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September Solutions

Number Theory | Measurement | Geometry |
Patterns, Algebra, and Functions | Data, Statistics, and Probability |
Grab Bag

Remember: These are open-ended problems. There could be other solutions than the ones we are giving.

Number Theory

1. Look to see if there is some kind of logical order to the answer. For example, combinations starting with 7. There are many, many possible answers.

2. If there is no overtime and it is a 40 hour week, then there is no difference. If you can get overtime, then getting paid hourly is better. If you are working less than 40 hours, then the $300 is better. Check to see the reasoning.

3. Watermelons are 8 pounds. Cantaloupes are 4 pounds. 2 watermelons and 1 cantaloupe weigh 20 pounds.

4. During the 9th day. Check reasoning skills.

5. 19 miles


Measurement

6. 5 ways. (1,48), (2,24), (3,16), (4,12), (6,8)

7. Area of the original = 169 inches
Perimeter = 52 inches
New Area = 84.5 inches
The ratio of area to area is 1/2 and the ratio of perimeter is 3 to 4 new to original.

8. (Cheaper carpet is $702.65, other is $939.53.) The savings is $236.88. But, you need to consider how much dirt would show, footprints, warranty. Check for reasons.


Geometry

9. Use string to get the diagonals. Where they meet is the center.

10. Octagons and hexagons. Triangles should touch at one vertex.

11. 888; MOM


Patterns, Algebra, And Functions

12. 77 on the island; 35 left

13. X + (X + 25) + ( X + 50) + (X + 75) =1050
4X + 150 = 1050
4X = 900
X = 225

14. 190


Data, Statistics, And Probability

15. 47 girls; 53 boys = .47 = 47%

16. 4/10 = 8/20 = 12/30 = 16/40 = 20/50 = 24/60
60 - 24 = 36 so there are 24 oak trees

17. Check students' graphs


Grab Bag

18. 37 floors + basement

HOW DID YOU DO?

 

September Problems

Back to Open-Ended Math Index