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Lesson Objective: I can… Understand that a letter is an expression or an equation can represent a number. When that number is replaced with a letter, an expression or an equation is stated. Discover that the commutative property of addition and multiplication, the additive property of zero and the multiplicative identify property of one

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4 + 0 = 4 4 x 1 = 4 4 divided by 1 = 4 4 x 0 = 0 1 divided by 4 = ¼ 1. How many of there statements are true? 2. How many of those statements would be try if the number 4 was replaced with the number 7 in each of the number sentences? 3. Would the number sentences be true if we were to replace the number 4 with any other number? 4. What if we replaced the number 4 with the number 0? Would each of the number sentences be true?

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What if we replace the number 4 with the letter g? Please write all 4 expressions from the previous slide by replacing 4 with g. 1. Would all of these be true (except for g = 0) when dividing?

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g + 0 = g *Remember a letter in a mathematical expression represents a number. 1. Can we replace g with any other number? 2. Choose a value for g and replace g with that number in the number sentence. What do you observe? 3. Repeat this process several times, each time choosing a different number for g. 4. Is the number sentence true for all values of g? 5. Write the mathematical language for the property below.

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g x 1 = g *Remember a letter in a mathematical expression represents a number. 1. Can we replace g with any number? 2. Choose a value for g and replace g with that number in the number sentence. What do you observe? 3. Is the number sentence true for all values of g? Experiment with different values before making your claim. 4. Write the mathematical language for this property below.

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3 + 4 = 4 + 3 3 × 4 = 4 × 3 3 + 3 + 3 + 3 = 4 x 3 3/ 4 = ¾ Replace the 3s in these equations with the letter a.

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Choose a value for a and replace a with that number in each of the number sentences. What do you observe? Are the number sentences true for all values of a? Experiment with different values before making your claim. Now write the number sentences again, this time replacing the number 4 with a variable, b. Are the first two number sentences true for all values of a and b? Experiment with different values before making your claim. Write the mathematical language for this property below.

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1. Which of these properties of numbers is the easiest for you to remember? Why? 2. Which of these properties is the hardest for you remember? Why? Evaluate your Learning: 1 2 3 4 How will you “Sharpen your saw?”

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