# 45 and A Change in Order

45 is a composite number. 45 = 1 x 45, 3 x 15, or 5 x 9. Factors of 45: 1, 3, 5, 9, 15, 45. Prime factorization: 45 = 3 x 3 x 5, which can also be written 45 = 3² x 5.

When 45 is a clue in the FIND THE FACTORS puzzles, always use 5 and 9 as the factors.

When I introduce the FIND THE FACTORS puzzles to elementary school students, I only print copies of level 1 and level 2 puzzles. After students have completed those puzzles, I will demonstrate how a level 3 puzzle is completed.

A few students have downloaded the puzzles at home. One very bright sixth grade student was able to complete a level 6 puzzle with the help of his dad.

Kids can be very determined. They may die several times fighting dragons, but they will eventually find the way to save the princess. They can be just as determined to find the way to write the numbers from 1 to 12 in the top row and the first column to make the puzzle work as a multiplication table, especially when I compare it to winning a computer or video game.

Many students tend to guess and check and will get frustrated unless they are shown how to solve the puzzles logically. Frustration can be the enemy of determination.

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles. If you click on the excel file you may notice that I have changed the order of the puzzles on the main page.

If the puzzles are printed on both sides of a sheet of paper, the paper can be cut down the middle. In this way I can print puzzles for an entire classroom using only half as much paper.

I instruct students to treat the sheet of puzzles like a computer game and see what level they can achieve. They know upfront that I will be extremely surprised if any of them find all the factors to all six puzzles. That statement motivates some students while it reduces stress in others. Not all students like solving the puzzles, but it is a joy to observe the ones who do.

Here is solution for last week’s level 1 puzzle:

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