Sequences
A list of numbers in a particular order.
What is a sequence?
Figure 1 has 5 tiles, Figure 2 has 9, Figure 3 has 13. How many tiles does Figure 4 have?
What is 17?
The amount added or subtracted each time.
What is the constant difference?
Which doesn't belong: 2,5,8,11 or 9,9,9,9? Explain.
Accept any well-supported reasoning.
Create a sequence with a constant difference of 6.
Any valid example.
Find the constant difference: 4, 7, 10, 13, ...
What is +3?
Figure 1 has 5 tiles, Figure 2 has 9, Figure 3 has 13. How many tiles does Figure 10 have?
What is 41?
The amount multiplied or divided each time.
What is the constant ratio?
Describe 2,4,8,16,32 using only words.
Each term is double the previous term.
Create a sequence with a constant ratio of 4.
Any valid example.
Find the constant ratio: 2, 6, 18, 54, ...
What is ×3?
Figure 1 has 5 tiles, Figure 2 has 9, Figure 3 has 13. Which changes in the pattern: the figure number or the constant difference?
What is the figure number?
A student says 5,8,11,14,17 has a constant ratio. Agree or Disagree? Explain.
Disagree, because it is a constant difference.
Describe 100,95,90,85,80 using only words.
Each term is five less than the previous term.
Which grows faster over time: adding 4 each term or multiplying by 2?
Multiplying by 2.
Find the 8th term: 4, 7, 10, 13, ...
What is 25?
Figure 1 has 5 tiles, Figure 2 has 9, Figure 3 has 13. Why can different strategies lead to the same answer?
Because they represent the same pattern.
Does 4,8,16,32 have a constant difference or constant ratio?
What is constant ratio?
Describe 1,1,2,3,5 using only words.
Each term is the sum of the previous two terms.
Write the next two terms: 3,8,15,24,35,...
What are 48 and 63?
Name one strategy for finding a later term without listing every term.
Examples: use a table, look for a pattern, write a rule.
Explain why extending a table works.
Because the pattern continues consistently.
Does 100,90,80,70 have a constant difference or constant ratio?
What is constant difference?
Why is explaining your thinking important?
It helps justify and communicate reasoning.
What is the constant ratio for the following sequence?27,9,3,1
What is 1/3 or dividing by 3?