This two-part lesson is based on the Laws of Arithmetic lesson that is part of the Mathematics Assessment Project. In today's lesson we follow my standard Do Now Strategy to begin the lesson. Although I often create Do Nows that have problems that connect to the task that students will be working on that day, here I want students to review this area diagram that they encountered on the preassessment (see Equivalent Numerical Expressions Day 1). By analyzing someone’s idea and writing their thinking, students are engaging in MP3 (Construct viable arguments and critique the reasoning of others).
I have students participate in a Think-Write-Pair-Share about Daniel’s idea. I want students to recognize that according to the order of operations, Daniel’s expression will not match the area diagram. I ask students how Daniel could add something to his expression to make it match. I am looking for students to see that by adding parentheses, (5+3) x (5+3), it will work. If I have time, I ask for students to share other equivalent expressions that match the area diagram.
At this stage of this two-day lesson my goal is for my students to make connections between the work they have been doing with equivalent expressions and the commutative and distributive properties. Rather than give students wordy definitions, however, I present two examples of each property and have students come up with their own definition (see Commutative and Distributive Properties). I remind my students that we can use letters, or variables, to represent any number. I plan to ask, "How could we represent this property with variables?" If students are noticing patterns and relationships, they will be able to come up with their own example using variables (MP7, MP8).
As we move on to this activity, I have students join their partner from yesterday's lesson (see the lesson for an explanation of how the groups were formed). To begin our work, I have a volunteer review the rules and expectations on 1.14 Matching Part 2. Then, I ask students to share out the strategies that students used yesterday. We discussed these at the end of the lesson, so I am interested in seeing if students volunteer strategies that their peers' used. Finally, I ask students if they have any questions. Once the questions are asked and answered, I pass out the materials and students start working.
As students work on the Matching Task, I walk around and monitor student progress. I am observing what strategies students are using and I am monitoring behavior.
Many students may struggle at first, and this is okay. If a partner pair is stuck, at first I will not intervene. I want students to find ways of applying what they know to find matches. If students raise their hand and ask for help, I may ask some of the following questions:
If students successfully find the matches, I ask them to use blank cards to create a different expression that is equivalent to each area diagram. If they complete this task, I will have them pair up with another partner pair to compare their matches. For partner pairs who need an extra challenge, I will give them the Matching Challenge cards.
I have a volunteer read the directions on the Making a Poster handout. I set up the card sets, scissors, glue, and poster papers in the room. I will call partner pairs a few at a time to collect the needed materials.
As students work I walk around and monitor student progress. I make sure that partners are working on different matches. If students struggle, I refer them to my exemplar.
If students successfully complete the poster, I give them the following choices:
I begin today's Closure by asking students to explain the Commutative Property of Addition, the Commutative Property of Multiplication, and the Distributive Property in their own words. I ask students to share out struggles that they encountered during this two day investigation and how they overcame them.
I have students clean up and organize their cards. Instead of giving a ticket to go, I collect and look at student work.
I hand out the HW Post-Assessment. When I look at the post-assessments I will make comments/questions on student’s thinking. I will staple students’ pre-assessment to the post-assessment so students can observe and compare their thinking from the Pre-Assessment and the Post-Assessment.