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Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
Lesson Segment 1: Identify Commutative, Associative and Identity Properties
Q. How did you do the problem in the Starter? Did anyone do it differently? Is there another way to work the problem that would make it easier to do?
Go over the essential questions with the students telling them they will need to be able to answer them at the end of the lesson.
A property is simply a true characteristic or attribute of something. Do “Stand Up If” where you as students to stand up if you name a property that is true for them, personally.
Stand up if…
Operations have properties, or true characteristics, too. Addition is an example of an operation. Think of three other operations.
Have students make a foldable where flaps open in the center to make four sections like this
Have students use the graphing calculator to review commutative, associative and identity properties as explained in the TI-73 Equivalency attachment. After discussing a property, and Trying several examples, have students write three examples of that property and an explanation for how that property works under the appropriate flap of the foldable.
Lesson Segment 2: Properties of 0
Multiplication by 0
Division by 0
1. First dividing the tiles into 12 equal groups. Ask, “How many tiles in each group?” Have them sketch the groups and write 12/12 = 1 tile in the group.
2. Next, have them divide the color tiles 6 equal groups. Ask, “How many tiles in each group?” Sketch the groups, and write 12/6 = 2 tiles in each group.
3. Next, have them divide the color tiles into 4 groups. Ask, “How many tiles in each group?” Sketch the groups, and write 12/4 = 3 tiles in each group.
Q. As we divide the 12 into fewer groups, what is happening to the number of tiles in each group? Predict: Will that pattern continue?
4. Next, have them divide the color tiles into 3 groups. Ask, “How many tiles in each group?” Sketch the groups, and write 12/3 = 4 tiles in each group.
5. Next, have them divide the color tiles into 2 groups. Ask, “How many tiles in each group?” Sketch the groups, and write 12/2 = 6 tiles in each group.
6. Next, have them divide the color tiles into 1 group. Ask, “How many tiles in each group?” Sketch the groups, and write 12/1 = 12 tiles in the group.
Q. Has your prediction proven to be true so far?
7. Last, have them divide the color tiles into 0 groups. As they look for ways to form no groups, they will try to form one group or they will say they will use no tiles. But, that is not what they are being asked to do. Guide their discussion to the fact that there is no way to identify what a no groups look like. So, there is no way to make no groups when you have any number of items. Thus, dividing by 0 is undefined or impossible. Have them try 12/0 on their calculator. Have them try dividing several numbers by 0. Show them this is different from when we have no tiles and try to make 12 groups. Have them try this on their calculator.
Have them write examples for multiplying by 0 and for dividing by 0 and write in their own words what happens when multiplying by 0 and when dividing by 0 under the properties of 0 flap of the foldable.
Lesson Segment 3: Modeling, Applying and Recognizing Properties
Sing the attached Properties Song with the students a couple of times.
Do Stand-Up-If where students stand up if the statement is true. As they stand or remain sitting, ask them which property helped them to know this.
Round The Room Writing Properties
Assign rotating roles: Scribe, Editor, Encourager, and Coach(es). The scribe writes only what the coaches suggest. The editor makes sure the expression looks correct and is large enough to be read across the room. As students move to each successive chart, the roles should be rotated giving each a chance to perform all the roles.
Lesson segment 4: Practice
Cooperative Activity: Do Round The Room Writing (instructions attached)
Assign any additional text practice as needed.
Using the TI-73 to Verify Equivalency
To validate a property, press . Type the expression on the left of the equal sign. Then, curser to the = sign. and press . Type the expression on the right of the equal sign. Curser to Done and press . If a 0 appears, the expressions are NOT equivalent. If a 1 appears, the expressions are equivalent.
Try several examples of properties to check for equivalency. Give the students some non examples using subtraction and division. Students should record the expressions on their paper and indicate whether they are equivalent or not.
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