Monday, October 26, 2015

Big Ideas

Over the past couple of weeks, some colleagues and myself put together a chart outlining Mariam Small's "Big Ideas" for the Ontario Math curriculum, and matched these with the specific expectations from it as well; specifically for Grades 6-8. If you are unfamiliar with Small's "Big Ideas", here is a link to a PDF outlining them, with examples. Our document can be found here.

Feel free to use the chart for your own long range plans, and please comment on this post if you notice any need for changes that we should/will make looking forward!

Bansho- A Mathematics Instructional Method

A colleague of mine the other day mentioned Bansho, and not having a strong math background from my teacher's college days, I had never heard of it before then. Having said that, after doing a bit of research and discussing Bansho's concept with them, I realized that more and more we are seeing this method of mathematical instruction make its way into our Ontario classrooms. I suppose then it is no surprise that the Ontario Ministry of Education has made many publications regarding this concept, one of which you can view here for more information regarding Bansho. ***UPDATE October 24th, 2015: here is also a lesson plan template/exemplar explaining how to structure a Bansho lesson.

My last blog mentioned Bump It Up (BIU) walls in the classroom, and Bansho provides the teacher as well as their students with the opportunity to create and assess student work in real time in an inclusive and cooperative educational environment. It focuses more on what Dan Meyer calls "patient problem solving" (see video below for more information on this concept), which is having students use their knowledge of math and how it works to problems in order to clarify students' understanding of how math works, and why it is meaningful.

Anyways, I wanted to post a blog about this to provide anyone who is interested with these resources to see how they can implement Bansho into their mathematics programs, and why it is a great tool for improving not only student success/understanding, but to help reshape/redefine the aging textbook/linear mathematic programs from the past. As Dan Meyer states, "Math needs a makeover", and here in Ontario we are doing this one classroom at a time!

Bump It Up Walls in the Mathematics Classroom

Ok, so Bump It Up Walls (or Interactive Performance Boards) have been around in many school boards for a few years and we are seeing them in almost every classroom. Personally, I really like the idea of what a BIU wall can provide my students, as each level clearly shows students what a particular level of achievement looks like. Besides this, students actively engage in the classroom with this wall by developing and deconstructing an assignment's success criteria and learning goals in order to gain a better understanding of what each levelled exemplar has and/or does not have. Thus, at any given point while constructing an assignment, they can look back at the wall, success criteria, rubric, etc. to help figure out where their work currently is and formulate steps of how to "bump it up". Similarly, this serves as a great tool to help students assess their peers work to provide meaningful and transparent feedback. If you'd like more information about what a BIU wall is, or what it looks like, you can check out Stephanie Kennedy's video explaining her BUI wall and/or read Raine6's blog about them. 

The purpose for my blog post today is to shed light on a BIU issue that I have struggled with to date, and that is how to formulate a successful BIU wall in the Mathematics classroom. My background has typically provided me with opportunities to engage with BIU walls in Language, Art and Social Studies courses, as these disciplines encompass tasks that include formulated writing via reading comprehension, research skills, creativity, etc. Thus, providing levelled exemplars is as easy as having students assess success criteria (SC) and mark sample questions; gauging which parts of the SC are evident, and which are not. Math is a little more tricky with regard to this type of marking, as often students understand math answers as either "correct" or "incorrect", so how can we assign levels when the perception of math as a discipline is so black and white?

After some research on the internet, and viewing countless amounts of Math BIU walls online, I'm starting to get the impression that the focus for a levelled approach in Math is on the process and representation of student answers, much like the Social Sciences/Arts BIU walls, however, there is a stronger emphasis of how the answer is represented. For example, depending on the success criteria, students are often encouraged to solve a problem however they see fit and, therefore, the levelled approach is based on what how student demonstrates how/what they know as opposed to an answer being "correct or incorrect". Here is a neat example video from Pat Johnson, showing his grade 1's Math BIU wall.

