Lesson plan - Study Island
|Math Lesson: Equivalent Expressions |Grade Level: 6 |
|Lesson Summary: |
|Students review properties of arithmetic operations and then relate concepts of balance to algebraic equations. They apply arithmetic properties to simplify |
|algebraic expressions. Advanced students are challenged to create equations that represent each property. Struggling students reason through simplifying an |
|algebraic expression. |
|Lesson Objectives: |
|The students will know… |
|an expression has infinitely many equivalent expressions. |
|The students will be able to… |
|apply the properties of operations to generate equivalent expressions. |
|identify two expressions are equivalent. |
|simplify expressions. |
|Learning Styles Targeted: |
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| |
|Visual |
| |
|Auditory |
| |
|Kinesthetic/Tactile |
| |
|Pre-Assessment: |
|Write the following equations on the board and then ask students to explain the properties of addition that each represents: |
|3 + 2 = 2 + 3 and 3 × 2 = 2 × 3 (Commutative property) |
|(3 + 2) + 4 = 2 + (3 + 4) and (3 ( 2) × 4 = 2 × (3 × 4) (Associative Property) |
|4(12 + 3) = 4(12) + 4(3) (Distributive Property) |
|3 – 2 = 1 and 2 + 1 = 3 (Inverse Operations of Addition and Subtraction) |
|6 ÷ 2 = 3 and 3 × 2 = 6 (Inverse Operations of Multiplication and Division) |
|3 × 1 = 3 and 3 ÷1 = 3 (Identity Property) |
|3 + 0 = 0 and 3 – 0 = 3 (Zero Property of Addition and Subtraction) |
|3 × 0 = 0 (Zero Property of Multiplication) |
| |
|Leave the properties on the board for reference throughout the activities. |
| |
|Identify students with little awareness of the properties of arithmetic. |
|Whole-Class Instruction |
|Materials Needed: notebook, pens, and pencils |
|Procedure: |
|Presentation |
|Give students 1 minute to conceive of a simple way to demonstrate balance and equality. Then have them demonstrate their creation to the class. It might be to |
|balance a pencil on a narrow rim, or balance on one foot. |
| |
|Then write the equation ab = ba and ask how the equation represents balance and equality. Explain that when the symbol = appears in an equation, both expressions |
|in the equation, if correct, balance because they are equal in value. |
| |
|Refer students to the properties of arithmetic from the Pre-Assessment activity. Explain that those properties are actually algebraic laws that they have been |
|using when they add, subtract, multiply, and divide. Those same properties apply in algebra. |
| |
|Students write the algebraic formulas for each of the properties by substituting the numbers for corresponding variables. Then students dictate the equations to |
|you as you write them on the board next to the arithmetic properties. |
| |
|Explain that these properties help simplify algebraic expressions and solve equations. |
|Write an equation for the commutative property 323 × 72 = 72 × n. Based on the commutative property, what is n? (323) |
|Have students suggest an equation to demonstrate the distributive property |
|such as 360 ÷ 24 = (240 ÷ 24) + (120 ÷ n). Based on the distributive property, what is n? (24) |
| |
|Write the expression 3n + 3n + 3n. Ask how it could be simplified (9n). Confirm that students understand the 3n + 3n + 3n = 9n, that these are equal expressions. |
|Guided Practice |
|Write the following expressions on the board and have students reason through combining terms to simplify each expression. |
|17x + 39x (56x) |
|15x – x – 7x (7x) |
|3x + y + x + y (4x + 2y) |
|5a + 6b – a + b – 4a (7b) |
|(7 – 4)ab (3ab) |
| |
|Confirm that only like terms can be combined and that the coefficients can be combined without affecting the value of the variables. |
|Independent Practice |
|Divide the class into pairs. Give students five minutes to do the independent practice activity. One student writes an algebraic expression (for example, 3x + 5x |
|or 7xy + 3x – 2xy + 9x) and the other student simplifies it. Students take turns writing and simplifying. Remind students they can only combine or simplify like |
|terms. |
| |
|Students in each group present one expression and how it was simplified. Students defend their reasoning. |
|Closing Activity |
|Refer to the Pre-Assessment activity and ask students how the properties of arithmetic are similar to and different from the properties of algebra. |
|Advanced Learner |
|Simplifying Expressions Using Properties |
|Materials Needed: notebook, pens and pencils |
|Procedure: |
|Challenge students to create equations with variables and coefficients that demonstrate each of the properties of algebra covered in the lesson. |
|Review results and allow students to explain their reasoning. |
|Struggling Learner |
|Translate into Symbols |
|Materials Needed: notebook, pens, and pencils |
|Procedure: |
|Pose this expression: 9(2r + 8t) + 4(2r – 8t). |
|Students use the distributive property to decompose it and the associative property of addition to simplify it. [(9x2r + 9x8t) + (4 x2r – 4 × 8t) = (18r + 72t) + |
|(8r – 32t) = 18r + 8r + 72t - 32t = 24r + 40t] |
|Review results and allow students to explain their reasoning. |
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