Primary students (K-2): number recognition, shapes, patterns, number line, even/odd numbers
Intermediate students (3-5): looking for patterns, multiplication, shapes, number line, even/odd numbers
I'm calling this one 'Patterns on the Number Line' but it really has to do with the pattern associated with the square number 36. The number line runs from 1 to 12. 6 is the center of all the patterns beginning with multiplying 6 by itself to get 36 - a square number. The two numbers on either side of 6, 5 and 7, are then multiplied by each other (below the line) to get 35 (written above the line). Then the two numbers on either side of the 5 and 7 - 4 and 8 - are multiplied by each other and so on.
Upper elementary students will easily be able to see the multiplication problems. The patterns associated with the square number 36 takes a lot of 'noticing' and I didn't really expect them to find any without some guidance. This would actually be a fun exercise to do in the classroom.
Notice how the numbers that were multiplied together are listed above the 6 on the number line: 36, 35, 32, 27, 20. Students can look at these numbers and find the pattern of consecutive odd numbers: 36 - 35 = 1; 35 - 32 = 3; 32 - 27 = 5 and so on.
Another pattern has to do with consecutive even numbers: 7 - 5 (7 and 5 are the two numbers multiplied together) = 2; 8 - 4 = 4; 9 - 3 = 6; 10 - 2 = 8
There's another pattern that has to do with square numbers.
6 x 6 = 36
5 x 7 = 35 (36 - 35 = 1 - the square number of 1 x 1)
4 x 8 = 32 ( 36 - 32 = 4 - the square number of 2 x 2)
3 x 9 = 27 (36 - 27 = 9 - the square number of 3 x 3)
2 x 10 = 20 (36 - 20 = 16 - the square number of 4 x 4)
To tie in even more squares, notice the purple and green and blue squares made by the lines...
"The bottom numbers are what you multiply to get the answer."
"I see a line from # 1 - 12."
"Triangles."
"A variety of addition problems."