Course Guide - USAID Teacher Education Project

c) Note the distributive property of multiplication over addition and the idea ofequivalency.c) Discuss what they learned about children's mathematical thinking from reading thearticle.4. Class Activitiesa) Begin the session by distributing copies of the article “Algebra in the ElementaryGrades? Absolutely!” Allow students to scan the article, noting that they will go intothe article in greater detail during the remainder of the class.Mention that this is not just an article that presents student work for analysis, but thatit provides insight into 7 year-old children's thinking as they are working on analgebraic activity involving patterns.As the students continue to refer to the article, have them note the role of the teacher.What does the teacher notice? What does she say? How might she use what she seesand hears during student work time to have a discussion at the end of class to bringstudents' ideas into sharper focus?b) Although you might not have enough coloured blocks for students to simulate theproblem, you can draw the first two examples on the board and then have studentscreate patterns of trees on blank paper.Note that this is really a "growing pattern" since it's a simulation of how a small treegrows from year to year. (On a practical note, keep in mind that all trees reach amaximum height and that even after several hundred years redwoods and giantsequoias in the US grow wider, not taller. But even these trees show a growth patternin the cross section of their trunk. Notice how the width of each year's growth layerdecreases as the years go by.)c) After students have drawn about 10 years growth for their trees, ask them to stopand consider a mathematical expression for the tree's growth. E.g., for x = years, (xtrunk sections + x leaf sections + the top triangle). Ask them how many shapes theydrew for any particular year.d) The summary is an opportunity to discuss three important mathematical concepts: