Mathematical Term for a Number to Double and Double Again Then Double Again
Developing algebraic ideas and language
Number tricks are fun for children. The fun, all by itself, is valuable, but is not mathematics. Merely understanding how the trick works is good mathematical, often algebraic, learning. And understanding a trick well enough lets children make upward their ain tricks.
"Think-of-a-number" tricks
These tricks come in ii types:
- Recollect of a number (but don't tell me), do some arithmetic with that number, and I tin can predict your result.
- Retrieve of a number, do some arithmetic, tell me your outcome, and I can instantly say what number you started with.
4th graders dearest these tricks! Nearly of them (and even some younger children) are likewise set up to understand how they work and even to learn to make upwards their own tricks! Without the loftier-school annotation, what they are learning is the ancestry of algebra!
The flim-flam
An example of predicting the answer:
- Think of a number.
- Add iii.
- Double that.
- Decrease 4.
- Cutting that in one-half.
- Decrease your original number.
- Your result is ane!
How it works
I say Think of a number. I don't know what number y'all are thinking of, so I just imagine a bag with that number of marbles or candies in it.
The handbag is closed, and tied, so I tin't run across in, just it doesn't matter. Your number is in there.
I know that if I tell you to add 3, I tin picture that bag and three extras, this style: 
When I tell yous to double that, I double the quantities in my moving-picture show similar this: 
And so, when I say subtract iv, I mentally erase 4 of the extras: 
From the motion-picture show, itself, I can be sure that you lot tin can cut that in half, and I picture this: 
The last teaching, subtract your original number, gets rid of the pocketbook! 
That's why I can predict your result without knowing what number y'all thought of. Your answer must exist ane.
Nosotros tin can summarize this in a table.
| Words for each footstep ——— | Pictures of the results |
|---|---|
| Call up of a number. | |
| Add 3. | |
| Double that. | |
| Subtract iv. | |
| Cut that in half. | |
| Subtract your original number. | |
| Now it is like shooting fish in a barrel to see… | The result is one! |
Inventing your ain tricks
Yous tin make upward tricks on your own equally long as your rules[1] allow you to:
- depict the pictures,
- employ whole numberless and whole marbles (no fair cut bags in half!), and
- subtract only the marbles you can see. (No fair taking marbles out of the bag. The bag might accept been empty!)
Drew, age ix, kept asking for new tricks, then started inventing tricks of his own. Here are two to practise on. Draw the pictures yourself, to figure out what the "magician" should predict the result volition be. And then brand up your own tricks.
| Fox 1: words for each stride——— | Flim-flam 1: Pictures |
|---|---|
| Think of a number. | |
| Double it. | |
| Add x | |
| Divide by two. | |
| Subtract your original number. | |
| Triple the outcome. | |
| Aha! | Your result is… |
| Trick two: words for each pace——— | Trick ii: Pictures |
|---|---|
| Think of a number. | |
| Add two. | |
| Multiply past 3. | |
| Add ii. | |
| Subtract your original number. | |
| Divide by ii. | |
| Subtract your original number again. | |
| Aha! | Your result is… |
Drew's inventions
Here are three tricks Drew invented. Draw the pictures to figure out how he can easily figure out your starting number!
| Drew'southward trick: words for each step——— | Fox i: Pictures |
|---|---|
| Think of a number. | |
| Add xx. | |
| Quadruple that! | |
| Divide by 2. | |
| Subtract your original number. | |
| Tell me your result… | |
| Aha! | You started with… |
| Drew's second pull a fast one on: words for each step——— | Trick 2: Pictures |
|---|---|
| Recollect of a number. | |
| Add 2. | |
| Double that! | |
| Subtract 4. | |
| Subtract your original number. | |
| Aha! | Your answer is your original number! |
| Drew's third fox: words for each footstep——— | Fox 3: Pictures |
|---|---|
| Think of a number. | |
| Add 5. | |
| Double that! | |
| Decrease your original number. | |
| Decrease 1. | |
| Subtract your original number. | |
| Aha! | Your answer is 9! |
- It is certainly possible to make up tricks without the restrictions given hither, just they are not suitable for almost students in elementary school. The algebra is non harder, but the pictures and arithmetics can be harder.
Mental 2-digit multiplication
The trick
You tin learn to multiply certain pairs of numbers, like 87×93 or 52×48 or 65×65 or 34×36 instantly in your caput.
How it works
Click here to acquire how to do this trick and to understand how information technology works.
Source: https://elementarymath.edc.org/resources/algebraic-thinking/
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