Course Guide - USAID Teacher Education Project

4. Class Activitiesa) Begin the session by distributing the handout of the water level and marathongraphs.Ask students how these differ from the discrete graphs they explored in the priorsession. Noting that they probably learned about line graphs as a secondary schoolstudent, ask if these two graphs could be considered line graphs. Have them considerthat each of these is a graph composed of several line segments, each constitutingsomething that was continuous, but which happened within a particular interval ortime frame.Ask them to pose a timeline about what different lines in the graph of water in a tubmight mean. Why does it begin and end at 0? What might account for the fall and risein the depth of the water.When analysing the marathon graph, draw attention to question 2, which asked aboutwhat happened during Interval C. What does a horizontal line on a graph mean?b) Distribute the handout of the Kitchry recipe, which asks students to consider howthe recipe will change if they needed to decrease or increase each ingredient in orderto serve different numbers of people. Have students chart and graph two differenttypes of ingredients: the lentils (a measurement expressed in pounds) versus thecardamom (expressed as a countable item). Can they predict what each graph willlook like?When they have completed the assignment, ask questions to help students analyse andcompare the two graphs. Then compare them to the coin, water level, and marathongraphs.Can the students have predicted what the graph would look like by using the table?What patterns do they notice? Introduce the idea of first difference, the differencebetween successive values for y. Note the lentil graph is called a linear function,whereas the graph describing the data is a single straight line.Finally, ask students to write an expression in symbolic terms that could serve as arule for this linear relationship.e) End the session by referring to the use of multiple representations (narrative, table,graph, and expression) that were used to solve the problem. Ask what connectionsthey saw among these different approaches to solving the problem. Ask what theythought were the advantages and disadvantages of each representation.Ask which one of these representations seemed most useful. If students offer astrategy that relies more on arithmetic than algebra try to steer the conversationtoward an algebraic approach.5. Assignments