What does the equals sign mean?

1. What does the equals sign mean? ========= TRN 01

2. This equals thatthis = 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___ . = TRN 01

3. = Wait Wait!! There’s More!! TRN 01

4. 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 = TRN 01

5. 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… TRN 01

6. 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  TRN 01

7. 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…. TRN 01

8. 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. = TRN 01

9. 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. = TRN 01

10. 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 TRN 01