Algebra+&+Patterning

return HOME] Share rich **ALGEBRA AND PATTERNING** problems with the group. For each problem you post, please include: - the appropriate grade level(s) - source of the problem

THE SLIPPERY FROG A frog climbs up the side of a well and slides back while resting. Every minute, the frog leaps upward 5 metres (and it leaps upward precisely at the end of the minute). Then it rests for a minute. At the end of the rest, the frog slips down 3 metres. At the end of the next minute it leaps 5 metres, then a minute later it slides down 3 metres, and so on. The well is 11 metres deep. - How long will it take the frog to get out of the well? - How can you figure out the answer for any depth well? - How long would it take to get out of a well that is 30 metres deep? 100 metres? 103 metres? //Junior/Intermediate, Unknown//

BOTTLE AND CORK A bottle costs $1.00 more than a cork. Together they cost $1.10. How much does each item cost? //Intermediate, Unknown//

PUMPKIN PROBLEM Ms. Fizzle brought in pumpkins for science class, one for each group. The first task was to weigh the pumpkins, but the scales they had wouldn't register any weight under 7 kg, and it seemed that two or three pumpkins were under that weight. The class decided that they could weigh the pumpkins two at a time, so they weighed each pumpkin with each of the other pumpkins. The weights registered on the scale were: 7 kg, 8 kg, 9 kg, 10 kg, 11 kg, and 12 kg. How many pumpkins were there, and how much did each weigh? //Junior/Intermediate, Unknown//

WEKA POST Weka Post is a new company that can deliver your letters. They have a unique set of six stamps that they believe allows you to put any exact amount of postage up to 63 cents, which is their top letter rate. Here is the set of stamps: 1¢, 2¢, 4¢, 8¢, 16¢, and 32¢. They also believe you need no more than one of each stamp to make any amount up to 63 cents. Are they right? //Junior, New Zealand Maths []//

CONFLICTING DATES Maki plays volleyball every third day of the month. She meets her mother for dinner every seventh day of the month. How many times in a month will Maki have a conflict between volleyball and dinner with her mother? //Junior/Intermediate, Unknown//

TABLE ARRANGEMENTS Ms. Liu is organizing a party. She would like to have it at a restaurant. The restaurant has 36 square tables. Ms. Liu does not want all her guests sitting apart so the tables will need to be arranged all together. If each table side can sit one guest, how can the tables be arranged in rectangles to satisfy her demand? What is the maximum and minimum number of guests Ms. Liu can invite? //Primary/Junior/Intermediate, Unknown//