clements project ii-part i, ii, iii
TRANSCRIPT
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Project II – Part I
Adam Clements
October 07, 2012
BIG Idea
The BIG Idea of my Unit Plan is that multiplication can mean growing in that a product is so many times
bigger than one of its factors.
Multiplication is intertwined in most of our daily lives, whether we are conscious of it or not. When we
go to the store and need to buy multiples of one type of item, we multiply to figure out cost. When
trying to re-organize our desks, we try to figure out how much space we have and we multiply to figure
out how we should organize things so they fit. When we go to recess, we think about how fast we run
comparing their speed to how fast we are going and multiplying how much faster we are than they are.
The idea of multiplication is large, but not large enough to be a big Idea. For this unit, students will be
focused on multiplication, but in a more specific way.
Up to now, students have focused on multiplication as group of so many. For example if John has seven
baskets of 6 apples, he has 7 groups of 6 which is 42. Students will be expanding their idea of
multiplication and making connections to the work they have been doing with multiples and multiple
towers in order to think about multiplication as growing. For example, if John has seven baskets of 6
apples he has 7 times the amount of apples that are in one basket. Another way to think of this is that
his total 42 apples, is 7 times larger than one basket of 6 apples. This is purposeful because it begins to
re-frame multiplication in a way that allows students to transition into multiplying fractions which can
be thought of as shrinking.
Topic: Understanding multiple ways to multiply multi-digit whole numbers.
Strand: Operations (Multiplication)
Objective: Students will solve multi-digit whole numbers multiplication problems by independently
working using paper and pencil and be able to explain their reasoning for how they got their answer.
BIG Idea: Multiplication can mean growing in that a product is so many times bigger than one of its
factors.
Common Core State Standards
[5.NBT.5] Fluently multiply multi-digit whole numbers using the standard algorithm.
- CCSS Unpacking: Student: “I can multiply multi-digit numbers by hand.”
- Explanation: “This standard refers to fluency which means accuracy (correct answer), efficiency
(a reasonable amount of steps), and flexibility (using strategies such as the distributive property
or breaking numbers apart also using strategies according to the numbers in the problem, 26 x 4
may lend itself to (25 x 4) + 4 where as another problem might lend itself to making an
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equivalent problem 32 x 4 = 64 x 2. This standard builds upon students’ work with multiplying
numbers in third and fourth grade. In fourth grade, students developed understanding of
multiplication through using various strategies. While the standard algorithm is mentioned,
alternative strategies are also appropriate to help students develop conceptual understanding.
The size of the numbers should NOT exceed a three-digit factor by a two-digit factor.”
(Unpacking Content for 5th
grade Common Core Sate Standards for Mathematics, North Carolina Department of Public Instruction: Instructional
Support Tools. 2011. http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf )
- Connection to BIG Idea: In discovering multiple strategies to solve multi-digit multiplication
problems, students will observe that there is more than one way to reach an answer to a
problem. Students will be encouraged to find the relationships between the algorithms and
look for what mathematical facts they share in common. They will also reflect on which makes
more sense to them and why. This will help them connect to their own learning and how the
algorithm is able to use equivalence to transform the calculation into a simpler one.
- Examples:
There are 225 dozen cookies in the bakery. How many cookies are there?
Student 1 - Solution
225 x 12 = ?
I broke 12 up into 10 and 2.
225 x 10 = 2,250
225 x 2 = 450
2,250 + 450 = 2,700
Student 2 - Solution
225 x 12 = ?
I broke up 225 into 200 and 25.
200 x 12 = 2,400
I broke 25 up into 5 x 5.
So, I had 5 x 5 x 12 or 5 x 12 x 5.
5 x 12 = 60. 60 x 5 = 300
I then added 2,400 and 300
2,400 + 300 = 2,700
Student 3 - Solution
I doubled 225 and cut
12 in half to get 450 x 6.
