Math Reflection Week 12
Using Games in Math
As a conclusion to our course, we looked at a number of math games in class that could be incorporated to strengthen mathematical skills taught in the classroom.
My game was called "Gem Mining" which can be accessed by clicking on this link. This game is ideal for the grade 5 level under the Number Sense & Numeration strand with a focus on fractions: mixed numbers and improper fractions.
The overall expectations for this game according to the Ontario Mathematics Curriculum is to read, represent, compare, and order proper and improper fractions, and mixed numbers (78). The specific expectations are:
-Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation (78)
-Demonstrate and explain the concept of equivalent fractions, using concrete materials (78)
This is what the game looks like:
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Milhomens, Britney. (2017, December 1).
Screenshot of
Gem Mining. [Personal Photo].
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In the game, students need to chip away at the rocks in order to represent the fraction. This part of the game already engages students who are visual learners because they can learn about how fractions are represented visually. (One of the mathematical processes). The next part of the game is to convert the fraction into a mixed fraction. The visual aids help students think about whole numbers compared to parts. This game is engaging because there is no time limit, and students can continue playing until they receive 3 stars in the game which is good for a reward system.
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Milhomens, Britney. (2017, December 1).
Screenshot of
Gem Mining. [Personal Photo].
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Milhomens, Britney. (2017, December 1).
Screenshot of
Gem Mining. [Personal Photo].
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There were a lot of other fun games that I thought were really good for students of all ages. One that caught my attention was called "Math Buzz" which can be played by clicking this link. The game looks like this:
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Milhomens, Britney. (2017, December 1). Screenshot of
Math Buzz. [Personal Photo].
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I thought this game was great because of the rage of grades available to choose from and the topics that you could pick. For example, I chose to play at a grade 4 level and I chose to do addition. The game progresses from level to level in a similar way as may mobile games such as Candy Crush or Panda Pop. The grade levels go from Pre-K to grade 8 and there are a range of topics to choose from for each grade level. It has a lot of engaging music and graphics and all the goals relate somehow to bees which is fun and engaging.
Here are a few snapshots of the game so you get a better idea:
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Milhomens, Britney. (2017, December 1).
Screenshot of
Math Buzz. [Personal Photo].
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Milhomens, Britney. (2017, December 1).
Screenshot of
Math Buzz. [Personal Photo].
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Milhomens, Britney. (2017, December 1).
Screenshot of
Math Buzz. [Personal Photo].
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Math Reflection Week 11
Using Technology in Math
This week we looked at how technology can be incorporated in math. Over the last few weeks, we have been looking at digital games that could be used in the classroom to help reinforce learning. Two of my peers presented their activity today and they showed how you can use other online resources to facilitate learning in the classroom while you are doing your lesson.
Anthony showed us a site called abcya.com that is free for students and teachers to use at home or at school. He showed us a fraction strip resource that could be used to replace more traditional paper fraction strips. Not only does this save paper, but it also makes it accessible for any student at any time. Students do not always have access to fraction strips at home, but this online site makes it easy to bring these fraction strips home. He used this site to look at comparing and adding fractions but it can also be used to look at equivalent fractions.
Here is a screenshot of what the site looks like:
The fraction strips on the left of the screen can be dragged anywhere on the white canvas. You can link them together or put them under each other to see the comparison of a part of a fraction to a whole.
You can use these fraction strips to add, subtract and compare fractions. The fractions are also put in such a way that you can see equivalent fractions (ex: 2 halves are equivalent to a whole).
Alexa used a resource in class for the measurement strand. She used an online geo board to talk about area and perimeter of shapes. She had her group make shapes and find the area and perimeter of each shape. She was also able to allow students to make connections between each shape. For example, the purple rectangle had the same perimeter as the orange rectangle but the same area as the blue square.
Here is a screenshot of the website to get a better idea of how it looks:
The elastics on the bottom are colour coded so you can make different shapes and compare them. There are also smaller geo boards and geo boards that are differently shaped.
