Learning Made Fun

Don't Be Scared of The Magic Square (Strategy Guide)

3/20/2017

I remember doing magic squares when I was back at school, and to be honest I recall finding them confusing and frustrating at best! There are a few different ways to presenting Magic Squares. In my recent Math Quest: 'Raiders of The Lost Egg', Chapter 3 'Dodger's Party' I chose to give the Magic Number to the students to work with and have a number of tiles filled in already. I figured this way it would take a lot of the usual frustration out of Magic Squares and help level the playing field for everyone to attempt. However, these magic squares still require some strategic thinking and of course math.

I always believe in giving students the opportunity to think about their own strategies and ways to attack magic squares, but I also don't like to leave anyone feeling completely helpless and left behind. So this strategy trick I am about to explain is aimed at giving to those who are getting fed up with the activity and need a helpful nudge to power on.

So, first I recommend allowing students to see if they can figure out a strategy on their own. You could then discuss/share with the class about what students came up with and what they are finding difficult. Getting too stressed? Then carry out the modeling of completing these as I have outlined in this post to take the frustration away!

Below are images of Chapter 3 "Dodger's Party" (I've shown the Chapter presented in each of the difficulty levels). In this chapter, students are faced with some angry cutlery and crockery released by the dodgy rabbit, Dodger. To turn them back into regular items, the magic squares must be completed. It might look a bit overwhelming at first, but there is an easy strategy to conquering these magic squares at all levels 'Easy, Medium & Hard.' I will show and demonstrate a simple strategy that works with all of these Magic Squares

EASY

MEDIUM

HARD

Below I will go through each level and show an example of how I would tackle each, including my thought process. I believe if you can get the idea of a way to look at these, then working through each should be much less frustrating! Then Dodger's horrible party can be put to an end!

EASY LEVEL

5 + 3 = 8
15 - 8 = 7

In the example to the right, the magic number is 15. So, all rows, columns and diagonals must equal the sum of 15 to be completed correctly.

Step 1. First look for where only one number is needed to complete a row, column or diagonal. As circled, there is only one spot needed to complete the middle row, because the numbers 5 and 3 are already given.

Step 2. Add 5 and 3 together (= 8). So to work out the last remaining square, subtract 8 from the magic number 15. This equals 7. Giving the first completed row of the magic square.

Step 3. As in Step 1, look for where another row, column or diagonal only needs one more spot filled. In this EASY 3 x 3 grid, there are a few options here to choose from. In the image to the right I've chosen the diagonal, where I only need the bottom left square to complete.

Step 4. Exactly as in Step 2, first add the known numbers.
2 + 5 = 7
Then, subtract that total from the Magic Number
15 - 7 = 8

Keep carrying out Step 1 and 2 after completing each row, column or diagonal until the whole square is complete.

Step 5. Once your magic square is complete.Check all of the sums to make sure each row, column and diagonal equal the magic number.

The same strategy applies for the harder ones. I'll demonstrate these steps in both the 4 x 4 grids in MEDIUM, and the 5 x 5 Grids in HARD.

MEDIUM LEVEL

The Medium Level of Chapter 3 "Dodger's Party", contains 4 x 4 grid Magic Squares. These are a bit more challenging than the easy version, but the strategy to attacking them is the same! It just means a bit more math work in this step up.

In the example to the right, the Magic Number is 46. So, each row, column and diagonal need to equal 46.

Step 1. Look for a row, column or diagonal where only one spot is needed to complete it. There are four options that I can see in the example, but I will just circle the most obvious one to begin with.

Step 2. Add all of those numbers together:
7 + 12 + 19 = 38
Then subtract this total from the Magic Number
46 - 38 = 8
Pop the 8 in the empty spot.

Step 3. Rinse and repeat steps 1 and 2 until the whole square is complete. The key is to keep looking for those special rows, columns or diagonals that only have one spot to solve. Solving those starts to open up more rows, columns and diagonals that can easily be completed with confidence (and no frustrating trial and error).

Step 4. Check that the sums of each row, column and diagonal equal the magic number to make sure you have done it correctly.

See, there ain't nothing scary about this tea party!

For the HARD Level of Dodger's Party, the Magic Squares are 5 x 5. These look a little bit more daunting than they really are . . . but, they do require a bit more skill in hunting for that secret row, column or diagonal to help progress through the square smoothly. More math is involved too since more numbers will be required to be summed up, and the magic numbers get bigger.

Again, I will demonstrate with the same steps used above (Easy and Medium) to show the completion of the more challenging one.

HARD LEVEL

Achieve Chapter 3 of the Math Quest using the same strategy as in the above demonstrations. You just may need to crank up the brain power a bit more to tackle these though. Watch out cranky teapot!

Step 1. Look for a row, column or diagonal where only one tile spot is empty. I chose the most obvious one in the example to the right. Can you find the other?

Step 2. Add up all of the numbers in that row.
13 + 2 + 21 + 24 = 60
Subtract 60 away from the magic number 70.
70 - 60 = 10
Write 10 in the empty tile.

Step 3. Rinse and repeat Step 1 and 2. The key is to look for those easy to solve spots. When you only have one tile left in a row, column or diagonal . . . it takes out the frustrating aspect of trial and error.

Step 4. Check that all of your sums in each row, column and diagonal add up to the magic number.

So that's the special strategy to conquering the challenge faced at Dodger's Party.

The full resource that I have been referring to during this Magic Square post is down below. You can click through to find out more about it in my TPT store. It is a fun math quest involving six challenging chapters to work through. Students can end up with one of four possible endings.

A fun video hook is also provided to introduce the activity to your students and create excitement. Great for extra practice and review, early finishers, enrichment, or the sub tub.

Individual levels can be purchased separately, or bundled at a reduced price to allow for differentiation.