Intersecting lines -- streets and avenues and their intersections -- are one very useful model for multiplication.
Setup of activity
A tiny town has 5 streets (draw five vertical lines) and only three avenues (draw three horizontal lines intersecting the avenues). At each intersection, there is a stop light. How many stop lights? (15) And then the town grew! They needed another street. How many more intersections are there now? (another 5) How many stoplights total? (20)
Teacher “summarizes” what we know by writing 5 _ 4 _ 20, while saying (but not writing) what those numbers represent. “Oops! I forgot to show that we are counting the crossings and not the total number of roads, so I’ll add the crossing sign 5 × 4 and the equal sign to show that the number of crossings 5 × 4 equals 20.” (See photo below.) Streets × Avenues = intersections
Purpose: Both practice and concept are part of this activity. The practice, which must continue beyond this teacher/led introduction, builds confident familiarity with small multiplication facts (through 5 × 6). Children can get that practice from work on their own, drawing maps of tiny towns (5 streets × 6 avenues at the most, for starters) and counting the intersections/stoplights; or making arrays of city blocks (with tiles) of the same dimensions and counting the blocks (not the streets and avenues that separate them, or the stoplights at their corners). The conceptual part is in the “how many more intersections” when one new street or avenue is added. If we have only avenues and no streets (or only streets and no avenues), there are no intersections (anything × 0 is 0); and if we have exactly one street then the number of intersections is the same as the number of avenues (any number × 1 is that number). Also, if I know 2 × 7, then 3 × 7 is just 7 more. (Children are often not sure whether to add another 3 or another 7 until they have internalized the image of another line and how many crossings it will make.)
On their own
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