Course Guide - USAID Teacher Education Project

3. What is essential to know or do in class?a) Have a whole class discussion of the "Graphing Equations" homework, exploringthe relationship between a quadratic equation in its expanded y = ax 2 + bx + c formand the shape of its graph.b) Introduce Algebra Tiles as a way to model quadratic equations in factored form.c) Link the Algebra Tile model (using x as a variable) to the partial productmultiplication model used in arithmetic.4. Class Activitiesa) Begin by reviewing the homework assignment, "Graphing Equations."Students were asked to draw the graph of equations by using a graphing calculator,sketch the graphs, and then make conjectures between a graph's shape and thecoefficients of the terms in its equation.Ask questions such as:• What happened when the coefficient of "a" was negative?• Will the parabola open “up” or “down”?• Did any of the equations shift to the right or left of (0,0)?• Which coefficient seemed to cause that?• Which coefficient made a graph wider or narrower?• What does the coefficient "c" show?• Did you find any pattern for "b"? (You may need to point out that c, whichlooks as if it has no variable, really has x to the 0-power, which is equal to 1.A discussion on this point is not warranted now, but it does show students thatthere is a pattern to the exponents of x in the equation.)Students may have been confused by the factored form in the last two equations, sincelast week's lesson on order of operations did not mention exponents. This is anopportunity to ask them how they interpreted 2(x − 4) 2 . Mention that the factoredform will become clear once they have worked with their Algebra Tiles.b) Review the partial product method for multi-digit multiplication by havingstudents decompose 23 x 17 onto graph paper: 20 units + 3 units horizontally, and 10units + 7 units vertically. What does their filled-in grid look like? (200 units + 30units + 140 units + 21 units = 391 units) Now ask them to draw a quick diagram onblank notebook paper with just the numbers 20 and 3 horizontally and 10 and 7vertically. Can they quickly multiply those numbers to fill in the grid? Whatnumbers did they come up with? Ask if it mattered in finding the answer that theyused actual units vesus numbers once they understood the process.Remind students that when they decomposed the numbers 23 into (20 + 3) and 17 into(10 + 7), they were creating factors that will help them think about quadraticequations when they use Algebra Tiles.