I then doubled 450 again
and cut 6 in half to get
900 x 3 which is 2,700
Student 4 – SolutionI drew an array model for 225 x 12…. 200 x 10, 200 x 2, 20 x 10, 20 x 2, 5 x 10, 5 x 2
200 20 5
10 2,000 200 50
2 400 40 10
(Unpacking Content for 5th
grade Common Core Sate Standards for Mathematics, North Carolina Department of Public Instruction: Instructional
Support Tools. 2011. http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf )
2,000
200
400
50
40
+ 10
2,700
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Work with a partner to solve and explain various problems using teamwork, active listening skills, and by
responding respectfully.
- Students will be learning how to have a discussion and work with a partner during the literacy
lesson which is happening simultaneously. They will be expected to participate, stay on topic
and on task, build off other's ideas, use positive body language, ask questions for understanding,
listening, think, and then respond, use other's names, be positive and encourage others, and
support their opinions with evidence.
Relevance to Student’s Lives
Multiplication is a foundational mathematical principal. For this and many other reasons, it is extremely
important for students to understand. Students may see this connection in many real life examples. For
example, baking cookies requires that you might have to double or triple a recipe. Going to the store
and buying multiples of the same item means you will have to figure out how many times bigger the
total price is compared to the price of one item. Riding a bike uses multiplication skills in that if you
have traveled a certain distance in a certain amount of time, you could use that information to figure
out how many times father you have to repeat that to get to your destination. If you a student is having
a sleepover, he or she may need to figure the total floor space he or she has available. One sleeping bag
takes up so much space, how many will fit in the entire room.
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Project II – Part II - A
Adam Clements
October 07, 2012
Pre-Assessment
Creating the pre-assessment was actually surprisingly a challenge. It was hard to not just write down a
few math problems and see if the students could solve them. I found it helpful to really focus on the big
idea and go from there. What can my students actually do? How could I get them to show me more of
their thinking? Still, I thought it was important to include the standard “solve and find the answer” type
of question since that is such a heavy driving force behind the MEAP and the main CCSS that I will be
using. [5.NBT.5] “Fluently multiply multi-digit whole numbers using the standard algorithm.” However I
focused it and explicitly told them that these are MEAP-like questions. I want to help them understand
that not all of math is dictated by the kinds of questions the MEAP will ask, but that by understanding
math more deeply, hopefully they will find those types of problems easier to solve. Even if the skills andabilities that they work on don’t necessarily help them arrive at the correct answer, they should at least
help them figure out obviously wrong answers.
Since my learning goals focus on multi-digit multiplication and recognizing multiple strategies to solve
them, I wanted to use the pre-assessment to figure out a few different things. First I want to see if they
already recognize some of the strategies or algorithms. Perhaps they have learned similar strategies in
previous grades. Knowing this will be helpful to build off and then relate it to multiplication with multi-
digit numbers which will later translate itself to fractions and decimals. Second, I want to not only see if
they are able to use the strategies and algorithms correctly, but also to find out if they can actually
understand why they work. Third, I wanted to see if they could catch on to some of the patterns someof the different strategies use, without being explicitly taught them. How developed is their pattern
recognizing skills? Lastly, how do they understand multiplication? By having them explain it to
someone else, I will be able to see how well they have mastered the concept and where they are in their
understanding of it (groups of so many vs. transitioning into relationships of how much larger or
smaller).
I also kept in mind my learning goals and math practices. Since we will be focusing on constructing
viable arguments and critiquing the reasoning of others, I decided to see how they would handle a
question that asked them to do this. By looking at someone else’s work and trying to figure out how
they solved it or where they went wrong, it uses higher leveled-thinking skills and more math knowledgeto think of and eliminate reasons that would explain it. During the unit, I will be integrating the
discussion skills that they will be learning in literacy and applying them to discussions in all content
areas. Getting to see how they talk about other’s work and how they explain something that is not
theirs will be helpful to see what skills they have and which we will need to develop.
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Analyzing the Pre-Assessment
Well the students kind of freaked when they had to do this pre-assessment. It was shortly after they
finished MEAP testing, so I think that they may have viewed it as another test that they weren’t going to
feel good about. They started after I gave directions and within a minute it became clear from the
puzzled looks on the student’s faces that they were not understanding what was being asked of them.
