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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 π‘ represent the number of triangles, and let π represent the number of quadrilaterals.

- a. Write an expression, using π‘ and π, 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.

- We need to have 1 person open their envelope to see how many shapes are in there!

- 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 partnerβs 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)?

- a. Rewrite 5π₯ + 3π₯ and 5π₯ β3π₯ by combining like terms.
- Write the original expressions and expand each term using addition. What are the new expressions equivalent to?

- b. Find the sum of 2π₯ + 1 and 5π₯.

- 2x + 1 + 5x = 7x + 1

- c. Find the sum of β3a + 2 and 5a β 3.

- -3a + 2 + 5a β 3 = 2a β 1

- ππβπ = ππ+ππ+ππ = ππ
- πβ (πβπ) Associative property of multiplication (any grouping)
- πβ (πβ π) Commutative property of multiplication (any order)
- ππ 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.

- 3(2π₯)
- 4π¦(5)
- 4 β 2 β π§
- 3(2π₯) + 4π¦(5)
- 3(2π₯) + 4π¦(5) +4 β 2 β π§
- Alexander says that 3π₯ + 4π¦ is equivalent to (3)(4)+ π₯π¦ because of any order, any grouping. Is he correct? Why or why not?

- We found that we can use any order, any grouping of terms in a sum, or of factors in a product. Why?
- Can we use any order, any grouping when subtracting expressions? Explain.
- Why canβt we use any order, any grouping in addition and multiplication at the same time?

- Write an equivalent expression to
2π₯ + 3+ 5π₯ +6 by combining like terms.

- Find the sum of (8π +2π β4) and (3π β 5).
- Write the expression in standard form:
4(2π) + 7(β4π)+ (3 β π β 5)