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Main Curriculum Tie:
Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
Starter: Accessing prior knowledge
Lesson Segment 1: (Accessing prior knowledge) What is the product of any number and 1? What is the sum of any number and 0? How does applying the commutative or associative properties affect the sum or product? How can I demonstrate the use of the distributive property of multiplication over addition?
Team Contest: Use the #1 question on the starter to review properties by asking students to look at property words on the board. Tell them you can compute much faster and easier by using these properties. Have students take out a paper for an assignment activity called “Properties Guess”, and number the paper a-f. As you mentally compute each starter problem, have students quietly discuss with their team and write which property or properties they think you applied. Ask students to respond after they have written the property they think you applied. Any team who correctly identified the property(s) earns a point. You may need correct their thinking as you go over each problem. After discussing an expression, have students write the correct property and how it was applied to simplify each expression on their paper.
Tell students these properties work for addition and multiplication with variables too. If they have their properties foldable from September Lesson 7, they could use it to compare. Make this foldable for properties with variables. Fold both edges toward the center. Clip on the dotted line to the fold to make four shutters. Inside students should write examples of the application of these properties using variables. Work with students to write simple algebraic examples such as:
a + b = b + a
Lesson Segment 2: How do properties help me simplify algebraic
Accessing and building background knowledge:
In our language we often simplify expressions. For example, we could say, “Hi there. How are you doing? Or, we could say, “Hey, Sup?” The meaning is the same, but the second expression is much shorter and simpler than the original expression. In mathematics we want to write expressions as simply as possible, but do not want to change their meaning or value. We want the simplified expression to be equivalent to the original, longer expression.
Ask the following questions and have students record the examples on their Team Contest record paper.
Q. When we say two expressions are equivalent what does that mean? For example when we say 3 + 1 is equivalent to 4 (or 3 + 1 = 4), what does that mean? The equal sign tells us one expression is equivalent to the other or in other words, the expressions have the same value.
Q. If two expressions are equivalent, must they always look exactly the same? What
makes you think so?
Q. How can we know whether two expressions are equivalent if they don’t look alike? One way to verify that two expressions are equivalent, is to simplify each expression.
Example 1: 2 • 6 = 3 • 4
2 • 6 simplified is 12
Example 2: 3(2 • 5) = (3 • 2)5
3(2 • 5) is 3(10) =30
Example 3: 3(5 + 6) = 3 • 5 + 3 • 6
3(11) = 33
Tell students these ideas about equivalency and simplifying apply with variables as well as numbers. We use properties to simplify algebraic expressions. When we simplify an algebraic expression using properties, we can compare the original expression with the simplified expression to make sure they are equivalent. A simplified expression is always equivalent to the original. Students will be simplifying algebraic expressions, and then substituting values in the expressions to verify equivalency.
Work with the class to complete the Simplifying Algebraic Expressions worksheet.
Lesson Segment 3: How can the distributive property be applied to algebraic
Assign text practice as needed.
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