UMLN February 2015
San Antonio, Texas
Presentation:
Intentionality around the SMPs:
Through the Lens of Rich Tasks
Task for Elementary
Problem string:
300 ÷ 3 =
120 ÷ 3 =
420 ÷ 3 =
Directions for first problem string: Note the use of color.
1. Write only the first problem on chart paper (300÷3 =).
2. Ask, “who has an answer”, and complete the equation (300÷3 = 100).
3. Ask participants to share with their shoulder partner how they solved the
problem. Then popcorn out some responses. There should be at least three
approaches or strategies.
a. “I know if I take three hundred of something and put it in three
groups there would be 100 in each group”
b. “I know 3 ÷ 3 = 1, so 30 ÷ 3 = 10 and 300 ÷ 3 would have a answer
(quotient) that is ten times bigger than 30 ÷ 3, or a 100 times bigger
than three divided by 3.”
c. “I think of multiplication. I know that 3 times one hundred is 3
hundred. Therefore, 300 divided by 3 equals 100.”
4. Add the second problem using a different color marker (120 ÷ 3=)
5. Ask, “who has and answer”, and complete the equation.
6. Have participants see if they can solve the problem in the three ways the
first problem was solved, and share with their table group.
7. Write the third problem using a third color. (420 ÷ 3 =). Have participants
work with a partner to solve.
8. Find a participant that has used the first two problems to solve the third
problem and have them share with the group.
9. As the participant shares his/her strategy, draw the arrays using color to
match each component. Say, “ I am going to draw an array to help show your
thinking. What should the first array look like?” Answer, “ It should have a
short side representing the factor 3. There should be 300 inside the array
representing the dividend, and there should be a long side which will
represent the other factor or the quotient.”
10. Write the equation using colors to match the arrays, and have participants
discuss the relationship of the quantities in the visual model (the array) and
the equations. Have a short discussion about why use color?
3
300 ÷ 3 =
120 ÷ 3 =
100
420 ÷ 3 =
40
300
120
420 ÷ 3 = (300 ÷ 3) + (120 ÷ 3)
140
=
100
+
40
Part two:
T/F?
80 ÷ 4 = (80 ÷ 2) + (80 + 2)
1. Write “T/F?” and the equation on chart paper.
2. Say to participants, “Work with a partner to determine if the equation is true
or false, and be able to justify your conclusions in at least two different
ways.”
3. Offer a context for this problem. “Say I have a total of 80 skittles and I wanted
to share the skittles equally with four of you. How many skittles would each
person get?”
4. Visit each table group as they work, clarifying expectations as needed. You
may need to suggest they approach the problem by justifying without
calculating, and ask them to use arrays to justify their conclusions.
5. Have groups share their approaches.
6. Draw arrays to model the connections to the equation and a visual
representation when discussing possible approaches.
7. Have a discussion about why decomposing the dividend works in the first
problem string, but decomposing the divisor does not work in the T/F part of
the task. Ask participants, “what misconception is addressed through this
task, and why this is a rich task that supports applying the SMPs.”
80 ÷ 4 = (80 ÷ 2) + (80 + 2)
4
80
2
=
80
2
+ 80