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substitute number variables and compare the results to concrete models and tables
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An expression for the mass of two cans and five marbles is 2 c + 5 m. Find the total mass, if each can has a mass of 200 g and each marble a mass of 75 g.
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write expressions involving variables using standard mathematical conventions
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An equal-arm scale is balanced when there are 3 marbles on one pan and 410 g on the other. Write an equation to show this relationship.
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analyse relations graphically to discover how changes in one quantity may affect others
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[No example for this prescribed learning outcome.]
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graph relations, analyse results, and draw conclusions
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Measure the sides of each of these squares.
What is the perimeter of each square? Make a graph by plotting the length of the sides on the horizontal axis and the perimeters on the vertical axis. Describe the pattern made by the graph.
From the results of this graph, make a rule for finding the perimeter of a square. Explain how you could verify your rule.
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solve and verify simple linear equations using a variety of techniques
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Jill had some marbles in a bag. After Jay gave her 7 more, she had 12 marbles in all. How many marbles were in the bag at the start?
Jose wrote this equation.
M + 7 = 12
He used a balance scale model to solve it.
Use Jose's method to show how you would solve Bill's problem. Bill had 6 books. Tereko gave him some more, and then he had 10 books. How many books did Tereko give Bill?
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use patterns and relationships to represent and solve problems by translating everyday language into mathematical symbols and vice versa
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Celine wants to put 12 small square tables together
to make one larger rectangular table to use for a class party. She is using square tiles to experiment before she moves the tables.
Use 12 tiles to find all possible arrangements and record your solutions on grid paper. Make a chart
to show each solution.
- What is the area of each large table?
- What is the perimeter of each large table?
- Which has the smallest perimeter?
Try the same experiment with 15 tiles, 24 tiles, and
30 tiles. Compare your results. Is there a relationship between the shape of a table and its perimeter?
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explain how to solve simple problems using informal algebraic methods
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When you double Daniel's age and add 10, you get
his mother's age. Write a mathematical expression that shows Daniel's mother's age.
Nat had some stamps. He divided them into sets of
six to put in his album. He made 17 sets. How many stamps did Nat have?
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Patterns and R elations (Variables and Equations)
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