Description For Unit of Instruction

The initial plan for our unit was to teach about number places and delve into the hundreds
place including addition and subtraction with those hundreds place numbers. However, upon
immediate introduction to our pre assessment, our students provided ample coverage of mastery
of hundreds place concepts. As we discovered this we began to assess multiplication, the
students understood basic third grade grouping concepts, so we began to pre assess for fractions.
We knew that we did not want to get too far into third grade concepts and keep the understanding
closer to their grade. The small amount of information we were given about our students
informed us that our students were above grade average, but we did not know to what extent.
These findings will be further discussed in the pre-assessment section, but what was found is that
the students had a basic understanding of fractions, but lacked basic understanding of key
vocabulary and how fractions can be split into multiple different parts depending on the
denominator.
As a team, we decided to teach on fractions due to the age and grade of these students.
They are on their way to second grade and already demonstrate understanding on second grade
standards of place value “​2. NBT.A.1: Understand that the three digits of a three digit number
represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.”​.
We decided that we would introduce a third grade concept due to the fact that they had not yet
received instruction on those topics. We taught on fractions because this would be a topic that
they would benefit from knowing and that could help them as this topic was introduced into their
classroom seeing that fractions can be a difficult concept to grasp for young learners. Providing
these students with introduction to fractions and qualities of fractions would allow them to
further their knowledge as these concepts were introduced in their classrooms and they could
remain above their level.

Pre-assessment
Pre-assessment goal: This assessment was informal due to the changes we had to make due to the
ceiling effect on our original assessment. The standard we had planned to assess and teach on
was mastered by the students and they proved that within the first ten minutes of the
pre-assessment. We adapted the plan to cover other various second grade topics without delving
into third grade concepts. During our revised pre-assessment, we determined that our goal was to
assess what exactly the students knew about fractions and parts of a whole, if any at all. We had
 determined that if they did not know anything about fractions, that we would not introduce those
topics yet, however the students provided ample understanding that fractions came from a whole
split into equal parts. The questions we asked covered basic vocabulary, the basic definition of a
fraction, and what a fraction would look like and how it would be said out loud.

Reliability, Validity and Bias: The pre-assessment was delivered orally and through small
writing on the board for questions that needed a visual and then we provided the students with
the choice to answer on paper or orally for most questions with exception to the questions that
required writing or drawing. Due to the last minute changes that were made to the
pre-assessment, the validity and reliability of the pre-assessment was questioned. To help with
the question of reliability and validity, we pre-assessed again as we entered into the second day
of teaching. The questions that were asked did measure what we needed to have measured for the
students’ understanding. The teachers did not assist the students in answering the questions, but
would repeat the questions to help for clarification.

Administration Conditions: The pre-assessment was administered orally and written on the
whiteboard. It was given in two parts, one at the end of the first day and again at the beginning of
the second day. Due to the needs of our students, we provided options of how they wished to
answer the questions. One student chose to answer the question on the whiteboard and the other
student chose to answer the question verbally and on paper. Students were assess for
approximately 20 minutes on the first day and then approximately 15 minutes the second day.

Pre- assessment Questions and Standard aligned to the Pre-Assessment:

​ Understand a fraction 1/​b as the quantity formed by 1 part when ​a whole is
Standard: 3.NF.A.1
​ partitioned into ​b equal parts; understand a fraction ​a/b as the quantity formed by a parts of size
1/​b. *limited to denominators of 1,3,4,6, and 8.

1. What is ½ of a whole? (Demonstrating that fractions are a part of a whole)

a. Students will demonstrate this through drawing a picture of a circle with half of the circle
colored in.
2. Write out ½ in number form. (Demonstrating that they understand how a fraction is written,
with a numerator and denominator, even if they do not understand the vocabulary just yet.)
a. Students will write “½” on the board.
3. Color in three pieces of your 7 piece pizza, what would the top number in your fraction
be?
a. Students will demonstrate this by correctly writing the fraction out, and point, verbalize,
etc. which number the placed on the top of their fraction.
4. Color in four pieces of your 8 piece pizza, what would the bottom number in your fraction
be?
a. Students will demonstrate this by correctly writing the fraction out, and point, verbalize,
etc. which number the placed on the bottom of their fraction.
5. Which number is the ​numerator ​in a fraction?
a. Students will demonstrate mastery of this concept by correctly identifying the numerator
by either pointing to the top number of the fraction, circling or underlining the top
number, or by stating that it’s the number on the top of the fraction.
6. Which number is the ​denominator ​in a fraction?
a. Students will demonstrate mastery of this concept by correctly identifying the
denominator by either pointing to the bottom number on the fraction, circling or
underlining the bottom number, or by stating that it's the number on the bottom of the
fraction or the amount of equal parts in the whole.
* Results were recorded based on understanding. A 2 was given for mastery of the question
and student’s answer hitting target answer; 1 was for partial understanding, meaning they
missed some of the target answer; and a 0 was recorded for no understanding.

Questions/Prompts Student #1 Student #2

#1 2 2

#2 2 2

#3 2 1

#4 1 0

#5 1 1

#6 1 1
 Concluding our revised pre-assessment, there is not much that we would have changed.
We did discuss how it would have been better to include more questions regarding other
fractions other than one half due to how one half is a common fraction and there could be more
fractions that they would not have understood. What helped us to understand that was the
following questions where the students had to draw fractions with the denominators being 8.
Pre-assessment Results

Measures of Dispersion and Central Tendency: Due to the informal assessment the students
received scores between 0-2. We only has two sets of data and both students are very close to
level of understanding so our data is very close. For each individual question we had a mean of
1.8 with a range of 0-2. Our range over the whole test was 7-9 when comparing our two students’
scores. The mean and median were both 8 out of 12, there was no mode.

Analyze the data and Summary: ​The data provides information that the students have a base
knowledge about fractions. The students however do not have full understanding of the
numerator and denominator. From the data we can see that the students know the basic set-up,
but need to know further more about how the numerator and denominator play into fractions.
The students still need to learn more about how one whole can be split multiple different ways.
The interpretation from the data tells us that the students know how to write a fraction and how
to color it in, but do not understand that the same whole can be split into different equal parts
with different denominators. From we decided that the students need to become more familiar
with the numerator and the denominator, to help with furthering their understanding, we would
compare fraction sizes and then delve into equivalent fractions after those concepts were
understood.

Reflection of results: We are basing data off of two students’ data and concluded that the
students’ demonstrate a good basis of understanding with fractions, which was the goal. In
relation to the standard, the students still require further instruction. We wanted to make sure
that we were not introducing a brand new concepts to them. However, they knew much more
than we had planned so we concluded that we would further their knowledge through comparing
fractions and identifying fraction equivalents which we knew they have not yet covered since
they did not fully understand topics such as numerator and denominator where they would need
to know those before understanding comparing and equivalents.