BC Education - Preface: Using this Integrated Resource Package

PREFACE: USING THIS INTEGRATED RESOURCE PACKAGE

This Integrated Resource Package (IRP) provides basic information teachers will require in order to implement the Mathematics 8 and 9 curriculum. This document supersedes the Mathematics 8 and 9 Integrated Resource Package. The information contained in this IRP is also available via the Ministry web site: http://www.bced.gov.bc.ca/irp/irp.htm . The following paragraphs provide brief descriptions about each section of the IRP.

The Introduction

The Introduction provides general information about Mathematics 8 and 9, including special features and requirements. It also provides a rationale for teaching Mathematics 8 and 9 in BC schools.

Mathematics 8 and 9 Curriculum

The provincially prescribed curriculum for Mathematics 8 and 9 is structured in terms of curriculum organizers. The main body of this IRP consists of four columns of information for each organizer. These columns describe:

provincially prescribed learning outcome statements
suggested instructional strategies for achieving the outcomes
suggested assessment strategies for determining how well students are achieving the outcomes
provincially recommended learning resources

Prescribed Learning Outcomes

Learning outcome statements are content standards for the provincial education system. Prescribed learning outcomes set out the knowledge, enduring ideas, issues, concepts, skills, and attitudes for each subject. They are statements of what students are expected to know and be able to do in each grade. Learning outcomes are clearly stated and expressed in observable terms. All learning outcomes complete the stem: "It is expected that students will . . . . ". Outcome statements have been written to enable teachers to use their experience and professional judgment when planning and evaluating. The outcomes are benchmarks that will permit the use of criterion-referenced performance standards. It is expected that actual student performance will vary. Evaluation, reporting, and student placement with respect to these outcomes depend on the professional judgment of teachers, guided by provincial policy.

Suggested Instructional Strategies

Instruction involves the use of techniques, activities, and methods that can be employed to meet diverse student needs and to deliver the prescribed curriculum. Teachers are free to adapt the suggested instructional strategies or substitute others that will enable their students to achieve the prescribed learning outcomes. These strategies have been developed by specialist and generalist teachers to assist their colleagues; they are suggestions only.

Suggested Assessment Strategies

The assessment strategies suggest a variety of ways to gather information about student performance. Some assessment strategies relate to specific activities; others are general. These strategies have been developed by specialist and generalist teachers to assist their colleagues; they are suggestions only.

Provincially Recommended Learning Resources

Provincially recommended learning resources are materials that have been reviewed and evaluated by BC educators in collaboration with the Ministry of Education according to a stringent set of criteria. These resources are organized as Grade Collections. A Grade Collection is the format used to organize the provincially recommended learning resources by grade and by curriculum organizer. It can be regarded as a "starter set" of basic resources to deliver the curriculum. These resources are typically materials suitable for student use, but they may also include information primarily intended for teachers. Teachers and school districts are encouraged to select those resources that they find most relevant and useful for their students, and to supplement these with locally approved materials and resources to meet specific
local needs.

The recommended resources listed in the main body (fourth column) of this IRP are those that either present comprehensive coverage of the learning outcomes of the particular curriculum organizer or provide unique support to specific topics. Further information about these recommended learning resources is found in Appendix B.

The Appendices

A series of appendices provides additional information about the curriculum, and further support for the teacher.

Appendix A lists the curriculum organizers and the prescribed learning outcomes for each grade for the curriculum.
Appendix B consists of general information on learning resources as well as Grade Collection organizational charts and annotations for the provincially recommended resources. New resources are evaluated and added to the Grade Collections on a regular basis.
Appendix C contains assistance for teachers regarding provincial evaluation and reporting policy. Prescribed learning outcomes have been used as the source for samples of criterion-referenced evaluations.
Appendix D acknowledges the many people and organizations that have been involved in the development of this IRP.

Explanation of Section

Curriculum Sub-Organizer as seen on the World Wide Web

Mathematics 8 - Patterns and Relations (Patterns)

Mathematics 8 - Patterns and Relations (Patterns)

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

Internal links to each
section of the document

Prescribed Learning Outcomes

PRESCRIBED LEARNING OUTCOMES

It is expected that students will generate and analyse number patterns.

It is expected that students will:

generate number patterns exhibiting arithmetic growth
use expressions to represent general terms and sums for arithmetic growth, and apply these expressions to solve problems
relate arithmetic sequences to linear functions defined over the natural numbers
generate number patterns exhibiting geometric growth

Suggested Extensions

SUGGESTED EXTENSIONS

To extend students' understanding of patterns, they could:

represent a pattern using mathematical expressions and equations, and verify by substitution

Suggested Instructional Strategies

SUGGESTED INSTRUCTIONAL STRATEGIES

Looking for patterns and making generalizations from them are mathematical skills useful in investigating and solving real-world problems. The variables, expressions, and equations used to describe patterns and relationships are the basis of students' study of algebra.

Have students work individually or collaboratively to explore patterns by:

working at concrete activities using simple cases (e.g., dividing a circle by lines to create patterns)
developing a pattern using, for example, two or more shapes, colours, or textures
differentiating between growing and repeating patterns
changing a growing pattern to a repeating pattern
changing a given pattern to a new one
determining the formula to extend the pattern

Encourage students to use concrete materials where possible (e.g., algebra tiles, algebra lab gear, two-colour counters). Remind them that there are many possible ways of describing patterns.

Ask students to bring in examples or pictures of patterns from their surroundings (e.g., flower petals, architecture, needles on a tree, ploughed fields). Invite them to make conjectures about the patterns. Ask students:

How did these patterns occur?
How would you go about finding or creating a pattern?

Display a table of ordered pairs. Have students work with partners to determine the rule that was used to generate each pair. Students could then create patterns using their own rules and challenge their partners to generate the rules from the patterns.
Have students work in groups to examine graphs from a variety of sources and attempt to interpret their meaning.
Brainstorm terms that have the same meaning, such as sum, difference, product, and quotient. Have students develop posters of these terms, which can be put up in the classroom.
Ask students to suggest one number each, and respond to their numbers with others based on a pattern or equation. Ask students to plot each pair of numbers. Continue until students can guess what the pattern is.

Suggested Assessment Strategies

SUGGESTED ASSESSMENT STRATEGIES

Students use higher-order thinking skills to identify patterns and to generalize. Assessment should provide opportunities for students to demonstrate their problem-solving skills.

Question

As students solve problems using patterns, variables, expressions, equations, and graphs, ask them to explain the methods and processes they are using. Provide feedback to students concerning their application of problem-solving approaches.

Collect

Ask students to annotate their work to describe the processes they use to solve problems. Alternatively, students could provide brief descriptions of which processes did and did not work.

Self-Assessment

Work with students to generate a set of criteria that can be used to evaluate problem-solving skills. Use the criteria to create a rating scale that students can use to evaluate their own skills. Criteria should demonstrate:
- a willingness to persevere to solve difficult problems
- flexibility in trying different approaches<br>
Note: Refer to Suggested Assessment Strategies In Problem Solving section