Course Guide - USAID Teacher Education Project

symbol manipulation informally before being introduced to these procedures in aformal manner.3. What is essential to know or do in class?a) Have students solve the Tiling the Pool problem, which involves a growth pattern,by using multiple representations as solution strategies. After working with one-digitnumbers for the side length of the pool, can they extend their pattern rule to a poolwith the side of 50 units? For a pool with a side length of unspecified units?b) Have students represent a variety of solutions in symbolic format, then use symbolmanipulation to demonstrate that all their correct solutions were equivalent.c) Introduce the idea that although all their solutions were equivalent, they might notlook the same if the problem was solved without a corresponding coloured diagram.Use the coloured transparency to emphasize that while solutions may bemathematically equivalent, they are not necessarily the same in a real world situation.d) Have students connect the various representations they used in solving thisproblem.4. Class Activitiesa) Introduce the Tiling the Pool problem by distributing the student handout. Refer tothe directions, answer any general questions, and have students work in pairs to solvethe problem.Allow plenty of time for this, since students will be creating diagrams, a table, agraph, and several symbolic expressions that all represent the same situation.Listen to their conversations during this assignment as they pose tentative ideas andresolve them.b) After students have finished finding symbolic expressions, bring the grouptogether and ask about the symbolic expressions that their pictures, table, and graphhelped them discover. Have students report out their expressions and note them onthe board. Some student contributions may be:• 4s + 4• 4 (s + 1)• 2s + 2(s + 2)• 2s + 2s + 4• 4(s + 2) - 4• s + s + s + s + 4Ask how these (correct) expressions, which all look different, can be proved equal. Ifsomeone mentions the distributive property, follow through on this. If not, this is thetime to formally introduce the concept. If a student suggests an expression that is noton the above list, have them try to show equivalence.