Miss M's Learning Space

This week was our final week of presentations and our last traditional class, and therefore my last reflection post. We went over technology in the classroom in general, but specifically their applications within the data management and probability strand. The first resource was Prodigy , which I discussed in detail in my post from week 8 , so I won't go into detail about it here. In addition, we talked about an activity called story graphing . The idea is students graph some variable over a series of time. Based on the above story, students could get a variety of specific height answers since they're making an estimation, but hopefully their graph would look something along the lines of: This activity allows students to interact with, and clearly understand, what a graph means . I would consider this an appropriate activity for students in grades 5-8 as a part of the data management and probability strand. Another interesting activity is the video below. It doesn...

This week we discussed data management and probability. The main thing to remember when teaching data management is the quality of the data (i.e. is it meaningful and accurate). One way the data can be made less meaningful is if the sample size is too small. For example, if we only sample 3 people in a class of 45 then the results of the sample will not apply to the entire class. I'm going to organize this post similarly to my week #9 post in that I'm going to outline several strategies/activities that can incorporated into lessons for data management and probability. Terminology: Probability Line It's important for students to understand the terminology that's used when talking about probability. Below is an example of a graphic that could be posted in the classroom for students to refer back to regularly.  MathIsFun.com (2014). Probability Line [Online Image]. Retrieved from: http://bit.ly/1MpzS9B  Having an anchor chart in the room like this one will h...

This week we discussed various units of measurement and various types of measurement. For example, we talked about measuring in bps, metres, kg, and minutes as well as how to calculate area, perimeter, and speed. I'm going to discuss in this post some of the activities I found to be the most engaging for students. Video Clip The first activity is a video by John Green called 36 Unusual Units of Measurement . It discusses bizarre (but very real) units of measurement that are no longer commonly used. This video can lead into discussions surrounding what it means to be a unit of measurement (i.e. everyone needs to agree what 'one' of the unit is, but other than that they can be fairly arbitrary) and some other units of measurement not often discussed in schools (ex: GB). I showed this video to the class I'm observing and got mixed reviews. Some students absolutely loved the video since they read a lot of John Green books. Others simply enjoyed the content and ...

I never understood the connection between patterning and algebra until this past lesson; we seek out patterns, and then algebra is how we communicate patterns to each other. We start in elementary school by describing and representing patterns, then in middle school we model and predict patterns (through algebra), and then in high school we solve and analyze those patterns.  Since I'm observing a grade 7 class right now, I'm going to focus on strategies at the grade 7 level. In grade 7 students move beyond extending a pattern to the next three items, and start being able to calculate patterns at any point, and students begin to see patterns as relationships. For example, if a car is moving at 50km/h consistently for 3.5 hours, how far will they have travelled? If we chart it on a 'T' chart we can see the patterns:  MacCuish (2015).  Based on the above diagram, students can easily see that as time increases by 30 minutes (0.5 hours) then the distance tra...

This week we talked about proportional relationships; specifically ratios and rates. Rates and ratios are concepts that are introduced initially in grade 4, but are developed later on in grade 7. There are several different types of rates and ratios (rates, part-part ratios, part-whole ratios, equivalent ratios, etc), and I'm not going to go through them all. Instead I'd like to focus first on some engaging ratio problems, and a potential strategy for teaching them. The engaging math word problem is as follows: Based on the diagram below, which of the lots is fuller? MacCuish (2015). Parking lot ratio question.  The above question is based on one I found at EDUGains in one of their ' Big Ideas ' resources (page 3).  If the question is written out it is as follows: in parking lot A there are 24 of 40 spots filled. In Lot B there are 56 of 80 spots filled. Which parking lot is fuller? Students may get caught up with the 'absolute' numbers and think...

This week we continued with our number sense and numeration discussions but focused on operations involving integers (specifically: addition/subtraction and multiplication/division which leads into discussions around BEDMAS and perfect squares/square roots). In terms of building up to discussions around perfect squares/square roots it's important to lay a solid foundation. The diagram below demonstrates what an integer is , and it's important to spend time with moving around the number line (i.e. adding/subtracting both positive/negative integers). Below, there is an image of a number line; all whole numbers (both positive and negative) are integers. Begin by adding/subtracting whole numbers along the number line. For example, -3 + 2 = -1. NCS Pearson (2015). Integers [Online Image]. Retrieved from http://bit.ly/1LfGsfj.  Once students have a good understanding of what integers are and how to work with them, you can move on to multiplication/division (again using the n...

This week we continued to explore several strategies outlined in our textbook  Making Math Meaningful  (Small, 2012). Specifically, strategies regarding operations with decimals and fractions, and understanding the relationship between the two.  It's easier, in my opinion, to start with fractions. There are several strategies for operations (multiplication, division, addition, subtraction) involving fractions that were presented in class. In terms, again, of classroom application I would begin with addition/subtraction since that would help develop an understanding of what fractions are before continuing onto multiplication/division. The most effective way, I thought, of explaining addition/subtraction of fractions was the visual representation we explored. It compares the fractions to a whole so students can estimate whether the result will be less than or greater than one. Using lego or strips of paper (which is what we did) you can add fractions with different de...

This week we explored several strategies outlined in our textbook Making Math Meaningful (Small, 2012), including strategies on prime factorization, mental math, estimation, and place value. I talked more about prime factorization last week, and this week I'm going to explore mental math strategies.  I’ve never really thought about how to teach concepts such as mental math strategies, since by this time in my life they come quickly, but Keenan, Casey (2014, August 23). Screen-grab from Number Talks Strategies [Online Video]. Retrieved from:  http://bit.ly/1MQnDFV now that I’ve been introduced to the strategies it makes a lot more sense. It’s interesting to see all the different mental math approaches laid out since they help you realize that there are multiple ways to get to the same answer and may help students feel more confident if you change the focus from what your answer is to how you got to that answer. I think this concept of mental math would be well intr...

Like I mentioned in my introduction post, I have always loved to do math. It makes sense to me; I understand how to manipulate the tools I'm given in order to solve the problems I'm faced with. To me, math is logical and non-subjective. However, many may disagree with me. I know my mum, for example, hates math. She is also a teacher and dreads having to teach math. And in our class at Brock I know some of the people at my table have expressed their frustration with math as well. Zimmerman, Alycia (2013, December 27) Using Lego To Build Math Concepts . Retreived from http://bit.ly/1inCRzE Why is that? Is the blame on the student for not engaging or on the teacher for not explaining in different ways? Or is it society for popularizing the idea that math is intangible for some people? I know when I was in school it was almost 'cool' to not be good at math, and ripping on math was commonly accepted. I think if we want to change attitudes and engage students about math...