Grade 6 - 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 use relationships to summarize, generalize, and extend patterns.
It is expected that students will:
- construct a visual representation of a pattern to clarify relationships and to verify predictions
- summarize a relationship using everyday language in spoken or written form
- create expressions and rules to describe patterns and relationships (e.g., area, perimeter, volume)
- interpolate number values from a given graph
- predict pattern relationships
To view the prescribed learning outcomes for Patterns and Relations (Patterns) in other grades click on an icon below.
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SUGGESTED INSTRUCTIONAL STRATEGIES
The study of patterns and relationships, while still involving visual representations, begins to be more formalized at this level, as numerical or algebraic rules are established to describe patterns and relationships. However, students should also study patterns as a link to understanding mathematics
and their environment. Many Grade 6 students
will benefit from the visual and tactile support that manipulatives provide.
- Have students study problems that are rich in pattern development. For example:
- How many squares in a checkerboard?
- How many handshakes would result in a group of seven people if everyone shakes everyone else's hand?
- How many blocks are there in the tenth step
of a step design?
| PEOPLE | 1 | 2 | 3 | 4 | 5 | ? --» | 10 |
|---|
| HANDSHAKES | 0 | 1 | 3 | 6 | 10 | ? --» | ? |
|---|
- Use the following questions to help students reach a conclusion for the problem related to handshakes, which is described above:
- What is the next number in the people row?
- How are the number of handshakes
increasing?
- What is the difference between each column?
- If there were ten people rather than seven, how many handshakes would there be?
- What can we do to the numbers to predict the number of handshakes?
SUGGESTED ASSESSMENT STRATEGIES
As students engage in problem-solving activities, encourage them to talk or write about the strategies and processes they use. Determine how they generate and use mathematical rules, and to what extent they recognize how a pattern grows and
how it can be predicted.
Observe
- Examine students' work for evidence of the strategies they used to solve a particular problem:
- Have they developed a chart or picture sequence to show an understanding of the problem? How effective or appropriate is it?
- Have they created a number sequence to show the pattern? To what extent is it logical and helpful?
Self-Assessment
- Have students assess their own work by explaining:
- the problem in their own words
(understanding)
- how they worked to solve the problem (process)
- the relationship they discovered (solution)
- how the problem or the strategies they used could be applied in a new situation
Collect
- Have each student develop a collection of the problems they solved over a period of time.
Have them include problems from other subject areas and from outside school. Review the collections to assess growth and changes in students' understanding and use of patterns.
You may wish to have students review these collections and write a summary in their math journals listing things that they notice about
their work.
RECOMMENDED LEARNING RESOURCES
Print Materials
- About Teaching Mathematics
- Discovery Kit - Double Tangrams
- Games in the Teaching of Mathematics
- Historical Connections in Mathematics
- Kids 'n' Calculators: How to Use the Calculator as a Teaching Tool
- Linking Mathematics and Language: Practical Classroom Activities
- Math Bridges: Everyday Math for Home and School
- A Mathematical Pandora's Box
- Mathematical Reasoning Through Verbal Analysis: Book 2
- Problem Of The Day
- Quest 2000: Exploring Mathematics Grade 6
- Using Calculators Is Easy: Complete Guide For The Classroom
Video
Software
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©Copyright 1996
All Rights Reserved.
BC MOECurriculum Branch.
Maintained by:Mathematics Coordinator
Revised: October 20, 1997
BC Ministry of Education