Analyzing how someone else figured out a problem is a very challenging task and requires a lot of
thought. Most of these students (based on their math interests assessments done earlier) have set in
their minds that math is out of a textbook and are just problems that you have to complete. What I am
asking them to do is not out of a textbook and requires multiple different parts of the brain to solve and
complete. Having this new information leads me to believe that I will need to be much more deliberate
in scaffolding the skills of partner talk and comparing different solutions of problems. Since they are so
unfamiliar and inexperienced with looking at other people’s work let along talking about it, I think it
would be a good idea to give them conversation starter cards will help them to have a script that they
can follow to help build these conversations.
Many of the students are also able to do the multi-digit multiplication. Some but not all, are able to use
the standard algorithm to complete the problem. However, when asked to explain their strategy or how
they solved it and why, they admit that they “are not good at explaining.” These students will be a
strength in the lesson because the understanding is there and they have some knowledge of how to
solve a multi-digit problem. I can help build off that by providing open ending problems that push and
encourage a student to represent how they solved it in different ways like with pictures or with words.
Some of the students seemed very uninterested in even attempting the pre-assessment. They gave it
one look, decided they had never seen something like it before, and completely gave up and were
unwilling to even try. These same students have admitted in a previous math interest survey that they
do not like math, they do not believe they will need it in their future to be successful, and do not buy-in.
I will need to really connect the content that my unit is focused around to something that really
interests these students. Many of them enjoy videogames so I believe this will be very instrumental in
helping them buy-in to doing the math activities.
What do I know about my students now?
- I know some of my students are involved/invested in math. Based on my math attitude survey,
many of my students (Ky’Juan, Destin, Sarina, Luke, Rayna, Precious, Nevaeh, Brooklyn, Victoria,
Bernardo, Rayn, Lamariyee) said they agreed or strongly agreed that they loved math. Having
an interest in a subject is half of the battle. When someone in interested in a topic, they are
more willing to pay attention, use their brain to answer questions, and think beyond the
standard.
- I know some of the students (Correanna, Dezirae, Brent, Alex, Indya, Joel) marked that they
disliked math, and Brent, Alex, and Joel said they strongly disliked math. Brent is very smart.
While behavior can sometimes be an issue, mostly this is because he is simply not engaged in
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the learning. Often he says he is bored. Whether the material is too easy for him is still unclear.
What is clear is that Brent has an active mind that thrives on creativity. When asked what his
favorite parts of school are beside recess, he talks about activities where they got to build
something, or were given a task and they had to figure out an answer. He is an independent
worker when on task and very capable. Joel also strongly dislikes math, but most likely because
he doesn’t fee successful at it. Joel missed 80% of 4th grade because of suspensions and an
expulsion. With the change in schools and districts, he somehow slipped through the cracks.
However, on the math interest survey, he marked doing many of the activities I had listed that
use some form of math or math skills. Helping him connect those ideas/skills to “school math”
may help him feel more successful in the subject.
- I know that students have been working with multiples and factors. The year started out with
skip counting and creating number patterns. Most caught on very quickly to the basics. We
spent more time on skip-skip counting. For example if I said I am counting by 5’s and I want to
know how many people will have said a number when I get to the 14th
person. We then moved
to focused skip counting and filled in the Sieve of Eratosthenes discovering which numbers were
prime and only had factors of 1 and itself. This went well and students quickly caught on to the
idea of prime and composite. We then moved into multiple towers and looked for patterns with
different starting numbers. After, we moved into more complex puzzles that helped extractthese emerging ideas of factor pairs, multiples, and the basics of multiplication and division.
Many students got stuck here. We worked for about a week, working through these kinds of
problems together as a class. They are now at the point where they are working in small groups
to solve them. (ex: If I start at 120 and count to 360 and said between 15 and 35 numbers, what
number(s) can I count by?)
What is the nature and content of the final assessment for this unit?
