Investigations in Multiplication

“Efficiency and economy simply do not make good pedagogy.”

― Paul Lockhart

We teach a subject not to produce little living libraries on that subject, but rather to get a student to think mathematically for himself, to take part in the process of knowledge-getting.”

― Jerome Bruner


  1. Review Game: Half-Blind Teacher


Students use white boards or paper to show the teacher the answers to 3 types of review problems:

* Powers of 10 multiplication & division
* Multiplication Diamonds

* Drawing fraction multiplication


Follow up the review game with this set of classwork problems:

(Link to Puzzle Point instruction page)

2. Introduction to Order of Operations, and a “Mad Dash” Game


3. Multiplication with Blocks – Alpha Beta Gamma Game


4. Guessing Game – Powers of 10

This is purely a guessing game – there is no need to keep score or track correct answers. However. it’s a good idea to reward participation.

After the game, a review sheet:

5. Multiplication and ART

Here are a couple choices that involve the multiplication table. The links below include instructions. These files use Google docs, but could be adapted to paper and pencil.

These projects are based on work by a blogger called “@mathrecreation”


6. Order of Operations, Part 2

Another “Mad Dash” game to build students’ comfort with the rules for order of operations.


7. Investigating Students’ Visualization of Multiplication

This lesson encourages the development of flexibility around multiplication by asking for multiple representations of mental math questions.

The lesson is based on lesson from Jo Boaler’s book “Mathematical Mindsets“, page 58.

8. Two-digit Multiplication Puzzles

9. Mental Multiplication Shortcuts – Friendly Numbers

In honor of Valentines Day! Are there numbers that love each other??

You might use white boards with this activity, and have students hold up their answers.

PUZZLE TIME – Binary Puzzles: Binairo and Heyawake. These are both clever and enjoyable logic puzzles. There is a short video explanation for each puzzle. The website does not provide solutions, but does confirm correct solutions. So students can email you a screenshot of any puzzles they solve correctly. (for puzzle points!)


10. Mental Multiplication Shortcuts – MORE Friendly Numbers

11. EVEN MORE Mental Math Multiplication Shortcuts

12. Review Day – Chips Game

Instructions on how to play this game


Puzzle points for fast finishers:

Quiz #4, Trimester 2 – What about Assessment?

Link to blog about the philosophy behind our assessments.




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