Middle School Math Project - Mystery Number

I have always tried teaching students about Number Theory near the beginning of the year so that we can all have an understanding of the vocabulary that we will all need for the rest of the year.  I put some mystery number challenges in with some of the problem solving that I do with my students and they all enjoyed them.  We started creating our own and voila a new project was born.  Students have found this project fun just because they can make a puzzle with it and challenge others.  I have also had students put these on the display board outside of the room (another teacher's idea: not mine) and they attract quite an interest from other students.  The general idea is to learn things like prime, factors, multiples, but you could challenge students to put many other concepts in.  The criteria that I give them is below. 

Mystery Number

Name:

Goal:

To learn different mathematical vocabulary and use it to communicate clues.

To learn how to use number concepts such as multiples, primes, factors, sum, product, quotient

T o learn the divisibility rules.

To make a creative display for outside the classroom

Project:

You are going to choose two different numbers and create clues that lead to the Mystery Number.

Your clues can’t be too obvious that makes it easy, but also need to lead to only one number.

Numbers must be displayed in some kind of creative style so that we can display them in the hallway.

Both mystery numbers must have answers that are hidden.

Mystery Number 1   Must be two digits You must use only four clues Clues  must lead to only one number Must use mathematical vocabulary in all clues Must use different types of clues using different kinds of mathematics

Mystery Number 2   Must be greater than 99 Must use only five clues Clues  must lead to only one number Must use mathematical vocabulary in all clues Must use different types of clues using different kinds of mathematics

Assessment:

Content

·         Did you use mathematical vocabulary

·         How challenging were your clues

·         How well did you communicate

·         How many different types of math did you use in your clues                                      /10

Accuracy

·         Do your mystery clues lead to one answer

·         Do your clues lead to a correct answer

·         Are you using the vocabulary correctly                                                                         /10

Presentation

·         Is your presentation organized

·         Is the presentation neat

·         Is the presentation creative                                                                                                    /10

/30

 

An example would be something like:

I have a two digit number

It is a multiple of 4

It is a square number

One of its factors is 9

 

Don't underestimate how hard this project is for some students.  The key is that there can only be one answer and many students have difficulty obtaining only one answer and have to continuously rework their clues.  I get students to check other students work.  It definitely helps everyone get that general understanding of some of these number concepts that students forget every year.  They get practice with multiples and factors and prime numbers as well as many other aspects of mathematics. 

 

Let me know what you think.