What does the equals sign mean? ========= 11/12/2018 TRN 01

This equals that this = that Lots of folks see an equals sign and figure that that’s what comes before the answer to a math problem. So, the equals sign “points at the answer.” 1 + 1 + 1 + 1 = __4___ . = 11/12/2018 TRN 01

= Wait Wait!! There’s More!! 11/12/2018 TRN 01

It’s 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 = 11/12/2018 TRN 01

Are the rules changing? No… an equals sign can still point at the answer. There’s 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… there’s more to hairy four-leggedness than dogs. There are horses, cats, cows… (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.) 11/12/2018 TRN 01

We 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  11/12/2018 TRN 01

You know this already… Back to that dog. You could call it “that curly-haired dog.” You could call it “Gravity,” because that’s 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 creature That stinky but adorable creature = Gravity…. 11/12/2018 TRN 01

Which side of the equals sign? We’re accustomed to seeing problems like this: 3 + 7 = _____ and filling in 3 + 7 = 10 . Since we’re describing **exactly** the same thing, though, it doesn’t matter where each expression goes. = 11/12/2018 TRN 01

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 we’re done putting those parts together, they’ll have the same value as the whole thing… whichever side of the equals sign we’re working with. = 11/12/2018 TRN 01

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 + 7 4) 6 + 4 = 5 + 5 then matching exercises to match pics and equations… And add animation so stuff comes in one line at a time A 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. 11/12/2018 TRN 01