Archive for December, 2010

Does our math education impact how we value math (or don't)?

Wednesday, December 29th, 2010


The author of Social Media for Trainers and I have been having an interesting debate about the place of higher math education in schools. I had read her book and found it useful, so I looked up her Facebook page. There, under the heading, “Stop teaching math,” she placed a link on her Facebook page to the blog article titled “The Case Against Math.” Of course I found this provocative and clicked over to read the article.

While I agree with the thesis of the article – that the way we teach math and value it as a proxy for measuring intelligence is not useful, and that it should be changed – I do not think we should reduce or eliminate it as a requirement in education. Instead, I agree for the most part with how the article’s author puts it:

“If we must teach math, teach it  as if math was just one aspect of the larger concepts and questions that are the main thrust of education: critical thinking, problem solving, communication, empathy, and creativity. If we must teach math, teach it through music, art, science, technology, history, cooking, construction, engineering etc. because math as an abstract system is useful to very few of our students. If we must teach math, focus less on the answers and the algorithms for specific types of problems and focus more on the questions and the processes of problems.”

I do think that teaching math in an integrated way is best, but I also see merit in teaching math as a subject unto itself, as long as it’s taught in ways that make sense. The process of teaching through problem solving and from conceptual to abstract allows math to make sense to all students I’ve encountered, and problem solving therefore becomes a fun challenge, not a chore.

As I mentioned on the Facebook page, I once had a friend who was working as a carpenter. He asked for my help in figuring out how long a piece of wood needed to be to complete an attic renovation project. I showed him how to solve the problem using the Pythagorean theorem. This was before I became a teacher, but he told me that if he had had teachers like me in high school, he probably would not have left school, as this was useful stuff to know.

The author’s response was to ask 3,000 Twitter followers for examples of using advanced math in their everyday lives. She received one tweet about a problem similar to the carpentry one, and one about helping a child with trigonometry homework.

This doesn’t surprise me if the vast majority of her followers are Americans. I would love to know, though, if we would get a different response from people raised in other countries, especially those in countries that have consistently scored highly in math. If no studies have been done on this, I would like to study it myself. Does how we are raised to think of math affect how we use it (or don’t) in our daily lives, or is the subject objectively useless to all but scientists and engineers and taught only as a carry-over from ancient times? What do you think?

UPDATE: I discussed this topic today with a student of mine who is “unschooled” and started fifth-grade Singapore math with me when she was 15 years old. Two and a half years later, she is at high school Algebra level. Her main interest is fashion design, and she’s been attending high school fashion design classes for a couple of years. She told me that she was pleased to put her fraction knowledge to use in her sewing class last spring. That’s only one story; do you have your own?

Math Sentence Frames Wiki

Wednesday, December 15th, 2010


In a training today, I learned about sentence frames. These are helpful for English language learners, and also native speakers, to develop understanding of math concepts by filling in a statement with blanks in it.

In researching this further, I came across a wiki that contains a number of sentence frames for various California math standards categorized by grade level. These can be used in any context to fit your math teaching. You can even contribute your own sentences by joining the wiki.

Go to the wiki here:

New Multiplication Activity Available – Free!

Wednesday, December 15th, 2010


For my educator friends and colleagues, I have added a new multiplication chart lesson plan, complete with reproducible handouts, to It is free to download and use. It can be used in a classroom, in a homeschooling setting, or in a special needs or remedial context.

The lesson is aligned to the Common Core Standards and includes objectives, materials, and descriptions of procedures, follow-ups and adaptations. Please let me know if you find it useful, and if you do, please add a rating to the TeachersPayTeachers site.

Download the lesson plan here.

Tips for Times Tables and Dividing

Monday, December 6th, 2010


Teachers in my math workshops like me to share some multiplication and factoring tips I teach my students. These help with number sense as well. I hope they can be useful for you too.

Tips for Multiplying Whole Numbers

  • Times 2: Double the number. If multiplying by 2, the result will always be even.
  • Times 3: Triple the number. Products alternate odd and even (3, 6, 9, 12, etc.).
  • Times 4: Double the number twice. The result will always be even.
  • Times 5: The result must have a 5 or a 0 in the ones place.
  • Times 6: Triple the number and double it, in whichever order is easiest.
  • Times 7: These must be memorized. (Please add a comment below if you know a trick for these!)
  • Times 8: Double the number once, double it again, and double it a third time. The result will always be even.
  • Times 9: Two tricks here for multiplying single digits by 9. 1) The fingers trick: see
  • 2) Take the number you are multiplying by 9, for example 7. The tens digit will be one less than the multiplier (6, in this example). The ones digit will be whatever it takes for the two digits to add up to 9. In this example, 6 + 3 = 9, so the answer is 63.
  • Times 10: The concept here is that when multiplying by 10, it increases by one place value. So 1 x 10 is 10, 10 x 10 is 100, etc. Thus you append a 0 to the number, increases the value by one place. The result will always be even.
  • Times 11: For 1-9, the result is always that both digits will be the same as the multiplier, for example, 3 x 11 = 33. For two-digit numbers 10-19, there is a cool trick. The first digit will be the same as the first digit of the multiplier; the second digit will be the two multiplier digits added together; and the last digit will be the second digit of the multiplier. For example: 11 x 18 = 198, 11 x 13 = 143, etc. Just sandwich in the sum of the multiplier’s digits between the multiplier’s digits to get your product!
  • Times 12: Same as the 6 trick, but double the result.

