Week of November 24th – Math Technologies

Exploring Resources

In this week’s session, we explored different types of math technologies. I will share a small collection of the resources we explored.

Graphing Stories: Graphingstories.com. This neat website is a resource that can be very valuable for teachers to get their students familiar with graphs. Students start with “stories” in video forms and have to try to plot the data on graphs. Students can decide the labels for their axis and then plot the points. Here is an example of our graph for “Height of Waist off the Ground” while watching a man on a swing.

Teachers can further extend this knowledge with reverse application and give the students graphs and have them attempt create a story.

Prodigy: https://www.prodigygame.com/. This website is Ontario-based math game for grade 1-8! Students battle against monsters, using math questions, to win coins and items. The game features customizable assessments and questions chosen by teachers to evaluate students. Teachers can choose from over 600 topics and view the students results in a highly organized way. Students can use several in game supports, including manipulatives and text-to-voice. Their profiles feature customizable avatars that use only first names of students to protect privacy. Parents are also invited to support their students learning.

Desmos Graphing Calculator: https://www.desmos.com/calculator. This online tool is sophisticated, but can be simplified by teachers to can explore mathematical language, ex. vertical and horizontal translations. Check it out!

Reflection

Technology is a key part of 21st century learning and it would be foolish and naive to leave it out of mathematics. This session was a key part to my continued growth a math educator. Reviewing the tools available and learning how to apply them has helped me gain confidence towards teaching different concepts using technology.
When I was in high school, I loved using the graphing calculators to explore tables of value and equations. Now, the tools we have available to explore and inspire math creativity seem endless. We can practice our math we learned in class or take chances to create new things in a fast and fun way. I’m excited to enter the teaching field with the skills to find and critically evaluate tools to use for math. I also have been consistently highlighting different math resources and games throughout my blog series. This collection will be helpful as I move into the lesson planning and internship stage of my teaching block.
This first semester of math has been great for me. I started with a closed mind about math and my willingness to teach it. As we continued our sessions and I listened to ideas and collected resources, I became more confident. Now, I find some excitement in being trying out some of the activities and games in my teaching placement. In December we will be starting Data Management, so I hope to try incorporating Graphing Stories to get my students critically thinking about what graphs represent.
– A

 

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Week of November 17th – Data Management & Probability

Exploring Resources

This week’s math learning presentations focused on Data Management and Probability. We started by exploring experimental probability, then looked at theoretical probability and finished with a lesson on data collection. For the data collection, we were introduced to appropriate question construction. Questions should be clear and have discrete categories. We were asked to make our own questions and choose a fun way to collect data. My group chose the question, “Whose coffee do you prefer?” and gave 4 discrete options: McDonalds, Tim Hortons, Starbucks and Second Cup. Counters were placed in cups as a method to collect the data. The picture below is an example of this method we used.

After the lesson we explored several other probability resources. This included a “Horse Races” probability game. Students will use a chart to keep track of horses numbered 2-12. When you roll the dice (2) and land on a number, you move the corresponding numbered horse forward one space. The first horse to the finish line is the winner. Student’s can place bets on the horses they think will win. After the first round, it is imperative the educator stops the game and asks questions about theoretical probability. Students should note the numbers that have a higher chance of being rolled. An example of a lesson plan that uses this game can be found HERE, and bonus, it actually includes an online version of the game you can play!

For grades 4-6, OntarioMathResources.ca features a small but useful curation of data management and probability resources to help teachers get started with their lessons. Take a look.

For grades 7-8 , the Mathematics Assessment Resource Service has other probability and data management lesson plans and activities. It is definitely worth it to check it out.

Lastly, many of our presenters touched on the language of probability. When studying and teaching probability it is really important to be consistent with your language use and to clarify the meaning of the language to the students. The probability line, from mathisfun.com, is a great visual to explain the probability language on a scale of 0 to 1. I highly suggest showing some form of this visual with your class or working together to co-create something similar.

Reflection

I really enjoyed exploring some of the probability resources. I think this is an area of math that is fun and exciting, especially theoretical probability. One of the presenters talked about the misconceptions surrounding the independent and dependent events. I think this is one area of probability that I should become very familiar with before I start teaching because it will elicit many questions from the students.

I was talking to some teachers in Ontario, and many expressed that probability is usually left to the end of the year and sometimes gets overlooked due to time constraints. I think that as a teacher in the Ontario context, I need to be aware of this phenomenon and try my best to make data management and probability as important as the other strands in the math curriculum. As a kinesiology graduate, statistics and statistical significance were important concepts that underlined almost every single peer-reviewed study. I hope that I can pass on my knowledge of probability and significance with interesting and relatable material and context for students.

– A

Week of November 10th – Measurement

Exploring Resources

This week we looked at measurement topics such as perimeter, area, volume, mass, time and angles.

The concept of time as a measurement can be a little difficult to understand. We at different strategies to estimate, measure and record time. Students need to know the difference between analog and digital clocks. A really fun and interactive game we used to test the knowledge of analog clocks was a “clock bingo” game. The students each receive a bingo card with analog clocks and the teacher calls out/displays digital corresponding times. This activity is most suitable for grades 3-4. I also stumbled upon a cool Pinterest board that has neat activities for teaching time. You can check this out if you’re looking for some ideas.