- As of now, I would like to do some type of project based assessment paired with a more typical
paper and pencil test assignment. I am definite in that I want to have two summative
assessments in two different mediums. Often students have more knowledge than what we areable to test, so by testing it in different ways we as teachers can get a better perspective of what
they actually know. The project would perhaps focus on them creating a lesson for how to
teach one of the strategies of multiplying multi-digit numbers that they will have learned. This
would assess how well they understand the strategy, whether they can effectively explain how
to use it and why it works. This would cause students to think of it from a mastery point of view
and teaching it to a small group would allow for feedback and discussion.
What don’t I know about my students? (content knowledge/critical thinking/process or skill demonstration)
- I don’t have a very good sense of what math the students actually know. How well developed
are their basic skills. When they multiply, have they been exposed to it enough that the answersare routine? Were they able to memorize basic math facts, but not understand the concepts
behind them?
- I don’t know how well they will respond to more open-ended thinking. Many of them have
expressed that they would rather just work some problems out of a book so they can be done
with math. Others seem to enjoy the few investigatory activities we have done thus far. I think
that the activities I use over the course of the unit will need to be engaging and reach across a
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wide spectrum of intelligences, interests, and learning styles. If they are in their seats every day
for every lesson, I have not done my job well.
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Name: _________________
Student Number: ________
Date: __________
Mr. C needs to grade some multiplication homework. Can you help him figure out if the students got the problems
right and how they might have gotten their answers. If they made a mistake, where did they get confused?
5
x 6
225
x 12
450
225
675
22x 8
1. Are they correct? Explain how they solved the problem? How would you solve it?
2. Are they correct? Explain how they solved the problem? How would you solve it?
3. Are they correct? Explain how they solved the problem? How would you solve it?
467 = ____________
A) 4 + 6 + 7 B) 40 + 60 + 70
C) 400 + 6 + 7 D) 400 + 60 + 7
4. Explain how you know.Alex scored 109 points on each
level of his video game. If Alex
is on level 13, how many total
points has he scored?
5. Explain how you know.
6
6
6
6
6
___
___
___
___
12
18
24
20 x 8 = 160
2 x 8 = 16
176
____
1
_________+
____
2250
____ ____
____
____
____
____
____
450
225
450 <
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Can you solve the puzzle?
Example: 8.
MEAP TEST
Mark is in second grade and
just starting to learn about
multiplication.
Can you explain to him what
8 x 3 means?
6. Explain it to Mark. 7. Can you explain it in a different way?
200 20 5
10 2,000 200 50
2 400 40 10
300 70 9
40
6
Mr. J and Mr. C teach in a room
that is about 60 feet wide and 40
feet long. Mrs. Seagren and Miss.
Hamlin teach in a room that is half
as wide, but has the same length.
10. How do the dimensions and area of Mr. J/Mr. C’s classroom compare to
Mrs. Seagren/Miss. Hamlin’s room? Draw a picture to prove your answer.
9. How could this help you solve 379 x 46?
11) 7 x 6 = ____
⃝ A. 49
⃝ B. 13
⃝ C. 36
⃝ D. 42
12) 10 x 56 = ____
⃝ A. 56
⃝ B. 560
⃝ C. 5,600
⃝ D. 540
13) 13 x 6 = ____
⃝ A. 78
⃝ B. 120
⃝ C. 72
⃝ D. 118
14) 223 x 48 = ____
⃝ A. 10,344
⃝ B. 4,089
⃝ C. 49,876
⃝ D. 10,704
Use the space below to show your work.
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Project II – Part II - B
Adam Clements
October 07, 2012
Formative Assessment
Unit Big Idea: Making a shift in thinking that multiplication can mean growing in that a product is so many times
bigger than one of its factors.
Day Topic Standards/Goals Formative Assessment
1 - Math Game
- Intro Problem
- Students will apply their
multiplication background
knowledge and skills during a
math game played against a timer.
- Students will be able to solve a
multi-digit multiplication problem
in an open-ended manner.