For interests sake, here is a link to some Pintrest BIU wall exemplars!

Wednesday, October 14, 2015

Baseball & Math

So I'm sitting in my living room, coming down off my high from the Blue Jays win and being the nerdy teacher that I am, I think..."How can I incorporate the world series into math lessons?"
So I look up online and of course there are hundreds of baseball themed math lessons. Obviously I wasn't the first person to think of this.
I found a few interesting activities off this website
I think the easiest connection between baseball and math is statistics. You can have your students try to figure out Jose Bautista's playoff batting average by calculating the number of hits and divide it by the number of at bats. Even students that don't follow baseball can relate because it's just a different example for calculating mean.
Who else has used athletics or baseball in their math lesson planning? How effective is it for those students that are athletic and can relate to baseball a lot more easily?

Friday, October 9, 2015

Class Kick

I came across an app that is really interesting and can be beneficial to students and to educators. The app is called Class Kick. It's basically an online classroom. Teachers can create the classroom online through this app and can post assignments, quizzes, blog forums.

The app and website have available resources for teachers to use to create different assignments and tutorials on how to navigate the Class Kick app. I watched a video on how to create an assignment and saw how easy it was to use. You can basically copy and paste images of worksheets or draw in questions with the cursor. Another really neat aspect of this app is that you can correct students work in real time. You can view which students are having problems (they have the option of clicking a button that is a hand so the teacher will see that they have raised their hand for help)

Does anyone have any actual experience with this app? I wonder how effective it can be. It seems like it would be a great tool for the classroom, maybe as supplementary work.

Thursday, October 8, 2015

Teaching Math using Statistics in Sports

  Simple addition methods can be taught through sports statistics. For example, in order to figure out the number of point a team has, you must calculate the number of wins and ties in relation to how many points are allotted for both these factors. If each win counts as two points and each tie is worth one, these numbers can be calculated to determine the number of points. Thus, the number of wins and ties has a direct relation to a number of points a team has.

   The steps to this problem can be followed like so: If a team has 30 wins and 0 ties and each win is worth two points, the number of wins would be multiplied by 2 in order to get the number of points earned (30x2=60). Another example which can be used as a next step would be to add in the number of ties to the equation. If a team has 30 wins and 15 ties (ties = 1 point), how many points do they have? (30x2 + 15x1 = 75 points). In this equation, the number of wins are multiplied by two while the number of ties are multiplied by 1. After this step is completed, both values are added together to calculate the number of points the team has.

   I believe this is an excellent lessons to teach students how to use their multiplication and addition skills. I also think that relating this lesson to sports will create a higher interest in the students. While doing this lesson, a number of sports pictures and statistical sport standings can be used to keep the lesson interesting. I also believe this will help students who actually play sports by giving them the tools needed to understand how to calculate statistics.

Understanding Fractions Using Food

Fractions can be a tough math unit to teach to younger grades. It may be even more difficult when students are not as interested in the lesson due to the difficulty of it. Therefore, as teachers, we must find other interesting ways to engage the students with our lessons. In most cases, students won't even realize they are learning! I believe incorporating fractions with food such a pie or pizza (or any type of food that can be divided into fractions) would be a great way to teach younger students.

In this type of lesson, a pizza can be divided up into fractions. For example, if we slice a pizza into 8 parts and give away 2 pieces, what would my fraction be? Once students understand the basic principles of fractions they will be able to answer questions like this one. Asking students if they like certain foods like pizza, cake, or pie at the beginning of the lesson will get their attention. It's not even necessary to introduce the lesson as fractions! After a couple examples the teacher could explain what fractions are and how we can use them in this manner.

This strategy is important because it gives the students something to relate to. The teacher may also reward the class by brining in the foods used in the example for an end-of-unit task. This will also give the students something to look forward to and keep their participation levels up.

