ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] ACC-7 (7) 21 :

21. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem. [Grade 8, 11]

[MA2019] REG-8 (8) 11 :

11. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.

In this video lesson, students recall one way of understanding equivalent expressions, that is, the expressions have the same value for any number substituted for a variable. Then they use properties they have learned to write an equivalent expression using fewer terms. Students informally practice combining like terms, though the language is not yet introduced.

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] ACC-7 (7) 21 :

21. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem. [Grade 8, 11]

[MA2019] REG-8 (8) 11 :

11. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.

In this video lesson, students are working toward gaining fluency in writing equivalent expressions. The goal of this lesson is to highlight a particularly common error: mishandling the subtraction in an expression like 8–3(4+9x). To this end, students first analyze and explain the error in several incorrect ways of rewriting this expression. Then, they consider the effect of inserting parentheses in different places in an expression with four terms.

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] ACC-7 (7) 21 :

21. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem. [Grade 8, 11]

[MA2019] REG-8 (8) 11 :

11. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.

In this video lesson, students have an opportunity to demonstrate fluency in combining like terms. They also look for and make use of structure (MP7) to apply the distributive property in more sophisticated ways.

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] REG-7 (7) 9 :

9. Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, 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.

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.

[MA2019] REG-7 (7) 21 :

21. Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.

In Module 3, Topic B, students use linear equations and inequalities to solve problems. They continue to use bar diagrams from earlier grades where they see fit but will quickly discover that some problems would more reasonably be solved algebraically (as in the case of large numbers). Guiding students to arrive at this realization on their own develops the need for algebra. This algebraic approach builds upon work in Grade 6 with equations (6.EE.B.6, 6.EE.B.7) to now include multi-step equations and inequalities containing rational numbers (7.EE.B.3, 7.EE.B.4). Students solve problems involving consecutive numbers, total cost, age comparisons, distance/rate/time, area and perimeter, and missing angle measures. Solving equations with a variable is all about numbers, and students are challenged with the goal of finding the number that makes the equation true. When given in context, students recognize that a value exists, and it is simply their job to discover what that value is. Even the angles in each diagram have a precise value, which can be checked with a protractor to ensure students that the value they find does indeed create a true number sentence.