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

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

- (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.

- 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

- 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