Natural Math Multiplication Course

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Join our course Maria Yelena

April 7 update

The course was successfully crowd-funded – thank you for the support! There are more than 580 participants. Registration is now closed. If you missed it, subscribe to our newsletter to be notified of future courses!

If you registered before April 7, you should be receiving course emails. If you have not heard from us by now:

  1. Check your spam folder for emails from
  2. If you can’t find any, email and ask for help

We invite parents, teachers, playgroup hosts, and math circle leaders to join us in April for an open, crowd-funded online course about multiplication. Each week there will be five activities to help your kids learn multiplication by exploring patterns and structure. To get your course completion badge, do at least two activities every week. The course starts April 6 and runs for four weeks. Dr. Maria Droujkova and Yelena McManaman are designing and leading the activities.

Each activity will have adaptations for toddlers (2-4), young kids (4-6), and older kids (7-12). If you want to remix activities for babies or teens, we will help!

Preliminary Syllabus

Week 1: Introduction. What is multiplication? Hidden dangers and precursors of math difficulties. From open play to patterns: make your own math. 60 ways to stay creative in math. Our mathematical worries and dreams.

Week 2: Inspired by calculus. Tree fractals. Substitution fractals. Multiplication towers. Doubling and halving games. Zoom and powers of the Universe.

Week 3: Inspired by algebra. Factorization diagrams. Mirror books and snowflakes. Combination and chimeras. Spirolaterals and Waldorf stars: drafting by the numbers. MathLexicon.

Week 4: Times tables. Coloring the monster table. Scavenger hunt: multiplication models and intrinsic facts. Cuisenaire, Montessori, and other arrays. The hidden and exotic patterns. Healthy memorizing.

Natural Math Multiplication

Questions and Answers

March 22
Q: I am trying this out. Can I contribute money later in the course?
A: We greatly appreciate all the contributions participants made so far to support the development of the course. Thank you! Toward the end of the course, we will analyze course data, and announce development plans for the next stages of the multiplication project. If you like where this is going, you can continue crowd-funding then.

March 20
Q: Where are your 12 multiplication models?
A: We edited the Welcome! PDF file to spell out the link, since some readers weren’t showing it. Here the models are:

March 19
Q: I registered for the course, but I did not get a download, or submitted any information. Is this normal?
A: You are supposed to get access to a PDF file as soon as you register. You should also receive an email confirmation with a link to the same file. Please check your spam folder. We will send you a starting survey in a few days. Meanwhile, you can directly download that Welcome to the Course PDF file:

March 18
Q: Do I need separate registrations or “copies” of the course for each child? Do other parents from my learning coop have to register?
A: People who register accept certain leadership within their families, math circles, or other local groups. They figure out tasks, organize activities, and report back to our course community. Everyone who wants to grow in this math leadership can register, whether only one person, or multiple people from the same local group.

March 17
Q: What if I have a spring break or travels during April? Can I still participate?
A: Yes! We will keep the course tasks open for responses for two extra weeks in May.

Q: Will I be able to see the materials after the course is over?
A: Yes! The materials have open licence, Creative Commons, so you can always view and share. Big thanks to everyone who is supporting Moebius Noodles!

Q: I am in Australia. Will this work with my time zone?
A: Almost all course activities happen on the course forum. You can do the activities and post your results any time. We will have a couple of live meetings, but they are optional. We will upload full recordings of the meetings.

22 comments on “Natural Math Multiplication Course
  1. HoneyBunch says:

    Hi Maria,

    I am very interested in this online course. Could you please let me know how can I subscribe?


    • MariaD says:

      Hi HoneyBunch,

      I added a line with instructions about the missing button. The registration plugin does not work with older Internet Explorer versions. Please let me know if you still can’t register, and I will work on it some more!

  2. Nichole Oursler says:

    Please include us in the multiplication course in April. Thanks!

    • MariaD says:

      Hi Nichole,

      I added instructions on what to do if you don’t see that “Register” button. Thanks for your interest! I am looking forward to seeing you in the course.

  3. Lisa McCarville says:

    Wow this course is going to be amazing. Can’t wait.

  4. Lisa Merwin says:

    I am curious. Are the activities things that I would use in my classroom? If so, there is a small Easter break problem with the month of April.

    • MariaD says:

      Lisa, thank you for your question. I added it (and the answer) to the description. You can use some of the activities with large groups, and also you can shift the schedule of the course to fit around your spring break!

