Today we extended our work with rational numbers.
We looked at the method for solving problems using the guess and test method.
Worksheet for Aug29 HWK: Questions 3,7,8,9
Essentially we need to realize that problem solving with rational numbers is the same as any other kind of problem solving. Follow the steps
- Understand the problem
- Find all the crutial numbers and relationships or rules in the problem
- Make a plan
- What approach are you going to take – what can you figure out from what you have
- Carry out the plan
- Try out your plan and make some guesses at what the answer might be, check to see if they work with the rules that were given in the question
- Look Back
- Make sure that all aspects of the problem have been satified.
HELP SECTION:
for those of you who check this blog, I will help you complete one homework question, here’s #3
The number of kilometres in the perimeter of this park is 8 greater than the number of square kilometres in its area. What is the width? Use a calculator to help.
- Understand the problem
- Perimeter (2 x Length + 2 Width) is 8 more than the area (Length x width)
- the length is 6 km
- Make a plan
- Im going to look at the diagram and estimate how big the width is, then find the perimeter, and the area and find the difference between them (subtraction)
- Carry out the plan
- The length looks about three times the width, so if the length is 6, I’m going to try 2 as the width.
- Perimeter = 2l + 2w = 2 x 6 + 2 x 2
- 12 + 4 = 16
- Area = l x w = 6 x 2 = 12
- Perimeter – Area should be 8, 16 – 12 = 4
- The result is too small, so I will try again with a width of 3
- Perimeter = 2l + 2w = 2 x 6 + 2 x 3
- =12 + 6 = 18
- Area = l x w = 6 x 3 = 18
- Perimeter – area should be 8, but 18-18 =0
- So lets try going the other way, width of 1
- Perimeter = 2l + 2w = 2 x 6 + 2 x 1
- =12 +2 = 14
- Area = l x w = 6 x 1 = 6
- Perimeter – Area = 14 – 6 = 8
- Look Back
- We look back to see that the Perimeter of the park (2l + 2w)(2×6+2×1 = 14) – area of the park (l x w) (6×6=6) = 8
- Therefore, the width must be 1km.
good luck on the rest.
DK