Solving Equations and Inequalities

By (date), (student) will be able to solve for unknown variables in real-world problem situations by setting up an equation or inequality in the form px + q = r and p(x + q)... = r or px + q > r or px + q < r, where p, q, and r are specific rational numbers. When given 5 problems in writing, (name) will solve 3 problems correctly.
  • By (date), using a problem solving checklist, (student) will be able to solve for unknown variables in real-world problem situations by setting up an equation or inequality in the form px + q = r and p(x + q) = r or px + q > r or px + q < r, where p, q, and r are specific rational numbers. When given 5 problems in writing and a problem solving checklist , the student will solve 3 correctly.
  • By (date), (student) will be able to solve for unknown variables in real-world problem situations by setting up an equation or inequality in the form px + q = r and p(x + q) = r or px + q > r or px + q < r, where p, q, and r are specific rational numbers. When given 5 problems, where all the numbers are whole numbers less than 10, in text and read-aloud , the student will solve 3 correctly using tactile manipulatives such as algebra tiles and a problem solving checklist to complete the problems.
  • By (date), (student) when given 5 algebraic problems in text, verbal or pictorial forms , the student will be able to match the equation or inequality that illustrates the problem situation by selecting the card that shows the correct equation or inequality when given a choice between 2 cards. Student will complete task correctly for 3/5 problems.

UDL Strategies About UDL

  • UDL I 3.3 Guide information processing, visualization, and manipulation
    Instead of just providing the students the equations and asking them to find the value of the variable the teacher can provide a scaffolded problem solving checklist that prompts the student on each step of solving the equation.
  • UDL II 5.1 Use multiple media for communication
    Instead of the student writing out the equation/inequality of the problem, the student can use algebra tiles to illustrate and solve the problem situation algebraically. Instead of students having to perform arithmetic mentally, they can use a calculator to solve steps of the equation.
  • Vary demands and resources to optimize challenge
    If students are discouraged by the difficulty of the task, teachers can differentiate the degree of difficulty of the task so that students develop confidence and are more motivated to complete higher level tasks. For example if students are competent in solving two-step algebraic equations without a problem solving checklist but still like the scaffolded guide, teachers can encourage students to use the checklist for the first two problems and then remove it for the next two.

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Common Core Standards

7.EE.4 Solve real-life and mathematical problems using numerical and algebraic expressions and equations
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. 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? 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.

Standard Staircase

Solving Equations and Inequalities Current Goal

By (date), (student) will be able to solve for unknown variables in real-world problem situations by setting up an equation or inequality in the form px + q = r and p(x + q) = r or px + q > r or px + q < r, where p, q, and r are specific rational numbers. When given 5 problems in writing, (name) will solve 3 problems correctly.

Operations Using Scientific Notation

By (date), when given problems where decimal and scientific notation are used, (name) will use mathematical operations (i.e. addition, subtraction, multiplication, division) and choose correct units to solve (4 out of 5) problems.

Referenced Strategies

  • Math Manipulatives

    Manipulatives are physical objects that aid understanding of mathematical concepts or processes by allowing students to physically demonstra...

  • Read Aloud

    Read Aloud refers to presenting written text in an auditory format. The teacher can read aloud to the class or students can take turns readi...

  • Calculator

    A calculator is a mathematical tool that can perform basic to complex mathematical operations. A simple calculator usually has functions for...

  • Picture Choices

    A type of multiple choice adaptation where the student answers a question or prompt by selecting or sequencing the correct picture(s) (optio...

  • Algebra Tiles

    Algebra tiles are manipulative objects of different colors or shapes that are used to represent integers and variables. They can be used to ...

  • Problem Solving Checklist

    A problem solving checklist is a checklist that can be used by a student and/or class that outlines the steps necessary to complete simple o...