Unit 2 - Expressions and Equations

This unit builds on what students learned in 6th grade regarding mathematical properties. They will continue to build on their knowledge of the order of operations and other mathematical properties, and use these properties of operations to rewrite equivalent numerical expressions. The students should continue to use properties that were used with whole numbers in Grade 6 and understand that these properties apply to integers, rational and real numbers as well. Students will also have the opportunity to write expressions and equations in more than one format and understand that they are still equal. They will be given the opportunity to use variables to represent quantities in real-world problems.

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**MGSE7.EE.1** Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

**MGSE7.EE.2** Understand tat rewriting an expression in different forms in a problem context can clarify the problem in different forms in a problem context can clarify the problem and how the quantities in it are related. *For example, a + 0.05a = 1.05a means that adding a 5% tax to a total is the same as multiplying the total by 1.05.*

**MGSE7.EE.3** Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, factions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing 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 and hour, or $2.50, for a new salary of $27.50.*

**MGSE7.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.

**MGSE7.EE.4a** 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?*

**MGSE7.EE.4b** Solve word problems leading to inequalities of the form px = q > r or px + q< r, where p, q, 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 a t least $100. Write an inequality fo the number of sales you need to make, and describe the solutions.*

**MGSE.EE.4c** Solve real-world and mathematical problems by writing and solving equations of the form x+p=q and px=q in which p and q are rational numbers.