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Background For Teachers:
The associative property is the rule that refers to grouping. For addition, the rule is "a + (b + c) = (a + b) + c". In numbers, this means 2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.
The commutative property is the one that refers to moving numbers around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.
The identity property teaches us that any number multiplied by 1 will always equal that same number.
Finally, the zero property of multiplication teaches
us that any number multiplied by 0 will always equal 0.
Intended Learning Outcomes:
4. Communicate mathematical ideas and arguments coherently to peers, teachers, and others using the precise language and notations of mathematics.
The purpose of this invitation to learn is to help students understand that posters are used for a variety of reasons, many of which focus on advertising, communication, and information. Before beginning this activity, place a variety of posters around the room. Most classrooms already have posters hanging in them but for this activity try and hang some new or different posters that are new to the students.
Begin by saying, “As you may have noticed, I have hung some different posters around the room. I want you to take a few minutes, wander around the room, and look at the posters. As you wander, I want you think about the questions I am going to write on the board.” Write the following questions on the board: Why do we have posters (what do posters do)? Are there different types of posters? Which ones do you like the best?
Then say, “The questions I want you to think about are: Why do we have posters (what do posters do)? Are there different types of posters? And which ones do you like the best? After you have wandered around the room, I want you to take a minute or two and write down your thoughts in your math journals.” Give the students two or three minutes to look at the posters before sending them back to their desks to write in their journals.
After the students have written in their math journals, start with question one and say, “Let’s talk about why we have posters. Does anyone have any ideas about why we have posters?” Let the students share their ideas. Help them come to the understanding that posters are used to advertise things, communicate ideas, entertain, and share information.
Then ask, “How many of you think that there are different types of posters? Do we have different types of posters in our classroom?” Call on different students to point at different posters throughout the room. As you point them out, compare different posters, finding similarities and differences.
End this invitation to learn by discussing the third question. Say, “So, which posters did you like the best?” As you call on students to share, follow up this question with the famous “Why?” It is important that students explain why they like the posters. This will help them as they design their own posters in the next activity.
This activity is going to focus on helping students remember the commutative, associative, distributive, and identity properties of addition and multiplication by having the students create posters that they will hang around the school or classroom. However, this activity is not going to focus on teaching the properties. If the students haven't written these properties down in their math journals yet, have them write them down as you review.
Millis, B.J. (2002). Enhancing learning-and more! through cooperative learning. Idea Paper # 38. The Idea Center, 211 South Seth Child Road Manhattan.
In this article, Millis explains the power and effectiveness of cooperative learning. Not only is cooperative learning an effective teaching strategy, it “promotes a shared sense of community” in the classroom because “learning, like living, is inherently social.” As students learn to work together through cooperative learning, they develop trust with each other and are given an opportunity to develop self-efficacy. As teachers come to understand how to implement cooperative learning, “student learning can be deepened, students will enjoy attending classes, and they will come to respect and value the contributions of their fellow classmates.”
Willis, J. (2007). Cooperative learning is a brain turn-on. Middle School Journal. March pgs. 4-13.
Judy Willis states in her article that research has shown that “in math collaboration, students learn to test one another’s conjectures and identify valid or invalid solutions.” This happens because cooperative learning provides students with the most opportunities to ask questions, express ideas and opinions, and come to conclusions that they might not otherwise have through whole group instruction. Teachers can increase student understanding and involvement by increasing the amount of cooperative learning in their classrooms.
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