How to Eat an Elephant
"How do you eat an elephant?"
"How?" asked the frustrated fourth grader.
"One bite at a time," smiled the teacher*, and though the child moaned in response, the point had been made.
Any time you have a child who is struggling with acquiring a skill, ask yourself how you can break the skill down into manageable chunks so that "the elephant" can indeed be eaten a little bit at a time.
One skill set that many children struggle to master is learning the basic multiplication facts. Often times, such struggling students become overwhelmed by what appears to be the insurmountable task of memorizing innumerable answers to a vast array of unrelated facts. Over the years, I have found the following exercise a simple but powerful tool that not only breaks the skill down but gives the child visual evidence of his/her progress over time.
You will need:
- graph paper (use regular as shown or 1/2" or 1" for younger students or those with visual-motor delays)
- pen for teacher, pencil for student
- timer (kitchen timer, egg timer, stop watch, the timer app on your phone, etc.)
- Decide if you want the child to work on facts from 1-10 or from 1-12. If you will be working on 100 facts, count across and down 11 graph squares. If working on 144 facts, count 13 across and down.
- Starting in the upper left hand corner, make a multiplication sign. From there, write the numbers 1-10 or 1-12 across the top and again going vertically down the left hand side below the multiplication sign. To save time in the future, you may photocopy the master.
- Cut the graph paper out according to the size you will be using.
- Explain to the child how to fill in the chart and/or show him a completed one. Let him know he may skip around (ex. do the 1s, 2s, 5s, and 10s first). Encourage him to finish an entire series both horizontally and vertically before moving on to a new one.
- Set the timer (or better yet, let the child set it) for a predetermined amount of time (I'd suggest 5-10 minutes initially) and let the child begin, working until the timer rings or he has filled in as many squares as possible.
- Check for accuracy (or allow the child to use a completed chart to do so). Erase any incorrect answers and have the child highlight any empty squares (including those that are now empty due to being erased).
- Work on this body of facts over the next couple days and then decide with the child (guiding when necessary) the next set of facts to tackle. Strategize with him on ways to remember or figure out products in that group (see tips below).
- Repeat daily, highlighting as before. Point out to the child that the highlighted area (which indicates the facts he does not know) is shrinking.
In the illustration above (please note, this is just one sample of how a child's progression might go), the chart at the top shows all the 1s, 2s, 3s, 5s, and 10s being completed along with most of the 11s. Even so, you will notice that some of the 12s are completed because one number in some of their factor pairs is a part of a formerly mastered series. In that chart, there are 35 out of 144 squares left empty. The second chart adds in the 9s which results in 29 out of 144 unknown. In the third chart, only 17 squares remain empty after the 12s have been completed, and in the final chart, just 10 spots are blank after the 4s have been mastered. You may also state these statistics in positive terms if that appeals to you and your child more (i.e. 109/144, 115/144, 127/144, and 134/144 learned).
In doing this exercise, the child will be able to see:
- the relationships among the numbers.
- that he knows more facts than he doesn't.
- that if he knows 3 x 4, he also knows 4 x 3.
- that the more simple facts he learns, the more difficult facts he will automatically learn as an outgrowth of the simple ones.
- his progress is visible right before his eyes.
- that "the elephant" isn't all that big after all!
- 2s - count by twos (ie. write a number, skip a number, and so on)
- 3s - count by threes (ie. write a number, skip two numbers, and so on)
- 4s - add four to the previous number
- 5s - do the sing-songy 5, 10, 15, 20 that is used in hide and seek (play hide and seek if you like!)
- 9s - point out the following pattern: in every product in the nines sequence, the digits add up to 9 (ex. in 18, 1 + 8 = 9; 27, 2 + 7 = 9; 36, 3 + 6 = 9 and so on - even the 9 + 9 in 99 = 18 and then 1 + 8 = 9). There is also a trick with fingers that I can share if interested.
- 10s - each digit in ten's place goes up by one as the series progresses
- 11s - for most of them, you will see double digits or "twins" (ie. 11, 22, 33, 44, etc.)
- 12s - add 10 and then 2 more to the previous number in the series
Notice, if your child learns nothing more than the above tricks, he will only need to memorize 6 x 6, 6 x 7, 6 x 8, 7 x 7, 7 x 8, 8 x 8 and 11 x 11 because, although there were ten squares left, understanding factor pairs reduces the actual number of unknown facts. Integrate this quick exercise into your child's daily math routine, and consider setting goals and awarding small rewards as your child's number of unknown facts shrinks.
*my good friend Cathy