This is a great resource to use in class because the elastics are virtual (which helps with behavioural concerns while doing activities requiring the use of elastics) and they are colour coordinated so you can create multiple shapes on one board and keep track of it.
These tools can help teachers with their effective mathematics instruction. There are a number of effective resources that can be used throughout all math classes such as manipulatives, children's literature, games and technology. Technology can make it easier to differentiate instruction for students who are struggling or need more support in math.
Here is a screenshot of what the site looks like:
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| Milhomens, Britney. (2017, November 24). Screenshot of Fraction Strips. [Personal Photo]. |
You can use these fraction strips to add, subtract and compare fractions. The fractions are also put in such a way that you can see equivalent fractions (ex: 2 halves are equivalent to a whole).
Alexa used a resource in class for the measurement strand. She used an online geo board to talk about area and perimeter of shapes. She had her group make shapes and find the area and perimeter of each shape. She was also able to allow students to make connections between each shape. For example, the purple rectangle had the same perimeter as the orange rectangle but the same area as the blue square.
Here is a screenshot of the website to get a better idea of how it looks:
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| Milhomens, Britney. (2017, November 24). Screenshot of Geo Board. [Personal Photo]. |
The elastics on the bottom are colour coded so you can make different shapes and compare them. There are also smaller geo boards and geo boards that are differently shaped.
This is a great resource to use in class because the elastics are virtual (which helps with behavioural concerns while doing activities requiring the use of elastics) and they are colour coordinated so you can create multiple shapes on one board and keep track of it.
These tools can help teachers with their effective mathematics instruction. There are a number of effective resources that can be used throughout all math classes such as manipulatives, children's literature, games and technology. Technology can make it easier to differentiate instruction for students who are struggling or need more support in math.
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Math Reflection Week 10
Data Management & Probability
This week we looked at Data Management and Probability which is the last strand covered in the Ontario mathematics curriculum. In this strand, students "learn about different ways to gather, organize, and display data. They learn about different types of data and develop techniques for analysing the data that include determining measures of central tendency and examining the distribution of the data. Students also actively explore probability by conducting probability experiments and using probability models to simulate situations" (Ontario math curriculum, page 10). This strand can be used to bridge over previous concepts learned such as fractions, decimals and percents.
This week, Emily presented an activity using data management and probability by connecting it to real-world situations. Most Peel region schools take part in ROPSSAA (the Region Of Peel Secondary Schools Athletic Association). She created an activity relating a long jump event to stem-and-leaf plots which is one way that students can organize data. First she had my group stand up and participate in a "long jump." She measured how far we jumped twice using a measuring tape and wrot our distances on the worksheet. Then we ordered the data from least to greatest and displayed the data on a line graph.
After making previous connections (ordering from least to greatest and using line graphs), we were able to order the data on a stem-and-leaf plot. From here, we were able to see who would be able to move onto the ROPSSAA tournament (no surprise- my lack of height did not give me an edge in this competition so I was unable to move on).
Here are the results of our jumping distances displayed on a stem-and-leaf plot:
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| Milhomens, Britney. (2017, November 17). Stem-and-leaf plot. [Personal Photo] |
As you can see, Danial and Stephan jumped the furthest so they will be moving onto the ROPSSAA tournament. I really liked this activity because it gets students up and moving around. They are also able to apply their own measurements to this activity so it's not just a problem that the teacher gives them to solve. They are making up their own data inputs so that they can display it using stem-and-leaf plots. From here, students could find the mean, median and mode to apply their learning further.
