Page 116 - IM_Algebra2_FL Print Sample.pdf
P. 116
Student Task Statement
Here is a visual pattern of dots.
0
1
2
3
4
5
0
1
1. Describe in words how to produce one stage of the pattern from the previous stage.
2. Complete the table for , which is the total number of dots in stage of the pattern.
3. Explain why and
4. Explain why
5. Use the recursive rule
6. How di cult would it be to calculate using the recursive de nition?
Student Response
1. A new row of dots is added to the end, an equal number of dots to the stage number.
2. See table.
3. Sample response: Both of these describe how a new stage is built. Stage 4 is built from Stage 3, adding a row of four dots, so . Stage 5 is built from Stage 4, adding a row of ve dots, so .
4. Stage is built from Stage , adding a row of dots. Then .
5. so . Then , so .
6. It would be very di cult, because you would need to calculate every single result along the way.
. for any .
to nd and .
0
1
2
3
4
5
0
1
3
6
10
15
Unit 1
Lesson 5: Recursive De nitions 51
