Day 2 first day Objective: I can learn the properties of operations.

Journal Evaluate 6s – 3t if s = 4 and t = -2

Review Evaluate 3m-4 if m = -3

Quiz Evaluate 3(h+2) if h = -4

Notes Our number system has properties … many that you already know and understand.

Notes We know that 1 +5 = 5 + 1. But we don’t have a name for that.

Notes Commutative property: The order that you do the problem doesn’t change the answer.

Notes Let’s try it for multiplication. Choose two numbers we can multiply.

Notes Let’s try it for multiplication. Choose two numbers we can multiply. Now reverse them, do we get the same answer?

Notes Let’s try subtraction. Choose any two numbers.

Notes Let’s try subtraction. Choose any two numbers. Now reverse them, are they commutative?

Notes Finding an example that DOESN’T work is called a “counterexample”. We just found a counterexample that subtraction isn’t commutative.

Notes The commutative property only works for addition and multiplication. It doesn’t work for subtraction and division.

Notes If I have the problem 1+(2+3), what step do I do first? What will my answer be?

Notes If I move the parentheses … (1+2)+3, does that change the answer?

Notes This is the associative property. The way addition and multiplication groups itself, does not change the answer. It doesn’t work for subtraction and division.

Notes Here are some other things we know about math, we just don’t know the names.

Notes Here are some other things we know about math, we just don’t know the names. 9 + 0 = 0+11 = 537+0 =

Notes This is called the “additive identity” property. Whenever we add 0 to something, it equals the other number.

Notes Try these problems. 6 *1 = 1 * 45 = 367 * 1 =

Notes This is called the “multiplicative identity”. Any number multiplied by 1 equals the other number.

Notes Last property: 356 *0 = 0 * 533 = 11 * 0 =

Notes This is called the “multiplicative property of zero” Anything that is multiplied by zero equals zero.

Notes Name the property: 2 *(5*n) = (2*5)*n

Notes 3x +0 = 3x

Notes 42 +x +y = 42 +y + x

Notes Alana wants to buy a sweater that costs $38, sunglasses that cost $14, jeans that cost $22, and shirt that costs $16. Use mental math and the properties to find the sum.

Notes Simplify and justify each step. (7+g) +5

Notes (m*11) *m

Notes 15 +(12 + 8a)

Notes (5n * 9) * 2n