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# What?

In reference to Hiebert, et al.s The Nature of Classroom Tasks, students will be given the
space to vocalize their questions, misconceptions or understandings of subtraction concepts to encourage
reflection. Throughout their discussion they will be given appropriate mathematical tools, such as being
able to use their bodies as direct models, to explore and solve for their wonderings. In keeping with the
idea that students should begin with problems [and] develop methods for solving them (Heibert et al.,
1997, p. 22), the students will engage in discussion based on their previous subtraction work to discover
areas where they can grow. Since the students have a residue of subtraction operations and how to
compute problems such as 3-1=2,concepts, building a better understanding of number sense and
demonstrating the purpose for subtractionon this knowledge will hopefully reinforce increase and clarify
their understanding of subtraction as a means of separating.

Why?
As I walk around the room providing individualized assistance during worksheet-based math
lessons, I notice many students having trouble figuring out related concepts of addition and subtraction.
For example, I have observed all of the students in my selected small group write a problem like the
following: 1+2=3, therefore 1-2=3. Their understanding of how and why number relationships affect the
relationship between addition and subtraction is lacking. There is no use of direct modeling through
manipulatives in my classroom. Students are encouraged to draw pictures, but there are some students
that still seem to need a bodily-kinesthetic way to enhance their comprehension. These specific students
seem to dismiss drawing pictures and seem embarrassed to count on their fingers. Through the use of
manipulatives and targeted discussion (Kazemi and Hintz, 2014) I will be able to address these persisting
issues. I think that by asking students to justify their work they will increase their understanding of
subtraction concepts.
I also notice my classroom mentors push for worksheet completion over conceptual
understanding. My goal for this lesson is to slow down the problem solving process and give a small

group of struggling students the space to better understand the relationship between addition and
subtraction rather than trying to rush through a worksheet.
How
The pedagogical focus of my lesson is selecting and using representations to make mathematics
meaningful and draw connections between mathematical concepts. I plan to attend to this focus through
engaging in a student directed discussion using their prior work as a catalyst for their wonderings. I plan
to document their wonderings on a whiteboard for reference throughout the lesson. By using their prior
work to teach the lesson I am integrating the math curriculum and connecting to their whole group math
instruction. Lastly, I plan on using the students themselves as manipulatives to explicitly show the
relationships between parts and whole in a subtraction problem. I will provide students with part-partwhole worksheets should they wish to record their thinking.
Lesson Plan Template
Goals / Objectives
SWBAT increase their understanding of what subtraction means and how to model it using numbers 09SWBAT increase their understanding of subtraction concepts.
Standards:
CC.2.1.2.B.2: Use place-value concepts to represent amounts of tens and ones and to compare two digit
numbers.
CC.2.2.1.A.2 Understand and apply properties of operations and the relationship between addition and
subtraction.
Materials and preparation
1.
white board and markers
2.
previously completed math worksheet from Chapter 2 of My Math
3.2.
part-part-whole worksheet (optional/ if time)
Learning environment and management issues
1.
I will use the carpet space in the back of the classroom for this lesson as it has enough space for a
group of 6-8 students to move around freely. It also is separated by a whiteboard from the rest of the
classroom which will minimize distractions for all students.I will conduct this as a whole class lesson and
keep students in their current desk clusters of 4-5 students.
2.
Materials will be brought to the carpet area by teacher and passed out as needed. Students will be
prepped on appropriate ways to used the materials.passed out by an elected materials manager