Money is Math

Using money in math can be a very effective way to teach addition in the classroom. In this case, coins can also be used as a supplementary tool in addition to students writing. Money as a symbol of numbers can be related to addition as well as fractions. For example, using quarters can help student remember how many quarters are in one whole or in this case a dollar. In addition, students can learn that a dime is 1/10 (one-tenth) of a whole which also means it takes ten dimes to make one dollar. Other example are obviously using nickles or pennies to make a dollar.

   I believe that this method is also useful in terms of teaching students how to add. Asking students to make a dollar using more than one type of coin would be an excellent way to stimulate their minds. Understanding math using money is not only something that is beneficial in the classroom, but is also something that students will be doing a lot of in their futures. This is why I believe using money is an excellent tool for math class.

Wednesday, October 7, 2015

Mathematics Question Amazes the Internet

Mathematics Question Amazes the Internet Christina Whates
In a society that is primarily dominated by social media it really isn't surprising when something goofy or phenomenal becomes viral on the internet, but the article below does surprise me. A couple months ago (see problem below) a Singapore (grade 5) math question flooded the internet with questions of how, what, why and the most common, WHAT IS THE ANSWER? I stumbled upon it myself and became stumped. I was actually flabbergasted at how difficult the problem was for me to solve. I guess my real question is does our curriculum lack the ability to build our problem solving skills? People questioned whether the problem was really too difficult or the mere fact that maybe we need to sharpen up our problem solving skills. The article states that statistics show that students from Singapore score significantly higher than any other country in mathematics, but what does that say for us Canadians? Should we be doing something different too? I'm not sure what the answers are to these questions, but I can't lie I was pretty impressed that grade 5 students can solve problems like the one below.

Does our Mathematics Curriculum need a Facelift?

Does our Mathematics Curriculum need a Facelift?
Christina Whates

Dan Meyer proposes that we need to change our approach when it comes to mathematics in the classroom that encourages inquiry thinking. Often our lessons present mathematics in a manor that is strictly on a memorizing basis. Students answer all questions in a similar way - they find the same three pieces of information plug it into an equation and away they go. But are we really teaching students to become critical thinkers? How could incorporating real life questions that students can actually relate to change how students see mathematics? Dan Meyer has fully convinced me that if teachers create problems that allow students to question and apply real life situations, it will increase their problem solving abilities as they progress into adulthood.

                                               Dan Meyer: Math class needs a makeover

Mean Median Mode – Kinesthetic Based Learning

         Mean, Median, & Mode for the Kinesthetic Learner
       Christina Whates    

Teaching mean, median, and mode can become a routine lesson, but there are always ways to make mathematics lessons interactive for learners. I have included a short, but detailed lesson teaching mean, median, and mode.  I decided to use Smarties instead of M&M's to keep my lesson nut free. Considering all the allergens present in elementary schools today peanut free is always the best option, and including a treat can always be fun! I bought a box of Smarties for a dollar, so an easy way to make this lesson more cost effective is to have students
work in pairs.

Ontario Curriculum (Grade 5):

  • – read, interpret, and draw conclusions from primary data
    – calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs (future lessons students can extend their knowledge by graphing what they found).
Included is a definition of Mean, Median, and Mode. These are just rough examples of what can be done as a class. Together a definition of each can be created with an example, that can be posted on the class math bulletin board.


1) Provide students with Smarties.
2) Organize the Smarties.
3) Calculate Mean, Median, Mode.
4) If time is permitted students can organize the data into a graph.

Sunday, October 4, 2015

Funtastic Graphing

I came across a few great examples of graphing activities to get kids involved in hands on data collecting in a fun way! Some are quite classic activities, but sometimes a helpful reminder is needed to remember that these activities exist and are easy to implement into the classroom. Here are three examples of fun and interactive graphing activities:

1. Graphing: Facebook Birthdays: This activity pulls in technology and social media into the math class! Have students graph the frequency of birthdays each month on Facebook by "friending" other students in class as their data set, and observe what patterns may occur throughout the year!

