About This Chapter
Standard: 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. (CCSS.MATH.CONTENT.7.EE.B.3)
Standard: 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. (CCSS.MATH.CONTENT.7.EE.B.4)
Standard: 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? (CCSS.MATH.CONTENT.7.EE.B.4.A)
Standard: 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. (CCSS.MATH.CONTENT.7.EE.B.4.B)
About This Chapter
Students who have mastered the Common Core standards for algebraic equations will be able to solve mathematical and real-world problems using both numerical and algebraic equations and expressions. They will also be able to work with rational numbers in various forms to construct and solve equations and word problems using variables. The lessons in this collection can be used to help students learn about the following:
- Inverse operations
- Solving rational equations
- Writing and solving problems with one variable using addition, subtraction, multiplication and division
- Translating math sentences to inequalities
- Solving linear inequalities with one step
- Graphing inequalities
You'll be able to tell when your students have mastered these standards when they are able to write, solve and graph simple equations and inequalities using variables to represent quantities.
How to Use These Lessons in Your Classroom
Here are some suggestions you can use to help implement the tools in this collection into your curriculum.
Use Video Lessons and Quizzes to Supplement Homework
Have students watch the video lessons before completing their regular homework assignments. This quick refresher can help to remind students of the concepts they've learned that day in class.
Create Word Problems
Watch the lessons on writing and solving word problems with one variable. Ask each student to write a word problem using one unknown variable. Collect and shuffle the problems, then pass them back and ask students to solve them.
Work Together to Answer Practice Questions
Divide students into small groups and have them work together to solve the problems in the practice quizzes. Have students share their answers and any questions that arise with the class after the exercise.
1. Inverse Operations in Math: Definition & Examples
In mathematics, inverse operations are operations that 'undo' each other. Most operations have an inverse. This lesson describes the most common operations and their inverses, and it provides some examples and a quiz to cement your knowledge.
2. How to Solve a Rational Equation
A rational equation is one that contains fractions. Yes, we will be finding a common denominator that has 'x's. But no worries! Together we will use a process that will help us solve rational equations every time!
3. Writing & Solving Addition Word Problems with One Variable
After watching this video lesson, you will be able to write and solve addition word problems. Learn how to read your word problem, write out the algebraic equation, and then solve it for the unknown variable.
4. Writing & Solving Subtraction Word Problems with One Variable
You will be able to solve subtraction word problems after watching this video lesson. Learn how to take your word problem from words into an algebraic expression that you can solve.
5. Writing & Solving Multiplication Word Problems with One Variable
After watching this video lesson, you should be able to take a multiplication word problem and translate it into an algebraic expression that you can solve. You will also learn how to solve these problems from the expressions that you write.
6. Writing & Solving Division Word Problems with One Variable
After watching this video lesson, you should be able to solve word problems that involve the division operator. Learn how to write your math problem using an algebraic expression and then solve it.
7. Translating Math Sentences to Inequalities
Watch this video lesson to learn how you can easily translate math sentences into inequalities. Once you know how to do this, solving word problems becomes that much easier.
8. Solving One-Step Linear Inequalities
In this video lesson, you will learn how you can solve any kind of linear inequality that only requires one step. Learn when you need to subtract, when you need to add, when you need to multiply, and when you need to divide.
9. Graphing Inequalities: Practice Problems
If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.
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Other chapters within the Common Core Math Grade 7 - Expressions & Equations: Standards course