Transcript Lines and Dots

Whiteboardmaths.com
7 2
1 5
© 2009 All rights reserved
Teacher Guidance
A simple (hand-shaking type) investigation based on a set of
Mystic Roses. Students may or may not already be familiar with
the sequence of triangular numbers and some groups may be
aware of the general formula. The slight complication here of
course is that the L = (p -1)p/2.
Obviously it is a matter of tailoring the presentation to suit the
particular group. You may wish to add in formulas etc as you see
fit. Low ability groups can still get quite a bit out of it and if all
else fails slide 8 will keep them occupied (and hopefully thinking).
Printable worksheets are available at slides 6 and 7 should you
wish to use them.
There is more advanced work on triangular numbers in the
presentation “Stairs and Steps”.
Lines and Dots
Draw the patterns shown plus the next two in the sequence and investigate
the relationship between the number of lines and the number of dots.
Dots
Lines
1
0
2
1
3
3
4
6
Lines and Dots
Dots
Lines
1
0
2
1
3
3
4
6
5
10
6
15
7
21
8
28
Complete the table for
the diagrams shown.
18 Point Mystic Rose
Can you use the rule
that you found to
calculate the number
of lines in this 18
point Mystic Rose?
Black 15+ 2 + 3 + … +15 + 16 + 17 = 153
or (17 x 18)/2 if you
are familiar with the
formula for triangular
numbers.
18 Point Mystic Rose
1 + 2 + 3 + … +15 + 16 + 17 = 153