The Factor Tree

Objective: To guess the prime factors the other player used to generate a number using a factor tree.

Number of Players: 2 or more.

Materials required: A pen and a sheet of paper for each player.

How to Play: Players take it in turns to set and solve problems. A single round consists of the following steps:

Step 1:The player setting the problem takes three or more prime factors and multiplies them together. To begin with, it is best to use the smaller prime factors 2, 3, 5 and possibly 7 (depending on the times tables knowledge of your child). The same factor can be repeated. Examples are:

2 x 2 x 3 = 12

2 x 5 x 3 = 30

7 x 2 x 3 x 2 = 84

Step 2: The player who is setting the problem tells the second player the answer to the multiplications. The second player then breaks that number down in successive steps until she has reached all the prime factors used to make the original number.

Step 3: Players compare the numbers used to create the problem. If the player solving the problem has broken the number down correctly, they gain one point. If that player has not broken the number down correctly, the player setting the problem gains one point. If the player setting the problem did not set the problem correctly, the solving player gains one point.

Modifying the game: This game can be played with three or more people. Players take it in turns to set problems and the other players race to solve it correctly. If the fastest solver has the correct answer, she gains the point. If the fastest solver has made a mistake, the second fastest solver's answer is checked and so on. If none of the solvers have the correct answer, the player who set the problem gets the point.

Learning: If played using the factor tree form shown in the picture, the children playing will learn to correctly structure a factor tree. This is an essential precursor for factorizing in algebra and equation solving, a skill that is essential all the way up to senior high school mathematics.