Martian Counting Goals: To extend and deepen students' understanding of base ten by establishing a base six notation. To use the base six notation to add, subtract, multiply and divide, to gain a deeper understanding of base ten algorithms. Year level:  Advanced Year 6 or above Group size: Groups of 2-3 working together on the worksheet followed by a full class discussion. Equipment:  Pen and paper, straws, rubber bands Martian counting worksheet Martian counting solutions Time: 30 - 40 minutes Activity Instructions: 1. Print the accompanying handout Martian counting worksheet and Martian counting solutions 2. Allow the students to discuss their ideas as they complete the worksheet. The main role of the teacher is to pull together the ideas at the end, rather than teach base six notation. Teaching Notes: Give the base a name ie base six represents a martian hand. In this case you would count one, two, three, four, five, martian hand, martian handy one, martian handy two etc When you reach 6 lots of martian hands make up another name! The students will definitely have fun with this. Step 1-Counting: Children as young as 5 or 6 can play games where counting is done in a base other than ten. Step 2-Addition: Note when "trading" occurs. This is designed to help students think about the normal (ie base ten) rules that they use for addition. Step 3-Subtraction: Likewise with "decomposition". This is designed to help students think about the normal (ie base ten) rules that they use for subtraction. Step 4-Multiplication: Most children learn about multiplication by ten as a special rule (ie add a zero). Here is an opportunity to rethink these rules and why they work. When a number is multiplied by the base number, (normally ten but six here) all the digits move into the next largest column. (A number slide is perfect to show this.) Step 5-Division: On earth we divide our one into ten equal pieces. On Mars they choose six. Otherwise the notation is similar. Students are asked to use straws to try to understand some divisions. Something special happens when dividing by six; the digits are the same but move into the next column on the right. This is exactly what happens with earth numbers although students are often taught rules about "moving the decimal point". We prefer to say that the decimal point does not move, the digits move into the next smaller column. Again, a number slide is perfect to show this. Step 6-Which zeros matter?: Many students on Earth are confused about this. This example is to promote discussion. Step 7-Rounding: On earth we have rules like: "5 or more, round up". By considering base six, students are forced to rethink this rule.