Teresa-Marie's Math Blog: November 2016

Saturday, 19 November 2016

Time for Measurement!!!

On your mark, get set, and time to measure...It's the Session 9 Measurement Olympics!!!

via GIPHY

This week by far has been my favourite week of activities. Over the years, one of my favourite units in math is measurement; partially because I had little difficulty understanding the concepts of the unit. This week, the teacher candidates had the pleasure of exploring various hands-on activities involving the unit of measurement. As you read further on in this post, I will further discuss the engaging and interactive activities that educators can use to help students understand measurement concepts.

One way in which to get students excited about a new topic or concept is through the use of media. Whether it be an infographic or video, students will become engaged with visual; and prepared to learn more about the concept. Therefore, this is exactly how we started our lesson. Our instructor chose to display a kid-friendly video on measurement using a TV show "Sesame Street." The video allows students to be introduced to measurement terms and concepts before the commencement of the unit.

Firstly, the class got to explore an interesting activity named "Area Dice." This is an interactive game where students are able to practice plotting points on a cartesian plane; as well as practicing the concept of area. Students work in pairs and are given one sheet of paper with boxes; a piece of graph paper if the teacher chooses. The students are responsible of rolling the die twice in order to attain the measurements for the length and width for the area. Once this is completed, the student will shade in the appropriate area. The goal of the game is to shade in as much area as possible on the sheet. This activity is a great way for students to interactively practice getting familiar with area. Shading in the area will help students to visualize what consists of length and area. In sum, the "Area Dice" game provides students with an outlet to practice and develop their skills in the concept.

After this intriguing activity, we played, what I think, is the most interactive activity yet. This activity involved incorporating the aspect of the olympic games and the math concept of measurement. Each student would be put into a group with at least 4 other members. Each group receives a paper indicating the 5+ stations, or "games," that each member of the group will be able to participate in. The students as a group work together to make an estimate of the measurement, followed by checking the actual length of the measurement. This game promotes the development of collaborative working skills; while helping to improve the retention of measurement concepts. I really enjoyed this activity as an engaging lesson for students. Working collaboratively will help students learn measurement concepts while applying them to real situations. Below is an image of the worksheet of the various stations that can be given to students:

In my opinion, I felt that this week was the most intriguing week yet. Using the concept of olympic games would make learning the unit of measurement engaging to students. In future classes, I can see myself using this activity since it is a great way to create an active learning environment for students.

Friday, 11 November 2016

Geometry and Spatial Sense

This week's sessions focused on exploring problems dealing with geometry. Throughout my math classes over the years, geometry was a unit I was on the fence about. I would retain some concepts of the unit and struggle with others. But as the years progressed, I was able to gain a grasp of the geometric concepts.

Initially, a couple of the teacher candidates gave a demonstration on a activity a teacher could do in constructing geometric figures with a Grade 5 classroom. This activity was called "Marshmallow Geometry." Firstly, a review was done of different shapes; focusing on the number of faces, edges and vertices each shape has. After this quick recap, each table was given toothpicks and small marshmallows. Each person at your table had to chose a shape and make a 3-D representation of the shape; whether it be a prism or pyramid. I thought this activity would be very interactive for students. Allowing the students to be able to make the shapes themselves will help students to visualize the shapes when it comes time to drawing them on paper. Although the marshmallows may pose an issue, depending on the maturity of the class, a teacher could easily change the marshmallows to a non-edible item. Overall, this is an engaging activity that I could see using in my future classroom. Here are some pictures displaying this fun activity.

Once this demonstration was complete, we continued to explore various other activities that could be done in the classroom in regards to geometry. Each candidate was given a sheet of paper divided into boxes. Each box contained a number of shapes with a total number of sides. Students would then have to fill in each box of the different shapes that would satisfy the two requirements. For example: 2 shapes, 8 edges -> possible answers could be 2 squares or 2 rectangles.This activity could also be done in collaborative setting, in pairs or the class as a whole. The teacher could use paper bags labelled with the number of shapes and total edges. The class could then guess as to what shapes are in the bag to satisfy the two requirements. In short, this activity would be an engaging way to help students develop their confidence in recognizing the different shapes, how many vertices and how many edges each one has. Here is an image of the practice worksheet.

