Step by step

Alright, today I’m going to be sharing with you a little bit about a section that was very difficult for me to understand. I struggled with multistage experiments. Here’s a few examples of what those types of problems typically look like, as well as my thought process when I’m solving them.

There are 60 employees in a certain firm. We know that 36 of these employees are male, 12 of these males are secretaries, and 24 secretaries are employed by the firm. What is the probability that an employee chosen at random is a secretary, given that the person is a male

What I’ve found messes me up in these problems, is understanding exactly what’s happening in the problem. So, let’s start there. What information do we have?

There are 60 employees total.

36 of those are male

12 males are secretaries

There are 24 secretaries total

Alright, now don’t let all that information scare you. I’ve found that it’s super helpful to just break it down step by step and checking along the way helps in solving these problems.

Remember that we are looking for the probability that a random male is selected, is a secretary. There is a lot of unnecessary information in this problem that could be confusing.

There are 36 male secretaries. Which gives you 36 males to choose from. 12 of those males are secretaries. So: 12/36 is the probability of randomly selecting a male that is a secretary. This would simplify down to 1/3.

I hope this helps anyone else who also gets things mixed up during multistage experiments.

A square is a rectangle?

Yes. You read that right. A square IS a rectangle.

Sidenote: As I was typing this title my younger brother is sitting next to me and he reads this and replies “yeah, so a rectangle is a square” PERFECT TEACHING MOMENT!

So naturally, I had to take advantage of this and test out my own skills with a quick lesson. My brother is 9 so this is great practice. Here is essentially how this conversation went; and I’m happy to say that he now has a pretty good understanding of this concept as well!

My response to his statement that a rectangle is a square is no. Initially he was confused, much like I was when I first learned this concept. What helped me was drawing out a visual. One square and a rectangle next to each other. Now, list some of the characteristics of each one. There are more, and he could be more specific but; this is what he came up with.

Square:

4 sides
equal sides
4 right angles

Rectangle:

4 sides
4 right angles

With this, I had him check off the things that matched from the square to the rectangle list. Notice anything? Everything that’s on the rectangle list is also on the square list. That means yes, a square is a rectangle. It has 4 sides and 4 right angles. BUT we aren’t finished yet. Look at the rectangle list. There’s one thing left over. Does a rectangle have to have 4 EQUAL sides? No! So it can’t be a square!

It was just a quick spontaneous lesson, but I also found some cool interactive websites with activities for students learning basic geometry.

https://www.mathsisfun.com/quadrilaterals.html

http://interactivesites.weebly.com/geometry-shapes.html

Fun with candy!

Hey guys! So, I am ALL for making math as fun as possible. Recently in class we did a super fun activity using M&M’s. Not only is this project fun and engaging, but delicious too! We did this through the online course and had to go buy m&ms and submit pictures of our results but this would totally work in a classroom too! It is perfect for teaching probability.

Here’s how it works:

Each student would be given one bag of m&m’s.
Then, count the total number of m&m’s in their bag
Next, students will sort out the colors and count how many of each color there are
Record/graph
Find the probabilities

We did have an assigned packet that went along with this. The beauty of an assignment like this though is you can make changes and make it your own. Here’s a few examples of problems that can be solved using this data:

Graphing- especially for younger students this is a great way to teach them how to make a graph using their sorted m&m’s.
Probability (which is mainly what we used it for). Students could find the probability of finding a red m&m in their package. Ex: If there are 25 m&m’s in a package, and 6 of them are red, the probability of picking up a red m&m is 6/25 or 24%.
Making predictions- get their brains thinking and wondering. Students will take an educated guess on a given probability

I’ll attach some images so that you can get a better idea of what I’m talking about.

http://indulgy.com/post/eVGltx1MS1/m-m-math-use-when-teaching-money

M Math estimation, sorting, addition,comparing number, problem solving... — http://snippetsbysarah.blogspot.com/2011/09/m-math.html

Reflections, Rotations, translations, oh my!

Hey there everyone! Today I wanted to share with you all this super cool program called DESMOS. We all know that graphing can sometimes get a little messy, and if you’re not careful when drawing out points or lines you could end up with a wrong answer. Desmos can help with that! It’s an online program geared entirely towards all sorts of graphing problems. It’s interactive, and you can click around on the screen, and change around points to see what happens to the graph.

I think Desmos is a great tool for both students and educators! As an online student, I don’t always feel like I have the best understanding of some of the topics we cover because I am not good at learning from the book. I am very much a hands on learner who has to actually work out a problem in order to grasp the concept. Desmos allows me to do that even while taking a course online. It also seems like a great resource for teachers because not only can they choose from the Desmos database, they can also create their very own lesson and activity.

It’s definitely something worth checking out!

https://www.desmos.com/

Here’s another great video that covers the basics of transformations! Good, simple information! https://youtu.be/GqHWdTLL8Qw
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