Aren’t ladybugs magical? Did you know that these adorable polka-dotted crimson creatures are only called *ladybugs* in the U.S.. In the U.K., and other English speaking countries, they’re called* ladybirds*. Ben Orlin, wrote and sketched some math-related differences between U.K. and U.S. here on his awesome blog, *Math with Bad Drawings.* Here’s an example of a U.S. and U.K difference from Orlin’s post.

What the heck does math/s have to do with ladybugs? Well, this week’s magical math/maths book has ladybirds/ladybugs galore.

**The Book**

Written and illustrated by Alison Limentani, this picture book was published in 2016.

The simple text calls for some powerful mathematical thinking. The book begins with the statement:

“10 ants weigh the same as 1 ladybug.”

“9 lady bugs weigh the same as 1 grasshopper.”

The book continues in a similar way comparing the weights of the previous animal with the next, counting down from 10 ants, 9 ladybugs, 8 grasshoppers, all the way to 1 swan.

At the end of the book, the ladybugs/birds make a bountiful return when compared with the weight of one swan. Limentani’s vibrant and endearing illustrations on a bright blue backdrop make sure the multiplicative relationships in this book take center stage.

**The Math**

Since the number of animals varies from 10 to 1, there are opportunities for young ones to count. However the main mathematical idea in this book is multiplicative reasoning, and more generally proportional reasoning.

The essence of proportional reasoning is the consideration of a number in relative terms, rather than absolute terms. For example, 1 ladybug weighs the same as 10 ants. 9 ladybugs weighs the same as 1 grasshopper. And the related implicit question, how many ants does it take to equal the weight of one grasshopper?

Here is a nice summary document outlining the concept of Proportional Reasoning from the Ontario Ministry of Education (2012). Below is a web of interconnected Proportional Reasoning Concepts from the document. Note the Scaling concept from last week’s post. A key component of proportional reasoning is to reason* **multiplicatively* instead of additively.

In addition to comparing weights, the end pages provide an opportunity to discuss quotative division with decimals. Here is a post by Chris Hunter about using Limentani’s book as a jumping off point for quotative division.

Finally, the last page shown above gives the weights of each animal which connects to systems of measurements. Note the use of ounces with decimals. 3.2 oz? Ugh! [ Why don’t we use metric in the U.S. again? Perhaps it has something to do with Pirates?]

**The Magic**

The book afforded skip-counting opportunities for my daughter. She used a counting by ten strategy that she is working on (she is in kindergarten) and was able to get 90 ladybugs weigh the same as 1 grasshopper.

Towards the beginning of the book, my son surprised me with his multiplicative reasoning and creative mental math skills. As the number got larger, he listened more and added aloud less. At the end, I challenged him to figure out how there came to be 362, 880 ladybugs. I told him: “This is a big problem. So you’ll need to take your time.”

Less than 5 minutes later he came back in the kitchen asking: “Can use a calculator?”

I paused, “Where are you?” He explained how he got 72 ladybugs in 1 stickleback fish. Using addition similar to this: 9+9=18 AND 18+18=36 AND 36+18=54 AND 54+18=72.

After seeing his work, I thought again about the calculator. * It will make it more fun for him.* Realizing that, I agreed. And that is where it took a magical turn.

Here is his work.

He described adding on the calculator, until here (pointing to 15,120): “That’s when I started multiplying. ”

Surprised I asked: How did you know to multiply?

He replied: “It is faster. It was likes groups of.” [Using a repeated addition connection to multiplication.]

Then, as if that wasn’t enough, he started analyzing that last page on his own.

“That’s interesting.” He remarked, noticing a pattern on righthand page. We discussed and discovered much to chat about regarding decimal numbers, patterns and relationships (also that lb means pounds). For us, the math/maths magic in *How much does a ladybug weigh?* was immeasurable. Making it is #21 on our list list of magical math books.

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Thanks and see you next Monday! #mathbookmagic