17. Examining Student Thinking:
Geometric patterning tasks
Two 3rd grade tasks and associated student work
samples
Questions to consider:
What mathematical ideas do these tasks draw out?
What do you notice? What do you wonder?
What surprises you?
What are the implications for your practice?
18. A Typical Algebra Task
How many squares will be in the 25th arrangement?
Figure Number
1
2
3
Total Number
of Squares
5
7
9
19.
20. A Revised Version of
The Algebra Task
Investigate and report all you can about this pattern.
Figure Number
1
2
3
Total Number
of Squares
5
7
9
21.
22.
23.
24. Investigate and report all you can about the following growing pattern.
Figure Number
observations about the
pattern
a rough sketch or
picture of some larger
figures in this pattern
some different ways of
'finding' the total
number of tile in any
figure in pattern (like
methods of counting, a
table, a graph, a
formula or rule)
Which figure has 120
tiles? How did you
decide? What is
another way to
determine this?
How would you
convince somebody
else that you are right?
2
3
Total Number
of Tile
You may want to consider
including things like:
1
3
8
15
25. 120
Total Number of Tile
100
80
60
40
20
0
1
2
3
4
5
6
7
8
9
10
Figure Number
Figure
Number
Total Number
of Tile
1
2
3
3
8
15
4
5
6
7
8
9
10
26.
27. Investigate and report all you can about the following growing pattern.
Figure Number
observations about the
pattern
a rough sketch or
picture of some larger
figures in this pattern
some different ways of
'finding' the total
number of tile in any
figure in pattern (like
methods of counting, a
table, a graph, a
formula or rule)
Which figure has 120
tiles? How did you
decide? What is
another way to
determine this?
How would you
convince somebody
else that you are right?
2
3
Total Number
of Tile
You may want to consider
including things like:
1
3
8
15
Editor's Notes
Definitions “Continuum of knowledge and skills” means the Oregon Academic Content Standards. “Proficiency” means demonstrated knowledge and skills which meet or exceed defined levels of performance.
Definitions “Continuum of knowledge and skills” means the Oregon Academic Content Standards. “Proficiency” means demonstrated knowledge and skills which meet or exceed defined levels of performance.
Definitions “Continuum of knowledge and skills” means the Oregon Academic Content Standards. “Proficiency” means demonstrated knowledge and skills which meet or exceed defined levels of performance.
“An ideal learning environment or experience occurs when both teachers and students seek answers to each of these questions” (Hattie and Timperley 2007, 88).
