Identify, create and extend numerical patterns.
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?
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.
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
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.
- 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 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 Item 1
What are the fourth and fifth terms of the sequence below that follows the rule “subtract 4”?
34, 30, 26, ____, ____
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Access Points
|Access Point Number
|Access Point Title
| Extend a numerical pattern when given a one-step addition rule (e.g., when given the pattern 5, 10, 15, use the rule add 5 to extend the pattern).
|Decomposing Into Equal Addends
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.
|Adding Odd Numbers
Students are asked to consider what type of number results when adding two odd numbers and when adding three odd numbers.
|Adding Odds and Evens
Students are asked to consider the parity of the sums of two even numbers, two odd numbers, and an even and an odd.
|Patterns Within the Multiplication Table
Students are asked to find the missing numbers in a column of a multiplication table by using a pattern found within the table.
|Multiplication of Even Numbers
Students are asked to determine if the total number of students in five classes will be even or odd.
|One with a Bun (Exploring the Multiplicative Identity Property of 1)
In this lesson students will explore the Multiplicative Identity Property of 1, using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication equations, and identify patterns in a set of multiplication facts to develop understanding of the Multiplicative Identity Property of 1.
The lesson uses a movie making theme to teach the characteristics and purpose of arrays, as well as the vocabulary, factor and product.
|Arrays Show the Way to the Multiplication Chart
This is an introductory lesson to explore the use of arrays to solve multiplication problems. Students build arrays and save the arrays in a class Multiplication Chart. They learn to use arrays to find products and factors, and by placing them in the Multiplication Chart, they learn how to read the chart. They learn how to write equations to represent situations that are modeled with arrays. An overall theme is the organization of the multiplication chart and how it includes arrays within.
Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property. Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application problem on an Exit Slip.
|Fall Fun and Games! (Exploring the Commutative Property of Multiplication)
In this lesson, students will build and manipulate a variety of arrays in the context of creating games for a Fall Festival. They will practice using the Commutative Property of Multiplication to find related multiplication facts.
|Apples, Oranges, and Bananas of Math?
In this lesson, the students will work in independently or in small groups to write equations to represent situations as well as their own math riddles around the concepts of multiplication. The teacher will use the book, The Grapes of Math by Greg Tang, to support this lesson.
Original Student Tutorial
Original Student Tutorial