Generating equivalent expressions
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Generating Equivalent Expressions. Each envelope contains a number of triangles and a number of quadrilaterals. For this exercise, let 𝑑 represent the number of triangles, and let π‘ž represent the number of quadrilaterals. .

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Each envelope contains a number of triangles and a number of quadrilaterals. For this exercise, let 𝑑 represent the number of triangles, and let π‘ž represent the number of quadrilaterals.

  • a. Write an expression, using 𝑑 and π‘ž, that represents the total number of sides in your envelope. Explain what the terms in your expression represent.

  • b. You and your partner have the same number of triangles and quadrilaterals in your envelopes. Write an expression that represents the total number of sides that you and your partner have. If possible, write more than one expression to represent this total.

  • c. Each envelope in the class contains the same number of triangles and quadrilaterals. Write an expression that represents the total number of sides in the room.



  • d. Determine the number of sides that should be contained in your envelope if each envelope has 4 triangles and 2 quadrilaterals. NO COUNTING!

  • e. Determine the number of sides that should be contained in your envelope and your partner’s envelope combined.

  • f. Determine the number of sides that should be contained in all of the envelopes combined.

  • g. What do you notice about the various expressions in parts (e) and (f)?







Find the product of 2 and 3
Find the product of 2π‘₯ and 3. equivalent

  • πŸπ’™βˆ™πŸ‘ = πŸπ’™+πŸπ’™+πŸπ’™ = πŸ”π’™

  • πŸβˆ™ (π’™βˆ™πŸ‘) Associative property of multiplication (any grouping)

  • πŸβˆ™ (πŸ‘βˆ™ 𝒙) Commutative property of multiplication (any order)

  • πŸ”π’™ Multiplication

  • If a product of factors is being multiplied, the any order, any grouping property allows us to multiply those factors in any order by grouping them together in any way.


Simplify
Simplify equivalent

  • 3(2π‘₯)

  • 4𝑦(5)

  • 4 βˆ™ 2 βˆ™ 𝑧

  • 3(2π‘₯) + 4𝑦(5)

  • 3(2π‘₯) + 4𝑦(5) +4 βˆ™ 2 βˆ™ 𝑧

  • Alexander says that 3π‘₯ + 4𝑦 is equivalent to (3)(4)+ π‘₯𝑦 because of any order, any grouping. Is he correct? Why or why not?



  • Write an equivalent expression to a sum, or of factors in a product. Why?

    2π‘₯ + 3+ 5π‘₯ +6 by combining like terms.

  • Find the sum of (8π‘Ž +2𝑏 βˆ’4) and (3𝑏 βˆ’ 5).

  • Write the expression in standard form:

    4(2π‘Ž) + 7(βˆ’4𝑏)+ (3 βˆ™ 𝑐 βˆ™ 5)


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