00-Math 7a-CC2 Ch6

In Section 6.1, students compare expressions to determine whether one is greater than the other by simplifying. To do this, they use algebra tiles on an “Expression Comparison Mat.” They investigate the legal moves of removing zero pairs from one or both sides of the mat and removing or adding balanced (matching) sets of tiles from each side of the mat as they try to simplify expressions without changing the relationship between them.

In Lesson 6.1.3, students will begin to record the expressions they have compared symbolically as inequalities. They learn how to represent solutions to an inequality on a number line and to interpret the meaning of a number line graph in a specific situation. In Section 6.2, students begin working with Equation Mats. Building from their work comparing expressions in Section 6.1, they transition to looking for values that make two expressions equal. Students learn how to write an equation, solve for a variable, and record their solving steps using algebraic notation. Students will also learn to verify their solutions by evaluating equations for a specific value. They will work with equations that have no solutions as well as those that have infinite solutions. While students practice writing and solving equations, they return to their work with the 5‑D Process and begin to write and solve equations that summarize relationships found in word problems. Students construct equations after completing the Describe/Draw and Define steps of the process and possibly one or two trials. They see that solving the equation is another strategy for solving the word problem once the variables have been defined.

In Chapter 6, making sense of problems is your main goal for Mathematical Practices. Students will be using appropriate tools, expression mats with algebra tiles, to focus on comparing algebraic expressions. 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.

7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

a) Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

b) Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.