Students will use this lessons in this module to help them build on their experiences with algebraic expressions and one -step equations in 6 grade. The expressions , equations and inequalities encounter will involve a wide range of rational numbers and require two steps rather than one. The students will write equations and inequalities for problem situations, interpret the meaning of the quantities in the problem, create tables of values, graph problem solutions, and make connections across the representations.
Students will have the opportunity to develop an understanding of expressions, equations, and inequalities by thinking creatively as they write and solve each and apply them to real world situations producing solutions and products.
Standards: Mathematics, Grade 7, Expressions & Equations
- MGSE7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- MGSE7.EE.2 Understand that rewriting an expression 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, fractions, 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
- 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, 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