Expressions, Equations and Inequalities
Students will deepen their understandings of relationships between quantities as they write and simplify expressions, equations, and inequalities that represent real world contexts.
Note: Lessons will vary in length, depending on the amount of time you have with students, the resources that you choose to accompany the unit, the level of rigor within each learning target, and any other factors that may contribute to the pacing of your learning progressions. It is recommended that you adjust the pace and length of each learning progression(s) accordingly in response to these factors.
These learning progressions were developed using Next Generation Learning Standards and were crosswalked with the Common Core Standards.
Download the complete Grade 7 Unit 2 framework to customize for your own planning.
Essential Outcomes
- NY-7.EE.1 : dd, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
- NY-7.EE.2: Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related. e.g., a + 0.05a and 1.05a are equivalent expressions meaning that “increase by 5%” is the same as “multiply by 1.05.”
- NY-7.EE.3: Solve multi-step real-world 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. Assess the reasonableness of answers using mental computation and estimation strategies. e.g.,
- 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.
- NY-7.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 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. e.g., The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
- Note: The words leading to in the standard may require students to simplify or combine like terms on the same side of the equation before it is in the form stated in the standard. This standard is a fluency expectation for grade 7. For more guidance, see Fluency in the Glossary of Verbs Associated with the New York State Next Generation Mathematics Learning Standards.
- NY-7.EE.4b: Solve word problems leading to inequalities of the form px + q > r, px + q ≥ r, px + q ≤ r, or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem. e.g., 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.
- Note: The words leading to in the standard may require students to simplify or combine like terms on the same side of the equation before it is in the form stated in the standard.
Essential Questions and Big Ideas
- How do I identify equivalent expressions?
- Expressions with the same variable can be combined or subtracted.
- Coefficients of like terms can be combined or subtracted.
- How can I represent percentages mathematically?
- Percentages can be represented as a decimal to the hundredths.
- A percentage multiplied by a variable represents a percentage of that amount.
- How can I represent areas and perimeters mathematically?
- Side lengths can be represented using variables.
- With a known area or perimeter, a side length can be solved for in an equation.
- How can I solve real world problems using equations/inequalities?
- Constants can be moved to the same side of an equation.
- When a coefficient with a variable is found to equal a constant, the constant can be divided by the coefficient to find the value of the variable.
Download the complete Grade 7 Unit 2 framework to customize for your own planning.