Let’s do some Calculus 👨🏽🏫🧓🏽!
If the word Calculus psyches you out 😯, relax, you got this 😁.
Two news items before we, do some Calculus:
Go here to read recap of Habits Strategy session on Sept 21st.
Go here for Goals Strategy Session details on Sat. October 26.
- This Goals Session builds on the Goals article written last month. Students struggling with their September Goals would benefit from attending.
Edison here, and welcome to another edition of Edison’s Math School 🏫
where the motto is, ... math made easier❗
If the word Calculus psyches you out, 😯 relax, you
got this 😁. I’m your teacher on this ride, and everything will be fine, … if you accept that patterns are a core way to pick up math faster. Do that and it becomes a game of Spot the Pattern!
And that’s true even if you’ve never seen Calculus (age 5 to 16) or a parent who gave up on Calculus decades ago or a rusty grandparent or …
Patterns are so widespread in math that they get shortened into
a Rule or Law or Formula or Theorem. And though those Rules or Laws allow you to do math much quicker (they’re all just shortcuts to doing a math question), I’d say where the real ‘fun and joy’ happens is when you go ‘pattern searching’ 🕵🏽♀️!
What’s a pattern?
A pattern exists when you’re given three numbers or things in a sequence, and you can predict the fourth (and fifth and sixth and …).
Here’s an example: For the sequence 5, 7, 9, ?, a) What’s the pattern, b) What’s the fourth term?
Answer:
a) Looking at 5,7,9 you’ll notice the numbers are going up by two (or two is being added each time) so then
b) the fourth number follows that pattern, it’s 9 + 2 or 11 😊! Easy-peasy!
Refresher on patterns
The Grade 5 to 7 questions below have the first three terms of a sequence, and your task is to: a) State what the pattern is and b) Use your pattern to predict the fourth number.
I’ve done the first one for you,
Patterns don’t work with two, you always need three.
Want proof? For questions 1) & 2) and 3 & 4) the first two terms are the same (1,2 and 2,4), but once you know the third term, WHAM, you can predict what’s next! Cinch!
Recap
Know three of something then, you can spot the pattern and predict what comes next!
Time to go ‘pattern searching’ in Calculus
Today In Edison’s Math School, I’ll show you how patterns work in Calculus.
Here in Ontario, Canada Calculus is first taught to 17-year-olds (grade 12, last year of high school).
Now onto Calculus. Below are four columns, Column 1 (lists the question number), Column 2 (listed as y, has questions), Column 3 (listed as y’ has the answers) and Column 4 (is writing the pattern). Your task is to a) see the pattern for 6) to 8), and there’s two happening, and b) Predict the answer to questions 9) and 10).
In Calculus this concept is called Derivatives, and here’s what question 7) looks like in a Calculus course (asked two different ways).
What grade are you in?
If you’re in Grades 5 to 8 (age 10 to 13) 👦🏽🧒🏽, Derivatives have something to do with RATE.
If you’re in grade 9, 10 or 11 (age 14 to 16), Derivatives build on SLOPE.
In 12 Advanced Functions? Builds on RATE OF CHANGE.
Now let’s make this interesting … and raise the stakes!
Okay, you’re on a roll and know the pattern from 6) to 10) above, next question is a piece of cake … a cake walk … easy pickings.
You a) Make up two Calculus Derivative questions and then b) Write the answers in the table below.
Okay, if you’re having so much fun 😁 and beaming with joy 😆 over your success with showing Calculus who’s the boss, well, well done 😊, high five 🖐🏼! And if you’re thinking, “Is that it, as this is a walk in the park, child’s play for me 👶🏽 … too easy 😛!”, well, here are your three final questions that raise the stakes.
They’re sneakier questions, not tough, as there’s no such thing as a tough question in math. Find the derivative of the following questions:
You just did ten Calculus questions!
Amazing! You did it 😊! Didn’t that feel good?
If yes, then keep doing pattern searching … as ‘Spot the pattern game’ makes math a breeze! Until next time, Edison’s Math Class is over for today.
Edison 👨🏽🏫🧓🏽
Edison’s Math School 🏫
… making math easier❗