Instead of giving a sample lesson, here are some examples of scenarios and appropriate versus inappropriate responses.

John says that the factors of (x-4)(x+8) are -4 and 8.

Incorrect: “John, does -4-4=0? No, then you did something wrong?”

Correct: “John, what steps did you take to get there? ... Instead, let’s take the

opposite of -4 and see what we get.”

Sally says that on a right triangle with given sides 6 and 8, the third side is 100.

Incorrect: “Sally, you’re not finished. You forgot to take the square root of 100.”

Correct: “What formula did you use to solve this, Sally? Let’s try it as a class.”

Michael says that x+x equals x².

Incorrect: “That’s a tricky one. What did you do wrong, Michael?”

Correct: “That’s incorrect. Let’s try it together Michael, and remember what we do

when we add like terms.”

Jessica says that the natural log of

Incorrect: “That’s wrong. Jessica, why is it wrong?"

Correct: “That’s not quite right. Let’s try that again together.”

Cooper says that 7% written as a decimal is .7.

Incorrect: “Now Cooper, we remember that we have to move the decimal two

places.”

Correct: “Cooper, when we convert percentages to decimals, what process to we

take?”

John says that the factors of (x-4)(x+8) are 4 and -8.

Incorrect: “John, that is correct! I’m so happy you got that because that was a

tricky question.”

Correct: “Good job, John.”

Sally says that on a right triangle with given sides 6 and 8, the third side is 10.

Incorrect: “That’s awesome, Sally!!”

Correct: “Good, Sally, and can you tell us how you got that?”

Michael says that x+x equals 2x.

Incorrect: “Next question: who can tell me what 3x+5x equals?”

Correct: “Good, Michael. Now can someone tell me what 3x+5x equals?”

Jessica says that the natural log of

Incorrect: “That’s awesome, Jessica! I’m so proud you got one right.”

Correct: “Excellent answer, Jessica. How did you get that without putting it in the

calculator?”

Cooper says that 7% written as a decimal is .07.

Incorrect: “Wow, that’s impressive Cooper!”

Correct: “Good Cooper, now can you do the next one?”

John says that the factors of (x-4)(x+8) are -4 and 8.

Incorrect: “John, does -4-4=0? No, then you did something wrong?”

Correct: “John, what steps did you take to get there? ... Instead, let’s take the

opposite of -4 and see what we get.”

Sally says that on a right triangle with given sides 6 and 8, the third side is 100.

Incorrect: “Sally, you’re not finished. You forgot to take the square root of 100.”

Correct: “What formula did you use to solve this, Sally? Let’s try it as a class.”

Michael says that x+x equals x².

Incorrect: “That’s a tricky one. What did you do wrong, Michael?”

Correct: “That’s incorrect. Let’s try it together Michael, and remember what we do

when we add like terms.”

Jessica says that the natural log of

*e*is 0.Incorrect: “That’s wrong. Jessica, why is it wrong?"

Correct: “That’s not quite right. Let’s try that again together.”

Cooper says that 7% written as a decimal is .7.

Incorrect: “Now Cooper, we remember that we have to move the decimal two

places.”

Correct: “Cooper, when we convert percentages to decimals, what process to we

take?”

John says that the factors of (x-4)(x+8) are 4 and -8.

Incorrect: “John, that is correct! I’m so happy you got that because that was a

tricky question.”

Correct: “Good job, John.”

Sally says that on a right triangle with given sides 6 and 8, the third side is 10.

Incorrect: “That’s awesome, Sally!!”

Correct: “Good, Sally, and can you tell us how you got that?”

Michael says that x+x equals 2x.

Incorrect: “Next question: who can tell me what 3x+5x equals?”

Correct: “Good, Michael. Now can someone tell me what 3x+5x equals?”

Jessica says that the natural log of

*e*is 1.Incorrect: “That’s awesome, Jessica! I’m so proud you got one right.”

Correct: “Excellent answer, Jessica. How did you get that without putting it in the

calculator?”

Cooper says that 7% written as a decimal is .07.

Incorrect: “Wow, that’s impressive Cooper!”

Correct: “Good Cooper, now can you do the next one?”