[5.NBT.5]
Anecdotal Record:
Requirement 1: Solves the problem using any
strategy that makes sense to them and is able to
express their thinking through pictures and words.
3: Is able to express their strategy extremely
effectively through pictures and words.
2: Is able to show their work or ideas through
pictures and words.
1: Attempts to draw a picture and writes something
about how they solved it.
0: No effort.
*The anecdotal records will be kept together for
further reference and evaluation of growth. Student
who are not showing growth will receive 1:1 attentio
during work times.
2 - Discussion Centers
- Discussion Practice
- Students will apply the
discussion skills of Reply, Reason,
and Reflect by discussing as a class
a puzzle problem that they have
solved in a group. They will use
prompt discussion starter cards toengage in a full class discussion
where they will verbally share
their ideas, ask questions, and
make comparisons.
Anecdotal Record:
Requirement 2: Discusses the problem with their
class using the discussion R’s.
3: Full participation and is actively listening and
contributing to the conversation without needing to
use the discussion starter cards.2: Contributes to the conversation in a thoughtful
way and uses the discussion cards as a guide.
1: Relies heavily on the discussion starter cards and
barely participates in the discussion.
0: No effort.
Exit Pass: “State and describe one of the discussion
R’s that we are using during out discussions. Give an
example of something you could say during a math
discussion.”
* After upon review, students that don’t complete thetask with satisfactory answers, will be called to the
back of the room tomorrow and I will review the
discussion R’s with them as a small group.
3 - Video Game
Problem Intro
- Halloween
Problem
- Students will be able to solve a
multi-digit word problem in an
open-ended way by working with
a partner and then explain their
reasoning and engage in a
mathematical discussion with
their classmates.
[5.NF.5.a]
Anecdotal Record:
Requirement 1: Solves the problem using any
strategy that makes sense to them and is able to
express their thinking through pictures and words.
3: Is able to express their strategy extremely
effectively through pictures and words.
2: Is able to show their work or ideas through
pictures and words.
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- Students will apply their
multiplication background
knowledge and skills during a
Halloween themed math game
played for points.
1: Attempts to draw a picture and writes something
about how they solved it.
0: No effort.
4 - Video Game
Problem cont.
- Students will be able to solve a
multi-digit word problem in an
open-ended way by working with
a partner.
[5.NF.5.a]
Anecdotal Record:
Requirement 1: Solves the problem using any
strategy that makes sense to them and is able to
express their thinking through pictures and words.
3: Is able to express their strategy extremely
effectively through pictures and words.
2: Is able to show their work or ideas through
pictures and words.
1: Attempts to draw a picture and writes something
about how they solved it.
5 - Video Game
Discussion
- Intro to Video
Game Project
- Students will apply the
discussion skills of Reply, Reason,
and Reflect by discussing as a class
a puzzle problem that they havesolved in a group. They will use
prompt discussion starter cards to
engage in a full class discussion
where they will verbally share
their ideas, ask questions, and
make comparisons.
- Students will summarize the
components and requirements of
the Video Game Project they
remember by writing them in theirown words from their memory.
Anecdotal Record:
Requirement 2: Discusses the problem with their
class using the discussion R’s.
3: Fully participation and is actively listening andcontributing to the conversation without needing to
use the discussion starter cards.
2: Contributes to the conversation in a thoughtful
way and uses the discussion cards as a guide.
1: Relies heavily on the discussion starter cards and
barely participates in the discussion.
0: No effort.
Requirement 3: Solves a multiplication problem usin
the understanding that multiplication can mean
growing in that a product is so many times biggerthan one of its factors.
3: Fully understands the concept and is able to teach
it to someone else.
2: Uses background knowledge and highlighted
strategies of multiple towers to understand the
concept and can use it to solve problems.
1: Understands the concept but is having trouble
applying or explain it as related to a specific problem
0: No effort.
Exit Pass: “After just having heard an overview and
explanation of the Video Game Project, summarizethe components and requirements of the project by
writing them in your own words. Also include one
question you have about the project.”