If students do not have profiles of their own, you could use this similar idea on the website Fakebook, where students could create fake profiles to collect data as an alternative.

2. Paper Airplane Graphing: Have students design and test different paper air plane models, and collect data about how far each one flies! Students will graph the different distances in order to figure out which model produces the best results. This would be great for middle school classrooms.

To make this more challenging, you could have students change variables on one plane model (adding weight, changing wing length) to make a cross curricular connection to scientific investigation, and the engineering design cycle.

3. Candy Graphing: This would be a perfect activity to perhaps put into practice in preparation for the Halloween season! Place a mixed amount of candy (or M&Ms/Smarties/jub jubes) into a jar and have students guess how many of each colour are in the jar. Students will then be able to sort, count, and graph the results. Additionally, you could use pre-packaged candy bars and create a large-scale graph on the classroom floor as another visual alternative.

This would be a good introductory graphing activity, but of course it would be incredibly important to consider the potential for classroom allergies, and dietary restrictions.

Making Math Notes Interactive

Interactive notebooks have become increasingly popular, and I have noticed them widely appearing on education websites. These are great resources to help students create notes that are engaging and help to highlight the major concepts for a particular topic. As you will see below, I found the following images of an interactive notebook on another blog: Interactive Notebook Entry: Graphing Using Slope-Intercept Form 

Personally, I am a big fan of this concept, and could see myself using these widely in my classrooms to incorporate principles of metacognition into the math classroom; it can be challenging for students to learn how to effectively take notes, and turn a blank notebook page into great study notes for the future. If you would like to learn more about math interactive notebooks, and see a few more examples of their implementation, visit the following website: Everybody is a Genius: Interactive Notebooks

Example: Interactive Notebook for Graphing Using Slope-Intercept Form

Slope Intercept Foldable (y=mx+b) and Brief Notes over Rearranging Equations

Outside view of y=mx+b Foldable

Inside View of y=mx+b foldable.  The x and y flaps define y as the dependent variable and x as the independent variable.

Frayer Model over Y-Intercept
Notes over graphing using slope-intercept form.  This page is kinda blah. 

Reminders of which way to rise/run to get a positive or negative slope.  Some of my students found this really confusing.  Need to fix in the future! 
View of Left and Right Page in INB.

Battleship: Cartesian Edition

Re-creating an in-class version of the classic game Battleship is a great way to get student engaged and practicing how to plot points on the Cartesian Plane! The website Education World has a detailed activity plan to show teachers how to implement this strategy into classrooms.

Simply put, students plot points on their grids to represent their ships of different sizes before facing off against one another to see if they can locate and sink each others ships. 

This activity can be modified for different age groups to show plotting points in one quadrant, two quadrants, or all four quadrants depending on the grade level and needs of the teacher. I can also see the potential for a larger scale version of this activity using painter's tape and tiles on the classroom floor as the coordinate system guide. This activity is well explained in the clip below by teacher/youtuber Mr. Dunaway of the Mr. Dunaway's Math Videos channel:

Hands-On Visualization: Orange Peel Geometry

Visualizing how formulas came to be is no easy task, especially for students who struggle in math. It is important to accompany algebraic models with visual ones, in order to enhance understanding for all students. One area where this can implemented is explaining surface area formulas; incorporating nets is a great example of showing a visual (and even kinesthetic) representation of these concepts. One great example I have come across to visualize uses an orange peel to help show the relationship between area of circles, and surface areas of spheres.
Basically students measure the diameter of the orange, and draw four circles with the same diameter. Students then peel and flatten the orange peel and try to fit together the peel into as many circles as needed. Students will observe that the surface area of the orange is equal to the same amount as the area of the four circles that have the same diameter. This will help students to see how the two formulas are connected to each other! Plus they have the chance to get kinesthetic during class.

You can find this activity on the Math Solutions Webpage and searching for the activity "Orange You Glad...?" in the search bar. Happy teaching!