LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

Divide the class into small groups (Orange and Green), and distribute one blue, one red, and one yellow cup to each group, along with 100 counters.

The colors of the cups do not affect the activity. Any color may be used.

Each group needs to place the blue cup on the left, red cup in the middle, and yellow cup on the right.

Students should sit facing the overhead so they can see the responses to record in their group journal.

“I would like each group to put 15 counters in the blue cup, 8 counters in the red cup, and 9 counters in the yellow cup.”

Remind students that they should track the steps they are following by drawing pictures in their journal as the teacher records on the overhead.

The teacher keeps track of student responses on the overhead while students keep track of the responses in their journal.

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“How can we find out the total number of counters in all three cups?” (Pour them out and count them or add the three numbers in each cup.)

“Now, I’d like the Orange groups to pour their counters from the red cup into the blue cup and the Green groups to pour their counters from the red cup into the yellow cup.”

“How can we find the total number of counters in the cups that have been combined?” (Pour them out and count them or add the numbers from the two cups together.)

“Suppose we didn’t have cups to pour our counters into. How could we show mathematically that we want to add the counters in those two cups first?” (We could use parentheses to indicate that we want to add those two cups together.)

“How would you write that as an algebraic expression?” (15 + 8) + 9 and 15 + (8 + 9)

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“Yes, when you write the expressions, use parentheses to indicate what you want to combine together. So let’s put parentheses in our problems and see what we get.”

Orange group should add:

(15 + 8)   +   9

        23   +   9

Green group should add:

15   +  (8 + 9)

15   +  17

“Do you now have the same values to add?” (No. Orange has 23 + 9, and Green has 15 + 17.)

“What do you get as the total of all three cups?” (32)

“So would everyone agree that

(15 + 8) + 9 = 15 + (8 + 9)?” (Yes, because both algebraic expressions are equal to 32.)

Be sure to insert the equal sign between the two expressions on the overhead.

“This is an example of the associative property of addition.”

“What does the word ‘associate’ mean?” (to hang out with someone, to do things with someone, etc.)

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“The associative property of addition states that the sum stays the same when the grouping of the addends (numbers being added) is changed.”

“Why is our problem an example of the associative property of addition?” (because we grouped together different numbers to add first, but it did not change our sum)

“Do you think this would work for decimals?” (Yes.)

“Can you give me an example?” (A common example would be a money problem.)

“Can you give me an example with a variable?” [Example: 5 + (x + 2) =
(5 + x) + 2]

“Do you think the associative property would work for multiplication?” (Yes.)

“Work with your group to write two mathematical expressions that would illustrate the associative property of multiplication.”

Allow groups time to write their

expressions, then as a whole class check

the examples.

“The associative property of multiplication states that the product stays the same when the grouping of the factors is changed.”

Remind students that only the grouping of the numbers can be changed, not the order.

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“We are going to try one more problem with your cups. You will need only your blue and red cups.”

Have each group count 25 counters in the red cup and 43 counters in the blue cup.

“Suppose we want to double all the counters but don’t want to count them all out. Let’s look at how we can do that.”

“Orange groups, I want you to add the counters in your cups then double the total.

“Green groups, I want you to double the counters in the red cup, double the counters in the blue cup, then add the two totals together.”

Give students time to accomplish their task.

“Orange Groups, what was your answer?” (136 counters.)

“Green Groups, what was your answer?” (136 counters.)

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“Both groups got the same answer. However, they used different steps, so let’s think about how we could write each group’s steps mathematically. Remember, you can use parentheses to indicate what you want to do first in a problem.”

“What algebraic expression would you use to write the mathematical steps you took?”

Orange group 2(25 + 43);

Green group 2(25) + 2(43)

Allow time for each group to work on writing its steps mathematically, then record the steps on the overhead.

So the steps would look like this:

2(25 + 43)    =    2(25) + 2(43)

2(68)            =    50 + 86

136              =    136

“Since both groups got the same answer, we can write 2(25 + 43) = 2(25) + 2(43)?” (Yes.)

“Who can describe the correct calculations for this equation? (On the left side, you would add 25 + 43 before multiplying the total by 2, and on the right side, you would multiply 2 times 25 and 2 times 43 then add those two values together.)

Point out to students that 2(25) and 2(43) is another way to show multiplication without using the “´” (times) symbol.

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

Here we have used the distributive property which states that when one of the factors of a product is written as a sum, multiplying each addend before adding does not change the product.”

“Who can give me an example with a variable?” [Example: 2(x + 5) = 2x + 2(5)]

“Would this work if we wanted to triple the number of counters?” (Yes.)

“How would we write that?”

3(25 + 43)   =    3(25) + 3(43)

3(68)          =    75 + 129

204            =    204

“Would this work for decimals?” (Yes.)

“Work in your groups to write a decimal example that that illustrates the distributive property.”

Allow groups time to work on their examples, and then check the examples as a whole class.

Distribute the Properties-Check Exit Assessment to students to complete before leaving class.  Answer key provided.