Transcript Beth Alvarez - George Mason University

Using Multiple Strategies to Complete
Multi-step Addition and Subtraction
Problems
Dale City Elementary
Host teacher: Beth Moore
Team Members: Beth Alvarez, Cheryl
Ayres, Alise Brooks, Kathe Carney
Lesson Goals
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Professional Learning Goal:
We will develop math lessons that address students
at all levels and allow them to participate in inquirybased activities.
Student Learning Goal:
The students will participate appropriately and learn
from their peers.
The students will learn new strategies to solve word
problems.
Math Task
There are 23 students in our class. We want to
walk 230 laps on the track.
a. If each student walks the same amount, how
many laps will each student walk?
b. What if the students do not have to walk the
same amount, how could the class get to 230
laps?
Describe the Math Task
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We focused on part a of the problem in the initial
explanation and in the concluding discussion. The
second page (part b of the problem) was to provide
extension for students who were able to complete part a
successfully.
SOL Objectives:
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2.6B Find the sum of two whole numbers whose sum is 99
or less, using various methods of calculation.
2.7B Find the difference of two whole numbers, each of
which is 99 or less, using various methods of calculation.
3.4 Estimate solutions to and solve single-step and
multistep problems involving the sum or difference of two
whole numbers, each 9,999 or less, with or without
regrouping.
4.4D Solve single-step and multistep addition, subtraction,
and multiplication problems with whole numbers.
Student Work
Desirae
overheard the
answer of 10,
but her work
showed no
understanding of
how to get there.
Student Work
Jaedyn counted
out 23 tens rods.
She showed a proof of an
intuitive understanding
that the answer was 10,
not a strategy to find the
answer of 10.
Student Work
Kevin counted 23
tens using hundred
flats and tens rods.
Kevin also showed a
proof of an intuitive
understanding that
the answer was 10,
not a strategy to find
the answer of 10.
Revisions to Original Lesson (3rd grade)
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We reworded the story to decrease misconceptions such
as doing 230 times 10.
We made the numbers smaller to bring them into a
range where the students are more comfortable
working.
We changed the numbers to decrease the likelihood that
the students would be able to answer intuitively without
working through the problem.
We decided to limit the number of manipulatives
available to help the students choose tools that would
be really helpful for this problem.
Beth Alvarez
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1st Grade Study Lesson
Revisions to Original Lesson (1st grade)
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I changed the numbers to 3 students and 12 laps. I
also gave the students names instead of just saying 3
students.
When I presented the lesson, I started with a story
problem aloud with 2 students and 6 laps. I used 2
students in the class to help demonstrate the problem
and we solved it as a whole group. Then I read the
story that the students were going to solve in pairs.
The only manipulatives provided to the students were
cubes and the option to draw a picture. They were told
that they could ask for something additional if they
needed something specific, though no one did during
the lesson.
Revisions to Original Lesson (1st grade)
Angie used 3 cubes and
moved them around the
track 12 times total.
Maya drew 12 lines and
made three groups out of
them.
Some students misinterpreted the question and assumed the each student would walk 12
laps. These students needed to have the task explained in their small group.
Alise Brooks
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2nd Grade Lesson Study
Math Task – Modified 2nd Math Question
Modified Question for 2rd Grade:
There are 6 student who want to walk a total 42
laps. If each person wants to walk the same number of
laps, how many laps will each student walk?
Objective that we worked on was 2.6B Find the
sum of two whole numbers whose sum is 99 or
less. Using various methods of calculation.
Find solutions to and solve single-step and
multistep problems involving the sum.
Alise Brooks - Misconceptions
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Several children added
42 six times.
(42+42+42+42+42+42=
____).
Some children tried to
count by tens and ones
(4 tens and 2 ones).
Some children knew to
make 6 groups, but did
not know what to do
next.
Add
6+6+6+6+6+6+6=42
Alise Brooks - Success
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Used cubes to make 6
stacks of 7 to get to
the amount of laps.
Some children put 42
tally marks in 6
groups until they
reached 7 laps.
Some of children were
able to figure out in
their head and
multiply 6 X 7 = 42.
Cheryl Ayres Fourth Grade
The Fourth Grade problem
was modified to read: There
are 28 students in our class.
We want to walk 308 laps
on the track. If each
student walks the same
amount, how many laps will
each student walk?
Revisions to Original Lesson (4th grade)
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The numbers the
students worked
with were more
challenging.
Students divided a
3 digit number by a
2 digit number.
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A wider range of
solutions to the
problem were
encouraged and
accepted.
Some students
drew pictures while
some students
used multiplication
to solve a division
problem.
Analysis of Lesson (4th grade)
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Students found
dividing a 3 digit
number by a 2 digit
number to be
challenging.
Some students
had difficulty
deciding where
to start.
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Some students
relied on creating
visual
representations
while others wanted
to make an open
array.
We had productive
discussions about
“friendly numbers.”
Fourth Grade Successes
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Some students
were able to
skip count by 28
until they
reached 308.
They understood
that they
skipped 11
times.
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Some students
used
multiplication to
help them solve
the problem.
Multiplication
was seen as the
inverse of
division.
Kathe’s Special Education
Students- Grade 4
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This class used the revised question
from Beth’s lesson on the first day;
the second revised question was
presented on the second day to
assess generalization of these math
concepts and the ability to develop
more than one strategy for this type
of problem.
Kathe’s Special Education
Students – Grade 4
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This class is comprised of 6
students with significant emotional
and learning disabilities; in addition,
there are severe weaknesses in
communication and ESOL. The
math discussion was limited to
responses to the teacher’s probing
questions. Students demonstrated
their strongest intelligence when
problem solving.
Kathe’ s Special Education
Students – grade 4
Fatu set up her students as six groups; then she dealt
laps to each student until she reached the total of 96
laps. Then she proceeded to use the “box model” for
multiplication to check her results.
Nayeli is an ESOL student who is a
selective mute; she visualized the
students as a column of snap blocks and
then used cm cubes to represent the
laps. She used the traditional algorithm
to check her work.
Kathe’s Special Education
Students-Grade 4
Kendric attempted to use the
manipulatives to solve the problem; he
was not able to picture how to do this,
so he used the game Circles and Stars to
model his problem-solving.
Lierin’s basic problem solving revolved
around her artistic intelligence. She drew
team captains and counted the laps.
However, when she got to ten, the
solution became obvious.
How Lesson Study Supported Our
Professional Learning
o the wording and numbers in a problem
affect the students’ ability to solve
the problem
o manipulatives need to be made
available in a thoughtful way
o it is best to group students in pairs
Further Questions to Explore
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fractions
division
arrays
grouping