We did a lot of other fun and engaging activities in class. One that I thought was fun was using graphical representations to show the length of nails (mm) found in packets of 'assorted' nails. We were given a list of 50 numbers that we needed to organize into intervals or 5 or 10. The class was split in half so my group had to organize the numbers in intervals of 10. These results would be contrasted to the results if you organized the data into intervals of 5. We used the intervals 10-19, 20-29, 30-39, 40-49, 50-55. From here, we organized the data into a bar graph. The mm intervals was on the y axis and the number of nails was on the x axis. Here was our graph:
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| Milhomens, Britney. (2017, November 17). Horizontal Bar Graph. [Personal Photo] |
After counting up the number of nails in each interval, we were able to make a horizontal bar graph. We were able to see that most nails were those in the 40-49mm length range. Creating a bar graph helps you see data visually that you cannot see if you were given a list of random numbers.
We were able to compare our bar graph with the bar graphs that did intervals of 5 and we noticed that smaller intervals had smaller bars on the bar graph, but it was more precise.
Students are able to use a wide variety of different visuals when plotting data to visually see it which helps to make connections.
The text had a lot of great activities that could be used in the classroom. One that I could see myself adapting to my classroom was in chapter 21 of Making Math Meaningful to Canadian Students, K-8 (2017) which is activity 21.9. In this activity, the teacher asks students to do a survey of 10 people on the playground to see whether they prefer crunchy cookies or chewy cookies. They can make a tally chart and then a picture graph, using cookie pictures.
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Milhomens, Britney. (2017, November 17). Activity 21.9. [Personal Photo]
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Next week I'll be looking using technology in math!
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Math Reflection Week 9
Measurement
This week we focused on measurement. We watched a Sesame Street video in class where Elmo talks about the different ways he could be measured:
There were a lot of measuring activities done in class today. One group was led by Greg and he did an activity that involved measuring the classroom by using a metre stick. The group measured the width, length and height of the classroom and windows. This was a great activity that could be used in a primary-junior classroom and it is especially good for kinaesthetic learners. It helps students visualize how big something is by using the metre stick and things that can be measured such as the classroom.
Alessandro presented a measurement activity using unconventional materials (Small, 19.2). Our task was to get up and order our group from tallest to shortest. From there we were told that we needed to measure ourselves using a water bottle. First we guessed how many water bottles tall we were, and then we measured using the water bottle. We found that it would be easier to measure the water bottle using a metre stick, then measure ourselves with the metre stick. We determined the water bottle was 20cm tall and we used our height to divide by the height of the water bottles. I discovered that I was 8.25 water bottles tall! I thought this was a good way to incorporate measurement using everyday objects.
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| Knoch, Kim. (2010, May 15). jars. [Online Photo] Retrieved from |
In class we were able to practice our area and perimeter skills. We started out with 4 tiles. From there, we needed to find the minimum and maximum amount of tiles needed in order to make a perimeter of 16 units squared. Emily and I found that adding 3 tiles is the minimum, while adding 12 tiles is the maximum number of tiles needed to make a perimeter of 16 units squared.
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| Milhomens, Britney. (2017, November 10). Minimum tiles. [Personal Photo] |
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| Milhomens, Britney. (2017, November 10). Maximum tiles. [Personal Photo] |
These were our results:
The textbook had a lot of fun and engaging activities that could be used for teaching measurement.
One that stood out to me was activity 19.17 that deals with spatial reasoning. Students need to use 36 square tiles to make as many rectangles as they can. Students work systematically, starting with a rectangle with a width of 1 unit and recording the data in a table. From here, students can see how the area is the same, but the perimeters may be different. This differs from the activity above where the perimeter stayed the same, but the areas were different.
Stay tuned next week!
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Math Reflection Week 8
Geometry and Spatial Sense
This week we focused on geometry and spatial sense. Spatial sense is "the intuitive awareness of one's surroundings and the objects in them" while geometry "helps us represent and describe objects and their interrelationships in space" (Ontario curriculum, p 9). Students learn to recognize basic shapes, compare shapes, distinguish their attributes or classes and consider their location and movement.
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| Milhomens, Britney. (2017, September 15). Navanya- Hidden Heart. [Personal Photo] |
I did some art activities with the students I tutor when they did math activities that required them to hide an object they drew using shapes drawn over top of it.
