Samantha HorschUnderstanding and Teaching Patterns and Functions Task #2A: Patterns and Functions Content Standards3rdGrade 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 TrainingDayNumber of TimesRan around theField2639412515Solution: 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 therule 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 3rdgrade, 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. 5thGrade 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,___,158Solution: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