This Scholastic blog has 10 great hands on strategies for teachers to use when approaching area and perimeter. In fact, one of our presentations included an activity from here. Students are to write their names in block letters on centimetre grid paper. They must find the perimeter of each individual letter and then combine the perimeters to find the total perimeter of their name. This is a great activity for the beginning of the year too as these names can go on the students math binders or as a name tag on their desks. Below is from Ellena’s math blog.. this is her example for our class!

Woolley, E. © 2015 Retrieved from http://woollenamath.blogspot.ca/2015_11_01_archive.html
One presentation explored volume. In grade 6, students must learn to estimate and measure volumes using the metric system. A neat activity we tried was using the cm block cubes manipulatives to estimate the volumes of empty boxes before we calculated their actual volumes. We tried this strategy on a rectangular prism (box of Kraft Dinner) and a triangular prism (Toblerone bar). When teaching measurement, it is important to remind students to be watchful with their units. Perimeter is linear (cm), area is in two dimensions (cm squared) and volume is in three dimensions (cm cubed)! The Khan Academy has a great set of tutorials for this topic.

Lastly, in our class we viewed a great resource for a “Minds On” portion of a lesson. This video is about unusual units of measurement and can be really useful to help students break the rigidity of thinking around the ways we measure. It also offers a bit of history on where our current measurements come from and it is simply entertaining and funny! Take a look!

Reflection

My father is the proud owner of an audio/visual company here in Ontario. Many summers I spent time working with his employees at various hotels, schools or office board rooms all over Canada. I can’t stress enough how valuable it was to know basic measurement principles. Every day we are encountered with measurement and conversions, but in my case it was extremely important to be accurate. We had to know the perimeter of the rooms, the lengths of the tables and screens, the volume of the speakers that needed to be cut flush into the wall. Having the measurement knowledge was extremely beneficial to me when realizing I had to make these calculations.
As we explored these concepts in our class and through the readings, my feelings we’re reaffirmed. My classmates highlighted relevant applications of measurements in our lives, especially with unit conversions and time. I feel extremely confident going into my classroom to teach this unit, regardless of age. I can’t wait to allow my students to explore measurement with manipulatives, make estimates, and then go out and apply their knowledge to real life situations. I also enjoyed adding to my knowledge base. Watching the unusual measurement video gave me some insight to where these expressions originated from.
– A

Week of November 3rd – Geometry & Spatial Sense

Exploring Resources

This week’s learning activities were centered around geometry and spatial sense. For 2-D shapes we used geoboards and toothpicks to demonstrate the qualities of the shapes. For 3-D shapes, we used clay and toothpicks to recreate the dimensions according to specific instructions. We also looked at creating nets of 3-D shapes and had time to construct various 3-D shapes using some pre-made nets.During the symmetry session, we had an opportunity use mirrors. We completed some half drawn images from a worksheet and also created half of an original drawing that was to be completed by a partner. The presenter also shared a tool from MathIsFun.com that allows you to create symmetrical drawings. Lastly, we looked at dissecting and combining shapes. Using tangrams was a fun way to explore the properties of 2-D shapes.

Near the end of our session we also reviewed some really cool applications that I would like to share! Click the links for more detailed reviews and to download.

Osmo is a one-of-a-kind app. This amazing app kit comes with a camera mirror as well as tangram pieces, letters and numbers. Even though it is on the pricey side, this app has some amazing classroom applications. One tangram activity has users creating shapes physically and the camera reads the pieces and displays the shape on the screen. Check out this video to see for yourself.

 

Slice It! is a neat app that requires users to slice shapes into a predetermined amount of equal pieces. It takes a good grasp of spacial sense to complete and is quite entertaining.

Foldify is an app that has users creating unique nets of 3-D shapes. Users can make simple nets or complicated nets (like a Spongebob character net) that have the option to be printed. Although its connection to the curriculum is more playful than serious, it is still fun for overall geometry knowledge and interest in the strand.

noiƚɔɘlʇɘЯ | Reflection

The lessons on Geometry and Spatial Sense definitely expanded my thinking as a math teacher. There are many valid and reliable resources that are available to create a fun and active learning environment. In my opinion, this unit of math is extremely hands on and visual. Students need to feel and see the shapes in order to get a fundamental understanding of their properties, especially with younger students. The use of tangrams, connect-blocks, toothpicks & clay, nets, or any other manipulatives to build and create 2-D or 3-D shapes has extreme value. I am excited at the opportunity to approach this part of the curriculum creatively with many good resources for my students. I really like the Osmo app. Even though it is expensive, it is a modern technology that beautifully combines kinesthetic and visual learning applications.
I also think it could be interesting to try and create cross curriculum activities that make use of geometry and spatial sense expectations. For example, I remember in Grade 5, my teacher had us constructing a method of transportation (ie. car or boat) in a woodshop type class. I would hope that as an educator I can build on an experience like this and incorporate mathematics expectations into an assignment to fully demonstrate the useful applications of math in our every day lives.
– A