Another fun demonstration was playing "Guess Who: Geometry" as an activity. Instead of using people, and asking yes or no questions about the characteristics of a person, the students use geometric shapes to play. Students play in pairs and ask each other questions about various characteristics of geometric shapes in order to figure out each other's shape.

The final demonstration focused on the Spatial Sense portion of the unit. Our instructor used the game Battleship to get students engaged about using a cartesian plane. This game allows students to practice plotting points on a white board cartesian plane. This is a great activity to use with students in order to help them develop their skills on plotting points. Here are some images of the fun activity.

In short, we explored many innovative activities to make learning geometry and spatial sense fun. I personally enjoyed the Battleship gam the most to use with future students. However, all these activities provided engaging environments for students to develop their skills in these math concepts.

Thursday, 3 November 2016

Patterning and Algebra

This week's session focused around the concept of patterning and algebra; and the various resources educators can use to help students improve their skills in this concept. Throughout my years learning math, I've always enjoyed learning the basic fundamentals of patterning and algebra. By high school, when the concepts became more difficult, the positive feeling started to dissipate. However, in general, I believe I have a strong basis of this concept.

Firstly, one of the teacher candidates gave a sample lesson for students. This activity involved practicing to identify various patterns based on images and a table. The handout provided a great way for students to develop a basis of identifying the pattern; what is the operation and number by which the pattern is increasing or decreasing? Overall, a great way for students to develop a foundation of the basic skills needed for the concept of patterning.

As a class, we continued this development of skills by practicing various problems about pattering and developing an algebraic expression. This was modelled by output # = input # x __. This algebraic expression will help students to predict what the pattern will look like for a higher term, such as 100. A sample problem is found below.

The next step our class took was to demonstrate these patterns with the use of manipulatives; instead of just a regular table. Each table was given a bag with various patterns indicated Each member of the table chose a pattern and had to construct this pattern with square coloured chips (math manipulatives). After each table was done making their patterns come to life, the class did a gallery walk to see the different ways in which people represented the pattern. As a class, we noticed that most individuals represented the pattern flat on the surface of the table. However, there were some individuals who chose to build the pattern by expending upwards; stacking the math chips on top of one another. I enjoyed this method a great deal since it would allow students to visually represent each of these patterns and hopefully make more sense of this math concept. Below are some images of this activity; the pattern with the rule beneath it.

We continued to build on this manipulative method by expanding on the original pattern. The algebraic expression that was used no longer just contained a number that is multiplied by the term number, but rather adding an operation; such as output # = 2 + 4. The representation of the constant number added a bit of an extra challenge. The same process occurred for these questions. Each member picked a pattern from the bag, then displayed this pattern on the table using the math chips. Once all tables were complete, the class completed another gallery walk. Here are some images of the representations of these patterns.

Lastly, the class was able to explore the innovative app called "Dragon Box." Our instructor described this game as an opportunity for students to practice algebra without viewing algebra in a traditional form. She also disclosed that she uses this app all the time with her students. Therefore, I thought this app must be a great source for students. At first, I found the game was a bit confusing. However, after playing around and figuring out the elements of the game, I could see how this would be a great game to help students develop their algebraic skills. Instead of solving for "x", students must try to isolate for the dragon. Through trial and error, students will become familiar with the process of eliminating various boxes to get the dragon by itself. As students progress, the levels will get harder and harder; which will help them develop their skills for the algebra concept. Despite having to pay for this app, I believe this would be a great app to use with students in the classroom.

To sum up, this week has proven to be very informative for the concept of patterning and algebra. Through the use of manipulatives and various technological resources, such as the app "Dragon Box," I believe I would use any of these resources in my classroom.