In level 3 of Hands-On Algebra, students continue their journey through basic algebraic concepts. 
This program involves the manipulation of pawns (kind of like chess pieces) and numbered cubes in order to set up equations on a balance. They use "legal moves" such as removing a pawn from each side, removing a zero in the form of a positive and negative pawn, and subtracting the same number from both sides of the equation to learn the rules of solving equations. Students also learn to translate word problems into a physical set up and solve them using the materials from the kit. Here's a breakdown of the lessons:
Lesson 1:  students gain familiarity with adding and subtracting positive and negative numbers using the colored cubes from their kit.
Lesson 2: Students solve simple algebraic equations involving negative numbers.
Lesson 3: Students solve algebraic equations that involve adding a zero in the form of opposite integers in order to set up equations involving the subtraction of whole numbers.
Lesson 4:  students are presented with equations that contain both positive and negative numbers, and 1 type of pawn on both sides of the equation.  They learn to  isolate X and solve as they have in the past. 
Lesson 5:  We extend the concept from lesson 4, and solve equations with both positive and negative integers and positive and negative Xs. 
Lesson 6: Review lessons 1-5 and learn to write equations for solving word problems that require the use of the level 3 skills learned so far. 
Lesson 7: Students solve equations containing multiples of parenthetical expressions involving negative numbers.
Lesson 8:  Students solve equations involving the subtraction of a multiple of a parenthetical expressions.
Lesson 9: Students transition to using the standard notation of negative x as (-x). Up to this point, the negative x has been represented by an x with a horizontal line, similar to an *.
Lesson 10: The concrete experiences of level 3 are transferred to a pictorial system using only pencil and paper. 
Lessons 11 and 12: These lessons are comprehensive reviews of all lessons in levels 1, 2, and 3, with an emphasis on more complex word problems.