Parts and Wholes

What does the equals sign mean? =========8/18/2013TRN 011

This equals thatthis = thatLots of folks see an equals sign and figure that thats what comes before the answer to a math problem.

So, the equals sign points at the answer.

1 + 1 + 1 + 1 = __4___ .

=

8/18/2013TRN 012

=Wait Wait!! Theres More!!8/18/2013TRN 013

Its true to a point What the equals sign is *really* doing is separating two ways of saying the same thing.

1 + 1 + 1 + 1

I could have also said 1 + 1 + 1 + 1 2 + 2

=4=

8/18/2013TRN 014

Are the rules changing? No an equals sign can still point at the answer. Theres just more to it than that. Most children learn what a dog is and, for a while, every animal in a yard is a dog. They grow and learn theres more to hairy four-leggedness than dogs. There are horses, cats, cows

8/18/2013TRN 015

(Unless you are like my friend who lives in Alaska, when the animals her kids saw were moose so they called a dog a moose the first time.) 5We need to advance our thinking. Just as we grow from big animals in a yard are dogs to dogs are just one of lots of kinds of animals we can grow from the equals sign points at the answer to the equals sign is between two ways of describing the same value.

Be aware of your old ways of thinking. Grow your brain 8/18/2013TRN 016

6You know this alreadyBack to that dog. You could call it that curly-haired dog. You could call it Gravity, because thats its name. You could call it that stinky but adorable creature! and it would still come to you and lick your face. Different names same things. Gravity = that curly-haired dog That curly-haired dog = that stinky but adorable creatureThat stinky but adorable creature = Gravity.

8/18/2013TRN 017

Which side of the equals sign?Were accustomed to seeing problems like this:

3 + 7 = _____ and filling in 3 + 7 = 10 .

Since were describing **exactly** the same thing, though, it doesnt matter where each expression goes.

=8/18/2013TRN 018

Anywhere you could spend a ten dollar bill, you could spend 3 one dollar bills and seven one dollar bills. They have the same value.

We can write = 3 + 7

The equals sign separates the expressions that have the same value. When were done putting those parts together, theyll have the same value as the whole thing whichever side of the equals sign were working with.

=8/18/2013TRN 019

Practice! Write ten equations of your own that show different ways of describing the value 10.

Examples:

1) 9 + 1 = 10 2) 8 + 2 = 10

3) 10 = 3 + 74) 6 + 4 = 5 + 5

8/18/2013TRN 0110

then matching exercises to match pics and equationsAnd add animation so stuff comes in one line at a timeA thing I want to make: pies and thirds and halfs andyou click on the number line to find them and then it shows you by splitting precisely into one third and two thirds. And you get to do it as many times as you want. Until you get 90% of them right. 10