Tips for Dividing or Factoring Whole Numbers

If you are trying to check to see if a number is divisible by another number, or can be factored by that number, or has a common factor with another number, these tips can be helpful.

  • Divisible by 2: Any even number.
  • Divisible by 3: Add up the digits as if they are all ones. If the sum is divisible by 3, the number is divisible by 3.
  • Examples: 143 -> 1+4+3 -> 8, so not factorable by 3. 144 -> 1+4+4 -> 9, so factorable by 9
  • Divisible by 4: If an even number is still even when you cut it in half, it is divisible by 4.
  • Divisible by 5: Any number ending in 5 or 0.
  • Divisible by 6: Any even number that fits the 3 rule.
  • Divisible by 7: Memorize these.
  • Divisible by 8: If an even number is still even when you cut it in half, and in half again, it is divisible by 8.
  • Divisible by 9: Same as 3 rule, except the sum of the digits must be a multiple of 9.
  • Divisible by 10: Any number ending in 0.
  • Divisible by 11: See the Times 11 rule and reverse it.
  • Divisible by 12: Any number that fits both the 3 rule and the 4 rule.

I also recommend Greg Tang’s book The Best Of Times, which is full of multiplication tricks like these, but in a fun, picture book format that children will enjoy experiencing.

A great video showing how to fill in a times table chart, and learn the facts while you are doing so, can be found here:

If you have learners who struggle to learn their multiplication facts because they have trouble memorizing or can’t learn through these tips, or are just kinesthetic learners, try playing games where children toss a ball back and forth while skip counting with different tables. If they don’t know the tables at all, they can use a chart on the wall for reference while they are learning. Like with any skill, practice and repetition will eventually lead to mastery.

NaNoWriMo YWP TGIO Party

Monday, December 6th, 2010


On Friday, my young writers and I had a Thank Goodness It’s Over party to celebrate our accomplishments during the month. The TGIO party is a well-established tradition for any NaNoWriMo group. I have always used it to showcase and celebrate each individual child’s writing.

We met at a family’s home, and each child had five minutes to read an excerpt from his or her story. I was impressed by the quality of the writing; three years of doing Nano for most of them has led to exceptional storytelling abilities in these young writers. During the reading part of the get-together, we had the usual stage fright issues, eventually overcome, and we had to practice being a good audience, also as usual.


The new experience was that one of the students had written a song and dance into his story, and he read us the description. His mother encouraged him to perform it for us, which he did. What followed was an expression of pure delight and joy as the boy rapped out a song and did a rhythmic, but hilarious, dance with it. We all laughed so much, along with him, that nobody managed to videotape the performance, but I did manage to snap a photo or two. That was an experience I will never forget.

After we all had a chance to read from our stories, we all enjoyed snacks, and the children played together. It was a perfect ending to a great program. The photo below is me with most of the participants (some couldn’t make it) holding their winner certificates.


NaNoWriMo is Over!

Wednesday, December 1st, 2010


Today is Wednesday, December 1, and November is finally over. All of the students in my program, Your Greatest Writing Adventure Ever, achieved their goals of writing a story in the month. The word count goals ranged from 1,500 to 4,700 words, and their ages ranged from seven to ten. What an amazing accomplishment! Not only the writing, but the fun they had doing it.

Nano Winner

I am so proud of everyone, but I’m also relieved that NaNaWriMo is over. In fact, doing this program is such a mammoth accomplishment that it’s pretty much a requirement to have a TGIO (Thank Goodness It’s Over) party at the end of the month. I will be attending two: the party for my students on Friday night, and the New York City party for grown-up Nano-ers like me who wrote the full 50,000 words. Time to celebrate our accomplishments! All the students in my program will have the opportunity to self-publish their illustrated works through On that note, my own novel, a futuristic biotech thriller, doesn’t really inspire me to revise and publish it. However, I do think it would make a good screenplay, so my rewrite may be during Script Frenzy in April. That may also be my next group writing program, so please get in touchif you would like your child to participate! Now that November is over, I should also be able to write for the blog more regularly again. I just did not have the time during this month. Writing 1,667 words per day in a story is quite a commitment! I’m glad for the experience, though, as it helps me relate even more to the struggles of my own student writers.


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