2nd Grade Math Lesson Study 9-27-16
Eastside and Enterprise Elementary Schools
Presented by Dr. Michele Douglass
What is working and what are the struggles?
It was reported that word problems are going better because of more familiarity
with the curriculum. Math mountains and counting are better, and decomposing
numbers is smoother. However, students are not using tape diagrams as smoothly.
In addition, two-step problems are a struggle.
MD reinforced that 2nd grade students should count by 2, 5, 10, and 100 from any
given number. She demonstrated a strategy to hold up a number and wave it to a
beat and give students a starting number to practice counting. Students need to see
numbers charts that go beyond 100, maybe to 300. Students need to see the pattern
on a chart and then do it orally. Have students transition to the next decade or
hundreds to get more practice on the hard part. In particular, more practice is
needed from the 90s to the next group. Also, they should practice counting
backwards to improve subtraction understanding. Strategies for adding and
subtracting have gotten better, using base 10, expanded form, alternative
algorithms, making 10's, doubles, doubles plus 1 and doubles plus 2. We should
assess what strategies students are using.
Fluency and Benchmarks
At grade two, students should be fluent in addition and subtraction up to 20. MD
introduced the fluency program and the initial assessments (90 percent is considered
fluent).
By quarter, this is a potential flow of learning:
Quarter One: +0, +1, -0, -1, -itself
Quarter Two: +2, doubles, making 10s (up to 10), counting on/counting up,
difference of one, difference of two
Quarter Three: making 10s within a problem (8+5), doubles +1, doubles -1, up and
down from 10
Quarter Four: compensation 6+8=7+7, doubles +2, other facts
An issue was mentioned with transferring math mountains to equations and back.
MD suggested starting with the easiest (quarter one) addition and subtraction to
scaffold this.
MD discussed strategies for addition and subtraction. For example, when counting
up or down, students should first use number lines. Also, when moving to larger
numbers, teachers should model by saying and writing the place value of the
numbers next to the actual numbers, “9 hundred minus 8 hundred equals 1
hundred.”MD recommended strategic anchor charts for making 10s to display in
the classroom. Group shared examples online to create their own.
Three strategies are shown below. First, adding up:
Going down to ten strategy:
Take from 10 strategy (from EngageNY):
Number Talks
The importance of Number Talks for English Language Learners was discussed, as
these students can be good at covering up. However, with a Number Talk you can
assess what they know and what they don't know. Teachers were interested in
trying to do it during breakfast, but it is recommended to have a meeting area aside
from the desks, with nothing in hand. A handout was provided for number talks
about how to organize it, strategically choose problems, procedures for avoiding
blurting out, and talk moves. You can have anchor charts to display during a
number talk. Students can indicate silently if they have 1, 2, 3, or more ways to
solve a given problem. The group practiced writing what the student is saying in a
valid numerical sentence. The way you write is a way to help students transition
into using symbols to show thinking. MD states that we should write all the number
sentences separately so students can learn how to use equations to prove a method.
The group watched videos from the book CD of second graders doing adding
strategies on double tens frames.
Daily Fluency and Number Talks
Depending on available time, MD suggested that students should alternate doing 10
minute number talks and fluency practice every day. Both of these practices build
mental math skills. It was explained that the fluency materials start with easy facts,
teaches new strategies and new facts in small chunks. It was suggested that
problems should also be written horizontally as a true test of rigor. There was a
group discussion about planning fluency for the rest of the year.
It was suggested that teachers should use a double ten frame in a plastic sleeve and
manipulatives for students to practice strategies. Teachers can also use a cookie
sheet with magnets and electrical tape to make a portable double ten frames. It was
suggested that there is also an app called “ten frames” that you can manipulate
on the overhead. Teachers use counting forward and back, but also need to expose
students to the strategies to start getting faster with facts and not always counting
one by one.
The question was asked when should students be weaned off the double tens frame.
The answer is that it is individual for each student as to when they should stop using
it. Teach students when it's a good time to use the ten frame and when they don't
need it because there are more mental math strategies that they can use.
Demonstration Lesson – Number Talk
MD showed students a set of dot patterns on a white board, and then would take the
board away and ask students how many numbers they saw. After polling the group,
she then would ask how they arrived at their number, and if any students found the
number in different ways. The Number Talk revealed students using counting all,
counting up, using doubles (revealed in the group discussion), and how students
grouped numbers.
By sitting in proximity, MD could see what students were doing with their hands,
eyes, and head movements to determine how they were arriving at their solutions.
She modeled how to teach various hand signals to students, and Talk Moves from
the Number Talk materials.