## Intermediate Math 1 - Expressions and Equations

## 1- Expressions and Equations 2- Geometry 3- Number Systems

4- Ratios and Proportions 5- Statistics and Probability

## Use properties of operations to generate equivalent expressions

7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. |
7.EE.1
I can apply properties of
operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients. |

7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” |
7.EE.2 I can understand that rewriting an expression in different forms in a contextual situation can shed light on the problem and how the quantities in it are related.For example: a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” |

## Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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.3.a I can solve multi-step contextual situations posed with positive and negative rational numbers in any form. (whole numbers, fractions, and decimals)7.EE.3.b I can convert between numerical 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.For example: 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?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. |
7.EE.4.a.1 I can develop and solve simple equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers, for contextual situations7.EE.4.a.2 I can solve a contextual situation numerically or by solving an equation and compare the processes involved in each case.For example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Numerically: 54 - 6 – 6 = 42, 42/2 = 21 so the width is 21 cm. Algebraically: 2(6) + 2w = 54, 2w = 42, w = 21 so the width is 21 cm. Compare and discuss the steps in each process. 7.EE.4.b.1 I can develop and solve simple inequalities of the form px + q > r and px + q < r, where p, q, and r are specific rational numbers, for contextual situations.7.EE.4.b.2 I can graph the solution set of an 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, solve and graph the inequality, and describe the solutions. |