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What a journey it has been with our math learning! Over the last 12 weeks, we have covered topics such as number sense and numeration (fractions, decimals, etc.), patterning and algebra, geometry and spatial sense, measurement, data management and probability and the types of formative assessments in math. In this blog post, I will discuss some things that really stood out to me during the journey!
Rates, Ratios, Percents and Proportions
Within our number sense and numeration strand, we covered proportional relationships. Here is an introductory video to ratios and proportions that will work well for junior-intermediate students during a Minds-On math lesson! Additionally, I created a math word problem catered to Grade 8 students, that allows them to calculate percentages as consumers making purchases. I think that students will be engaged with this problem because they can connect it to their own life experiences! Also, this problem will pave the way to financial literacy. I will discuss the specific and overall curriculum expectations along with the math processes used below: ⇩
My Digital Math Word Problem: To Buy or Not to Buy the Designer Backpack?
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| No attribution required. |
I received an enticing offer from COACH Canada in the mail. My offer (attached photo) states that I can save 20% if I spend $300-$500 or save 30% if I spend $500 or more. My budget is $555 before tax. I then looked to see what I can buy on the online store and picked this "too cool for school" backpack that caught my eye. The price tag is a modest $1300. (Here's the link to this fancy backpack: http://ca.coach.com/en_CA/coach-gotham-backpack-in-burnished-glovetanned-leather/11106.html?dwvar_color=JIMDB)
Will my budget be enough to purchase this backpack, with my discount offer before tax?
Answer:
Since I am purchasing an item over $500, I will get 30% off. Using percents I will convert 30% to a decimal out of 1.0, so I divide 30 by 100. I move the decimal place once to the left and I am left with 0.3.
Then, I multiply my total $1300 by 0.3 to see how much 30% of $1300 is. This gave me: $390.
I then subtract that 30% or $390 from my total cost to see my final price before tax. So $1300- $390 = $910.
I am over budget. To see how much more money I need, I subtract my budget from my discounted cost. So, $910 - $555 = $355. I need even more than 150% of my budget to buy this backpack. Looks like I won't be buying this pretty backpack anytime soon!
Review of Problem:
The strand that this problem directly relates to overall is number sense and numeration, dealing more specifically with proportional relationships. This question would be part of the Grade 8 math curriculum.
Overall Expectations for this problem:
• solve problems by using proportional reasoning in a variety of meaningful contexts (p. 111)
Specific Expectations for this problem:
– solve problems involving percent that arise from real-life contexts (e.g., discount, sales tax, simple interest) (p.112)
Math Processes involved in this problem (p. 110):
Reasoning and Proving:
• develop and apply reasoning skills to make mathematical conjectures, assess conjectures and justify conclusions, and plan and construct organized mathematical arguments
Connecting:
• make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts
Problem Solving:
• develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding
My Overall Reflections Throughout My Math Journey
Over this course, I made several connections to an inquiry question I formulated, where I asked myself, "how can I incorporate culturally diverse content during lessons throughout the curriculum?". I am sure many teachers have this question as well, since our goal is to make our classrooms as positive and inclusive as possible. I was able to find a wonderful video that contains excellent tips to guide my inquiry. Here, the teacher is focusing on an Afro-Centric math lesson. Take a look!
Concluding Thoughts
Over the last few weeks, I learned that as teachers, we must aim to engage our students in math, in order to create meaningful learning experiences. I would like to end off with a great math joke. I hope you understand it and if you do not, don't worry! You can google it! Also, you will eventually become familiar with the terms when you reach secondary school, if you are not there yet!
Overall Expectations for this problem:
• solve problems by using proportional reasoning in a variety of meaningful contexts (p. 111)
Specific Expectations for this problem:
– solve problems involving percent that arise from real-life contexts (e.g., discount, sales tax, simple interest) (p.112)
Math Processes involved in this problem (p. 110):
Reasoning and Proving:
• develop and apply reasoning skills to make mathematical conjectures, assess conjectures and justify conclusions, and plan and construct organized mathematical arguments
Connecting:
• make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts
Problem Solving:
• develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding
My Overall Reflections Throughout My Math Journey
Over this course, I made several connections to an inquiry question I formulated, where I asked myself, "how can I incorporate culturally diverse content during lessons throughout the curriculum?". I am sure many teachers have this question as well, since our goal is to make our classrooms as positive and inclusive as possible. I was able to find a wonderful video that contains excellent tips to guide my inquiry. Here, the teacher is focusing on an Afro-Centric math lesson. Take a look!
Over the last few weeks, I learned that as teachers, we must aim to engage our students in math, in order to create meaningful learning experiences. I would like to end off with a great math joke. I hope you understand it and if you do not, don't worry! You can google it! Also, you will eventually become familiar with the terms when you reach secondary school, if you are not there yet!
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Thanks for reading friends!
Love,
Teddy