Navanya drew a heart and then tried to hide the heart by drawing different kinds of shapes over top of it to camoflage it. Look closely to see if you can see it!
Navanya used her basic knowledge of shapes to draw rectangles, squares and triangles to name a few. Then she used other shapes that she made up to fill in the gaps to completely colour in the whole page.
Other students drew objects using basic shapes. One student named Ethan created a rocket ship and a glove with his shapes. He used his imagination and geometric properties of shapes to create his picture:
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| Milhomens, Britney. (2017, September 15). Ethan- Shape picture. [Personal Photo]. |
Nerenya and Ethan had a lot of fun using math to create their own creative pictures!
Rabia presented her math activity in class today. She used geometry to introduce two kinds of symmetry: rotational symmetry and reflectional symmetry. At first rotational symmetry was a little hard to understand, but she brought in manipulatives to help show the concept. Using pattern blocks, we were able to physically turn the shape to see if it had rotational symmetry.
She also let us use cube blocks to create a castle. The problem involved creating a castle for Princess Peach. We had to keep in mind that the castle needed to be symmetrical in order to please Princess Peach. This was the finished product of my castle:
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| Milhomens, Britney. (2017, November 3). Princess Peach's Castle. [Personal Photo]. |
My castle had one line of symmetry down the middle of the castle. Some of the other requirements for this problem was to rotate the castle to find how many rotational symmetries it had, and to change the castle so that it had more than one line of symmetry.
I really liked Rabia's activity because it was extremely engaging! Since I was engaged while doing this activity, I know that my students would be engaged too. This would be really helpful for students that need a visual representation to show rotational and reflectional symmetry.
Some of my other colleagues used puppets or marshmallow/toothpick manipulatives to go along with their math activity. These looked really engaging to use as well in the classroom! I liked the idea of building shapes using marshmallows and toothpicks to show edges and vertices in various shapes.
The textbook had a lot of engaging activities that I could do in my classroom. One that stood out to me was activity 17.8 where students develop their spatial reasoning. The activity involves cutting out a simple symmetrical picture out of a magazine, folding it in half, and cutting along the fold line. Students would glue half of the picture to a piece of paper and draw the missing half. I think this is a fun activity students could do to introduce them to bilateral symmetry.
Stay tuned for what week 9 has to bring!
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Math Reflection Week 7
Patterning and Algebra
This week we went over patterning and algebra. When I was in school, patterning was one of my favourite strands because sometimes it required being able to be creative! Here is an example of a patterning activity I did with a student who was in kindergarten:
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| Milhomens, Britney. (2017, September 15). Kindergarten Patterning. [Personal Photo] |
He used bingo dabbers to create his own pattern. (Considering his age, he decided to make his pattern a little messy because he figured out how much fun the bingo dabbers were!)
As students get into older grades, they start using equations to represent the pattern using numbers rather than words. Students can find the "nth" term by finding a simple formula that could be applied to any input. An example of this is the activity that my colleague, Dimitri, presented to my group. The task was to use manipulatives or an equation to find out the number of toothpicks you would need to make 10 squares in a row.
I appreciated being able to use the toothpicks he brought in to try to solve the question that way. Using maniuplatives would be really helpful for lower grade students. For higher grades, students can use manipulatives to see how the pattern is created, and then use an equation to find out the "nth" term, in this case, 10. Here was the information for the problem:
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| Milhomens, Britney. (2017, October 27). Patterning and Algebra. [Personal Photo] |
As you can see, the pattern adds 3 toothpicks for each new term number. But how can we calculate for the 10th term without adding 3 each time or using the manipulatives? Equations are the solution! Using the pattern we already know (adding 3 each time) we were able to conclude that the equation for solving for the "nth" term is: 3x+1. Now let's solve for the 10th term by placing the number 10 in place of the x!
3x+1= n
3(10)+1= n
30+1=n
31=n Voila!
