Students will learn how to identify factor pairs for any number 1-100. For example, 3 and 6 is a factor pair of 18 while 2 and 4 is not. Here's an interesting problem: Find the dimensions of the rectangle that has whole number side lengths, area 12, and perimeter 16. Students can find the answer by making a table, as seen here. After that, teach students how to solve Shikaku puzzles, then give your students some puzzles to solve. Puzzles of various difficulty are conveniently organized here. Additionally, here are some random Shikaku puzzles I've stumbled across. After your finished with Shikaku, explore the game found here and here. After that, give your students this challenge. Before attempting the challenge, students must be able to multiply two-digit numbers by two-digit numbers. They don't need to know the divisibility rule for 13, despite the name of the problem. Next, give your students the puzzle titled *Pattern 30* on this page. Next, give your students this challenge. The solution can be found using the reasoning provided by NRICH, or by drawing a graph of all numbers which may be adjacent. From this, it's easy to see the longest simple path has length 9. Either way, the reasoning is that if we try to include 7, we miss out on 3, 6, and 9, or 4 and 8. Which set we miss out on depends on our subsequent choices. Conclude by leading the investigations found here, here, and here. Two more instances of the *Tax Collector* game being played can be seen here. Also, go to this page and give the puzzles found on the slides *Hungry Monsters* and *Hungry Monsters Pt. 2.*

At this point, 4th graders don’t know the divisibility tests, so without this or the sieve of Eratosthenes, there’s no way they can test primality.

Watch these Khan Academy videos:

Do these Khan Academy exercises:

Next, give your students this challenge:

Make the equation below true by replacing each letter with a unique digit (0-9).

$$P + P + P = I = G + G$$Here's the solution:

\(P + P + P = I,\) and \(I = G + G.\) Thus, \(I\) must be divisible by 3 and 2. The only single digit number with this property is 6. Now we have \(P + P + P = 6 = G + G,\) so \(P\) is one-third of \(I,\) and \(G\) is one-half. So \(P = 2\) and \(G = 3.\) In conclusion, the equation is \(2 + 2 + 2 = 6 = 3 + 3.\)

Conclude by leading this investigation:

Lazy Lemur Puzzles

by MathPickle

4.OA.B.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.