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Activity 3: WHAT A DRAG!
In this activity, students will manipulate movable rectangles that represent partial
products of a multiplication expression, 13x11. In each activity tab students will
combine the rectangles to form one shape, and then discuss their strategy and explain
the relation between the numbers on their shape and the “Total Sum” that is displayed
on the screen.
Learning Objectives
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Students will explore various geometric combinations of partial products.
Students will create a multiplication expression from the partial products.
Students will see that their strategies for combining a static set of partial products
all result in the same final product.
Students will see that while the combination of a static set of partial products can
change, their sum will be constant.
Tab #1: Combining Static Partial Products (Part 1)
Have students open “Activity #3: What a Drag!” from the “Networked Documents” list,
and distribute the student worksheet. Project the iPad and display the first tab in the
activity. Displayed in the tab are four uniquely colored rectangles (blue, yellow, green,
and red). Inside each of the rectangles is a number that represents the area of the
rectangle. The rectangles can be moved, but their sizes cannot be adjusted. These four
rectangles are constructed such that it is possible to combine them to form a rectangle.
Also in the display is a dark blue line. When a student moves one of the rectangles
across that line the “Total Sum” value, located in the upper left-hand corner of the
display, is increased by the area of the rectangle.
Activity #3: What a Drag! Teacher Notes
Kaput Center for Research and Innovation in STEM Education
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NOTE: Refrain from stating that the rectangles in the display are partial products, or
that the numbers represent the area of the rectangles; let the students present their
descriptions and names for the rectangles’ properties first.
Instruct the students to move the four shapes to the left, across the line, and combine
them so they form one shape and then fill in the first question on their worksheet. When
they are done, instruct the students to log in and submit their work.
NOTE: For instructions on how students can submit their work consult the “Sketchpad
Explorer Guide”.
Once students have submitted their work, ask, “What were your strategies for
combining the shapes?” When a student group is describing their strategy, display their
work on your iPad for the whole class to see. After discussing the students’ strategies
ask the class, “Does the way you combined the shapes model a multiplication
sentence?”
Tab #2: Combining Static Partial Products (Part 2)
Have students tap the second tab located at the bottom of the screen, which again
displays four uniquely colored rectangles. As with Tab #1, the rectangles can be moved
but their sizes cannot be adjusted, and they are linked to the “Total Sum” value.
However, these four rectangles are constructed such that it is impossible to combine
them to form a rectangle.
Activity #3: What a Drag! Teacher Notes
Kaput Center for Research and Innovation in STEM Education
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Instruct the students to move the four shapes to the left, across the line, and combine
them so they form one shape and then fill in the first question on their worksheet. When
they are done, instruct the students to log in and submit their work.
Once students have submitted their work, ask, “What were your strategies for
combining the shapes?” When a student group is describing their strategy, display their
work on your iPad for the whole class to see. Also, ask the students to share the number
sentences they created to model the relationship between the four rectangles and the
“Total Sum”.
It is our expectation that student strategies may involve creating a rectangle with the
four partial products. In this case, the student strategy would not work since the four
rectangles were constructed so that they could not be combined into a rectangle. If
students make this observation ask the following questions:
• “Why do you want to create a rectangle?”
• “Why can’t you create a rectangle?”
• “What would you have to change to create a rectangle?”
Tab #3: Creating a Rectangle
Have students tap the third tab located at the bottom of the screen, which again
displays four uniquely colored rectangles. As with Tab #1, the rectangles can be moved,
but now the blue rectangle’s size can be dynamically manipulated by dragging the red
point located on the upper right-hand corner of the rectangle.
Activity #3: What a Drag! Teacher Notes
Kaput Center for Research and Innovation in STEM Education
4
Instruct the students to move the four shapes to the left, across the line, and combine
them so they form a rectangle and then fill in the first question on their worksheet.
Creating a rectangle using the four shapes will require the students to change the size of
the blue rectangle.
When they are done, instruct the students to log in and submit their work. Once
students have submitted their work, ask, “What were your strategies for combining the
shapes?” When a student group is describing their strategy, display their work on your
iPad for the whole class to see. If students have yet to call the rectangles partial
products ask, “Is there another term/phrase you can use to explain what these
rectangles are?
It is our expectation that some students’ strategies may result in “Total Sum” values
that are not equivalent to the original problem (i.e. not equal to 143). In these cases ask
the students, “Why is your ‘Total Sum’ different than the other students?” and “How
do the numbers on the shapes relate to the ‘Total Sum’?”
For example, students could have constructed a shape where the blue shape is 7x1, and
the “Total Sum” would then equal 120 (i.e. 10 x 12).
Tab #4: Creating a Rectangle with Different Partial Products
Have students tap the fourth tab located at the bottom of the screen, which again
displays four uniquely colored rectangles. As with Tab #3, the blue rectangle’s size can
be dynamically manipulated by dragging the red point located on the upper right-hand
corner of the rectangle. Also, the sizes of the three static rectangles are different than the
previous tabs (i.e. 56, 20, 35).
Activity #3: What a Drag! Teacher Notes
Kaput Center for Research and Innovation in STEM Education
5
Instruct the students to move the four shapes to the left, across the line, and combine
them so they form a rectangle and then fill in the first question on their worksheet.
Creating a rectangle using the four shapes will require the students to change the size of
the blue rectangle.
When they are done, instruct the students to log in and submit their work. Once
students have submitted their work, ask, “What were your strategies for combining the
shapes?” When a student group is describing their strategy, display their work on your
iPad for the whole class to see.
It is our expectation that some student’s strategies may result in “Total Sum” values
that are not equivalent to the original problem (i.e. not equal to 143). In these cases ask
the students, “Why is your ‘Total Sum’ different than the other students?” and “How
do the numbers on the shapes relate to the ‘Total Sum’?”
For example, students could have constructed a shape where the blue shape is 3x5, and
the “Total Sum” equals 126 (i.e. 7 x 18).
Activity #3: What a Drag! Teacher Notes
Kaput Center for Research and Innovation in STEM Education
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Activity #3: What a Drag! Teacher Notes
Kaput Center for Research and Innovation in STEM Education