Subtracting: whole - Part = part dividing: whole ÷ Part = part Finding Parts Subtracting: whole - Part = part dividing: whole ÷ Part = part

We’ve already learned : We add or multiply parts together to get a whole. Part + part = whole

Add or multiply 2 cats x 6 pictures = 12 cats. 3 rows of 5 bags of charcoal. Things added have to be the same thing – but you can multiply 2 cats times 6 pictures.

What about the opposite: Ways to find a missing part Subtracting: whole – part = part Or Part + (missing part) = whole We use subtraction to find that answer.

But both ideas are there… at the same time 

But both ideas are there… at the same time 

Subtraction – is it just “taking away?” Early understanding of subtraction is the idea of “taking away.” Take away a part from the whole, and you’ve got a part left. (pictures of something reasonably interesting being “taken away.” Naw, make it follow our little plot. We’re raising money by showing movies in the basement.

“Another taking away” example The Mary Ellen Carter Academy is going to show a movie! “Another taking away” example There were 30 folding chairs in the back of the bike trailer. Marco and Shauna unloaded 20 of them. There were ten left. 30 – 20 = 10 The whole bunch of chairs = 30 The part they unloaded = 20 The chairs left on the trailer = 10 If you have time, add Marco and Shauna to these.

You gotta sit somewhere! Parts and wholes Taking Away” The parts and wholes are still there; it’s just two ways to describe that same amount. 30 chairs in all 20 unloaded; 10 still on the trailer. Same chairs!

Popcorn, popcorn They started the movie with 30 dishes of popcorn. People bought 21 of them. How many did Clara and Mark eat and give to the birds so they wouldn’t go to waste at the end? (Draw this, and make it funny. Think about your characters on the ride in tomorrow.

Is that all there is? - Wait Wait!! There’s More!! 11/12/2018

How much do I need to add to *get to* my whole? In ‘take away’ situations, we start out with the whole thing… take something away… and figure out what we have left. What if we haven’t *gotten* to the whole yet, though… but we do know how big it is supposed to be?

We’re showing a move to make money, to pay for Internet for the year at the Mary Ellen Carter Academy. Want a ticket???

Whole: the 8 tickets that are her goal Part: the 5 she sold Monday We’re showing a move to make money, to pay for Internet for the year at the Mary Ellen Carter Academy. Want a ticket??? Clara wanted to sell 8 tickets to the movie. Monday, she sold 5. How many more did she still have to sell to make her goal? Whole: the 8 tickets that are her goal Part: the 5 she sold Monday Part: the 3 she still has to sell.

Wholes and Parts  You’re trying to find a missing part. The little part. You’re subtracting tickets from tickets, to find out how many *tickets* she still has to sell to reach her goal. (in the subtraction game, it’s same FROM same!) While you’re playing this and recording it, do the laser thing around the “whole” and then around the parts.

Wholes and Parts  When a question asks “what do I need to add?” even though the word “add” is used, since you’re looking for the *part* you’re going to need to subtract from the whole to figure that out!

You’re going to need drinks to go with that popcorn!

How many do I have to add? The Mary Ellen Carter Academy has a 10-gallon cooler to fill with punch to sell at the movies. Mark has poured 3 gallons in already. How much more can he add? What we didn’t tell you: that the Horizons School folks are showing movies that the boys wouldn’t want their parents to know they were watching. Then they decide that’s crossing a line, for some reason or another. If only b/c they don’t want to subject themselves to the nastiness.

How many do I have to add? … even though the word “add” is in the problem, I need to subtract to find my answer. Whole: The 10 gallons that go in the whole cooler. Part: the 3 gallons he’s put in already. Part: the 7 gallons he can add without spilling all over the floor. What we didn’t tell you: that the Horizons School folks are showing movies that the boys wouldn’t want their parents to know they were watching. Then they decide that’s crossing a line, for some reason or another. If only b/c they don’t want to subject themselves to the nastiness. 7 gal. part 10 gal. whole 3 gal. part

If I want to know *how much* to add… “I have 4 spoke cards on my bike. My friend has 10. How many will I have to add to catch up to her?” I need to subtract to find the part between my total and hers.

A third use for subtracting What’s the difference? How much more or less?

What’s the difference? Another kind of problem that we use subtraction to figure out is when we want to know the difference between two things. Carla is 60 inches tall; Gravity is 20 inches tall. How much taller is Carla than her adorable dog? Yea, we need more visuals here.

Subtracting: same to same Even though we’re talking about Carla and a dog, we’re comparing inches to inches. Subtract same from same! 40 60 20

Finding parts by dividing: Dividing: Whole ÷ part = part 12 ÷ 2 = 6 12/2 = 6 2 12 12 2 6

Division means something is “shared equally” – or the same amount is subtracted for a number of times.

Here we’ve got 5 columns of 3 bags of charcoal…

… Or, I can take away charcoal, five bags at a time… 3 times. the parts and the wholes are still in our minds at the same time…

Subtraction or division? Read the problem carefully and imagine what’s happening in it. Subtracting will be: taking things away – but not in equal amounts. Same thing from same thing. comparing two things (“how much smaller? How much more?”) Same thing compared to same thing. Figuring out what you need to add – to get to that whole, *after* you added…. Oh, yea, Subtract Same to Same. Dividing will involve: breaking things into equal-sized groups taking away the same amount, again and again.

Either way… If you know the WHOLE, and one of the PARTS, you can find the other part by SUBTRACTING or DIVIDING.

Subtracting Examples: One more time  : You’re subtracting the same thing from the same kind of thing. Eggs from eggs. Parts of Gravity from parts of Gravity. Pie from Pie.

Dividing Examples 5 rows of broccoli x how many columns of broccoli = 25 broccoli plants? Five… 2 cats x how many pictures = 12 cats. Six… 3 rows of how many bags of charcoal. gets you 15? 5. Dividing is more powerful and abstract than subtracting… but you do *not* have to divide the same thing by the same thing. I have 12 cats divided by 6 pictures; 15 bags of charcoal split into 3 rows of 5; 25 broccoli plants divided into 5 rows x 5 columns.

Division or subtraction? typical subtraction key words typical division key words Difference Minus Decrease Reduce Less than More than Left Dropped Change What do you add? How much more? Quotient Equal pieces Divide Split (evenly) Cut “how many in each...” Per Shared What do you multiply by? How many times? Have them separate *pictures* into those respective categories` Then have them *match* the pictures to the symbols Then tell stories and have them match the stories to the pictures Then, finally, TELL THE STORIES> ALSO ALSO MAKE A CONCEPT CARD WITH A PICTURE OF ADDITION AND A PICTURE OF MULTIPLICATION BOTH CONCRETE AND ON THE NUMBER LINE. Likewise adivision and subtraction