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Goal: Exponent rules and rational exponents

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Goal: Exponent rules and rational exponents

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Students should be able to explain how rational exponents relate to roots and radicals. For example, they should understand that x^(1/n) is equivalent to the nth root of x.​

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Develop a guided notes handout that walks students through the relationship between rational exponents and radicals. Include examples showing how x^(1/n) is equivalent to the nth root of x. Have students fill in key information as you explain the concepts.

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Lesson Practice 1A: Card Matching--pairs

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Lesson Practice 1A: Card Matching--pairs

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Create a set of cards with equivalent expressions using rational exponents and radicals. Have students work in pairs to match them. For example, match x^(1/2) with √x, x^(1/3) with ∛x, etc. This activity helps students visualize the equivalence between the two notations.

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Use diagrams or interactive digital tools to visually represent how rational exponents relate to roots. For instance, show how x^(2/3) can be visualized as taking the cube root of x squared.---graphing,

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Have students create a table comparing radical expressions with their equivalent rational exponent forms, helping them see patterns and relationships.

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Students should be able to rewrite quadratic equations so the equation can be solved using square roots.

Students should be able to rewrite quadratic functions so that the vertex is easily identified.

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Goal:  Write inequalities and show solutions on number lines

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Goal:  Write inequalities and show solutions on number lines

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Students should be able to write word sentences as inequalities, determine whether or not a value is a solution of an inequality, graph inequalities, and explain inequalities.

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Students should be able to explain how the equation in slope-intercept form is related to the coordinate plane. The equation, y= mx+b, where m is the slope and b is the y-intercept.

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Students will be able to give examples of linear equations with one solution, infinitely many solutions, and no solution. For example simplify an equation until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers)

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Students should be able to reduce complicated expressions by identifying factoring terms.

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Goal: Multiplying and Dividing Polynomials

Students should be able to multiply and divide polynomials and explain their relations to the system of integers under these operations.

coloring/ maze activities

interactive online games- (the students need to solve polynomial operation problems to be able to move to the next level of the game)

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Different graphs on cards and equations on cards and they have to match the graph with the correct equations.

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Create a bingo game with radical expressions to simplify

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. As you call out simplified forms, students mark off the corresponding unsimplified expressions on their cards. This gamifies the learning process and provides repetitive practice.

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Design a puzzle activity where students match simplified radical expressions to their unsimplified forms

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. As they correctly match pairs, the pieces come together to form a complete puzzle grid. This provides a visual way to reinforce the connections between simplified and unsimplified radicals.

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Cool Desmos activity

https://teacher.desmos.com/activitybuilder/custom/63f51763f720e0a8e00e5341

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resent students with a basic equation like x + 3 = 5. Ask them to:

Modify the equation to create infinite solutions (e.g., x + 3 = x + 3)

Modify the equation to create no solution (e.g., x + 3 = x + 4)

Explain their thought process for each modification

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Equation Crafting: Ask students to create their own linear equations for each solution type.

One Solution: Students create an equation that simplifies to x = a (where a is a specific number).

Infinite Solutions: Students create an equation that simplifies to a = a (where a is any expression).

No Solution: Students create an equation that simplifies to a = b (where a and b are different numbers).

Peer Review: Have students exchange equations and solve them, identifying the solution type.

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Four square method (I am sure it calls diffrently) for students who are visutal or need different ways. Picture is factored one so teach reversed