Edison’s Math School, The Input-Output-Machine: Partie deux de trois - MATH!
Any Input put into -> A Math Machine -> Gives an Output.
Edison’s Math School math today focuses on how to shift how you think about math to learn and understand it better.
The Input-Output-Machine of Life, Math, Learning & You: Partie deux de trois - Math
As you read in Partie un, Machines are a part of life, and the three-step process of Input-Machine-Output is integral to living life.
Math works in a similar way to life as it too has Input-Output-Machine. Thinking of math as an Input-Output-Machine, will shift how you think about questions that initially stump you as you’ll be thinking differently - what’s the input, where’s the output, how is the machine helping? You become more curious 👍! And it forces you to train yourself to think about math in the same way you approach life … and that helps you know how to learn better … which will help you remember longer 😊!
Learning & Math Words in Partie deux de trois - Math
LEARNING> Input, Output, Machine, How to learn (Learning, The Learning 5), Understand, The Fantastical (foundation), Reps (reinforce the understanding),
MATH> Input, Output, Math Machine, Rules, Expressions, Evaluate, Solve, Equation, Formula, Theorem, Rule, Percent, Add times, Sum, Doubled, Word Problems, Area, Rectangle, Angles, Triangle.
In grade 9 and above, some Input-Output-Machines become core to the course - called a Relation (gr 9 & 10) and Function (gr 11, 12, college & university).
Let’s find out about what math machines have to with The Fantastical 5
Machines in math, show up as Words, Symbols, and/or a Picture, so not surprisingly you need to know meanings of your math Words, Symbols and Pictures (that’s the purpose of your Fantastical 5 Summary Sheet). And that makes math machines easier to understand ✔.
What do Machines in math look like?
Expression (2 & 3 below), Equation (4), Word Problem (5 & 6), Rule (1 & 1b) Formula (7), Theorem (8).
What’s the Input, Output, Machine?
1) Machine Rule is ‘Adds three’
Machine? Input? Output?M? It takes any input you have an adds 3
I? could be any number, two (2) or 22 or 3000 or 0.5 or 1/3
O? For an input of ‘2’, Output would be 2 + 3Thinking Question: What’s an Input that would not work in this Machine?
1b) You won’t see “Adds three” as a question in math, but you will see it asked in, What’s the rule for 5, 8, 11 …❓
2) Evaluate 2 + 3
Input? Output? Machine?M? ‘+ 3’ (adds’ three)
I? 2
O? 2 + 3 or 5
Evaluate means find the number answer, that’s why we don’t stop at 2 + 3.
To get better with understanding which part of a question is the Input, Machine and Output, it helps to think of Math as you would in real Life: A washing machine does something to the input (of dirty clothes) … it makes them clean. Similarly in math, a Machine does something to an Input … to give an Output 🎡.
3) Evaluate 2x + 3 if x = 4
Input? Output? Machine?M? 2x + 3
I? x = 4
O? 2(4) + 3 or 8 + 3
or 11. Output is 11.
Thinking Question: How can you verify that your Output is correct? 🔍
Questions 1) to 3) above were asking to find the Output and gave the Machine and Input. But 4) below shows sometimes you’re asked to find the Input (warning: more thinking required 😊).
4) Solve 2x + 3 = 11
Input? Output? Machine?M? 2x + 3
I? ‘x’ and we have to find that.
O? 11
Solving 2x + 3 = 11 look like this,
2x + 3 – 3 = 11 - 3
2x = 8
2x / 2 = 8 / 2
x = 4
Input is 4, Machine is 2x+3, Output is 11.Thinking Question: What’s a picture for 2x + 3 = 11?
Sometimes the machine is given in words, and you have to find it, 5) below. Lot of thinking and translating ㊗ required.
5) Word Problem: The sum of a number doubled and three is eleven. What’s the number? [Input? Output? Machine?]
M?
I?
O?If you did it mentally and said the number is 4, that’s correct ✔. BUT … getting the right answer doesn’t prove you understand ☹, as the answer is only one part of The Fantastical 5️⃣
To understand this word question, translate the Words to Math Symbols (isn’t that the first two parts of The Fantastical 5?) and I wrote about that in Edison’s Math School Part 2 of x: Learning Math Words.
Starting translating, The sum of a number doubled and three is eleven. What’s the number?
Let ‘n’ be the number I’m trying to find.
Sum is ‘+’
double means times two or ‘x (2)’
‘is’ is =
eleven is 11Translated to Symbols gives, n x (2) + 3 = 11 or 2n + 3 = 11
Machine? 2n + 3
Input? n (need to find this)
Output? 11
The equation you found for the Word Problem is question 4) above. Neat eh 😊!
6) Word Problem: Determine fifty percent of twenty.
Input? Output? Machine?In Symbols, ‘Determine fifty percent of twenty’ can be translated to, 50% of 20
M? 50% of
I? 20
O?50% of’ means ‘½ of’ which means ½ x (one-half times)
50% of 20 becomes ½ of 20 becomes, ½ x 20 … which is a fraction multiplying question.
Remember ow to multiply fractions?
Go ahead, and you’ll see where your ‘divide by 2’ magically comes from.
I’m sure you did mental math and knew the output/answer is 10. And you probably did 20 divided by 2. But if I ask, why did you ‘divide’ ❓ … I’m guessing I would have stumped you ❓❓. The above input-Output-Machine explains why you divide by 2.
Two questions where the Machine isn’t given in the question. Hmm …
Your turn to find Input, Output and Machine
7) Measurement: Find the Area of a Rectangle with length of 10cm and width of 5cm. Input? Output? Machine?
M?
I?
O?
How did you do partner? Did you flex your muscle💪!
8) Geometry: Two angles in a triangle are 50 degrees and 70 degrees. What’s the third angle. Input? Output? Machine?
M?
I?
O?
How did it go partner? 👀
7) Machine is A = L x W, the Area Formula for a rectangle. And two inputs given, 10cm and 5cm.
Output will be A = 10cm x 5cm
or A = 50cm^2
8) Machine is the Rule or Theorem (SAT or ASTT), that angles in a triangle add to 180 degrees
50 + 70 + t = 180 📐
Where ‘t’ means the measure of the third angle.
This is now a Solving question, similar to 4).
Want to understand math quicker?
Want to understand math quicker?
Make it easier! Start thinking of Math questions, as Input-Output-Machine! And know your Fantastical 5.
Math isn’t difficult!
I take that back, ‘it’s difficult if you don’t understand it’, and today was all about waking up to understanding math better. Which then explains, why I forever tell, yell and spell out, “Math isn’t what makes math hard, it’s ...”.
Look at it this way, if you’re thinking, ‘math is hard’ then that’s your output. Which means you’re putting in the wrong inputs.
Look at it this way, if you’re thinking, ‘math is hard’ then that’s your output.
Which means you’re putting in the wrong inputs.
Until we meet learning again partner, time to put in the reps on what you now understand - find a math question and figure out the Input, Output and Machine. Then repeat.
Which gets us to You & Learning, Partie Trois de Trois. See you next week, when YOU, are the Star, you are Machine!
Edison 👨🏽🏫
Edison’s Math School 🏫
… making math easier❗