What are the chances that we have met here today again? They are certain I would believe! Here's a task for you, take a moment and watch this adorable children's story. Embedded in the story is a math lesson, try to see if you can figure out what strand of math it is!
Any thoughts? If you guessed PROBABILITY, you are correct! So friends, this week we will discuss the math strands of: Data Management and Probability.
Data Management: Stuck in the Middle
Data management is about recording, organizing and analyzing numbers. Some aspects of data management are averages/means, medians and mode. These are all tools used that help us organize and make meaning of numbers. Many people still confuse those three terms. They all have something to do with central tendencies and different types of middle points of number sets. Here are the definitions and how averages, medians and modes help us organize and interpret data.
Average/Mean
- HOW TO: Adding together several quantities in a SET and dividing it by the total number of quantities used.
- Average helps us understand the middle or central tendency of a quantity of numbers.
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| Harvey Mudd College (05 January, 2010). Example of a graph with a mean [Graphic]. Retrieved from http://bit.ly/2hyHDkQ |
Median
- HOW TO: Take the entire quantity of numbers you are using, call this your SET of numbers. Sort them consecutively from the least to the greatest. Find the number in the middle of the list. If the total quantity is even, take the 2 numbers in the middle, add them and divide them by 2, to find their average and thus your median of the SET.
- Medians help us with finding out the central number of a SET of numbers.
Mode
- The mode is the most frequently occurring number in a SET. Take your data set and record how many times each individual number occurs. The most frequent is your mode. There may be several modes or no mode at all.
Not so hard after all right? Anything can be accomplished with a little bit of practice! ⬇
Practicing the Means, Medians and Modes
Would you like to practice and fine-tune your skills? The Khan Academy is a renowned resource with hundreds of instructional videos, lessons and practice opportunities. Here is a practice page for mean, median and mode!
It is Certain That We Will Talk About: Probability
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| No attribution required. |
In her book "Making Math Meaningful to Canadian Students, K-8", Marian Small discusses that, "probability is the study of measures of likelihood for various events or situations. How likely it is to rain tomorrow, how likely it is that a contestant will spin a particular number on a game show, or how likely it is that a particular candidate will win an election are all examples of probability situations" (p. 628). Small (2016) also states that using pictorial models like probability lines are helpful because students can see, describe and compare likelihoods of events. A probability line has specific terminology and should be out of a whole, like 100 or 1, as in the image. It thus starts at 0 or impossible, continues to 50 or even chance, and stops at 100 or certain. These are all tools to help students visualize and understand the likelihood and chances of events!
Activities
I would like to share a super fun activity that I participated in this week. My colleague made a great worksheet that could be used as a Grade 7 activity. The Ontario Math Curriculum states that the 3rd overall expectation for Grade 7 students is, "compare experimental probabilities with the theoretical probability of an outcome involving two independent events". This activity demonstrated just that! It used 3 bags filled with a set amount of blue and red lollipops (i.e., bag 1 has 5 red, 5 blue, bag 2 has 8 red, 2 blue etc.). Our colleague drew these lollipops for 10 independent trials and we were to predict which bag she was using, based on the event probability. It is always so engaging when there are visuals and manipulatives to consolidate mathematical concepts. Using these resources helps teachers differentiate to visual and kinaesthetic learners and is a fun mind-break and observational time for the logical-mathematical learners!
Thanks for participating in blog today friends! There is a very likely chance I will be posting next week, so stay tuned!
Teddy
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