3.
One management concern is working the students while another lesson is going on in the same
classroom. I am concerned about noise. I will address this concern by speaking to the whole class about
using inside voices to be courteous of the others learning in the same room.keeping students standing in
the front of the room while the lesson takes place. I will attend to this concern by ensuring the standing
students are still engaged in the mathematical discussions taking place.
Plan (35 min)
1) theThe hook (10 min.)
I will remind students we have been learning about the relationship between addition and subtraction. I
number sentences, and the concept of taking away or adding to. As students answer, I will ask other
students to explain the first students answer in their own words.
I will hook students by presenting them with worksheets they have completed in a prior math lesson on
subtraction. I will purposely choose a worksheet from their textbook where I noticed this specific group
of students struggling. (My CM makes all students write the correct answers before they can leave the
math lesson, so all problems will have correct answers). I will ask students, What are some things you
are wondering about subtraction? I will record their wonderings on the whiteboard. If students are
having difficulty coming up with wonderings, I will remind them of the number talk we had last class that
focused on subtraction. I will offer them question starters like why? and how?
I will remind students that we are working on listening to one another and building up our understanding
as a team rather than getting correct or fast answers.
2) theThe body of the lesson (15 min)
Using the knowings or wonderings the students in have about subtraction, I will segue into a targeted
discussion focused on Kazemi and Hintzs Why? Lets Justify (2014). The body of the lesson will be
focused on the related concepts of subtraction and addition problems.
I will tell students we are going to create some of our own addition and subtraction situations. I will
establish norms for participation. I will tell students who wish to come to the front of the class to keep
their thumbs up on their desk. I will provide a number story for them:
Result unknown: there are 5 students waiting in line, 2 went to the bathroom. How many are still
in line?
Change unknown: There are 10 kids playing basketball. Some of them left. Now there are 7 kids.
How many left?
Initial Quantity unknown: There were some kids in line. 5 went to lunch early. Now 5 are still in
I will ask another volunteer to tell me what we need to do to make this number story using the students in
the class.
I will ask students some of the following questions to prompt their thinking.
1.
If we are using ourselves to model this problem, how many students do we need to start? Why?
2.
Now I want to separate some students. Look at the numbers on the board. How many students
should we separate?
3.
How many students are left standing?
4.
How can we get the students back together?
5.
Can someone show me how they would put this in writing?

6.
Why did he/she write it this way?
I would repeat this process with one or two more problems. If students seem to understand the process I
will ask them to develop their own number story. If it seems as if some students want to record their
observations I will give them the option to record on a part-part whole worksheet.
Using the most common questions or wonderings the students in my group have about subtraction, I will
segue into a targeted discussion focused on Kazemi and Hintzs Why? Lets Justify (2014). The body of
the lesson will be focused on the related concepts of subtraction and addition problems.
I will call on a student at random (using a cup of popsicle sticks with names on them) to choose a problem
they want to work on. A sample problem is Write a subtraction number sentence using the numbers 5, 3,
and 2.
I will tell the students that they are going to use their bodies to model our work. I will record 5, 2 and 2 on
the board as follows:
2
5
3
I will ask students some of the following questions to prompt their thinking.
1.
If we are using ourselves to model this problem, how many students do we need to start? Why?
2.
So we have 5 students standing. I want to keep track of our thinking. How can I write down what
were doing?
3.
Now I want to separate some students. Look at the numbers on the board. How many students
should we separate?
4.
How many students are left standing?
5.
How can we get back to 5 students?
6.
Can someone show me how they would write this problem?
7.
Why did he/she write it this way?
I would repeat this process with one or two more problems. If it seems as if some students want to record
their observations I will give them the option to record on a part-part whole worksheet.
3) closureClosure (7-10 min.)
Students will be asked to put their supplies aside. I will ask students What did you learn about
subtraction? Has anyones thinking about subtraction changed? How?
Assessment of the goals/objectives listed above
Students will be informally formatively assessed through their verbal and physical representations of their
thinking. I will ensure that each student has a chance to verbally justify their thinking regarding one of the
problems on their worksheet. I will record students reasoning on the whiteboard or blackboard. I will
also document the change in understanding using their prior worksheet from My Math as a start and my
own checklist as an ending point. My checklist will contain the following:
-Student explains what a subtraction sign means
-Student models separating when given a subtraction number sentence
-Student explains why a problem is a subtraction problem
-Student explains why the larger number goes first when writing a subtraction number sentence
-understands subtraction as taking away
-understands relationship between situation and number sentence.

## Anticipating students responses and your possible responses

a) I anticipate that some students will be distracted by other things going on in the room. I also
am concerned that some students will test behavior norms as they are unfamiliar with working in a handson math environment. I will address behavior norms that are consistent with classroom norms at the
beginning of the lesson and offer reminders throughout as needed.
b) Some students may feel frustrated if they do not understand a concept as easily as their peers. I
will prevent this by telling the students that we are working on understanding and problemsolvingproblem solving rather than speed and accuracy.
Accommodations
a) To accommodate for students that find the information challenging, I will offer the chance to subtract
using smaller numbers and assistance with direct modeling. If it seems like a student needs to diverge
from bodily-kinesthetic learning or needs to think in a quieter space, I will offer him or her the option to
work with a partner to discuss their thinking.
b) I am not anticipating students who need a greater challenge as I am selecting a group of students that
need additional support and clarification with subtraction concepts. Should a student need an extension I
will provide additional part-part-whole problems for them to apply their newly learned strategies.
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