Learning basic multiplication is easier if we have some association or “hook” with which to relate a particular problem. Here’s something I’ve done with 3^{rd} graders for those difficult factors of 6, 7, and 8.

I use one page per factor, so 3 sides, 2 sheets of paper per student. The students have already used Cuisenaire Rods to work out the products either on a meter stick or the 56-cm number line. Or sometimes they have colored the sevens (or sixes, or eights) on the number line, alternating different colors for each seven as shown here. Then they complete the problems at the bottom, one column at a time. Decide at which point you want them to cover up the number line.

The coloring is best done with colored pencils or fine point markers. You really need to monitor the precision of their coloring closely; if a student colors the third multiple of seven only to 20, then all the products greater than that will be off by 1. I have them circle each multiple as they get to it.

Students supply their own associations with a particular product. Of course, we discuss these as a group and write ideas on the board, but many numbers will call up different associations from different people, so students are free to write their own.

Download Multiplying With Associations.docx

Here’s a blowup of the above image.

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