grade 8 classes, I am particularly fond of the Overall Expectation for them to be able to use probability models to make predictions about real-life events (Ontario Curriculum, 2005: 118) because I am a huge advocate for making math applicable to the real world in order for students to be interested and engage.

Speaking of engagement, here is what I consider to be the fun part of learning and expanding on mathematical processes: games!

Probably a Favourite,(2015). Introduction Game

I am only going to talk about one probability game because I think it is just that good, especially for Junior grades. This game, Probably a Favourite, combines auditory instruction with interaction from the user. This game is amazing because it beings with students having to identify the different representations of a whole in a card memory and matching game. Once students have this skill adequately understood they can move onto the game. The game is told almost like a movie, with interaction from the user as well as auditory instruction from the game.

Probably a Favourite (2015).

The user is instructed to determine the probability of selecting a type of candy out of the group of candies in this virtual candy shop. This not only makes the user understand that this is an applicable, real world problem, but it also gets them to think about probability, fractions and understanding proportional and ratio thinking. This game would probably not be enjoyed by the Intermediate grades as it reinforces basics about the above mathematical processes they should be familiar with, but it does provide that solid foundation for students. Should I teach Junior level math, I would definitely utilize this game in the classroom.

I hope that the above information has been helpful to everyone, feel free to comment below if you have any suggestions or questions! Stay warm during the upcoming holiday season!

References 
Mrs. MacIntosh's Website (2015). Probability Online Games. http://www.tvdsb.ca/webpages/cmacintosh/mathematics.cfm?subpage=193944 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapters 19, 20 and 21: Integers. In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 

Length and Area, Capacity, Volume, Mass, Time and Angles, Week 9

Hello Everyone,

Katic, K (2015)©. Bluffers Park.

Welcome back to my math blog! I know that these past few weeks my posts have taken on a redundant pattern, Background from the Small Textbook, Curriculum Expectations and Fun Games, however I feel that this pattern is important to stick with for the fact of cohesiveness.

So here we go! As I have always said, it is important to get breaks from studying in order to clear your head. I did just that this week. My lovely sister and I went to one of my favourite spots in the whole world, and needless to say, it helped inspire my math photo word problem and clear my mind.

Katic, K (2015)©. Math Photo Word Problem.

This week, we have been involved in a discussion regarding length and area, and perimeter. The math activities taught in class were great! They really gave us some great activities to try with our own students. For example, my instructor wanted to get us up and moving, so we needed to all participate in a long jump activity in order to understand measurement and distance travelled. This is reaffirmed by the Small textbook, as it states that teachers generally move through three stages of measurement, in this order, Definition/Comparison, Nonstandard Units and Standard Units (Small, 2013: 414). Remember, we do live in Canada so anything discussed in measurement uses the metric system! Additionally, capacity, volume and mass are all measurements that are attached to 3D objects (see my Week 8 blog), so it is critical to understand 3D objects completely before moving onto this unit.

In regards to the Ontario Curriculum, Geometry and Spatial sense is particularly important for students to understand as it requires students to holistically understand the world around them. As such, by having a strong foundation of understanding spatial relations, it allows students to have a deeper understanding of number sense and numeration. The best way for students to develop spatial sense is through practice of visualizing, drawing, and comparing shapes and figures in various positions (Ontario Curriculum, p.9).

En Garde Math Game (2015).

Design a Party Math Game (2015).

The first math game that I found to be particularly amusing is called En Garde Geometry: Surface Areas, Perimeters. The objective of this game is rather simple, as it asks the player a question related to the topic and if the student gets the answer right, they get to attack their opponent! I like the theme and purpose of this game as students get a "reward" for choosing the correct answer. This math game supports Grade 4 level within the Math Curriculum.

The second math game Design a Party also supports Grade 4 level within the Math Curriculum. Students must understand the concept of perimeter and area completely for this game. The objective is to represent a variety of squares according to the math word problem at the side. If the student gets three "check it"'s wrong, then they will automatically have to start a new game. If students get the answer right they're prompted with a cheer, then they move onto the next puzzle.

I hope that this post has been useful for the readers, next week I'll be discussing some more interesting math topics so be sure to leave your questions or comments below. Keep warm, the weather has been very unpredictable...but it makes for some amazing photos!

References 
Katic, K (2015). Math Photo Word Problem 
math4children (2015). En Garde Geometry: Surface Area, Perimeters. Retrieved from http://www.math4children.com/Grade4/games/Geometry/geometry/ 
Math Play Ground (2015). Design a Party. Retrieved from http://www.mathplayground.com/PartyDesigner/PartyDesigner.html 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 16 and 17 In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 

2D and 3D Shapes, Location and Movement, Week 8

Hello Everyone!

Katic, K © (2015). In Class Nov. 2.

This past week, we were involved with a discussion about 2D and 3D Shapes, Location and Movement. In the Small textbook, Chapter 15 discusses 2D and 3D shapes while Chapter 16 discusses location and movement. Both of these chapters are extensive and offer great classroom based application of math

 In particular, I am a huge advocate for visually understanding math through images, and Geometry and Spatial sense is a great math strand for incorporating those all important math manipulatives.

