The fourth grade has been spending a good deal of time working with their math fact fluency. This week they explored geometric rectangular arrays. This approach helps to solidify concept development. Students worked cooperatively in groups of three or four and were asked to create different rectangles using 12 squares.
Groups came up with different examples such as 1x12, 2x6, 3x4. Each group drew out what they found on 1/2"squared paper and wrote their number inside and cut them out. Next, they were given the number 7 and all came up with 1x7. Students quickly made the connection to factors of the numbers given and related it to the idea of prime numbers. The groups then proceeded to draw out the rectangles for numbers 1-25. They quickly realized they needed to work efficiently and assigned numbers and tasks within their groups.
Once all the rectangles were cut and accounted for we discussed the patterns they saw and worked a bit on new vocabulary. The students were introduced to a way to transfer their rectangles numerically to a chart sharing the rectangles they cut. Laying down each rectangle to the upper left-hand corner of the paper and then lifting the bottom right-hand corner of their rectangle I wrote the number of squares of that array in the square on the 1/2" grid paper. In a rather short time, the students realized I was creating a multiplication chart. They gathered around checking the chart to prove to me their hypothesis was correct. Many students were completely surprised by this discovery.
The idea of the lesson was to involve students in an activity that explored how a multiplication chart could be generated from a geometric investigation of rectangles. Through this methodology, the students were able to see the interrelationship of the many areas of mathematics. The concepts reviewed help students to prepare for the more complicated computation of long multiplication and division that we will soon be embarking on.
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