Lesson plan - Study Island



|Math Lesson: Simplifying Expressions |Grade Level: 7 |

|Lesson Summary: |

|Students review properties of arithmetic operations, and then relate concepts to simplifying expressions with integers, rational numbers, and variables. Students |

|simplify a number of expressions as a class, and then students take turns writing simple expressions for partners to simplify. Advanced students are challenged to |

|create equations with rational numbers that represent each of the properties. Struggling students create examples of each property using integers. |

|Lesson Objectives: |

|The students will know… |

|that the properties of operations can be used as strategies to simplify expressions. |

|The students will be able to… |

|apply the properties of operations to simplify expressions. |

|simplify expressions with fractions, decimals, integers, and variables. |

|Learning Styles Targeted: |

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|Visual |

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|Auditory |

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|Kinesthetic/Tactile |

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|Pre-Assessment: |

|Write the following equations on the board, and then ask students to explain the properties that each represents: |

|3 + 2 = 2 + 3 and 3 × 2 = 2 × 3 [Commutative property: the order in which two numbers are added or multiplied does not matter.] |

|(3 + 2) + 4 = 3 + (2 + 4) and (3 × 2) × 4 = 3 × (2 × 4) [Associative property: when three or more numbers are added or multiplied, the answer is the same |

|regardless of the grouping of the factors.] |

|(12 ÷ 4) = (8 ÷ 4) + (4 ÷ 4) [Distributive property over addition: the factors in addition, subtraction, multiplication, and division can be decomposed and |

|operated on individually and then added together.] |

|3 – 2 = 1 and 2 + 1 = 3 and 6 ÷ 2 = 3 and 3 × 2 = 6 [Inverse operations of addition and subtraction and multiplication and division] |

|3 × 1 = 3 and 3 ÷ 1 = 3 [Identity property: any number multiplied or divided by 1 is itself.] |

|3 + 0 = 0 and 3 – 0 = 3 [Zero property of addition and subtraction/Identity property of addition] |

|3 × 0 = 0 [Zero property of multiplication] |

|Leave the equations on the board for use in the following activities. |

|Note students who appear to have little awareness of the properties of arithmetic. |

|Whole-Class Instruction |

|Materials Needed: None |

|Procedure: |

|Presentation |

|Henry David Thoreau, a famous writer and philosopher of the 19th century, said, “Our life is frittered away by detail. Simplify. Simplify.” To simplify an |

|expression or an equation in mathematics, you need to eliminate the detail by combining, calculating, and reducing so that it is easier to solve. The properties of|

|arithmetic and algebra help do that. |

|Ask students about a time they had to clean up a big mess. How did they go about it? [By organizing, sorting, and combining.] |

|Write this expression on the board (6 × 2) + 5 + (3 × 2) + 2. Have students devise their own methods to simplify the expression. Discuss how students simplified |

|the expression and record different approaches on the board. |

|Some may have multiplied 9 × 2 and added 7 because the distributive property allows the combination of numbers for multiplication. The associative property allows |

|the addition of numbers in any order. |

|Some may have multiplied 6 × 2 and added 5 to equal 17 and then calculated 6 + 2. |

|Consider how each of the following strategies could be used to simplify an expression. |

|Rewrite the expression so like terms are grouped together. For example, 3x + 5y + 2x – 6y can be rearranged to form the expression 3x + 2x + 5y – 6y using the |

|commutative property. |

|Simplify the expression by adding/subtracting the coefficients (numbers partnered with variables) of like terms. So, the expression 3x + 2x + 5y – 6y can be |

|simplified to |

|(3 + 2)x + (5 – 6)y = 5x + (-y) = 5x – y. |

|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 even when there are variables. |

|Now write this expression on the board, and ask students to use the distributive property to simplify it: 5(x + 14) [5x + 70]. Explain that x can represent any |

|number because it is a variable. |

|Next write each expression and work together to simplify them, asking students to explain their reasoning and identifying the fraction bar as the division sign and|

|using the order of operations correctly. |

|[pic] [pic] |

|x(5 + 3) [8x] |

|(17 × 18) + (3 × 18) [360] |

|3.3 + 3(6)(5 - 1) - 2 [73.3] |

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|Guided Practice |

|Write the following expressions on the board and have students reason through combining terms to simplify each expression. |

|1.7x + (39x)(5.6) [220.1x] |

|[pic] [pic] |

|[pic] [pic] |

|[pic] [pic] |

|[pic] [pic] |

|Confirm that only like terms can be combined, and the coefficients can be combined without affecting the value of the variables. |

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|Independent Practice |

|Divide the class into pairs. Give students five minutes to take turns in which one person writes an algebraic expression that includes rational numbers (for |

|example, [pic] or |

|[pic]) and the other person simplifies it. Remind students to only combine or simplify like terms. |

|Have students in each group present one expression and how it was simplified and have them defend their reasoning. |

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|Closing Activity |

|Refer back to the Pre-Assessment activity, and ask students how they used the properties of arithmetic to simplify the expressions. |

|Advanced Learner |

|Simplifying Expressions Using Properties |

|Materials: None |

|Procedure: |

|Challenge students to create equations with rational numbers, variables, and coefficients that demonstrate each of the properties of algebra covered in the lesson.|

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|Review results and have students explain their reasoning. |

|Struggling Learner |

|Translate into Symbols |

|Materials: None |

|Procedure: |

|Have students create an example of each of the properties using integers, and then compare their results and explain their reasoning. |

*see supplemental resources

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