We explored patterns in class by using games and looking at Pascal's Triangle! Pascal's triangle is a triangular array of the binomial coefficients. We figured out a lot of patterns within the triangle just by looking at it! Some of the games we looked at were input machines which can be played by clicking this link. In this game, you pick what the pattern would be (ex: add two then subtract 3 each time). Then you place an input number into the machine and get an output number after applying the pattern. This was really neat!
One of the things that blew my mind in class was when our teacher created a growing pattern that looked like this:
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| Milhomens, Britney. (2017, October 27). Growing Pattern. [Personal Photo] |
We were told to find the 10th term and add all the terms in the sequence (from 1-10). You could do so by adding the first and last term, the second with second last, etc. By the end, you would get a total amount of 100. The pattern in this sequence is to add two each time. The number for the first 10 numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19.
Let's rearrange these numbers into groups: (1+19) + (3+ 17) + (5+15) + (7+13) + (9+11). If you add these 5 groups, the total is 100 (20+20+20+20+20).
Our teacher visualized this using the manipulatives for the first 5 terms and this is where I was blown away:
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| Milhomens, Britney. (2017, October 27). Patterning Blocks. [Personal Photo] |
How cool is that?! Every week I seem to be more and more impressed by how math can be interesting and fun at the same time! Stay tuned for what week 8 will bring!
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Math Reflection Week 6
Number Sense and Numeration: Ratio, Rate and Proportion
Number Sense and Numeration: Ratio, Rate and Proportion
This week we focused on ratio, rate and proportion. While all of these terms relate to one another, they have significant differences.
We used a lot of examples of "everyday ratios." I did an example of an everyday ratio in my forum post this week:
The word problem below is one I created from an everyday experience. It talks about equivalent ratios and how to solve for a missing variable:
Lucky (the poodle) weighs 20 pounds.
How much more does Daisy weigh than Lucky?
The ratio of the weight of my dog Lucky to the weight of Nadine's dog Daisy (a boxer) is 1:4.
We can set up the two ratios to compare. We'll let "D" represent Daisy's weight.
1:4= 20: D
We can cross multiply to find the missing variable.
1 x ___= 20
1 x 20 = 20 (In order to get the number 20, we needed to multiply 1x20)
We need to multiply by the same number in order to get the missing variable.
4 x 20 = 80
D= 80
We know that Daisy's weight is 80lbs and Lucky's weight is 20lbs. Now we subtract to find the difference.
80-20= 60
Daisy is 60lbs heavier than Lucky.
The word problem below is one I created from an everyday experience. It talks about equivalent ratios and how to solve for a missing variable:
Lucky (the poodle) weighs 20 pounds.
How much more does Daisy weigh than Lucky?
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| Milhomens, Britney (2014, December 26). Lucky [Personal Photo] |
Mendes, Nadine. (2017, October 10). Daisy [Personal Photo]
I liked the ways in which my fellow teacher candidates found different ways of solving problems presented in class today. I also learned a lot about proportions that I had forgotten about since I was in school.
Keith did his lesson today on proportional relationships and he presented a series of questions that I was able to solve confidently. The first part of the question required finding the price of a list of groceries given set rates for them. From the rates for the items, you were able to deduce how much a set number of items would be.
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| Turner, Lindsey. (2008, January 20). Juice. [Online Image] Retrieved from |
You would be able to solve this by taking $3.00 and dividing it by 2 to find the unit price of 1 juice box (the answer is $1.50).
The second part of the question gave you an option of checking out from the grocery store in 3 lines.
Line A has 3 people with 2 items each. This would mean that there is a total of 6 items.
Line B has 1 person with 15 items. This would mean there is a total of 15 items.
Line C has 2 people with 6 items each. This would mean there is a total of 12 items.
Which line should you pick so you get home faster? The answer is Line A.
Our course text had a lot of great ideas for teaching about ratios, rates and proportions. It gives a list of appropriate manipulatives that can be used to represent ratio, rate and percent. Counters can be used to represent ratios while decimal hundredths grids and percent circles can be used to represent percents.
