Maria Miller Hello again!

Here are this month's collection of tips. 😀

  1. Math Mammoth news
  2. Visualizing factors (grades 4-7)
  3. A question on drilling the multiplication tables (grades 3-4)
  4. Geometric art project: flower design with with seven circles (grades 4-12)
  5. Data Science from Youcubed (grades 9-12)
  6. Just for fun!

1. Math Mammoth news

  • Grade 6, Canadian version is now available.
  • I'm working on a new book for the BLUE series, titled Geometry 4. This will cover geometry topics in the 8th grade level: geometric transformations (translations, rotations, reflections, dilations), common angle relationships (vertical angles, corresponding angles, alternate interior angles, etc., and interior and exterior angles of a triangle), and volume of cylinders, spheres, cones, and pyramids.

    This will probably be available within a month or so.

2. Visualizing factors

Look at this NEAT visual representation of the counting numbers:

(originally from Mike Naylor)

Check out also this animated visualization of the same... it is mesmerizing.

The first task to give to your students is to figure out HOW is it made? What is it based on? The last number on this chart is 49. Can you figure out how to make the next number, 50?

Malke shared a cool factor domino game with her readers. We played it, too. Here's one of our games:

Factor tiles in our factor domino game
(We had a few cards that were not the same size; just ignore that.)

Basically, you may put a card next to another if they share a factor. Using these visual dominoes makes children easily learn about factors and factorization. Please visit Malke's blog to read the rules and see more details.

Here are a few other things you can do with these cards:
  1. Organize them in some way. For example, you could find all multiples of 5, all multiples of 4, or all primes.
  2. Pick up two cards randomly and tell their least common multiple (LCM). This can easily be done if you notice their factorization from the visual (the LCM has to include all the factors from both numbers).

As to finding the greatest common factor, you can do that too, but I feel it would work better with bigger numbers.

3. A question on drilling the multiplication tables

A question from a customer, concerning MM grade 3:
We are getting ready to start Chapter 3 on the multiplication tables on Monday. I wasn't sure if I am supposed to drill the facts of 2 until they are memorized, before she starts the worksheets for 2, or should she do the worksheets pertaining to 2 and then drill until she has them memorized? She is really looking forward to learning her multiplication tables. It's so nice! 🙂 Thanks!

Chapter 3 in grade 3 is a comprehensive study of the multiplication tables, and when you're working on those, the BASIC idea is to stay on a particular times table until it is mastered. That can take a varying amount of days based on the child, how often you practice, what else is going on, etc. It is best to practice each table at least two times a day (because our brains will memorize things much quicker if things are reinforced often), but that doesn't have to take a long time at a time.

HOWEVER, you can also study some OTHER math concept(s), such as geometry, addition, or measuring at the same time, as long as these other topics don't rely heavily on multiplication tables (e.g. division or fraction arithmetic). So, you could in effect be studying in two chapters at the same time.

Also, incorporate some games to keep the learned facts "in her brain." The old idiom "use it or lose it" comes into play here. As she masters more facts, she will probably enjoy playing multiplication games, whether online, on the computer, or other types of games such as card games and board games.

See also:

4. Geometric art project: flower design with with seven circles

Here's how to make a flower design with seven circles using a compass, and then coloring it using 2, 3, or 4 colors (or however many of your own). I think it ties in neatly with mathematics, and lets students practice drawing circles with a compass.

My girls did this art & math project, well, 9 years ago, and loved it! See the pictures they made, and full instructions on how to draw this yourself:

Geometric art project: flower design with with seven circles

5. Data Science from Youcubed

Are you teaching high school math?

Check out the free Data Science course from YouCubed.
This curriculum will introduce students to the main ideas in data science through free tools such as Google Sheets, Python, Data Commons and Tableau. Students will learn to be data explorers in project-based units, through which they will develop their understanding of data analysis, sampling, correlation/causation, bias and uncertainty, probability, modeling with data, making and evaluating data-based arguments, the power of data in society, and more! At the end of the course students will have a portfolio of their data science work to showcase their newly developed abilities.

The curriculum will be adaptable so that teachers can bring in datasets or use what is provided to find datasets most relevant to their students. The course has received A-G approval in California, so it can be taken as an alternative to Algebra 2, or in addition to Algebra 2. It can lead to a pathway in calculus, statistics, data science, other STEM or humanities subjects.

6. Just for fun!

Thanks for reading! 🙂

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Till next time,
Maria Miller

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