The various presentation activities were great, I especially enjoyed the various hands-on activities. I have included an image of one of the activities the class did, which involved very simply plasticine and toothpicks. Following some requirements listed on a worksheet, students are expected to model a 3D shape. It's a great way to get students interacting with math and to think about math more visually.

Geometry and Spatial sense is particularly important for students to understand. It requires students to really understand the world around them, and by having a strong foundation of understanding spatial relations, it allows students to have a deeper understanding of number sense and numeration. The best way for students to develop spatial sense is through practice of visualizing, drawing, and comparing shapes and figures in various positions (Ontario Curriculum, p.9).

Topmarks (2015). Quadrilateral Quest.

There are two really fun games that I discovered this week that students can use to learn more about Shape, Location and Movement. The first game is called Quadrilateral Quest: Do You Know Their Properties? This game is a much slower paced game as it allows students to really think about the questions that are asked before they submit their answers, so if any student has math anxiety that is especially induced by higher paced games, this one would be a great alternative for them. This game meets the core curriculum expectations for Geometry and Spatial Sense for Grades 5 and 6 but can serve as a review for older students, or even as a starting point for younger, more mathematically inclined students.

Topmarks (2015). Coordinate Plane Jeopardy.

The second game is Coordinate Plane Jeopardy. If you read one of my previous posts, you know that I'm a fan of jeopardy games, they're a really fun way to get students working together to try to determine the correct answer. There are 3 different categories of questions and students can work indepedently versing the computer or they can work in small or large groups. It's a really great way to get students to think about the math involved while competing to try to get the right answer.

I hope that the above post will help pre and in-service teachers alike! If you have any questions or comments feel free to post them below. Stay warm this week, the cooler weather is quickly approaching!

References 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 15 and 16 In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 
Topmarks (2015). Math Games for 11-14 Year Olds; Quadrilateral Quest and Coordinate Plane Jeopardy. http://www.topmarks.co.uk/maths-games/11-14-years/shape-position-and-movement

Patterning and Algebraic Thinking, Week 7

Hello Everyone,

Katic, K (2015) ©. Patterning Worksheet.

This past week was the week that I was looking forward to since the beginning of the term...that's right presentation week! Every week throughout this course, a select few students are responsible for presenting a 10-minute lesson based off of one of the chapters in the Small textbook. It's great as it allows everyone to teach the class about a topic they have become an expert in, and it's so interesting to see what kind of creative solutions my peers come up with when presenting math. The section I was responsible for was the patterning strand for Grades 5s and 6s; it was actually a lot of fun seeing as this week was Halloween and I was able to create an engaging, fun presentation and worksheet using Halloween graphics!

Within the textbook, it gave quite a good background on patterning and algebra. Small discussed the importance of teaching students about patterns and pattern rules before students can be able to expand and create their own. As stated in the textbook, "A pattern rule is an unambiguous, unarguable description of the pattern; every element, including the first element in the pattern, must be described" (Small, 2013: 610). This is a critical element to understand with patterning as this is the foundation upon which students build and expand their mathematical knowledge off of. As such, this directly relates to pages 77 and 87 within the Ontario curriculum, where problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, and representing and communicating are all key processes and expectations that students are expected to utilize.

Teaching Treasures (2014). Triangles Puzzle 1. 

After doing extensive research about this topic to ensure my lesson went off without a hitch, I began to realize that, given more time during my presentation, I would have discussed tools and useful games that teachers can use to engage their kids. While it is admittedly difficult to make algebra fun, I found this great online resource that can aid kids with thinking algebraically. It's called Triangles Puzzle 1 located on the gamequarium website. This game meets the patterning and algebra expectations for Grade 6s (specifically on p. 95 under the variables, expressions and equations specific expectations). It is not as action packed as some of the other math games I have discovered, but it certainly contributes to algebraic understanding. Very simply, students are expected to find a pattern illustrated in the top two triangles (it is the same pattern rule), and then apply it to the bottom triangle. The answer is inputted into an answer box at the bottom, answer correctly and another puzzle will be generated.

Teaching Treasures (2014). Triangles Puzzle 2.

Expanding off of this game is Triangles Puzzle 2 located on the same website! It meets the exact same curriculum expectations as the Triangles Puzzle 1, however instead of trying to compete the bottom right triangle within the larger triangle, in this game students are expected to answer the middle portion of the triangle. In this game, it's great that there's a help button available for students if they really are stuck with trying to solve the pattern and determine the pattern rule. I believe that both of these puzzles are great resources for students to access in order to get them thinking about patterns and algebra.  By utilizing all of the above resources, I am hoping that I will become an effective math teacher one day who will be able to show my students that in fact, yes, math can be fun! I hope these expectations and games I have discussed above will help all of those who read my post. Feel free to post any questions or comments below! Have a safe and happy Halloween.