* I will use the responses to evaluate how much re-
explaining I need to do about the project tomorrow.
will also use that time to answer the questions the
students provided.
6 - Video Game
Builder Exploration
COMPUTER LAB DAY
- Students will explore the Video
Game Builder website and gain
familiarity with the controls,
It’s Your Turn to be the Teacher: Take your puzzling
journal home, to your neighbors, or to an afterschoo
program and complete the following with someone…
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layout, and how it works. □ Retell what you did in class today.
□ If able and you have computer/internet access, vis
http://www.sploder.com/free-platformer-game-
maker.php
□ Explain the requirements of the project
□ Tell how it relates to multiplication
□ Give an example of a problem you might solve
during your design phase of the project.
□ Ask them to try to solve the problem.
□ Show how you would solve this problem.
□ Discuss the two solutions using the discussion R’s.
7 - Video Game
Project Work Day
- Students will be able to design a
platform Video Game using a set
of requirements that ask them to
use multi-digit multiplication to
complete the task. The tasks
require students to begin to think
about multiplication in terms of
growing in that a product is so
many times bigger than one of its
factors.[5.NF.5.a]
Anecdotal Record:
Requirement 1: Solves the problem using any
strategy that makes sense to them and is able to
express their thinking through pictures and words.
3: Is able to express their strategy extremely
effectively through pictures and words.
2: Is able to show their work or ideas through
pictures and words.
1: Attempts to draw a picture and writes something
about how they solved it.0: No effort.
8 - Video Game
Project Discussion
- Video Game
Project Work Day
- Students will apply the
discussion skills of Reply, Reason,
and Reflect by discussing as a class
a puzzle problem that they have
solved in a group. They will use
prompt discussion starter cards to
engage in a full class discussion
where they will verbally share
their ideas, ask questions, and
make comparisons.
- Students will be able to design a
platform Video Game using a set
of requirements that ask them to
use multi-digit multiplication to
complete the task. The tasks
require students to think about
multiplication in terms of growing
in that a product is so many times
bigger than one of its factors.
Anecdotal Record:
Requirement 2: Discusses the problem with their
class using the discussion R’s.
3: Fully participation and is actively listening and
contributing to the conversation without needing to
use the discussion starter cards.
2: Contributes to the conversation in a thoughtful
way and uses the discussion cards as a guide.
1: Relies heavily on the discussion starter cards and
barely participates in the discussion.0: No effort.
Requirement 3: Solves a multiplication problem usin
the understanding that multiplication can mean
growing in that a product is so many times bigger
than one of its factors.
3: Fully understands the concept and is able to teach
it to someone else.
2: Uses background knowledge and highlighted
strategies of multiple towers to understand the
concept and can use it to solve problems.
1: Understands the concept but is having trouble
applying or explain it as related to a specific problem
0: No effort.
9 - Video Game
Project Work Day
COMPUTER LAB DAY
- Students will be able to create a
platform Video Game using their
designs and the multi-digit
multiplication problems that they
solved. The tasks require students
to begin to think about
multiplication in terms of growing
in that a product is so many times
Anecdotal Record:
Requirement 1: Solves the problem using any
strategy that makes sense to them and is able to
express their thinking through pictures and words.
3: Is able to express their strategy extremely
effectively through pictures and words.
2: Is able to show their work or ideas through
pictures and words.
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bigger than one of its factors.
[5.NF.5.a]
1: Attempts to draw a picture and writes something
about how they solved it.
0: No effort.
10 - Video Game
Project
Presentations
COMPUTER LAB DAY
- Students will be able to solve
multi-digit multiplication problems
based off someone else’s game.
The tasks require students to think
about multiplication in terms of
growing in that a product is so
many times bigger than one of its
factors.
Summative Assessment:
Their Video Game Project plans, the actual final
project that they created on the computer, and thei
ability to solve someone else’s game will all be taken
into account and evaluated based on a rubric.