  5. Jennifer Polizzi says:

    Where do I find the 12 models of multiplication mentioned in the PDF of the course introduction?

  6. hupparoo says:

    I am going to do these activities with my group on 4 Thursdays in a row. Would it make more sense for the group to start meeting on 4/3 or on 4/10? I want to make sure I build in lead time for acquiring supplies and planning the activities, but don’t want to wait too long and get behind.
    Rodi Steinig

    • MariaD says:

      Hi Rodi,

      Start on the 10th. Most activities of the first week are for grown-ups, so it will work better this way.

  7. Reeba Lynn says:

    the button “use this page” takes me to the page where I see a colorful square and “April 2014 – Open online course” but it and the link “join the course” below it, just take me back to the page that has a register button, but when I click on it, it changes to a “donate” button…..

    • MariaD says:

      Reeba, do you see the little window next to that second “Contribute” button, where you can type your price (0 and up)? If not, try using a different browser!

  8. Claire says:

    I’ve registered but I still don’t understand how this course works. Will you email the lessons in April? or do I have to go on your website to check lessons??

    • MariaD says:

      Hi Claire,

      Yes, we will start sending course updates in April, by email. You’ll have daily updates starting April 6. I did check that I have your registration. Glad to have you in the course!

  9. Carmen Downes says:

    I registered and paid for the course back on 18 March, but I haven’t heard anything since. Will further course information be e-mailed, or should I be seeing the activities posted somewhere else? We are excited to participate and don’t want to miss anything! :)

    Thank you!

    • MariaD says:

      Hi Carmen, glad to see your excitement! Have you missed the first assignment – how to teach your baby to find the surface area of a general paraboloid by surface integration? Just kidding – happy April 1st!

      I can’t wait to start, as well. We plan to email everyone a questionnaire today, and to start daily emails this weekend. Several people asked similar questions. So next time we organize a course, we will open the forum together with the registration. This way, people can start meeting one another and discussing their math adventures.

  10. Elena C says:

    Dear Maria, I am having a lot of troubles to register. I used Internet Explorer and Firefox but neither of them worked properly. When I click on button “contribute” in IE it gives me an error. When I use Firefox, I can not change the price tag. Has anyone else experienced similar problems? Thanks a lot.

  11. Erika says:

    Is it possible to use this course for teens who could use a boost & better understanding of multiplication?

    One is presently struggling in Algebra & the other is currently in pre-algebra.

    Thank you for your time, assistance & advice!

    • I think this course would be great, just great, for teens. I did the course with my 9-year-old daughter and some of her 10-year-old friends (all homeschoolers). We did it in my living room. When my teenage daughter would come home from school later on each of those days and see the materials and work done, she would be incredibly interested in the math that we had done, and asked if I could do some of the activities with her over the summer.

  12. Wes Rajesh says:

    Dear Madam,

    I listened to your video “Math Cafe: What is multiplication?” with great interest. Like you, I am too fascinated by patterns.

    My research suggests that multiplication or, more accurately, product is a thought pattern common to many forms of human expression. Just like you, I too studied the issue of metaphor in human expressions, but I did not limit it to mathematics.

    Multiplication is often introduced to children as ‘a kind of addition’. Three plates with four cookies each are typically presented as a single row of cookies which are then counted to find the total. This is only one way of thinking about products, however.

    I looked at the issue from a more general view point of cognition which suggests that one can think of multiplication 4 x 3 as an association between the value of 4 and its repetition (3 times), where 4 is a nested concept and 3 is a concatenation.

    Repetition is a straight forward concept, but understanding nesting could pose a problem. Nesting in this context is a special way of thinking in which value 4 depends on value 3, which depends on value 2, which depends on value 1, which depends on value 0. For value 4 to exist, all other values have to exist at the same time. Value 4 is therefore a state, and repetition is a process. Consider a container of water as an example – 1 litre of water includes 3/4, which include a half of a litre, which includes 1/4 litre, which includes no water. This could be represented as a group of nested circles. Remove any of these scales and one litre is no longer. On this account, product combines smaller scale nesting (e.g. 4 cookies or 1 litre) with the large scale repetition (e.g. 3 plates or 3 containers) or, in other words, the state of nesting with the process of repetition.

    All this might sound a bit obscure. If you are interested in the issue let me know by return email.

    My regards, Wes

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