Unit Plan

  1. Topic of the unit

Linear Equations and Systems (Unit 2)

  1. Grade level

9th Grade (High School)

  1. Name of the two lessons
    1. Equivalent Equations (Lesson 6)
    2. Explaining Steps for Rewriting Equations (Lesson 7)
  2. The New York State content and practice learning standards that need to be met in each lesson.
    1. Equivalent Equations (Lesson 6)
      1. 6.EE.A.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y+y+y and 3y are equivalent because they name the same number regardless of which number y stands for.
      2. HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
      3.  HSA-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
      4.  HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
      5. HSA-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.
    2. Explaining Steps for Rewriting Equations (Lesson 7)
      1. HSA-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.
      2.  HSA-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  3. Identify the Standards for Mathematical Practice to be addressed.
    1. Equivalent Equations (Lesson 6)
      1. HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
      2.  HSA-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
      3.  HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
      4. MP2: Students learned that equivalent equations are equations that have exactly the same solutions.
    2. Explaining Steps for Rewriting Equations (Lesson 7)
      1. HSA-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.
      2.  HSA-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
      3. MP3: Further develop the concept of equivalent equations. Students think about and explain how they know that the equations produced using acceptable transformations are indeed equivalent.
  4. Identify 3-4 learning objectives for the unit that align with the chosen standards.
    1. Students can understand the study of systems of linear equations, their solutions, and their graphical representation.
    2. Students can understand and recognize the graphical representation of a linear equation with two variables as the set of all ordered pairs that satisfy the equation.
    3. Students can understand how to write equations using numbers and variables to describe relationships and constraints.
    4. Students can understand how to use structure or rearrange equations to determine the slope and y-intercept of the graph of a linear equation.
  1. Identify the new vocabulary to be addressed.
    1. Equivalent Equations (Lesson 6)
      1. equivalent equations：Equivalent equations are equations that have the exact same solutions.
    2. Explaining Steps for Rewriting Equations (Lesson 7)
      1. Elimination：Elimination is a method of solving a system of two equations in two variables. A multiple of one equation is added to or subtracted from another to get an equation with only one of the variables. (The other variable is eliminated.)
  2. Present a list of activities (with timing) for each lesson, and questions that you, the teacher, will ask as part of the activities. 

    1. Equivalent Equations (Lesson 6)
      1. Warm-up (5 mins): Two Expressions
        1. “Were you surprised that these expressions have the same result for different values of n?” (No, because using distribution in the n denominator results in the same values, so the other parts with the  may do the same thing.)
        2. “If (or when) you tried using other values of n, what did you find?” (They were the same for all the different kinds of numbers we tried.)
        3. “Do you think that the two expressions will have the same value no matter what value of n is used? How do you know?” (Yes, because the distributive property shows that the numerators are equivalent and so are the denominators.)
      2. Activity (15 mins): Much Ado about Ages
        1. “Consider the equations you wrote for each situation. Are they all equivalent? Why or why not?”
        2. “What do you think it means for two equations to be equivalent?”
      3. Activity (15 mins): What’s Acceptable?
        1. Why do these operations result in equations with the same solutions?
      4. Cool-down (5mins): Box of Beans and Rice
    2. Explaining Steps for Rewriting Equations (Lesson 7)
      1. Warm-up (5 mins): Math Talk: Could It Be Zero?
        1. Give students quiet time to think, and ask them to give a signal when they have an answer and a strategy.
        2. Invite students to share their strategies, and record and display their responses for all to see.
      2. Activity (15 mins): Explaining Acceptable Moves
        1. Explain why certain actions are effective methods for writing equivalent equations?
      3. Activity (15 mins): It Doesn’t Work!
        1. Why do performing acceptable operations on these equations always result in equivalent equations with the same solutions?
      4. Cool-down (5mins): If This, Then That
  3. Design both formal and informal assessments to evaluate whether the learning objectives have been achieved. 
    1. Equivalent Equations (Lesson 6)
      1. A cardboard box, which weighs 0.6 pounds when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6+15b+4=25.6.

In this situation, what does the solution to the equation represent?

  1. Explaining Steps for Rewriting Equations (Lesson 7)
    1. The equation 4(x-2)=100 is a true equation for a particular value of x. Explain why 2(x-2)=50 is also true for the same value of x.
  2. References
    1. https://accessim.org/9-12-aga/algebra-1/unit-2/section-b/lesson-6/preparation?a=teacher
    2. https://accessim.org/9-12-aga/algebra-1/unit-2/section-b/lesson-6?a=teacher
    3. https://accessim.org/9-12-aga/algebra-1/unit-2/section-b/lesson-7/preparation?a=teacher
    4. https://accessim.org/9-12-aga/algebra-1/unit-2/section-b/lesson-7?a=teacher
    5. https://accessim.org/6-8/grade-6/course-guide/standards-reference?a=teacher#6eea4
    6. https://accessim.org/9-12-aga/algebra-1/course-guide/standards-reference?a=teacher#hsa-ceda2
    7. https://accessim.org/9-12-aga/algebra-1/course-guide/standards-reference?a=teacher#hsa-reia
    8. https://accessim.org/9-12-aga/algebra-1/course-guide/standards-reference?a=teacher#hsa-reia1
    9. https://accessim.org/9-12-aga/algebra-1/course-guide/standards-reference?a=teacher#hsa-ssea1
    10. https://accessim.org/9-12-aga/algebra-1/course-guide/standards-reference?a=teacher#hsa-reia