05-Math 7a-CC3 Ch2

This chapter lays a solid foundation for solving equations. A heavy emphasis is placed on using algebra tiles daily throughout Section 2.1 (see the “Required Materials” notes below) so that all students can access abstract understanding through the use of concrete manipulatives.

Students’ work with an expression mat, like the one shown at right, will help them gain a deeper understanding of “minus” and will address common errors that occur with simplifying expressions such as 2x − (3 − x).

Special care must be taken so that students will take full advantage of the algebra tiles. Your attitude will be critical in this regard. The tiles in this course afford students an opportunity to “see” abstract algebraic expressions and equations in two variables. They will be used throughout the course. They are certainly not mere toys or a diversion; rather, they will greatly enhance the learning of algebra for the majority of your students. Even if you are hesitant to use them, present them to the students in a positive manner.

Here are concrete steps to take so your students want to work with algebra tiles and do not resist using them:

• Make the problems more challenging. If students see the problems as something they can easily do in their heads, then it is understandable that they would not want to use the tiles. Therefore, do not hesitate to create new problems for your students that present the challenge that they need.
• From the beginning of the course, regularly praise students for being able to solve challenging problems. Most students who have more traditional math learning experiences are used to being exposed to simple questions before being exposed to more difficult challenges. With tiles, students are able to tackle challenging problems early on. Praising them for being able to simplify expressions like 3y + 2 + 2xy + 4x + y² + 4y + 1 on the first day will make them eager to tackle other challenging problems and to embrace the tool that helps them solve such difficult problems.
• Have students come up and use the display tiles at the board regularly. Many students will enjoy this opportunity and will appreciate having time to learn how to use the tiles when they are in front of the class.

In Chapter 2, students will be using appropriate tools, Expression Mats, Expression Comparison Mats, and Equation Mats, with algebra tiles, to focus on comparing algebraic expressions and solving equations. Throughout the chapter, it is recommended that you focus very clearly on the skills of abstract and quantitative reasoning, construction of viable arguments and critiquing of others’ reasoning, and attention to precision, both in student communication with others and their use of tools.

EE.7 Solve linear equations in one variable.

a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.