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Examples
Bailey collects 6 baseball cards every day. This generates the pattern 6,12,18,… How many baseball cards will Bailey have at the end of the sixth day?Clarifications
Clarification 1: The expectation is to use ordinal numbers (1st, 2nd, 3rd, …) to describe the position of a number within a sequence.Clarification 2: Problem types include patterns involving addition, subtraction, multiplication or division of whole numbers.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to identify, create, and extend numerical patterns using all four operations. Understanding of ordinal numbers from Kindergarten is the foundation for describing the sequence of numbers in a pattern.- “ Identifying” a numerical pattern requires students to determine when a pattern exists in a sequence of numbers, and to potentially determine a rule that can be used to find each term in the sequence. For example, students may be asked whether a pattern exists in the numbers 20, 17, 14, 11,... and to discuss possible rules used to determine the next term.
- “ Creating” a numerical pattern requires students to write a pattern given a rule and starting value. For example, students may be asked to write the first five terms of a sequence that begins with 500 and then create each successive term by subtracting 35 from the previous term.
- Finally, “extending” asks students to identify a future term in a sequence when provided with a rule. For example, students may be asked to find the next three terms in which each term is multiplied by 2 to get the next term 2: 1, 2, ___, ___, ___ (MTR.2.1, MTR.5.1).
- Instruction of this standard can begin by relating patterns to skip-counting to explore patterns in sequences of numbers and look for relationships in the patterns and be able to describe and make generalizations. When exploring patterns, teachers should allow for students to describe pattern rules flexibly. For example, in the pattern 6, 12, 18,..., one student may describe the pattern’s rule as “ add 6.” Another student may describe the rule as, “ add 7, then subtract 1” or “ list the multiples of 6.” Classroom discussion could compare these rules (MTR.2.1, MTR.4.1).
- Instruction should be limited to whole numbers and operations that are appropriate for Grade 3.
- This foundation for identifying and using patterns extends into Grades 4 and 5 to build algebraic thinking for functions in middle and high school.
Common Misconceptions or Errors
- Students can confuse a term’s number and its value in the sequence. For example, in the pattern 6, 12, 18,..., students can struggle to understand that even though 12 is the 2nd term, 6 is being added to it to find the value of the 3rd term (18). Encourage students to use precise vocabulary while describing patterns to address this confusion.
Strategies to Support Tiered Instruction
- Instruction includes explicit vocabulary instruction regarding patterns (first term, second term, third term..., rule, value, etc.). Instruction also includes relating the pattern to skip counting where appropriate.
- Example:
- For example, a 100 chart may be a referent that can be used for arithmetic patterns. The teacher makes connections between the rule and counting on the 100s chart.
Instructional Tasks
Instructional Task 1
- Part A. Write a pattern that shows the first 10 multiples of 6.
- Part B. What do you notice about the ones digits of the pattern’s numbers?
- Part C. What would you expect the ones digit of the 12th multiple to be? Explain how you know using the pattern you observed.
Instructional Items
Instructional Item 1
What are the fourth and fifth terms of the sequence below that follows the rule “subtract 4”?*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
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Formative Assessments
Lesson Plans
Original Student Tutorial
STEM Lessons - Model Eliciting Activity
This is a 3rd grade MEA that requires students to use mathematical patterns to solve the problem, along with the analysis of data. After reading One Grain of Rice by Demi, students will look for ways to help Rani's relative find a new pattern so she can secure a large supply of rice to feed the people of her province in India. The twist is likely to cause controversy, so prepare for some strong debates.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to consider what type of number results when adding two odd numbers and when adding three odd numbers.
Students are asked to consider the parity of the sums of two even numbers, two odd numbers, and an even and an odd.
Students are presented with an equation and asked to find a pattern within the equation and to determine if the equation is true or not.
Students are asked to determine if the total number of students in five classes will be even or odd.
Students are asked to find the missing numbers in a column of a multiplication table by using a pattern found within the table.
Original Student Tutorials Mathematics - Grades K-5
Determine if the sum of three odd or three even numbers will be odd or even as Lilly prepares for a math celebration in this interactive tutorial.
This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.
Student Resources
Original Student Tutorial
Determine if the sum of three odd or three even numbers will be odd or even as Lilly prepares for a math celebration in this interactive tutorial.
This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.
- Part 1 - Party Patterns: Odds and Evens in Addition
- Part 2 - Party Patterns: Odds and Evens in Addition
Type: Original Student Tutorial
