Pollinator puzzles help students with multiplication, division and problem solving. I often emphasize the nasty stinger on the bee to recalcitrant boys just to engage them viscerally ūüėČ Forgive me! lol

The class starts by collectively solving a¬†puzzle.¬†Here they must add numbers 1-20 around the flower so the petals are satisfied. Let’s see¬†how it works…

The numbers 5 and 20 can be put in the upper two slots. The light blue petal indicates that these two slots must add to 25. Light blue always means addition… 5+20 = 25 so this might be a good start…

What about the slot just¬†left of the 5? We see from the dark blue outside petal that the difference between its¬†two slots must be 12. Dark blue means subtraction. What two numbers under 20 have a difference of 12… one of them is a five…

Yes – 17 and 5 have a difference of 12. This is the only answer. So we know that if the initial 5 and 20 were correct – then this must be a 17.

Let’s look at the slot just right of the 20. Dark red means division. So we know that the two numbers in the dark red petal must¬†divide to give a half. Well 20/40 = 1/2, but 40 is too big. We are only using 1-20… so the slot must be a 10. 10/20 = 1/2.

Now let’s look at the slot left of the 17. Pink means multiplication – so we need to find a number 1-20 that multiplied by 17 gives 35…

Oh no! That’s impossible. So our initial guess of 5 and 20 must have been wrong. Is there anywhere where we might have a better chance of guessing correctly?

Absolutely… One such place are the two slots that must multiply to 35. These must be 5 and 7 although we don’t know the order. You can try both to see which one ends up¬†being useful…

This order doesn’t end up working… so the other one must if the puzzle is to have a solution.

I’ll leave it for you to work your way around. If you were doing this with a class you would never give them the big hint of where to start ūüėČ

Rafflesia are smelly big flowers pollinated by carrion flies. I put digits 0 through 9 into the slots for this smaller puzzle.

Try to solve it…

Answer coming up…

Students should be encouraged to create their own Pollinator Puzzles. Can they create three puzzles Рone that has a unique solution Рone that has more than one solution Рand one that is impossible?

Pollinator Puzzles

(MathPickle, 2017)

This puzzle gives students practice working with multiplication and division whilst working through¬†a puzzle. They are not quite as good puzzles – and have significantly less flexibility than the excellent Cartouche Puzzles. However, these puzzles are perhaps more aesthetically pleasing and¬†they’ve worked well in class.

Download puzzles here.

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Use the right tools!

Students should use the right tools: 0-99 wall charts, graph paper, mathigon.org. etc.

MP6 Be precise!

Students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist ūüėČ

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos ūüėČ For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)