One activity that really stood out to me was 14.3 where students use proportional reasoning. Students can use recipes to make connections and explore ratio ideas. The teacher provides students with recipes, indicating how many servings they are meant for, and have students adjust the recipes to serve more or fewer people. At first, students use multiples and factors of the intended number of servings. Later, this can be more complex by having students revise a recipe made for 6 to serve 8 people or by allowing students to choose the number of servings.
I learned a lot of tips and tricks this week about how to teach ratios and proportion!
The second part of the question gave you an option of checking out from the grocery store in 3 lines.
Line A has 3 people with 2 items each. This would mean that there is a total of 6 items.
Line B has 1 person with 15 items. This would mean there is a total of 15 items.
Line C has 2 people with 6 items each. This would mean there is a total of 12 items.
Which line should you pick so you get home faster? The answer is Line A.
Our course text had a lot of great ideas for teaching about ratios, rates and proportions. It gives a list of appropriate manipulatives that can be used to represent ratio, rate and percent. Counters can be used to represent ratios while decimal hundredths grids and percent circles can be used to represent percents.
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| West, Liz. (2007, February 28). Making Ginger Cookies. [Online Image]. Retrieved from |
I learned a lot of tips and tricks this week about how to teach ratios and proportion!
Math Reflection Week 5
Number Sense and Numeration: Integers and Exponents
Number Sense and Numeration: Integers and Exponents
This week we took a closer look at integers and exponents. We focused a lot on integers and my instructor gave a really good definition of what an integer is; "Integers are whole numbers that describe opposite ideas in mathematics." She showed us how integers can be represented using a number line. Integers can be either negative, positive or zero.
My favourite example used in class was the sea level chart.
Khirwadkar, Anjali. (2017). EDBE 8P29 Session 5(b) Slide 6
[PowerPoint slides]. Retrieved from Sakai Session 5
The number 0 is the sea level, the fish under water (approximately -20 to -110 meters) is below sea level while a plane above the sea (80 meters high) is above sea level. The pictures show both positive or negative integers depending on where they are from sea level (or 0).
This is a great way to introduce integers to my students. Using visual aids help them understand what integers are by visualizing them
[PowerPoint slides]. Retrieved from Sakai Session 5
The number 0 is the sea level, the fish under water (approximately -20 to -110 meters) is below sea level while a plane above the sea (80 meters high) is above sea level. The pictures show both positive or negative integers depending on where they are from sea level (or 0).
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| Carpenter, Shawn. (2007, January 31). Canadian Coins. [Online Image] Retrieved from |
My peers this week presented activities that related to the theme this week. My fellow classmate Stephan introduced an activity where we needed to toss the quarter 20 times. Heads was positive whereas tails was negative. I did an activity that was similar to this in elementary but we used it with a probability unit. I liked how he was able to implement an activity like this and relate it to probability and integers. As we tossed the coin, we recorded our results in a tally chart and on a number line. The person with the highest number won. I would use this experiment with my grade 7 students because it connects many math strands together. I could enhance this activity by using more than one different coin and making them represent other numbers. For example, a toonie's heads could represent +2 while the tails could represent -2. This would make it more challenging to chart results on a number line and tally chart. This is an activity I would definitely use in my own classroom since it does not require a lot of materials yet it teaches a variety of topics.
I've realized this week that activities and games are one of the best tools for students to learn math. Traditional teaching methods in math classes where the students do not understand the concept and merely follow rules and equations causes students to forget what they have learned. Memorization is not learning. Instead, students should be engaged in activities with their lessons that relate to real life situations. Students can use their problem-solving skills by making connections to everyday life.
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Math Reflection Week 4
Number Sense and Numeration: Fractions and Decimals
This Week we focused again on Number Sense and Numeration but this time we tackled Fractions and Decimals. I was extremely nervous this week! For my course, we were expected to present a math activity from our course text to the rest of the class that they could implement into their own classrooms. I was one of the people that got to pick last, so I got stuck with Fractions- something I am not personally comfortable with because I get stuck on them myself.
