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

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


  2. (5 min) FRACTION REVIEW
    • To add or subtract fractions: get a common denominator and add the numerators.
      Example: 1/2 + 1/4 = 2/4 + 1/4 = 3/4
      Note, by this time kids should be using horizontal bars for fractions so that they can more readily "see" the denominator in order to make it the same and also to cancel if possible. We write simple fractions horizontally in lesson plans because of the limitations of the keyboard.
    • To multiply fractions, multiply the numerators, multiply the denominators. The denominators do not need to be the same.
      Example: 1/2 x 1/4 = 1/8
    • To divide fractions, invert (turn upside down) the denominator, and then multiply.
      Example: 1/2 divided by 1/4 = 1/2 x 4/1 = 2
    • To operate on mixed numbers, always turn them into improper fractions.
    • Look for ways to cancel, and always reduce to lowest terms.


  3. HOW TO SOLVE A PROBLEM
    Ask the class to name three or four ways. Spend a couple of minutes talking about the following ways:
    • Draw a picture
    • Guess and check
    • Make a table or a list (one of my favorite)
    • Find a formula
    • Look for patterns
    • Try a simpler problem--use simpler numbers or smaller numbers

  4. USING ALGEBRA TO SOLVE A GEOMETRY PROBLEM (10 minutes)
    Remember:
    • The perimeter of a rectangle equals two widths plus two lengths:
      perimeter = 2W + 2L
    • A square has four equal sides: perimeter = 4 x S
    • Area of a rectangle is length times width: area = L x W
    • Sum of three angles in any triangle is 180 degrees: A + B + C = 180

    Ask the class to figure the following: The length of a rectangle is equal to twice its width. The perimeter is 138 feet. What are the dimensions? Demonstrate with a picture and algebra:


    x + 2x + x + 2x = 138
    6x = 138

    x = 23 feet
    2x = 46 feet

    Explain that you have to substitute x into the second formula (2x) to get the longer side.


    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?

    x + 2x + 2x + 5 = 180
    5x + 5 = 180
    5x = 175

    x = 35
    2x = 70
    2x + 5 = 75