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Formative Assessment: Anecdotal RecordsMr. Jaskolski / Mr. Clements – Attwood Elementary School – 5
thGrade
Main Focus/Purpose: ___________________________________________________________________________________
Date: _____________ Subject: _____________ Lesson: ___________________________________________________
3 = Exemplary: The student met all components of the requirement and exhibited thoughtfulness and mastery.
2 = Accomplishing: The student met most of the requirement components and completed them to satisfactory standards.
1 = Beginning: The student has a basic understanding of the requirement and needs more practice or instruction.0 = No Effort: The student was non-participatory in trying to meet the requirement.
Requirement #1 Requirement #2 Requirement #3
3 =
2 =
1 =
0 = No Effort
3 =
2 =
1 =
0 = No Effort
3 =
2 =
1 =
0 = No Effort
Rayn
Destin
Indya
Brent
Lamariyee
Coreanna
Nevaeh
Rayna
Lukas
Dezirae
Bernardo
Ky’Juan
Brooklyn
Joel
Sarina
Alex
Precious
Victoria
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Exit Pass
- I will take written responses to a question to assess student understanding of key concepts. Full participation
is required to get an idea of which students need more/less re-teaching.
It’s Your Turn to be the Teacher
- After important key lessons, I will pass this sheet out as homework. It will get the student thinking about the
topic outside of school and give them an opportunity to solidify the concepts they learned that day and
previously. Explaining it or teaching the idea to someone else is one of the best ways to check for
understanding. Also, it pulls in the community and gets the student and their family or community
connected in a new scholastic way.
Summative Assessment:
- Project:
o Students will create a platform video game. Using this medium they will create, identify, solve, and
explain three separate multiplication problems.
Explanation Connection to Big Idea Connection to Standards
Project
Students would develop some sort of project
that they will have worked on during the
latter part of the unit. It would showcase
their understanding and ability to represent a
solution to a multi-digit multiplication
problem in more than one way.
By creating a platform videogame,
students will be showing how they
can not only solve, but create their
own multiplication problems.
They will specifically be comparing
sizes to form multiplication
questions that focus on the
product being so many times
bigger than one of its factors.
[5.NBT.5] Fluently multiply
multi-digit whole numbers using
the standard algorithm.
[5.NF.5a] Interpret
multiplication as scaling
(resizing) by: 5.NF.5.a]
Comparing the size of a product
to the size of one factor on the
basis of the size of the other
factor, without performing the
indicated multiplication
Name: ______________________________________________________ Date: ______________
It’s Your Turn to be the Teacher... Directions: Take your puzzling journal home or to an afterschool program and complete the following –
□ Find someone who you can talk to for about 10 minutes.
□ Explain to them what you did in class today.
□ If you are able and you have computer/internet access, visit http://www.sploder.com/free-
platformer-game-maker.php and give them a tour of the website.
□ Explain the requirements of the project and tell how it relates to multiplication.
□ Give an example of a problem you might solve during your design phase of the project.
□ Ask them to try to solve the problem.
□ Show how you would solve this problem.
□ Discuss the two solutions using the discussion R’s.
Signature of who you taught the topic to: _______________________ Relationship: ______________
Comments:
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Puzzle #1:___
x___
Word Puzzle
My game has 4 times as many crystals as it does extra lives. I put 2 extra lives in my game.How many crystals does my game have?
Number Sentence
4 x 2 = 8
Solution
My game has 8 crystals.
Puzzle #2: ___ x ___ ___
Word Puzzle
My water pool is 11 cells wide. I have 22 total cells of water. How deep is my water pool?
Number Sentence
2 x 11 = 22
Solution
My water pool is 2 cells deep.
Puzzle #3: ___ ___ x ___ ___
Word Puzzle
My game is 20 cells wide. The total cell blocks used in my game is 13 times bigger than theone row of 20. How many total cell blocks does my game use?
Number Sentence
13 x 20 = 260
Solution
My game uses 260 cell blocks.
