HOW TO DO MAGIC SQUARE HOW TO

The Magic Squares task is an integral part of: Is it in Maths With Attitude? Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner. Maths300 provides a lesson plan, supported by software, that details how this lesson sequence can be carried through.ДЇor more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 98, Magic Squares, which includes an Investigation Guide and companion software. It helps if you have nine large tiles yourself, about 20cm 2, to demonstrate the problem on the community floorboard. Tasks can also be modified to become whole class investigations which model how a mathematician works.ДЄsk the students to tear a piece of paper into nine parts and number them. Whole Class Investigation Tasks are an invitation for two students to work like a mathematician. That is, each of the 8 totals is different. What happens if the condition is to arrange the digits 1 - 9 into the 3 x 3 square so that no row, column or leading diagonal has the same total. So, if every number was divided by 3, say, we would have a Fraction Magic Square, which is Task 37. It is based on the idea that if the same operation as is performed on every number in the square the result should also be magic.

HOW TO DO MAGIC SQUARE HOW TO

The remainder of the task allows students to discover how to make new magic squares from old ones. This strategy probably is easier to apply to the 4 x 4 case than the strategy of finding and managing all the quadruples that add to its magic total. Keep swapping until the diagonals also work. By swapping two rows or swapping two columns, you will not alter row or column totals but you will change the diagonals. Keep shuffling until the rows also add to 15. This will not alter the column total, but changes the rows. Firstly, set the tiles into three separate columns that each total 15.So really there is only one solution and the others can be created from it.ДЄnother strategy for tackling the problem is to break it into smaller parts. Further, looking along the top row reveals that each solution is the one to its left rotated 90В°. Studying this set of solutions more closely reveals that those in the bottom line are reflections of those above. We don't know which 5 triple goes in which of these lines yet, but by trying out possibilities and considering the triples that must be consequences in the border lines, we can find out.Д®ventually a solution will be found and it may appear in one of several variations: Only 5 satisfies that condition, so 5 must go in the middle and we now know the other parts of each triple it is lined up with horizontally, vertically and on the two diagonals. Four of these lines pass through the same square, the centre, which means one number must be in four of the triples. There are 8 of them, which is convenient because 8 lines of the magic square have to be equal. The next step in the problem might be to list all the triples that add to 15: So the sum of the three column totals is 45 and column totals are equal, so each one must be 15. The sum of 1 to 9 can be found in various ways. If those totals were then added that would be the same result as adding the nine separate digits because each digit is counted once in the three separate additions. Then the three columns will each add to the same total. Working backwards can help to find it out. Then they might begin to see that there are 8 lines which have to have the same total, so they need 8 number triples (made using the digits 1 to 9) that sum to the same number. It's likely students will begin this problem using a guess and check strategy. There is always more to a task than is recorded on the card. Iceberg A task is the tip of a learning iceberg. problem solving strategies, especially breaking the problem into parts and working backwards.Once solved the card invites the students to explore several What happens if.? questions. Sure, all the rows, columns and the two leading diagonals must add to the same number, but the first problem may by to calculate that number. Years 4 - 10 SummaryДЄ classic problem which is presented differently here because there are no clues.

How to do magic square