Samantha Horsch
Understanding and Teaching Patterns and Functions Task #2
A: Patterns and Functions Content Standards
3
rd
Grade Standard:
Standard - CC.2.2.3.A.4
: Solve problems involving the four operations, and
identify and explain patterns in arithmetic.
Problem
: Mr. Smith is running a race. The table below shows the number of times he ran
around the football field on 4 different days. Describe the pattern shown by the number of
times Mr. Smith ran around the football field.
Mr. Smith’s Training
Day
Number of Times
Ran around the
Field
2
6
3
9
4
12
5
15
Solution:
Students will identify the problem. They will underline important keywords that focus
on what the problem is asking. Students should understand that the data has been collected
over four days and that they are finding a pattern. Students will ask themselves, “How do I get
from 2 from 6?”. Students will say that you have to add 4. It is important that students check the
rule to be sure that it applies throughout the entire table and pattern. Students will ask
themselves, “How do I get from 3 to 9?”. They will understand that the rule is add 4. They will
then complete the next steps of applying the rule to day 4, and day 5, to determine that the
pattern is “add 4”.
Patterns and Functions:
Beginning the in younger grades, students learn how patterns repeat
themselves and can continue on for however long needed. In 3
rd
grade, it is important that
students understand now that they can apply different operations to patterns, such as addition,
subtraction, multiplication, and division. As students’ progress into the later grades, they will
utilize the operations to form patterns in equations and ratios.
5
th
Grade
Standard: CC.2.2.5.A.4
: Analyze patterns and relationships using two rules.
Problem:
Autumn and Nick each make a pattern.
Autumn’s pattern starts with 12 and uses the rule subtract 6, then multiply by 3.
Nick’s pattern starts with 8 and uses the rule multiply by 2, then add 2. What are the missing
numbers in the sequence?

Autumn’s pattern:
12,
18,
___,
90,
___
Nick’s pattern:
8,
___,
38,
___,
158
Solution:
Student’s will first differentiate the rules for each pattern. They will determine that
Autumn’s pattern is subtract 6, multiply by 3 and Nick’s pattern is multiply by 2, add 2.
Beginning with Autumn’s, students will have to start by determining the third number in the
sequence. Students will use the given rule. They will begin with the second number, 18. They
will first subtract 6 (18-6=12), then, they will multiply by 3, and get 36. They will then determine