Planning GuideGrade 2
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Increasing Patterns

Strand: Patterns and Relations
Outcome: 2

Step 3: Plan for Instruction

Guiding Questions

  • What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
  • What teaching strategies and resources should I use?
  • How will I meet the diverse learning needs of my students?

A. Assessing Prior Knowledge and Skills

Before introducing new material, consider ways to assess and build on students' knowledge and skills related to patterns. In Kindergarten and Grade 1, students have encountered repeating patterns. In Grade 1 the repeating patterns contained up to four elements in the core pattern and these were non-numerical: manipulatives, sounds, actions and diagrams only. In Grade 2, these patterns have been extended to contain as many as five elements in the core pattern and numerical patterns with numbers up to 100. Grade 2 is the first introduction to increasing patterns. In Grade 3 they will be reinforced and extended to include more complicated growing patterns, as well as comparing increasing patterns. In Grade 3, decreasing patterns are also introduced.

Some examples of ways to access students' readiness to be introduced to increasing patterns follow:

Given repeating patterns, can students continue the patterns correctly?

  • Start with the very basic student, action or sound patterns.
  • These could be two students standing and one sitting or two facing the door and one the windows.
  • Other patterns to use are clap, snap, clap, patch (hands open, palms down on quads) or twirl, touch your toes, touch your head and hands on your waist.
  • A pattern can be made with arm positions, such as a raised arm as in a right turn signal, out to the side like a left turn signal, dropped at one's side and then held out with hand raised as in a stop signal.
  • Patterns can be shown with boot or running shoe alignment, such as two facing one direction and the third in the sequence at right angles to the first two.
  • Class calendars often show repeating patterns and that is another opportunity to reinforce and extend the skill early in Grade 2.

For specific ideas, see 1a. Patterns can be considered in the context of the student day, such as the class schedule, opening exercises, recesses, movements in the gym, music, songs, and stories. Students can discuss repeating patterns in their home life and routines, such as lessons and practice routines, meals, getting ready for school, bedtimes and other such repeating sequences.

  • Identify the core in a repeating pattern. Given repeating patterns with three to five elements, can students identify in some way the core pattern?
  • Have the students translate repeating patterns into other modes. Ask the students how they could represent the patterns described above or others using colours, shapes, numbers, letters or other things. Unifix cubes can be used to show colour. Pattern blocks can be used to represent shapes.
  • Have the students verbalize their descriptions of patterns and the thinking that allowed them to deduce patterns or predict extensions of the patterns.
  • Have the students create repeating patterns and share them with the class, including numerical ones that are new to them in Grade 2.

Common misconceptions, do students:

  • include the first item in the next repetition of the pattern core as the last member of the pattern core? This often happens, since seeing the repeated item starting the next loop of the pattern is the first signal the student has that the pattern is repeating. Having students loop the pattern core elements and compare each to the next will help students who fall into this trap.
  • become confused when the same item appears in two places in the core pattern? Continue work with manipulatives complete core patterns. Translating to another mode such as letters may help these students see the core.

If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview, to determine the student's level of skill and understanding.

Sample Structured Interview: Assessing Prior Knowledge and Skills  Word Document

B. Choosing Instructional Strategies

Consider the following general strategies for teaching increasing patterns.

  • Start with physical materials that allow students to make changes to experimental extensions without fear of error.
  • Get students talking about how patterns can grow, so they learn from each other while accumulating the vocabulary necessary to describe increasing patterns.
  • Students often enjoy extending patterns and when doing so with concrete materials may extend these much further than in written formats.
  • Build the transfer from math concepts to other subjects. For example, while establishing the concept of increasing patterns, look for these cumulative songs and stories and share these in and out of math time. Some possibilities are the following books and songs, The House that Jack Built, Chicken Licke", The Old Woman and Her Pig, The Bag I'm Taking to Grandma's and The Great Big Enormous Turnip. There are many cumulative songs, such as "Old Macdonald Had a Farm," "The Old Lady who Swallowed a Fly," "I Had a Cat and the Cat Pleased Me," "The Green Grass Grows All Around," "Alouette," "The Twelve Days of Christmas," "Going on a Bear Hunt" and "An Old Austrian Went Yodelling." Librarians and music teachers will be valuable resources in collecting some of these to share with your class.
  • Consider the amount of materials required for some patterns that grow quite quickly. Their rapid growth and the limitations of space and materials may limit students to making only one step of the pattern at a time and then transferring it onto grid paper before building the next step. Groups of students could work together to reduce the quantity of materials required. Students, either individually or in small groups, can work with different manipulatives and/or patterns if supplies are limited and/or the increasing pattern grows quickly.
  • The brain is a pattern seeker and makes sense of the world through patterns. Helping students see pattern as a fundamental of mathematics and all learning will help them become better students.
  • Since pattern is critical to mathematical thinking, pattern work should begin early in the year and extend throughout the year's study of mathematics. This will influence students' beliefs about mathematics, which influences their learning.
  • Students who recognize that mathematics is based upon patterns will see relationships between problems and between mathematical concepts, finding it easier to learn and recall concepts and skills. They will likely persevere in problem solving because they expect the world of mathematics to make sense and possible solutions to exist.

C. Choosing Learning Activities

Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.

Sample Learning Activities
Identify and Describe Increasing Patterns in a Variety of Given Contexts; and Represent the Relationship in a Given Increasing Pattern, Concretely and Download Activities  Word
Identify Errors in Given Increasing Pattern Download Activities  Word
Explain the Rule Used to Create a Given Increasing Pattern Download Activities  Word
Create an Increasing Pattern, and Explain the Pattern Rule Download Activities  Word
Represent a Given Increasing Pattern, Using Another Mode; e.g., colour to shape Download Activities  Word
Solve a Given Problem Using Increasing Patterns Download Activities  Word
Identify and Describe Increasing Patterns in the Environment; e.g., house/room numbers, book pages, calendar, pine cones, leap years Download Activities  Word
Determine Missing Elements in a Given Concrete, Pictorial or Symbolic Increasing Pattern, and Explain the Reasoning Download Activities  Word
Extending Increasing Patterns Download Activities  Word