Counting Puzzles Stimulate Great Thinking

Please click on the thumbnails to enlarge the pictures.

These pictures show two recent student sheets that we have been working on in class. Both are designed to stimulate thinking about counting patterns. Often, students fall back on methods of solving these questions that are far from efficient. For example, a student might simply list all of the multiples of 25 in order to get to 300 and then state, after counting the written numbers, that it takes 12 people counting by 25 to get to 300. However, many students quickly latch onto the idea that it is much easier just to figure out how many 25s are in 100 and then triple the amount to get to 300.

On the "What's in Between" page, students have to sort through a multitude of important concepts in order to find the answers to these puzzles. For example, students must be able to find the mid-point of two numbers in order to find a reference point to know if a number is a number is closer to the numbers on the ends of the number line. Some students get really confused with larger numbers like 7,900 and 8,100. These same students would also have no trouble finding what comes exactly in the middle of 79 and 81. Sometimes, "ignoring the zeros" can be a great strategy. Students also have to be flexible and efficient when they are forced to find numbers that are multiples of two different numbers. If a puzzle said that the mystery numbers were said if you count by 125s and were also multiples of 500, then only certain numbers would qualify. I would try to think about multiples of 500 first, as that means only numbers that end in two or three zeros would qualify. See if you can find the puzzle with answers that are not quite correct.