Yesterday we launched into our first math lesson of the year. We looked at patterns in our place value system by using pattern blocks, a place value chart, and bar models.
The big message you want to take away is this: when something is “ten times as much as” something else, that means you have ten groups of “that something else.” And to say that something is “1/10 of” something else means we’ve taken a whole and divided it into 10 parts and are identifying what one of those parts is equal to.
An example can help.
What number is ten times as much as 4?
Ask yourself, what is ten groups of 4 equal to? 40. Another way to think of “groups of something” is multiplication. And when you think about it, repeated addition IS multiplication.
Add 4 ten times: 4+4+4+4+4+4+4+4+4+4 = 40.
Isn’t that the same as 10 x 4 or 4 x 10? 10 x 4 means ten groups of 4. And 4 x 10 means four groups of 10. Either way…you get 40!
Another big message you need to take away is that we can use a place value chart to see how many times bigger a number is compared to another number. Take 4 and 40. The 4 in 40 is one place value to the left of 4. When we move a place value to the left, a number is 10 times bigger. Move two place values, it’s 10 x 10 or 100 times bigger. Move three place values to the left, it’s 10 x 10 x 10 or 1,000 times bigger!
The opposite is true for moving to the right on a place value chart. A 4 is one place value to the right of 40 so 4 is 1/10 of 40. Yes, you could say it’s 10 times smaller and be accurate, but let’s try to stick with the 1/10 concept, okay?
Take 300 and 3. 3 is two place values to the right of the 3 in 300. Each place value to the right is 1/10 the value, so 3 is 1/10 x 1/10 of the value or 1/100 the size of 300. Not sure? Check it by multiplying 3 x 100 and see what you get?
Why am I sharing this? Because if you are one of the people who move onto writing your first instructional math film today, you are going to need to use VERY precise language that clearly explains what you’re saying.
I’m modeling how specific I want you to be with your terms. If your writing isn’t as specific as mine, you won’t start making Keynotes, using cameras or teleprompters, or editing your film. Any film is only as good as the writing behind it.
So, first math film challenge is this:
Take three numbers and explain their size relationship to one another. For example, 300, 30, and 3. I know that 300 is 100 times as much as 3 and 10 times as much as 30. I know 30 is 1/10 of 300 and 3 is 1/100 of 300. Those are the answers. Yay. But how do you SHOW this is true?
You could use a place value chart to show that moving to the left means ten or 100 (or whatever factor of 10) times as much as another number and that ten or 100 (or whatever factor of 10) times as much means ten or one hundred (or whatever factor of 10) groups of that something.
You could use a bar model to show how a whole can be decomposed into ten equal groups and that one of those groups represents 1/10 of a whole. If we decompose 300 into ten groups and equally share 300 amongst the groups, we can see that 1/10 of 300 is 30.
You could use pattern blocks to show how a whole can be divided into ten equal groups to show 1/10 of something. Say, 50. If you took 5 longs and exchanged them for 50 small cubes, you could divide those cubes into ten equal groups and get 5 things in each group. Therefore, 5 is 1/10 of 50 or you could say 1/10 of 50 is 5.
You could use pattern blocks to show a number 10 times as much as something else, too. Take 3 small cubes representing the whole number 3. If you make ten groups of three small cubes you have a total of 30 small cubes (or 3 longs) which is 30. Therefore, 30 is ten times as much as 3.
You might have noticed there are words that have been bolded throughout this post. These are vocabulary words you have GOT to know and understand and use in your script.
The first step in filmmaking is a concept. So think about the numbers you want to work with. Show the syntax on paper. Show me the syntax and be ready to explain it. Once you’ve got that, you can get writing. And once you’ve got a first draft, prepare to revise and rewrite it based on feedback you receive from peers (fellow classmates) and myself or Mr. Preston.
When your script is solid, you can start with a Keynote or possibly using a GoPro to show the syntax.
Ready! Set! GO!