Now look a different magic again take a look at the Add 6! let’s Let’s square. middle row. What do we have to do to start with the middle number and end up with 16? And what do we have to do to Subtract 6! start with the middle number and end up with 3? look at the middle Add 8! Now let’s column. What do we have to do to start with the middle number and end up with 18? And what do we have to do to Subtract 8! start with the middle number and end up with 9? So how could I write the middle row and column using addition and subtraction? Sure. To get the middle Does anyone see a pattern? row, we add and subtract the same number from the middle number. Same for the middle column, but with a different number. The middle row and columns are arithmetic sequences. Now try to build our own [Student volunteers a let’s What will you like the middle magic square that different number. Make sure a it’s number to be? from all of these others. [Draws positive integer between 5 blank magic square on board.] and 100, for simplicity.]
Now let’s look a different magic square. Now let’s try to build our own magic square that different from all of these others. [Draws blank magic square on board.] Let’s again take a look at the middle row. What do we have to do to start with the middle number and end up with 16? And what do we have to do to start with the middle number and end up with 3? Now let’s look at the middle column. What do we have to do to start with the middle number and end up with 18? And what do we have to do to start with the middle number and end up with 9? So how could I write the middle row and column using addition and subtraction? Does anyone see a pattern? What will you like the middle number to be? Add 6! Subtract 6! Add 8! Subtract 8! Sure. To get the middle row, we add and subtract the same number from the middle number. Same for the middle column, but with a different number. The middle row and columns are arithmetic sequences. [Student volunteers a number. Make sure it’s a positive integer between 5 and 100, for simplicity.]