gr9_Application+of+Linear+Relations

= Applications of Linear Relations =

//It is expected that students will://
 * Prescribed Learning Outcomes


 * B1** Generalize a pattern arising from a problem-solving context using linear equations and verify by substitution. [C, CN, PS, R, V]

If the school store sells gummy bears for 5 cents and sour keys for 25 cents and you have $1 to spend: a) Record in a table all the possible combinations of the number of gummy bears and sour keys that you can get if you have to spend all my money. b) Ask students to look for a pattern to determine how many sour keys they can buy if the number of gummy bears bought is given. i) Write the relationship as a linear equation. ii) Graph the linear equation c) Ask students to look for a pattern to determine how many gummy bears they can buy if the number of sour keys bought is given. i) Write the relationship as a linear equation. ii) Graph the linear equation || Verify that students can:
 * B2** Graph linear relations, analyse the graph and interpolate or extrapolate to solve problems [C, CN, PS, R, T,V] ||
 * **Planning for Assessment** || **Assessment Strategies** ||
 * * Propose rich problems such as the following:
 * write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table


 * graph a given linear relation. ||
 * * Have student match equations of linear relations with their corresponding graphs. Then have students generate a table of values for each pair of linear relations. Discuss with students the relationships between the numbers in their table of values. Extend the discussion to establish criteria for creating a new table of values to represent other linear relationships. Then have students create various tables of values that will produce linear relations, including horizontal and vertical lines. Have students trade with a partner and graph each other's tables of values to ensure they do actually produce a linear relationship. || Verify that students can:
 * match given equations of linear relations with their corresponding graphs
 * graph a given linear relation, including horizontal and vertical lines ||
 * * Provide students with a chart that indicates the winning times versus year for a certain winter Olympics event such as 1500m speed skating. Provide data for the last 10 consecutive Olympics leaving out data for two of the years. Have students interpolate what the winning time would have been for the two missing years, then have the students research the actual winning time to see how close they were. Have students extrapolate what the winning time will be at the next Winter Olympics. [|Link to Olympic Speed Skating Data (1924-2002)]


 * Provide students with a graph of the linear function of Fahrenheit versus Celsius. (ie. F=9/5C+32) Only graph the function for C between -5 and 30, labeling every point where C is a multiple of 5 . Ask students to use the graph to interpolate the approximate values for F given values of C such as C = -2 degrees and 12 degrees. Then asks students to predict what value for C would produce a Fahrenheit temperature of 0 degrees or 100 degrees. Have students work with a partner to determine the linear equation that represents the relationship between Fahrenheit and Celsius. Ask students to use the equation to check their interpolations and extrapolations. || Assess students abilities to:
 * extend a given graph (extrapolate) to determine the value of the an unknown element
 * interpolate the approximate value of one variable on a given graph given the value of the other variable
 * solve a given problem by graphing a linear relation and analysing the graph ||