I decided to pick an activity that was fun, engaging and could be used with students who have different learning styles. I also incorporated art since that's something I'm passionate about! I chose activity 12.16 which required students to use patterning blocks to make a creative design. People in my group made a bumblebee, a spaceship and a fish. One pair even made what looked like a backsplash for a kitchen.
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| Wikipedia Commons. (2012, January 11). Plastic pattern blocks [Online Image] Retrieved from |
First I went over some basic facts about fractions; what's a numerator? What's a denominator? Then I went over some common fractions that they would have already been familiar with; 1 whole, ½, ⅓ and ⅙. There were some of the pattern blocks I decided to use for the activity:
Using the manipulatives would help students that are more hands on; kinesthetic learners. I asked my fellow classmates to draw their designs on the paper provided and this step would help students that like to draw or use visuals; visual learners.
One my group finished drawing their designs, I asked them to regroup their design into whole numbers. Students are able to see visually how fractions can be regrouped into whole numbers without doing an addition sentence. However, I also asked my classmates to write an addition sentence so that they could see numbers being represented as visuals. Overall, everyone in my group was able to get the answer of 11 and ⅓ because they used visuals and counted the blocks or solved it using the addition sentence. My question could have been solved by simply changing the fractions into a lowest common denominator and adding from there--my group discovered this was possible as well so it was interesting to see how problems could be solved in different ways!
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m01229. (2012, December 30).
Hershey's Chocolate Bar. Retrieved from
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In class today we looked at chocolate. Not literally unfortunately, but we used a picture of Hershey's chocolate to consider representing fractions in different ways. We were told to write down different fractions that you can represent using a milk chocolate bar. I liked this idea because not only do I like incorporating any type of food into learning, but I see the value in implementing real-world objects into the math curriculum.
We also did a sub question where we needed to find out if the subs that were cut and shared at lunch among groups of students were fair or not. This one required that we try to use manipulatives (connecting blocks) to represent fractions and divide fractions. Again, I liked the idea that this involved food but it was also a good example of a good real-world example that could actually happen. Say you ordered pizzas for a party of 50 people, and there were some pizza boxes with pizza left over. One box may have half the pizza left while others may have 1 slice or three quarters left. One way you can figure out how much pizza you have left is to think of the boxes of pizza as fractions and add the fractions.
I look forward to learning about new ways I could make math both interesting and useful for the real-world in the classroom!
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Math Reflection Week 3
Number Sense and Numeration: Whole Number Operations
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Choi, Joseph. (2008, January 6). Sudoku. [Online Image] Retrieved from
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Today we focused on the curriculum strand Number Sense and Numeration. We had a student present a short lesson to the class about creating a game that develops a student’s fact fluency. He used the idea of a magic square where all the numbers in the rows, columns, and diagonals all add up to the same number. I found it challenging when it came to doing a harder example but through trial and error and guessing a sum, most people came up with the answer. It actually reminded me of sudoku!
We also went through different strategies or algorithms to solve addition and subtraction problems. I found these really interesting because I did not realize there were many ways to solve one problem.When I was in school we were encouraged to learn one way taught by the teacher so I did not know about different strategies such as the partial-sums addition algorithm that can be used to solve the same problem.
For example; this is how I would solve a two digit number:
1
49 I add the ones place first (9+2) to get 11. I had to carry over 10 ones to the tens
+ 22 place since the ones place cannot be larger than 9. Then I add the tens place
_____ (4+2) plus the one I carried over to get 7. This was the way I was taught in school.
71
However, there are other ways to solve a two digit number. The one that stood out to me was the partial-sums addition method. I will show that below using the same question as above:
49
+ 22
_____
40 + 20= 60 A student using this method would work one place-value column at a
9 + 2= +11 time, then adds the partial sums to find the total sum.
