# Multiplicative thinking with Anno’s Magic Seeds

### Anno’s Magic Seeds is a multiplicative picture book that can be used with older students.

An oldie but a goodie is how I think of this book. It is a classic and a keeper. Believe it or not I got my copy when a school library threw it out as part of their policy for culling old books. It was barely used so I snaﬄed it.

I was in a school library last week where the librarian has carefully maintained her collection of Anno books. They may still be in your school library too.

The thing I like most about this book is the way in which it shows how quickly a number grows when it is repeatedly doubled.

Many of the students I meet think of doubles additively and have never explored the way in which a quantity grows when it is repeatedly doubled.

Go back to my jigsaw puzzle blog post for ideas on how to correct this using jigsaw puzzle pieces.

Even older students need hands on materials to explore magnitude.

There is also much to be gained in relation to place value, as can be seen on the page below where groups of 10 make it easy to count.

Throughout the book there are problems to solve, such as:

“How many fruits will grow in Jack’s garden next fall?”

The answer is found by subtracting given quantities from the current number and then doubling what is left.

There are many ‘what ifs’ that spring to mind, for instance:

• “If the first pattern of subtract one from the current number and then double continued, how many seeds would there be at the end 5, 10, 15 years?”
• “How many years to get to a million seeds if the pattern continues?”
• “What if the pattern was subtract 2, 3, etc. How would the rate of growth change then?”

In essence, the book is also leading us toward ideas about proportional reasoning which has to be a very good thing, especially at years 6 and 7.

Doubling and repeated doubling for multiplication is the theme of Building Multiplicative Strategies: Strategy 2, which is part of the Building Multiplicative Strategies series.

Why not enjoy more picture books with older students and get them posing ‘what ifs’ of their own? And remember to share what works with us.

As ever: HAVE FUN!