Three Digits

Three digits A mathematical investigation Resources: digit fans, unit cubes

You start with three numbers – a 7, a 9 and a 4. Re-order them to make a new number, for example, 947, nine hundred and forty seven. What is the largest number you can make by re-ordering them? What is the smallest number you can make by re-ordering them? Can you list all the possible numbers that can be made with these three digits? (Clue – there are 6 different 3-digit numbers to find) Try again with the digits 1, 5 and 3. What is the largest number you can make by re-ordering them? What is the smallest number you can make by re-ordering them? Can you list all the possible numbers that can be made with these three digits? How can you be sure you’ve got them all?

Now for something slightly harder! Imagine you have 25 beads (or use cubes). You have to make a three-digit number on an abacus. You must use all 25 beads for each number you make. How many different three-digit numbers can you make? Write them in order.

Three digits Teacher notes. WALT: Ordering numbers, place value, problem solving. Each activity can be led from the front or worksheets may be copied and given out. Introduce the activity with a quick warmer on place value – what numbers in different columns represent, how we can tell they are tens or hundreds. Which numbers are larger? How do we tell, etc. Lead into the digit fans activity – 15 mins at most. Differentiate by adding a fourth digit. Discuss selecting a number for the first column (three/four choices) then the next column (two/three choices) and so forth. Lower ability will need cubes for the abacus activity. Group work. Describe how an abacus displays numbers (revision?) Perhaps encourage students to race to get all the answers (799, 899, 898, 979, 988, 997) Extend by adding (lower ability) or removing (higher ability) a cube. Discuss similarities with ‘Killer’ Su Doku game. Plenary: Have we achieved WALT? What ideas for further investigations can the students think of? -

list number of possible numbers for all viable amounts of cubes (1-27) using 2 or 4 digits on the abacus seeing how the maximum value increases as the number of cubes increases