_____
71
I will definitely use these various methods in the classroom so that I can introduce students to the multitude of different ways of problem solving. Activities like this suggests that there is more than one way of doing and teaching things.
One of my favourite parts of this week was using the base-ten blocks to add and subtract. I was familiar with the concept of using them to add but I do not remember using them in my classroom to subtract when I was in elementary school. I found it really cool to visually see how subtracting works when you have to regroup. When I was taught in school, I was told that this was how it was done and that was what I was supposed to do. I was not given an explanation of why things happen the way they do which is why I was really interested in watching the video and trying it out for myself!
This week taught me that there are other ways of doing things even if it looks like there is only one way to do it.
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Math Reflection Week 2
Problem Solving
This week we focused a lot about problem solving and different approaches and steps to take in the problem solving process. In class we looked at questions in a variety of different ways. We had a chart with numbers randomly placed and the goal was to find the missing numerical value in the last box. Upon looking at the chart, everyone immediately knew the answer was 55, but we did not consider how we may have gotten that answer.
At first it seemed simple. My group saw one pattern and said that was how we got the answer. We were encouraged to try to look at it in different ways to try to find other patterns to solve for the missing number. When we started thinking outside the box-literally- we discovered there are so many different ways of solving things, and there were some things we had not thought of!
I think the more we open our minds up to solving problems in different ways, the more we will be successful at teaching the same idea to students. If we have a fixed mind, our students will have a fixed mind also. Since students have different ways of learning, using one particular teaching method will not be beneficial. Instead, teachers need to look at the multitude of different learning styles and adapt the concepts to these learning styles. This creates a well-rounded student who is able to do things in a variety of different ways in the real world.
Sometimes there are approaches to a questions that will not be the way I would have approached it. But this course is teaching me not to look at math in a linear way. Math has a multitude of different directions. Even though there may be one answer to the problem (but not always!), there are a multitude of different ways to get to that same answer. I look forward to being able to use this knowledge in my daily teaching practice.
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Welcome!
My name is Britney Milhomens and I am in the Junior/Intermediate Consecutive program at Brock University. In this problem we take a variety of different courses to learn about different strategies and techniques for teaching. Some courses are more interesting than others. One course I inevitably have to take, is mathematics. I don't want to say that I dread this course, but it definitely is not the first on the list of my personal favourite courses.
I turned away from math in elementary school when I had a teacher that discouraged me. Instead of encouraging a growth mindset, she encouraged a fixed mindset where I was told that math was not for me, I was not good at it, and I would never amount to anything because I could not learn the concepts to her satisfaction. This did not change when I reached high school and the math became harder and harder. Since I did not effectively understand the concepts from previous years, this became a snowball effect when it came time to build my knowledge on previous concepts. It also did not help that discouraging teachers continued through my school years until I eventually decided not to pursue math past the required grade of grade 11.
This blog will be an exploration of my learning processes as I dive into the world of teaching mathematics in the Primary/Junior division. As an English major, math is a dusty subject. I mean REALLY dusty. In the last 4 years, I can accurately say I’ve taken one math course- and that was because it was required for my program. As an English and French tutor, I rarely teach math; and if I do, it is typically nothing past the grade 8 level. But even then, some of the concepts students learn in school, I am not able to remember how to do them!
The title of my blog is "Teaching & Learning." As the title of my blog suggests, I am a learning teacher. I know that as a teacher, my job is to educate others. However, I also know that as a teacher, my job is to continuously learn whether it is from my students, my pedagogical and content knowledge, or the environment around me. I expect that throughout this math course, I am not just going to learn the concepts I once learned in school, but I will learn how to teach these concepts effectively. My goal is to perpetuate a growing rather than a fixed mindset. The ultimate goal would be to be able to gain a love of math that has been strongly discouraged in my experiences time and time again. As a result, I hope that I will never discourage students from exploring mathematical strategies and concepts.
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