Another Anno book to stretch older students

Anno’s Mysterious Multiplying Jar is another Anno picture book for older students, but one with plenty of stretch potential.

While on the surface this looks like a simple multiplication book there is in fact a lot more going on in the back story.

The book introduces factorial numbers which will intrigue many of your students especially if you encourage them to get their calculators out to explore what happens to numbers when they grow factorially.

A factorial number is written with an exclamation mark at the end of it, for example 4!

4! means 4 multiplied by each of the preceding numbers, 4 × 3 × 2 ×1 and can also be written as 4 × 3! or 4 × 3 × 2!

In fact, when entering factorials on the calculator the display will soon run out of space and send you into exponential notation. But if you turn your phone sideways to turn it into a scientific calculator, you should see a x! button and that will enable you to explore just how large factorials get.

For example, 99! shows as 9.33262154439 E 155. This is a number that has 156 digits … and how many of the digits on the right-hand side of it will be zeroes (you might ask!)

There is much to enjoy and a lot of intrigue too in this book.

Above we see the images for 8 cupboards each with 9 boxes in so it seems that 8 × 9 will tell how many boxes altogether. Then wait a minute, there were 7 rooms each with 8 cupboards and there 6 houses each with 7 rooms so we soon see how numbers grow factorially. Hopefully your budding mathematicians will have fun with this.

A challenge could be to design and create a factorial sequence with objects, for instance one large box, inside are 2 smaller boxes inside each of which are 4 smaller boxes each containing a little package within which there are 5 small objects.

What fun to open up surprise package like that!

Want more help with teaching middle and upper primary students multiplicative strategies? Check out Building Multiplicative Strategies.