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UPDATE 3/17/19: The updated cards can be found in this post (Multiplication Subitizing Cards: An Upgrade to Building Fluency)

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Learning basic facts through tricks or aÂ mnemonic song lead students down a path of memorization, not understanding. Â I previously discussed the idea of conceptual development here. Â When students practice their multiplication facts, they’re expected to move from concrete to abstract too quickly. Â This takes time!!!

Moving too quickly forces memorization and avoids any possibility of multiplicativeÂ thinking. Â First students are asked to model 3Â rows of 6 using colored tiles…

Then after a day or two of exploring arrays, students are magically expected to remember that…

Intensions are good but strategy development is the key underpinning of automaticity. Â In the past I’ve asked myself the following questions:

• When do students practice multiplication that’s not written as AxB? (for the purpose of automaticity)Â
• When/how is multiplicative reasoning fostered?
• When do multiplication strategies become automatized?
• When do number strategies become number knowledge?

My answer to all 4Â questions….I useÂ multiplication subitizing cards with my daughter whose in 2nd gradeÂ so I figured I’d videotape and share.

My takeaways:

• It’s easy to identify which facts she’s comfortable with and has automatized.
• At 1:15– sheÂ demonstrates how she used multiplicative thinking for 6×6.
• At 2:00- she couldÂ use her understanding of the commutative property for multiplication to build fluency. Â She was quickly is able to recognize that 7×5=35 at 1 minute, but it took some time to figure out 5×7. Â She owns this strategy for addition so I’m waiting for it to click with multiplication….no rush:-)
• At 2:20– I missed a fact when she was wrong (doh!)
• At 2:48 and 3:55 she explains her multiplicative reasoning.

5 minutes spent purposefully building fluency and I gained so much information about my daughter. The great thing is that it works for every 8 year old…even the ones in your school.

Disclaimer: I didn’t create the cards and don’t know who did but they deserve a virtual math hug! Â If you know who did please let me know so I can give proper attribution!

Cheers!