It is difficult to comment on this class. This course was taught by Jana Wallace.
We focused a lot on geometer sketchpad which I was not familiar with at all. I was often lost and confused. I
didn't really feel like I got much out of this course.
Practicum Experience
We were not required to do any practicum work in this class.
Sample Piece of Work
Lost Buttons
In this lesson and the following one, students investigate
subtraction more directly, beginning with the easier “take away” mode. They model “take away” subtraction
with buttons and write subtraction sentences. They also work with the additive identity (0) as an addend and as a difference
and find missing addends.
Call
seven students to the front of the room and roll a number cube to decide how many will return to their seats. Have a volunteer
record on the board the subtraction equation the students acted out. Repeat with different sets of seven students. Then ask
zero students to sit down and call on a volunteer to record the sentence 7 – 0 = 7. Finally, ask
all seven students to sit down and ask a volunteer to record the number sentence 7 – 7 = 0 where
all can see it. Have the students identify the difference in each number sentence.
Ask
the students whether they have ever lost a button. [At this point you may wish to read Corduroy by Don Freeman. In
this story, a stuffed bear lost a button.] Now group the students in pairs and give each pair a bag of buttons, two number
cubes, and a copy of one of the Shirts Template.
Tell them to put six to 10 buttons on the shirt, and then take some buttons away as if the buttons had been lost. Ask them
to make a record of how many they started with, how many they “lost” and how many were left.
Call
attention to a chart with columns you have labeled “Number of Buttons,” “Number Lost,” and “Number
Left.” Display a shirt with six buttons and roll a number cube to see how many buttons to take away, for example, two
buttons. Then demonstrate how to enter this information in the chart. For example, 6 (written in purple), 2 (written in red),
and 4 (written in blue).
Next
ask the students to create new entries for the chart and to record them under their picture of the shirt using the colors
modeled on the chart. When they are ready, help them enter their findings on the class chart. Then ask them what would be
recorded if they started with 7 buttons and took 7 away. Repeat with a model for 7 – 0. Prompt them to add
entries to the chart. Now call on a volunteer to write each row of the chart as a subtraction sentence.
To
help the students become more familiar with the “take away” model for subtraction, ask them to choose a row of
the chart and make up stories about lost buttons using the numbers in that row. [Some children may need to use manipulatives
to complete this task.] Then demonstrate how to use the Sums to 10 chart to find the answer when they know the sum and one
addend. [Find the red addend. Go across the row until you get to the sum. Then go up the column to find the other addend.]
At
the end of the lesson, ask children to choose one of the number sentences derived from the chart. They should draw a shirt
with buttons on it and cross some out to illustrate one subtraction fact. Remind the students to write the number sentence
under the picture. The drawings would make an appropriate entry for their mathematics portfolio.
Questions for Students
What
happens when we take away four buttons from seven buttons? Can you show that with these buttons?
Which
difference on our chart was the greatest? If we use only 10 buttons, do you think we could get a larger difference? How?
What
would be the smallest difference we could get with eight buttons? How would you get it?
Suppose
you had five buttons. What would the difference be if you lost two buttons? If you lost zero buttons? How about if you lost
five buttons?
Look
at the chart we made. How did someone get a difference of five? Did anyone get a difference of five another way?
Can
you draw a picture to show that you had seven buttons and lost three of them?
If
you know there are seven buttons on a shirt and you can only see three of them, how many can’t you see?
Show
me how to use the Sums to 10
chart to find the addend that’s missing when the sum is six and one addend is two.
Assessment Options
At this stage of the unit, it is important for students to know how to:
model “take away” subtraction using the set model
identify differences and addends
recognize the effect of subtracting all and subtracting zero
find a missing addend
Teacher Reflection
Which pairs of students worked effectively together? Which pairs should be reconfigured?
Which students did not meet the objectives of this lesson? What caused them particular
difficulty?
Can most of the students justify the difference when one addend is zero? Can they justify
a difference of zero?
Can most of the children use the addition chart efficiently?
Which children met all the objectives of this lesson? What are appropriate next steps
for them?
What parts of the lesson went smoothly? Which parts should I change the next time that
I teach this lesson?
New Mexico State
Standards
Strand:NUMBER AND OPERATIONS
Standard: Students will understand numerical concepts and mathematical operations.
K-4
Benchmark N.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Performance Standards
Demonstrate an understanding of the place-value
structure of the base-ten number system.
Use ordinal numbers (e.g., what position?) and
cardinal numbers (e.g., how many?) appropriately.
K-4 Benchmark N.2: Understand the meaning of operations and how they relate to one another.
Use a variety of
models to demonstrate an understanding of addition and subtraction of whole numbers.
K-4 Benchmark N.3: Compute fluently and make reasonable estimates.
Performance
Standards
Use strategies for whole-number computation, with a focus
on addition and subtraction (e.g., counting on or counting back, doubles, sums that make 10, direct modeling with pictures
or objects, numerical reasoning based on number combinations and relationships).
Demonstrate a variety of methods to compute (e.g., objects,
mental computation, paper and pencil, and estimation).
Perform addition and subtraction with whole number combinations.
References
Freeman, Don. Corduroy. New York: Puffin Books, 1968.
The National Council of Teachers of Mathematics is a public voice of mathematics education,
providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest
quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions
of the Council.