16th Quick Step: Every math question can be done two-ways or more …
... the problem is, most students only know one-way.
Today, we talk math!
Who wants to start, you one-way or you two-way? Rock-paper-scissors … one-way wins.
Edison: One-way, welcome to the program. Can I call you 1-way?
One-way: Yes.
Edison: Tell me a bit about yourself 1-way.
1-way:
1] I’m quick to do 😊
2] I only know one-way to do a question,
3] I sometimes mix up what I’ve memorized cause I don’t understand what I’m doing ☹
4] I’m the answer to a, “How do I …?, question,
5] If a question stumps me it means … that my one-way isn’t helping ☹.
Edison: And what do you do if your one-way isn’t helping?1-way: … I give up.
Edison: 1-way you may want to check out Get rich quick. Get math quick.
Edison: Okay two-ways, you’re up. Can I call you 2-ways?
Two ways: Yes, 2-ways works. Good to be here. Happy to spread the ways.
Edison: Tell me a bit about yourself.
2-ways: I’m 2-ways and am very much the opposite of 1-way. I mean I make sure I know their one-way, but I also make sure I know a second-way.
Edison: Interesting. Keep going.
2-ways:
1] I’m slow … to do,
2] I know two-ways or more to do a question
3] I’m answering a, “Why do I …?, question which requires more thinking and that’s why it’s slow, and
4] If a question stumps me… in that instant the quick-one-way isn’t working. Then I just think of the second-way and use that.
Edison: What’s the second-way?
2-ways: You know, The Fantastical 5! … I think of the math I wrote on the Summary Sheet (the fundamentals) and use one of those to do the question.Edison: Hmmm. Interesting.
Edison: 1-way back at you, can I ask you some math questions?
1-way: Go for it.
Edison: As you might guess, they’re all, “How do I …?, questions, your specialty.
1-way: They complete me. Bring them on.
Edison: Okay, 1-way here are the questions, Grades 6 to 12 (age 11 to 17)
1. Gr: 6 How do I, Multiply 8 and 7 (8 x 7)?
Easy, memorize your multiplication tables … 56!2. Gr: 7 How do I, Find 50% of 80?
Just take a half of 80, which is 40.3. Gr: 7 How do I, Solve x + 3 = 7?
Just move the 3 to the other side and change the sign, … x = 7 – 34. * Gr: 7 How do I, If a $20 hat is on sale at 30% off, how much do I pay?
Just multiply $20 by 0.3 ... calculator says it’s $65. Gr: 8 How do I, Multiply negative two and three and negative two (-2 x 3)?
A negative and a positive makes a negative … -66. * Gr: 8 How do I, Multiply fractions, three-tenths times two tenths (3/10 x 2/10)?
Not sure … the denominators are the same … so … I just multiply the numerators?\(\frac{3}{10} \times \frac{2}{10} = \frac{3 \times 2}{10 }~or~\frac{6}{10} \)7. *Gr: 9 How do I, Multiply ‘a’ squared and ‘a’ cubed (a^2 x a^3)?
I forget the rule, but I think it’s multiply the exponents, to get a^68. Gr: 9 How do I, Expand 2(x+3)?
2x + 69. Gr: 10 How do I, Find the slope of y = 2x + 3?
It’s 2. Just think of y=mx+b10. *Gr: 10 How do I, Find the x-intercepts of y = (x+2)(x-3)?
Easy x = 2 or x = -311. *Gr: 11 How do I, Find the transformation on y = (x-4)^2?
It’s 4 left or is it 4 right … not sure.12. Gr: 12 Calculus Find the derivative of y = x^3?
Just use the Power Rule, y’ = 3x^2
Edison: Thank you 1-way.
Edison: 2-way can you help 1-way out with, Question 7., Gr 9: Multiply ‘a’ squared and ‘a’ cubed (a^2 x a^3)?
2-ways: Yup, that’s what I’m here for. If I’ve forgotten the quick way I’d look at the question and think about which of The Fantastical 5 helps. In this question there’s lots of symbols. I’d ask myself, what’s the meaning of the symbols? The exponent of ‘2’ in, a^2, is a symbol and means multiply ‘a’ by itself two times, a x a. And the ‘3’ in a^3, means multiply ‘a’ by itself three times, a x a x a. Then a^2 x a^3 becomes a x a x a x a x a. And ‘a’ multiplied by itself five times is, a^5.
…
Edison: That took a while, but you did say you were slow
2-ways: Slow and steady always wins the race! And The Fantastical 5 help, a lot!
1-way: Appreciate the lifeline 2-way.
2-ways. No problem 1-way. That’s why I’m here, to offer a second way.
Edison: 1-way, do you know a second-way to do Question 1, multiply 8 and 7?
1-way: No clue. Just memorized my multiplication tables.
Edison: And about Question 2, 1-way, Why is -2 x 3 is -6?
One-way: Don’t know. That’s how my teacher taught us, said a negative and a positive gives a negative, so I memorized it.
Edison: 2-ways, for Question 8., Gr: 9 Expand 2(x+3), 1-way said answer is, 2x + 6.
a) Come up with a second-way and a third-way or
b) Tell us why it’s 2x+6?
And c) could you be quick 2-ways?2-ways: No, I can’t be quick – thinking takes time. Give me a moment to ponder which of The Fantastical 5 to use … … Okay, got it, I’ll give you both: In words 2(x+3) is, two multiplied by ‘x’ plus three, so this is a multiplication question. That tells me a second way to do it, I’ll use the meaning of the symbol, ‘multiply’, which is repeated addition, 2(x+3) = x+3 + x+3. For the third-way, a Picture works (doing it with a visual) - Picture for multiplication is a rectangle and have to find the Area where length is 2 and width is x+3.
Edison: 1-way and 2-way, thank you for coming on the program and being my two guests today. I and the audience were taught some good lessons today. Goodbye.
Audience: … applause … applause.
Edison: What a show today! You heard it here, the Q & A chit-chat with 1-way and 2-ways. 1-way was quick to do and either got it or gave up. With 2-ways, explanation was slower, but it made sense. And the only difference between 1-way and 2-way, was that 2-way knows The Fantastical 5 (Summary Sheet).
Edison: Audience, questions?
Q1 Are 1-way and 2-ways good friends?
Q2 Why doesn’t a 1-way student take the time to learn 2-ways?
Q3 So 2-ways will always have more success on tougher questions?
Q4 I get it. It’s like 2-ways has back-up plan in case the 1-way doesn’t work out. And that means 2-ways will always be better than 1-way because they can problem solve better, right?
Q5 I’m a one-way student, and this explains a lot of my struggles in math. Merci.
Every math question can be done two or more ways.
Can you do your math two-ways?
EH
*P.S. Hey audience, Edison here. Did you know that Questions 4, 6, 7, 10 and 11 were done wrong? Are you a 1-way or 2-way student? Time to find out. Use The Fantastical 5, to find a second-way.
What’s EH? My initials for Edison Hopkinson, eh.
What’s ‘eh’? ‘eh’ is a part of Canadian culture - it’s how many of us snow angel making wonderful people finish off sentences.
Hey there’s 1-way over there eh! And that’s 2-way chatting with 1-way eh!