Grade 7 - Patterns and Relations (Variables and Equations)

PRESCRIBED LEARNING OUTCOMES

It is expected that students will:

• generalize a pattern arising from a problem-solving context using an open number sentence with appropriate variables
• substitute number variables and compare the results to concrete models and tables
• write expressions involving variables using standard mathematical conventions
• analyse relations graphically to discover how changes in one quantity may affect others
• graph relations, analyse results, and draw conclusions
• solve and verify simple linear equations using a variety of techniques
• use patterns and relationships to represent and solve problems by translating everyday language into mathematical symbols and vice versa
• explain how to solve simple problems using informal algebraic methods

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

SUGGESTED INSTRUCTIONAL STRATEGIES

• Graphs can be used to predict specific future events. For example, a graph of heights for the first bounce of a ball as it is dropped from successively higher points may be used to make a prediction for how high the ball will bounce.
  

  The two variables for the bouncing-ball graph are the height from which the ball was dropped and the height of the first bounce. Once students have been instructed in the basic techniques for assembling coordinate graphs, have them create their own graphs. Almost any source of data can be displayed on a coordinate graph. Other areas to explore: circumference/area, area/volume, rate of temperature change when melting ice, and so on.

SUGGESTED ASSESSMENT STRATEGIES

Question

• When students are presenting graphs to the class, ask them to write a list of questions to prompt class discussion. Consider the extent to which the questions allow their classmates to understand the relationships and to generalize in order to predict beyond the information provided on the graph.

• Provide students with a representation in one form (e.g., a graph) and ask them to develop at least two alternative ways of expressing the relationship (e.g., number sentences, equation, concrete model, table). Look for logic, the accurate use of symbols, and efficiency in their translations.
• Provide students with a simple linear equation and ask them to write an entry in their learning logs telling everything that the equation conveys to them: What does it mean? How do they know? Challenge students to take a simple equation (e.g., 2 + 3 = 5) and make it longer in a variety of ways, but still equal.
• Give students a simple problem. Ask them to develop (a) a graphic representation that would help clarify the problem and (b) an equation that they could use to solve the problem. Have them include a list of the decisions they made as they worked and the rationale for each.

• About Teaching Mathematics
• Games in the Teaching of Mathematics
• Historical Connections in Mathematics
• Interactions 7
• Linking Mathematics and Language: Practical Classroom Activities
• A Mathematical Pandora's Box
• Mathematical Reasoning Through Verbal Analysis: Book 2
• Mathpower Seven
• Minds on Math 7
• Nelson Canadian School Mathematics Dictionary
• Problem Of The Day

• Focus on Fractals
• Mathematics: What Are You Teaching My Child?

• The Logic Box
• Mathville
• Understanding Math

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