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The attached document is three entire units using algebra tiles to simplify algebraic expressions, solve equations, and factor polynomials.

The simplifying expressions unit begins by having students practice just representing expressions using algebra tiles and works through simplifying expressions including distributive property. It is paced to help students understand all the steps needed to simplify even the most difficult expressions. Each part includes a set of problems designed for students to work on in groups and then a practice worksheet that forces students to practice with algebra tiles.

The solving equations unit works through each type of equation making sure students have plenty of practice with two-step equations, variables on both sides, and multi-step equations. Each part includes a set of problems designed for students to work on in groups and then a practice worksheet that forces students to practice with algebra tiles.

Throughout the factoring polynomials unit, students will see the patterns and start to formulate a rule for factoring without using the model. This unit includes notes that specifically explain the rules while making clear connections to the concrete models. Each part includes a set of problems designed for students to work on in groups and then a practice worksheet that forces students to practice with algebra tiles.

Detailed answer keys are provided that show what is expected of the students. By using manipulatives and concrete examples, students excel at understanding these concepts. Here is the list of the progression of parts in each unit:

Algebra Tiles: Simplifying Expressions

Part 1: Writing and Simplifying Expressions (all positives)

Part 2: Writing Polynomials (with negatives)

Part 3: Simplifying Polynomials (with negatives)

Part 4: Simplifying Practice (this is just a practice worksheet)

Part 5: Distributive Property Day 1 (no negatives)

Part 6: Distributive Property Day 2 (with negatives)

Part 7: Distributive Property Practice (this is just a practice worksheet)

Part 8: Simplify Expressions and the Distributive Property

Part 9: Practice Problems (this is just a practice worksheet)

Part 10: Justify, Oops, Simplify (Higher Level Practice)

Algebra Tiles: Solving Equations

Intro: Scales Problems

Part 1: Solving Two-Step Equations

Part 2: Solving Two-Step Equations with Negatives

Part 3: Practicing Solving Two-Step Equations (this is just a practice work sheet)

Part 4: Variables on Both Sides (all positives)

Part 5: Variables on Both Sides (with negatives)

Part 6: Variables on Both Sides Practice (this is just a practice worksheet)

Part 7: Multi-Step Equations

Part 8: Solving Equations Practice (this is just a practice worksheet)

Algebra Tiles: Factoring

Part 1: Area Modeling

Part 2: Connecting to Equations

Part 3: Multiplying Binomials

Part 4: Dividing Polynomials

Part 5: Multiplying and Dividing Polynomials

Part 6: Factoring Trinomials

Part 7: Factoring Practice (this is just a practice worksheet)

Part 8: Factoring (Mixing Positives and Negatives)

Part 9: More Factoring Practice (this is just a practice worksheet)

Part 10: Notes on Factoring

Part 11: Review (this is just a practice worksheet)

The simplifying expressions unit begins by having students practice just representing expressions using algebra tiles and works through simplifying expressions including distributive property. It is paced to help students understand all the steps needed to simplify even the most difficult expressions. Each part includes a set of problems designed for students to work on in groups and then a practice worksheet that forces students to practice with algebra tiles.

The solving equations unit works through each type of equation making sure students have plenty of practice with two-step equations, variables on both sides, and multi-step equations. Each part includes a set of problems designed for students to work on in groups and then a practice worksheet that forces students to practice with algebra tiles.

Throughout the factoring polynomials unit, students will see the patterns and start to formulate a rule for factoring without using the model. This unit includes notes that specifically explain the rules while making clear connections to the concrete models. Each part includes a set of problems designed for students to work on in groups and then a practice worksheet that forces students to practice with algebra tiles.

Detailed answer keys are provided that show what is expected of the students. By using manipulatives and concrete examples, students excel at understanding these concepts. Here is the list of the progression of parts in each unit:

Algebra Tiles: Simplifying Expressions

Part 1: Writing and Simplifying Expressions (all positives)

Part 2: Writing Polynomials (with negatives)

Part 3: Simplifying Polynomials (with negatives)

Part 4: Simplifying Practice (this is just a practice worksheet)

Part 5: Distributive Property Day 1 (no negatives)

Part 6: Distributive Property Day 2 (with negatives)

Part 7: Distributive Property Practice (this is just a practice worksheet)

Part 8: Simplify Expressions and the Distributive Property

Part 9: Practice Problems (this is just a practice worksheet)

Part 10: Justify, Oops, Simplify (Higher Level Practice)

Algebra Tiles: Solving Equations

Intro: Scales Problems

Part 1: Solving Two-Step Equations

Part 2: Solving Two-Step Equations with Negatives

Part 3: Practicing Solving Two-Step Equations (this is just a practice work sheet)

Part 4: Variables on Both Sides (all positives)

Part 5: Variables on Both Sides (with negatives)

Part 6: Variables on Both Sides Practice (this is just a practice worksheet)

Part 7: Multi-Step Equations

Part 8: Solving Equations Practice (this is just a practice worksheet)

Algebra Tiles: Factoring

Part 1: Area Modeling

Part 2: Connecting to Equations

Part 3: Multiplying Binomials

Part 4: Dividing Polynomials

Part 5: Multiplying and Dividing Polynomials

Part 6: Factoring Trinomials

Part 7: Factoring Practice (this is just a practice worksheet)

Part 8: Factoring (Mixing Positives and Negatives)

Part 9: More Factoring Practice (this is just a practice worksheet)

Part 10: Notes on Factoring

Part 11: Review (this is just a practice worksheet)

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