Probability and Estimation

Why do we need estimates? Sometimes we do not want to know the exact answer but instead an estimate is more useful. We make estimates every single day and for many things in life. For example you may estimate how far you can get with the amount of gas in your tank or how long it will take you to get to a location if it is raining. Below is a photo of a jar filled with cookies that demonstrates an activity that is played at many wedding showers, birthday parties, or events that you may participate in life. You can get great at estimation by practicing and developing strategies that work for you.

Growth Mindset:
Our brains are like a muscle and it is important that we can work that muscle and let it grow and develop. Students should never feel like they are not good at math but instead keep trying and practicing and developing their skills because everyone is good at math it takes hard work and dedication. Below is a link to the website named Class Dojo that provides videos made for children explaining concepts such as your brain is a muscle and many more crucial topics.

https://ideas.classdojo.com/i/growth-mindset-1

Data Management and Probability:
Students love yo know what to expect and providing students with parallel tasks allows them to feel like they have some sense of control over their learning and allows them to take responsibility and initiative. Probability can relate to many different aspects of student's lives such as those who are interested in sports statistics. There are numerous games and online activities that allow students to practice probability such as Gizmos Reaction Time Game.

There are numerous data programs that you can find online to include in your lessons and explore data management units with. One of the programs that we explored in class was named Tinkerplots and there are numerous things you can do with inputed data. It is important to not just read the data but read between the data and read beyond the data as well. When teaching data it is not a matter of formulas but understanding the three measures of tendency Mean, Median, and Mode. 

Assessment of Math

Co-operative Groups:
A great way to get students moving around and getting physical such as making shapes with their bodies or attempting to make geometric shapes. It is important to be careful and not make students sit down for large periods of time because they can begin to lose focus and then they are not engaged in their learning. Everyone's voice in the classroom should be heard and there should always be opportunities for every student to contribute therefore provide students with oral clues. Grouping students in pairs is an effective strategy for collaborative work in math and if needed then students can compare their work with another pair beside them. If groups are too large that does not provide fair opportunities for everyone in the group to be a contributing member.

http://mathtechconnections.com/2015/12/24/differentiatedmathgroups/

Clapping Institute:
In class, the activity clapping institute was demonstrated to provide understanding that as educators it is important to give every student clear targets and share learning goals and clear success criteria. As educators we are not simply at the front of the class partaking in direct instruction but our role is to facilitate and guide students in their learning experience. When students are problem solving it is a great opportunity to assess their knowledge and application. Involving students in their own formative assessment allows them to set personal goals, opportunities to try again, and the result is that learning happens.

"Dont' Make Careless Mistakes"
Never tell students to not make careless mistakes. Mistakes are a part of the learning process and students do not mean to make careless mistakes it can be a cruel thing to say that can discourage students from progressing.

Keep Learning Goals Simple:
A great way of getting students to understand the learning goals is to collaborate with students to develop the success criteria. Monitor students progress and adjust instruction when appropriate. Not all teaching strategies are going to work out and keeping track and reflecting on lessons allows educators to make adjustments in the future based on what worked and what did not. It is important to have discussions with students to see what strategies are working best for them based on their learning styles and needs.

Measurement Math Activity

In this weeks class I had the pleasure of demonstrating a grade four or five math activity that could be used in the class to teach the unit of measurement to students. My classmates acted in the role of a grade four or five class and played the activity name banners. The idea of the game is to introduce the concepts of area and perimeters of simple shapes such as squares. Using 1cm squared graph paper the students were asked to write their names down and then calculate the area and perimeter of their name. In the photo below is a demonstration of a name banner that a student may create. The name banner activity is a great way to get students interested and engaged in learning about perimeter and area considering students love activities that are personal or individualized.



Another concept that we discussed in class is that when students can keep track of everything they've tried, they feel like they are making progress. Using charts to keep track of what students have done is a great way to track progress. It is important to reward hard work because the more time students spend on a task the better they get at it. Students must learn to establish a math mindset. Guided Inquiry Lessons are great because they are inquiry based and develop challenging concepts. It is important that what you are teaching is right for the grade level. Read expectations before and up to your grade level to know what they have learned in previous grades. The Minds On portion can be something that is considered review for the students to activate prior knowledge however the lesson should be something new. Consolidation is an important part of the lesson that allows students to discuss what they have learned in the lesson.

 The photo above depicts an activity that allowed students to learn the unit of measurement in groups and not only did it relate to real life but it was also a hands on activity that students could physically grasp the ideas of measurement. Students were able to calculate surface area using the toilet paper tubes and rulers and make connections between the surface area of various shapes.

The Greedy Triangle

What does Similar Mean in Math?

• Same shape
• Could be different size, colour etc. the colour does not affect what is happening mathematically

Teachers can use the smart board as an effective tool to teach Geometry for example using the smart board to demonstrate shapes that are congruent or similar. The smart board can be a great interactive way to demonstrate these shapes and have students come up to the board and rotate and move the shapes around to examine the relationships between the shapes. Mathematical vocabulary is a great way to start a class and ensure that the students are understanding the concepts before solving problems.

With regards to the topic of symmetry it is important to use real-life examples so that students understand what symmetry means. On both sides of the line of symmetry the shape is equal. Students can also use the smart board to understand that if you fold along the line of symmetry both of the sides are equal.

Using Children's Literature to Teach Math Concepts






There are many examples of children's literature that can be used to teach math concepts to students such as The Greedy Triangle by Marilyn Burns or her other novel named Spaghetti and Meatballs For All A Mathematical Story to teach perimeter and area. Reading to students aloud allows to involve them and make it engaging. It allows you to introduce topics and everyone enjoys being read to even older students.

Development of geometric thinking is key to the success of students in Geometry. It is important that students have a spatial experience and that problems include every day life scenarios. The best way for students to really understand Geometry is for them to be touching it, moving it, and cutting it. When students can physically experience geometry they are able to clearly understand the concepts. In Geometry all students should be using manipulatives because it develops a different area of the brain that is crucial for understanding. 

Mistakes Are Important

In math mistakes are an important part of success. Teachers should move away from the more traditional approach of teaching where students are afraid to make mistakes and fear asking questions because they do not want to look "foolish". Well questions and mistakes should be encouraged because that is an important stepping stone in learning. It is important that teachers change the way we encourage students and reward their efforts and hard work by saying compliments such as "You worked so hard, I am so proud of you" as opposed to "You're so smart" An effective video for demonstrating this concept is the Meet the Robinsons, You Failed! video available off of Youtube.




As educators it is important to use letters in equations that apply to the questions being asked. Instead of using X and Y because how many words really start with X and Y? We can use letters such as b for blocks or c for cats and so on. Students start to really understand proportional reasoning when they look at patterns with scenarios and examine the relationships in these problems. Incorporating the use of the smart board in math can also be useful for students to get engaged in their learning. For example one can explain mathematical vocabulary such as output, constant, and variable with visuals on the smart board such as demonstrated in the photo below.

Teaching students concepts such as what is increasing by the same amount each time? And therefore that would be your constant is an easier way of understanding functions than simply memorizing formulas and equations because then students have a much deeper understanding of equations and how to formulate one themselves.