References 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 22 In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 
Teaching Treasures (2014). Triangles Puzzle 1 and Triangles Puzzle 2. Retrieved from http://www.teachingtreasures.com.au/maths/yr7-puzzle1.htm 

Ratio, Rate and Percent, Week 6

Hi Everyone,

This week was dedicated to exploring and discussing ratio, rate and percent. As you will begin to see, many weekly topics covered in this mathematics course have real-world application. This one is no different. This topic can be extremely fun once it is fully understood!

Within the Small textbook, there are many useful activities for teaching ratio, rate, and percent to students. This chapter emphasizes the importance of reading symbols meaningfully when teaching this topic to your students. A mix of grid and non grid examples should be utilized so students get a sense of how percents, ratios and rates are all associated with various fractions of amounts (Small, 2013: 314).  It is also important to keep in mind that there are not always the best approach to solving certain solutions; it is important to give students the freedom to set up the solution strategy in whatever way makes the most sense to them.

That being stated, in the Junior and Intermediate level of math, students are expected to be able to build off of their preexisting knowledge, create and expand. The ratio, rate and percent topic falls within the number sense and numeration sections of the Curriculum, where students will be expected to represent, compare, and order numbers including integers by the time they are in Grade 7. They will also need to demonstrate an understanding of proportional relationships using percent, ratio and rate, expanding off of the preexisting knowledge of math in the Junior math level.

Every week, I try to continue building math game knowledge as a way to increase student's level of engagement. This week I discovered two really fun math games on the Math Playground Website. The first game is Math at the Mall. In this game, you select a player and have to walk around a virtual mall to complete math tasks. Upon successful completion of the math tasks at each store in the mall, the player receives a gold coin. The object of the game is to receive a total of four gold coins. While this game is not a high-paced game that involves competing with other players, I find this to work to its advantage. Students are able to take all the time they need to successfully and correctly complete the math problems posed, and when they are finished they are rewarded with gold coins. This game incorporates ratio and percent and successfully supports Grades 5 and 6 levels of the Math Curriculum. 

The second game is Ratio Stadium. In this game, it gives you a rate which you need to convert to the correct fraction in order to win against the other players. This game is great and supports Grades 6 and 7 levels of the Math Curriculum, specifically in regards to ratios and proportional relationships.

I hope these expectations and games I have listed in this post help all of those who read it! If you have any questions or comments feel free to post them below.

References 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 13: Ratio, Rate, and Percent. In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 

Integers, Week 5

Hi Everyone!

This week was dedicated to exploring and discussing integers. As with many topics discussed so far in this course, this topic is interesting because it has real-world application. As such, this topic is one that I find easy to understand and communicate to others.

Integer Contexts are hugely important to discuss with students to help them understand the larger idea. Some useful contexts Small (2013) addresses are temperatures, floors above or below a main level, being below or above sea or ground level, golf scores below or above par, and being in debt or not. For myself, I have always been able to understand integers through the context of temperature, however all of the above examples are all useful.

Katic, K. (2015). Orbit Integers Screenshot.

Within the Math Curriculum, integers become a focus in grades 7 and 8 within the Number Sense and Numeration strands. In grade 7, students are expected to represent, compare and order numbers including integers, demonstrate an understanding of adding and subtracting fractions and integers, and demonstrate an understanding of proportional relationships (Ontario Curriculum, p.99). In grade 8, students are expected to represent, compare, and order equivalent representations of numbers including positive exponents, solve problems involving whole numbers, decimals, fractions and integers, and solve problems by using proportional reasoning in a variety of contexts (Ontario Curriculum, p. 111). Understandably, each increasing grade gains a more complex understanding of mathematical processes, and integers are no exception, however, there will be students who genuinely need extra help in mathematics. This is why I believe that a variety of tools need to be used in order to enhance student learning, such as math games.

Katic, K. (2015). Spider Match Screenshot.

I have recently discovered two really fun games that students can access in order to further increase their knowledge of integers. These two games are specifically related to the grade 7 curriculum expectations, however students in grade 8 can also benefit from these games, and students in grade 6 who are demonstrating a thorough mathematical understanding. The first game above, the Orbit Integers Game, is a high paced, energetic game that brings out the competitive side in its players. Students compete against each other, or the computer, to answer the most mathematical questions correctly to try to finish first. This is a good beginner game for students as it only involves the addition operation.

The second game is the Spider Match Integer Game. Like the Orbit Integers game, it involves the competitive side of students, where they can play against each other or the computer. They must try to answer as many pairs as possible to equate to the number in the middle. The spiders eat the flies, where the flies represent either a positive or negative number. This game is one I would consider to be for students who have a more thorough understanding of integers, as opposed to the Orbit Integers game.

My next steps as an emerging educator will be to try to increase my teaching tool box, where I can access a variety of resources for my students to gain a more holistic understanding of the subjects I am teaching them.

References 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 14: Integers. In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada.