 Home Mathematics Modeling mathematical ideas: developing strategic competence in elementary and middle school

# MORE RELATED RICH PROBLEMS TO EXPLORE

1. Identify the next term in the sequence of growing patterns: 2. Consider the following growing pattern: 3. Consider the following growing pattern of tiles. • 4. How many tiles are there in the next stage? Explain your thinking.
• 5. How many squares are in a chessboard?
• 6. A small conference room has auditorium style seating. The last row has 19 seats and each successive row before it has 2 less seats. If the first row has one seat then what is the total number of seats in the room? (Hint: Try your pattern that you obtain at: http://completcccntcr.i;mu.edu/iava/sQuarenumbers/index.html)
• 7. Find the number of terms in the sequence: 7, 10, 13... 55.
• 8. A shopkeeper makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?
• 9. The first four figures of a pattern are shown. • 1. If the pattern continues, how many shaded squares will be in the 10th figure?
• 2. What percent of the 10th figure will be unshaded?
• 3. Each of the smaller squares has sides of length 3 units. For example, Figure 2 has a total area of 6 x 6 = 36 square units. What is the sum of the areas of the shaded regions in the first 10 figures of the pattern? Related topics