# Multiplicative Thinking Book 3

**Amanda Bean’s Amazing Dream**

I’ve chosen *Amanda Bean’s Amazing Dream* as the third book in our multiplicative thinking blog because it tells the story of Amanda who loves to count and skip count everything she sees.

She does not see the need for multiplication facts even though she is told that it is faster than counting everything.

The variety of multiplication opportunities in the illustrations abound and show equal sized groups, arrays, and the area model of multiplication, each in interesting everyday situations. Open this book on any page and the illustrations provide opportunities to identify multiplication situations and open up discussions about how to work out each multiplication.

For example:

The illustration above is the second page in a double page spread and shows:

- Five equal-sized groups of 4 lollipops. Would skip counting in 2s, 4s, 5s be a good strategy? Would doubling and doubling again and then counting on 4 more be a good strategy?
- A tall building which has 8 windows, some students will see 4 rows of 2 whereas others will see 2 lines of 4 which provides an early opportunity to talk about the commutative property of multiplication.
- That on closer inspection each window has 6 windowpanes allowing the extension of multiplication facts to, 8 × 6 or 4 × 12 depending on how students perceive the groupings and arrays.

We often overlook the identity property of multiplication and assume that students will know the 1s facts. This is not necessarily so. Often when asked 1 × 6 or 6 × 1 students will answer 7 treating it as an addition not a multiplication fact.

Looking at the page above, we can see examples of the identity property for multiplication, there is one row with 3 windows, 3 individual books in a cluster, 2 windows in 1 column on the door, each an opportunity to talk about the identity property of multiplication.

There is so much to explore on every page, but I do have one question in my mind, and that is why didn’t the illustrator create subitizable equal-sized groups of dots on the curtains in the above page?

My favourite page though is the array of trees shown below.

How best to work out how many trees? There are lots of opportunities for identifying sub-parts which could lead to working with the distributive property for multiplication. It might also reveal some misconceptions about how arrays work.

I would recommend that you take a close look at the illustrations on each page in this book and plan how you might use them to develop flexible multiplicative thinking. Finally, do not overlook the teaching and learning notes provide by Marilyn Burns at the end of the book.

For more about multiplicative thinking look at the following Natural Maths resources:

Building Multiplicative Strategies

Have a great week!

P.S. Johnny couldn’t help thinking that Amanda will probably grow up to be an accountant. She seems to be a ready-made Bean Counter!