Grades 2 to 3 - Patterns and Relations (Patterns)

The sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will investigate, establish, and communicate rules for numerical and non-numerical patterns that arise from daily and mathematical experiences, and use these rules to make predictions.

It is expected that students will:

identify, create, and describe number and non-number patterns
translate patterns from one mode to another using manipulatives, diagrams, charts, calculators, spoken and written terms, and symbols
explain the rule for a pattern and make predictions based on patterns using models and objects

To view the prescribed learning outcomes for Patterns and Relations (Patterns) in other grades click on an icon below.

SUGGESTED INSTRUCTIONAL STRATEGIES

Through concrete experiences students develop habits of finding, inventing, and using patterns to solve problems. Once they become familiar with repeating and growing patterns, they begin to associate and record numbers for patterns. They develop strategies for analysing and communicating patterns, which can then be connected to other areas such as the graphing of outcomes in data analysis.

Have students find patterns in the classroom (e.g., on the ceiling, on clothing); create patterns with manipulatives; and represent patterns in different ways, for example, with blocks, words, or illustrations.
Have students predict patterns. For example, use an overhead projector to project a partial pattern and have children predict the remainder.

Reproduced with permission from Curriculum and Evaluation Standards for School Mathematics: Addenda Series, Grades K-6: Third Grade Book, copyright 1992 by the National Council of teachers and Mathematics.
Ask students to play the following game in which they each share a calculator with a partner. Starting at 50, they take turns subtracting any one-digit number except zero. The player to reach zero first wins. Can students find a strategy to win? Does it matter who goes first? How do the rules work? Ask students questions such as: Suppose the rules change and the person who first reaches zero loses. How might this change your strategy?

SUGGESTED ASSESSMENT STRATEGIES

Children vary greatly in their ability to recognize patterns intuitively. They need many opportunities to talk about the strategies they use and to hear about the approaches used by others. When children work on problems that lead them into new areas of thought and synthesis (rather than those problems that have a "correct" answer), they predict, test, and talk about their understanding.

Observe

As students search for patterns in the classroom, notice how they approach the task. Which students seem to be analytical? Which students take a more global approach, looking for an entire sequence or pattern at once? Which seem to be random in their approach? Encourage students to talk about strategies and to experiment with different approaches.

Question

When students are predicting or extending patterns, probe their strategies and understanding by asking questions such as:
- How did you decide what would come next?
- What other possibilities did you consider?
- Try to think of something else that would work.

Collect

Students can develop pattern collections in which they keep or record interesting patterns that they find both inside and outside of school. You may wish to brainstorm possibilities or requirements with them, for example: include a pattern that someone in your family uses every day; a pattern that you find on the way to school; a pattern in your kitchen. Note qualities such as the level of complexity and abstraction in the patterns they find, the variation in the patterns they notice, and the language they use to talk about them.