Intended Audience: Teachers, prospective teachers, and parents (public, private, homeschool).
In this video, 7-year-old Autumn realizes that she does know the complete multiplication table! Here’s the story:
Autumn and I have been talking about multiplication and ways to think about multiplication since she was very young (see our other multiplication videos). However, we never tied all the facts altogether into a single table. So when one morning she confidently announced that she knew the multiplication facts up to multiplying by 5, I told her that she actually knew the multiplication facts up to 10. She refused to believe me! So we headed over to the studio and taped this video, partially to have her prove to herself she did know the facts, and partially to summarize all the great strategies we have been working on (in real life and in previous videos).
The video is awesome in that it captures on tape Autumn’s own disbelief in her own knowledge (education researchers take note). Start watching at 6:00 and see her reaction at 6:09–priceless.
For teachers and parents, this video makes three points to think about:
- Assessments such as the one in this video are important part of education because they help students recognize for themselves that they actually know the material. Autumn filled in every entry in the table, and it was only after she saw what she had accomplish did she realize she knew the facts.
- There are only 9(!) entries in the table that are tricky to memorize (watch starting at the 5:50 mark), not 121 as students sometimes think. The 9 entries reduce to just 6 after applying the commutative property (). They are:
These 6 facts can be effectively handled by linking them together by memorizing one fact, , and building to the other facts using the distributive property. The first fact can be given a story to help the child memorize it. (In our case, I told Autumn the story of “What is the answer to the ultimate question of life, the universe, and everything?” from Douglas Adam’s Hitchhiker’s Guide to the Galaxy. BTW: The answer is 42, which literally begs, “What is the question?”) The remaining entries are found using unit math, i.e., counting in different units, via skip counting. We have a lot of nice videos that introduce how to do this: Part I, Part II, Part III.
- Parents: This video once again shows that learning multiplication facts should not be done the old Textbook School Mathematics way where parents buy 121 flash cards and drill their child on all of them until she or he cries. That’s too many facts too quickly. There are better ways to learn the multiplication facts, and they all start with being selective about which groups of numbers are learned together. For Autumn, she learned them in different batches: grouping 2s in one batch, grouping 3s and 4s in a different batch, grouping 1s, 5s, and 10s in a third batch, the 9s by themselves, and the tricky facts, to , in a fifth batch. The batches can be learned simultaneously over a year or two (after the first batch of 2s is used to explain multiplication). The key is to remember to stay within the same batch during a learning session. Follow this advice, and learning the multiplication table can be a very pleasurable experience for you and your child!
A fun fact about the video: Autumn “hisses” like a cat at mark 7:45. We have three cats and enjoy imitating their silly behaviors as a family. If you have cats, you will probably recognize what Autumn was saying. If you have dogs, then the equivalent would be if your dog picked his ears up, tilted his head slightly, and stared at you with the look of, “Stupid human, don’t you get it?”
As always, comments are welcomed.
CHANNEL: Growing up with Eureka
© 2016 Autumn Baldridge and Scott Baldridge
Partially supported by NSF CAREER grant DMS-0748636