Year 2 Lesson Plan 25 - Using Algebra to Solve Geometry and Statistics Problems

  1. (5 min) Mental Math
    1. What is the square root of 25? [5]
    2. What is the square root of 16? [4]
    3. What is the cube root of 27? [3]
    4. What is the square root of 64? [8]
    5. What is the cube root of 64? [4]


  2. (15 minutes) Using algebra to solve geometry and statistics problems.
    Work these 4 problems on the board with the help of the kids:
    Geometry problem:
    The length of a rectangle is equal to twice its width. The perimeter is 138 feet. What are the dimensions?

    Equation:
    x + 2x + x + 2x = 138
    6x = 138

    x = 23 feet
    2x = 46 feet     		Geometry problem:
    The second angle of a triangle is twice the first, and the third is 5 degrees larger than the second. What are the three angles?

    Equation:
    x + 2x + 2x + 5 = 180
    5x + 5 = 180
    5x = 175

    x = 35   2x = 70   2x + 5 = 75
    Statistics problem:
    Here are Alicia's 5 test scores:
    88 90 80 89 91
    For her to get an "A"
    (average 90 or above)
    what should she score on a 6th test?

    Equation: (88 + 90 + 85 + 89 + 91 + X)/6 = 90
    Simplify: (88 + 90 + 85 + 89 + 91 + X) = 90 X 6 = 540
    Simplify: 443 + X = 540
    Simplify: X = 540 - 443 = 97
    She must score a 97 or above to get an "A"!     		Statistics problem: (from the 2013 Math Olympiad!)

    In Mr. Zeda’s class all the quizzes are 10 points. Julio current list of scores is 8, 4, 9, 8, 6.
    He takes the next one and his average doesn’t change. What did he score?

    Equation:
    (8 + 4 + 9 + 8 + 6)/5 = (8 + 4 + 9 + 8 + 6 + X)/6
    Simplify: (35)/5 = (35 + X)/6
    Simplify: 7 = (35 + X)/6
    Simplify: 42 = 35 + X
    X = 42 - 35 = 7
  3. Hand out the in-class exercises
  4. Hand out the homework as they finish the in-class