Question 1

We’re very much into number fact families in our house, where a number fact family is three numbers that can be linked to make a number sentence.  So, 3, 4, 7 is a fact family, because 3 + 4 = 7 and 7 – 4 = 3. The numbers 2, 3 and 6 are also a fact family, because they can be linked with × or ÷. I’m sure you’ve got the idea!

How can the numbers 1 – 9 be grouped into three fact families? To answer this, you need to use all of the numbers 1 – 9 and just three of the operations (+, -, × and ÷) to complete these number sentences.

Question 2

Ann is very much into beads and has made some really nice ones in bright primary colours.
“Wouldn’t it be nice if you strung them together to make a naturally mathematical design.” I said.
“And what is a naturally mathematical design.” she asked.
“Easy”, I replied, “use as many beads as you can, but don’t ever let a colour combination of two beads repeat itself. Here, look at this one.”

Question 3

We have always been fascinated by puzzles that use only the numbers 1 - 9 , and recently we discovered a slightly different one.

We found a way in which to position the numbers 1 – 9 in a grid so that the diagonals add to the same total.

Check this example out if you think we are tricking you!

But we were also hoping to do this so that no two consecutive numbers were next to each other, either vertically or horizontally.

Part 1
Please tell us where our example breaks the second rule.

Part 2
What are the largest and smallest diagonal totals can be made in which no two consecutive numbers are next to each other.

Part 3
Not more! There seem to be two diagonal totals that cannot be made without breaking the consecutive number rule. What are they?

Ooops, we nearly forgot! If you click on the diagram, you can open up an applet that will help you with this investigation. When you have an arrangement of the numbers 1 - 9 that is correct, you should:

1. Hold down <Alt> and press the <Print Screen> key. This lets you copy the screen and then you can paste it into a Word document.
2. Use the crop tool in Word which allows you to remove the bits of the picture that you don't want.
3. Then cut the diagram out of your document (<Ctrl> + <X>) and go to the Paste Special menu where you can paste it back again in .jpeg format. Otherwise your files will get very large.