Solving Story Problems Home Page
Level: Middle School Math (7th Grade)
Objective: The students will apply the correct geomtric formula in a
specific situation.
Objective: The students will solve for a missing quantity in a geometric
figure.
Objective: The students will apply the five step method of solving story
problems to solve a variety of story problems related to geometric figures.
Objective: The students will write their own story problems relating to a
specific situation.
Prerequisite skills:
1) The students have demonstrated the ability to draw geometric figures.
2) The students have demonstrated the ability to substitute values into a
formula.
3) The students have demonstrated the ability to solve an equation for a
variable.
Geometric Formulas
Perimeter (or Circumference) - The distance around a geometric figure.
Area - The amount of space enclosed by a geometric figure.
| Common Geometric Figures | Perimeter | Area |
| Rectangle | P = 2l + 2w | A = lw |
| Square | P = 4s | A = s2 |
| Triangle | A = (1/2)bh | |
| Trapezoid | A = (1/2)(b1 + b2)h | |
| Circle ( Use p = 3.14) | C = 2pr or C = pd | A = pr2 |
Five step method of solving story problems:
1. Read the problem - Figure out what the questions is asking
for. What are you trying to find?
2. Draw a picture - Read the problem again and develop a
picture of it in your mind. Look for word clues to help you decode the problem.
Draw a rough sketch that shows the situation.
3. Put the numbers in your picture - Take the numbers that are
stated in the problem and put those in the correct place on your drawing.
4. Do the calculations - Use a formula, if needed, and solve
for the unkown.
5. State the answer and check the result - Put the correct
units in your answer. Then check to see if your answer makes sense in the problem.
That is, does it answer the questions asked?
Word Clues
Words That May Suggest Addition
| total | sum | combined | together |
| and | how much | how far | how many |
| addtional | more |
Words That May Suggest Subtraction
| remain | exceed | difference | profit |
| change (money) | diminshed | how much more | how much is left |
| take away | reduced |
Words That Suggest Multiplication
| of | times | product | percent |
| each | cubic units | square units | per |
| how many | area | volume | reduced by a fraction |
| so many units at so much per unit | |||
Words That May Suggest Division
| each | average | equal parts | partition |
| shares | pieces | quotient |
Example Problems:
A rectangle is 20 inches long. Its perimeter is 68 inches. Find the width of the rectangle.
Step 1: Read the problem. What are you trying to find? The length and the width of a rectangle.
Step 2: Draw a picture.
|
Length
Width |
Step 3: Put the numbers in your picture. Width - w Length - 20
|
Length 20 Width - w w 20 |
Step 4: Do the calculations:
Using the perimeter formula for a rectangle: P = 2l + 2w
68 = 2(20) + 2(w)
68 = 40 + 2w
28 = 2w
14 = w
Step 5: State the answer and check the result. The width is 14 inches. Check: 14 + 14 + 20 +20 = 68
Your parents are going to retile the kitchen. The floor of your kitchen is 12 feet wide and 15 feet long. Each tile is 1 foot by 1 foot and cost $0.99 each. How much will it cost, without tax, for the tiles for your kitchen floor.
Step 1: Read the problem. What are you trying to find. The cost of the tile for the kitchen floor.
Step 2: Draw a picture.
Step 3: Put the numbers in your picture. Length - 15 width - 12
Step 4: Do the calculations.
A = bh A = 15 x 12 A = 180 ft2 If each tile is one square foot, then we have 180 tiles.
180 tiles x $0.99 per tile = $178.20
Step 5: State the answer and check the result.
$178.20 is the cost of the tile for the kitchen floor.