This session introduces the idea that there are different meanings of "more" and distinguishes between relative and absolute comparisons. To familiarize ourselves with the idea of equivalent ratios, we will use both additive and multiplicative methods to explore different ways of making similar figures. We will look at mixture problems and explore ratios without using algorithms to convert them to common denominators. Finally, we will examine characteristics of equations and graphs that represent direct variation.
Materials Needed: Graph paper, rulers, handouts of Quadperson, blank overheads
Groups: Discuss any questions about the homework. If time allows, take a few minutes to try out the number games with a partner. Pairs should show their networks to one another. One partner can choose a (secret) input, run it through the network, and reveal only the output. Then the other partner can use the "undoing" network to find the original number.
Groups: Take a minute and discuss iteration, along with Problems H4 and H5 from Session 3. It is likely to be a new idea.
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