As student enter the room, they will have a seat, take out their Problem of the Day (POD) sheet and begin to work on the question on the SMARTboard. The POD also allows students to use MP 3 continually based on the discussions we have about the problem each day.
POD-Write the expression 3 times 4 plus 12 - 6
The target for the day is also on the SMARTboard each day when students enter the room. The target for today’s lesson is to create expressions using numbers and pictures. I chose this question because it leads into what we are going to do in class today. I want them to experience expressing problems as mathematical operations. I also want to have the discussion about whether it is 3 x 4 + 12 - 6 or 3(4 + 12) - 6 or (3 x 4) + (12 - 6). What is the difference between these problems? Do those differences matter?
The exploration today will walk students through creating expressions using one-inch blocks and centimeter cubes. I will distribute a one-inch block to each student then walk them through the steps of Express This using the block as the variable and the centimeter cubes as the constants. At each step, students will write the expression that represents the step they just completed. At the end of the series of steps students will have a final expression to share.
Students will also create their own expression and a series of steps to guide a partner through determining the expression for the steps. Students will compare their partner’s solution to the work they sketched at each step in their problem.
I want the discussion as we work through the given sets of steps to not only focus on the volunteered expression or sketch that is shared but to determine if another representation is also appropriate. Is there another way to write the expression or draw the sketch? Using the distributive property is usually a difficult concept for students. Writing an expression that indicates the distributive property can be challenging for students who do not multiply the entire quantity by the indicated amount.
Draw a model that represents 3 times the quantity 4 minus 2. Write the expression after drawing the model.
I want to see if students are having any difficulty creating the model and/or writing the expression. If there are concerns, we can walk through the model during the next class. If there aren’t any concerns, I will ask a student to demonstrate a solution during the next class. If there is more than one solution, we can examine them to illustrate equivalent expressions.