September Solutions 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