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Shapeshifting Topic Mad  Science Topic Justice Topic Health Decisions Topic Personal Finance Topic Business Decisions

Math OER
 Turn In Problems 
 Health Decisions — Patterns 

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1. Triangular tables are placed in a row to seat more people. One table has 3 seats. Two tables have 4 seats. Create a formula where we put in the number of tables (as n) and get out the number of seats (as y).

y = n + 1 y = n + 2 y = 2n + 1 y = 2n + 2 y = n × 2

2. Now we switch to square tables. We still make a row of tables to seat more people. One table has 4 seats. Two tables have 6 seats. Create a formula where we put in the number of tables (as n) and get out the number of seats (as y).

y = n + 3 y = 2n + 1 y = 2n + 2 y = (n + 1)2 y = 3n + 1

3. This shape is sort of like a V or W that gets wider with more wiggles. What is the pattern for how many squares are in each row?

y = n + 2 y = 2n + 1 y = 2n + 2 y = n × 3 y = n2

4. How about this extra-wide plus shape? What is the pattern for how many squares are in each row?

y = 5n − 1 y = 6n − 1 y = 6(n − 1) − 1 y = 6(n − 1) + 5

5. How about this hollow diamond shape? What is the pattern for how many squares are in each row?

y = 4n y = 2n + 2 y = 4n − 4 y = 4(n − 1)

6. This shape looks somewhat like the stand that holds up a road construction sign. With each step it gets longer in each direction. What is the pattern for how many cubes are in each row?

y = 5n + 1 y = 5n − 4 y = 5(n − 1) + 1 y = 5(n − 1) − 4

7. There are many versions of an old story about the inventor of the game of chess. One version appears below. On which day will the total grains of rice exceed 3 million?

Day 20 or 21 Day 22 or 23 Day 24 or 25 Day 30 or 31

8. Two trains are approaching each other on parallel tracks. Both are traveling at 30 miles per hour. What is the overall speed at which they approach?

30 miles per hour 60 miles per hour 90 miles per hour 900 miles per hour

9. Continuing the previous problem, the two trains start 9 miles apart. How many minutes does it take for them to pass each other?

9 minutes 12 minutes 18 minutes 30 minutes

10. Continuing the previous problem, a fly zooms back and forth from the headlight of one train to headlight of the other. It starts when the trains are 9 miles apart. By the time it arrives at the other train, the two trains have gotten closer. It instantly reverses direction and heads back to the first train. And so on. The fly moves at 20 miles per hour. How far does it travel before the trains pass?

1 mile 2 miles 3 miles 9 miles