[Edit 4/14/14: If you came here looking for a blank multiplication grid, see this post for our PDF times tables.]
Three Free and Easy Ideas
During the 2007-08 school year I was a tutor with an agency serving the Los Angeles Unified School District under funding from No Child Left Behind (NCLB). A pre-test selected three California state standards that I was meant to enforce in each student, all of whom were unwilling and less than thrilled with school in general. I was on my own in terms of teaching materials and, feeling sorry for my bored kids and sensing the inefficacy of plain old worksheets, I found myself flexing my creative muscles to generate solutions, which I would like to share with any tutor or teacher who needs some inspiration.
In Praise of Play
At A C Bilbrew Public Library I met twice a week with a third grade girl, primarily to work on California Standard N.2.4: “Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers.” Though the pre-test did not identify single-digit by single-digit multiplication as one of her top three trouble spots, I quickly realized that the reason she was most often unable to solve the multi-digit problems was because she had not completely memorized her multiplication table. So, although technically I was only supposed to teach the three standards the pre-test identified, I obviously had to build a foundation before we could get anywhere with the long multiplication.
Actually, it wasn’t as simple as knowing whether she had memorized her times table or not. She was shy and afraid of displeasing the person quizzing her. So, at first, she just alternated through cycles of saying nothing and of spewing random answers, grasping for the one that would make me say “yes, that’s right” and move on. Before I could help this student memorize her multiplication table, I first had to get her to trust me and feel at ease. I noticed that she had a playful personality and responded well to humor and games, so my strategy became to design ways to turn multiplication into play.
While gazing upon a blank multiplication table (we now offer our own PDF times table here), I recalled a grid-based learning game of my early education, Number Munchers, and I thought I don’t have to design anything fancy; I have a gameboard right in front of me.
So I drew a set of maze-like obstacles in pen on a blank table and at the next session we played a game that fell somewhere between Number Munchers, checkers, and tag. The offensive player started at the left 5×0 position, while the defender started at either the top 5×0 or the bottom 5×10. The offensive player ran for the exit at the right hand 5×10 while navigating the obstacles and avoiding getting tagged out by the defensive player. It was turn-based, and in order to move, each player had to solve the desired adjacent square.
My third grader greatly preferred this game to any other method of rehearsing multiples that I had come up with and she requested to play it regularly, even after it was time to move on to address the standard directly and we had to leave the game behind.
To make our multi-digit practice problems more interesting, I wrote a (very bad) fantasy story and made it so that she had to solve multi-digit by one-digit problems to get the key to insert the missing words. It’s a straightforward premise and by no means original, but I’ve included a sample page here to illustrate the idea.
Engage Existing Interests
Some of the best mathematicians I know are not mathematicians, but carpenters, and it isn’t because all these woodworkers love math, but because math is an unavoidable part of what they do love, carpentry. Any 1:1 educator can use this principle to give a reluctant student a pathway into the subject at hand. A sixth grade math student I tutored in the Pico-Robertson neighborhood had exactly no interest in math per se, but he had a predilection for the natural sciences, specifically biology/zoology.
So I bought a large piece of poster board and I told him we were going to make a zoo. The standards we had to work on included some basic geometry, such as the measurements of circles and rectangles, so we drew the foundations of circular and rectangular cages in his zoo, and I had the student produce the proper measurements for me. Another standard we worked on had to do with rates of change. So when we had introduced a rabbit population or a tiger population, I had him predict population change over time given certain rates of growth or decline.
By engaging a student’s interests and embedding problem solving into play, it becomes much easier both to gauge what a student already knows and to spur the student towards practice and mastery. As a tutor I had the luxury of working with students 1:1, and even under the regulations that followed from the NCLB funding I had plenty of room for experimenting and plenty of time to get to know individual students, two things many classroom teachers can only wish they had. But whether you are a tutor, teacher, or even a professor, a little ingenuity can only improve upon the tired old worksheet of plain number problems.