F A T R N T EP N I D A Much of mathematics is based on patterns, so it is important to study patterns in math. We use patterns to understand our world and to make predictions. We will also use this skill later when we combine it with the problem-solving skill ‘solve a simpler problem’. The pattern above is a geometric pattern that has seven parts. They are circle, triangle, circle, heart, circle, star, circle. After the first cycle ends, the second cycle begins. This is what gives us the two circles together in the line. Patterns can be as simple or as complex as you want them to be, and both you and the students can create your own patterns to solve. The next slide has several pattern problems you can use in your classrooms. After that, the answers are given. Finally, I list other online resources you can use to find more pattern problems.

LIST THE NEXT THREE NUMBERS OF EACH PATTERN OR ANSWER THE QUESTION. 1)2, 5, 8, 11, ___, ___, ___ 2)0, 2, 5, 9, 14, ___, ___, ___ 3)1, 4, 9, 16, 25, ___, ___, ___ 4)32, 16, 8, 4, ___, ___, ___ 5)1, 2, 0, 3, -1, 4, ___, ___, ___ 6)1, 1, 2, 3, 5, 8, 13, ___, ___, ___ 7) FIND THE PATTERN AND COMPLETE THE NEXT LINE OF THIS TABLE

LIST THE NEXT THREE NUMBERS OF EACH PATTERN OR ANSWER THE QUESTION. 1)2, 5, 8, 11, ___, ___, ___ ANSWER: 14, 17, 20 (PATTERN = ADD 3) 2)0, 2, 5, 9, 14, ___, ___, ___ ANSWER: 20, 27, 35 (PATTERN = ADD 2, THEN ADD 3, THEN ADD 4, ETC.) 3)1, 4, 9, 16, 25, ___, ___, ___ ANSWER: 36, 49, 64 (PATTERN = EITHER ADD 3 THEN 5 THEN 7, ETC. OR TAKE 1 2, 2 2, 3 2, ETC.) 4)32, 16, 8, 4, ___, ___, ___ ANSWER: 2, 1, ½ OR 0.5 (PATTERN = DIVIDE BY 2 OR CUT IN HALF) 5)1, 2, 0, 3, -1, 4, ___, ___, ___ ANSWER: -2, 5, -3 (PATTERN = ONE SOLUTION IS ADD 1, SUBTRACT 2, ADD 3, SUBTRACT 4, ETC. ANOTHER WAY TO VIEW THIS ONE IS A MIX OF TWO PATTERNS THAT ALTERNATE 1, 0, -1, -2, -3, WITH 2, 3, 4, 5) 6)1, 1, 2, 3, 5, 8, 13, ___, ___, ___ ANSWER: 21, 34, 55 (THIS IS THE FIBONACCI SEQUENCE. AFTER LISTING THE FIRST TWO TERMS, WE GET THE NEXT TERM BY ADDING THE TWO BEFORE IT. DID YOU KNOW THIS IS SEEN IN NATURE? LOOK IT UP!)

LIST THE NEXT THREE NUMBERS OF EACH PATTERN OR ANSWER THE QUESTION. 7) FIND THE PATTERN AND COMPLETE THE NEXT LINE OF THIS TABLE This is Pascal’s Triangle. The outer two terms in each row are always 1. To get any of the inner terms, add the two numbers diagonally above it (example, 5 = 1+4 and 10 = 4 + 6)

MORE PATTERN PROBLEMS AND RESOURCES ONLINE