Name: ________________
Student Number: _______
Date: _________
BUILD YOUR OWN
the
adventures of
BLOCK
MAN
VIDEO GAME
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Puzzle #1:___
x___
Word Puzzle
My game has 4 times as many crystals as it does extra lives. I put 2 extra lives in my game.How many crystals does my game have?
Number Sentence
4 x 2 = 8
Solution
My game has 8 crystals.
Puzzle #2: ___ x ___ ___
Word Puzzle
My water pool is 11 cells wide. I have 22 total cells of water. How deep is my water pool?
Number Sentence
2 x 11 = 22
Solution
My water pool is 2 cells deep.
Puzzle #3: ___ ___ x ___ ___
Word Puzzle
My game is 20 cells wide. The total cell blocks used in my game is 13 times bigger than theone row of 20. How many total cell blocks does my game use?
Number Sentence
13 x 20 = 260
Solution
My game uses 260 cell blocks.
Name: ________________
Student Number: _______
Date: _________
BUILD YOUR OWN
the
adventures of
BLOCK
MAN
VIDEO GAME
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Make Your Own Video Game
- After working with multiple different multiplication puzzles, students will create their own
individual video game. They will be given a key showing them how big certain elements of the
game are. They will also be given graph paper to create their game on. The main point of the
assignment is to assess how well they are able to recognize multiplication problems from a real
world setting. Do they make the connection between their game and the relationships of size
and amount that exist within it? How many times bigger is one space compared to the other?
How many times bigger is the total number of villains compared to the total number of power-
ups? Do these relationships make sense in their game?
[5.NBT.5] Fluently multiply multi-digit whole numbers using the standard algorithm.
[5.NF.5a] Interpret multiplication as scaling (resizing) by: [5.NF.5.a] Comparing the size of a product to
the size of one factor on the basis of the size of the other factor, without performing the indicated
multiplication
- Students will be creating and solving their own multiplication problems. This allows for multiple
different entry points and shows me what type of multiplication problems they are most
comfortable with solving and how they solve them. They also have to create a multiplication
question. This allows me to see how much they have learned in terms of being able to
represent a multiplication problem as the product being so many times bigger than the factors.
What did students learn?
- Though the lesson, the major assignments were able to show me the progression of learning by
the students. The pre-assessment showed me where students were in their mathematical
thinking and ability to not only solve their own multi-digit multiplication problems, but how
comfortable they were with explaining someone else’s work and trying to figure out how they
solved it. Taking this information, I moved them forward to the first puzzle of the “stop the
clock” problem, which not only gave me clear insight into how well students were able to simply
solve a problem, but more so how well they were able to explain the relationships that existed
in the problem. The “Halloween Jelly Bean” problem allowed students to specifically focus ontrying to explain the relationship of multiplication in terms of so many times bigger. The
“Donkey Kong Tower Climb” and the “Extreme Basketball” video game problems game them the
opportunity to show how they could expand on what they have learned so far and explicitly
focus on trying to visually represent multiplication in terms of so many times bigger. They final
“Build Your Own Video Game” project gave them the opportunity to show how well they have
been able to take all of the scaffolded exploration, and create a product that deliberately
addresses the big idea of this unit.
- Many students succeeded during this unit. One particular student left most of her pre-
assessment blank or wrote in “IDK” (I Don’t Know). In looking at her progress, one can visibly
begin to see her making connections to the big idea. She begins to label her Donkey Kong video
game, showing the repeated addition and comparing the size of the first floor to the size of theentire tower. On her Video Game project, she was able to identify a multiplication problem and
frame it in terms of the big idea: “My game has 5 times as many crystals as it does have extra
life. I put 4 extra lifes in my game. How many crystals did I use?” She then showed that “5 x 4 =
20” and explained that her solution is “20 crystals.” Her video game also visually reflects this
problem and answer.
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Project II – Part III
Adam Clements
October 14, 2012
Differentiation Strategies
Student choice in theme of problems
During some of the activities, I will set them up to allow choice in theme. The content and
problems will be the same, but the topic that they are created around will differ. This allows
students who typically aren’t interested in a subject, the option to choose. Choice always brings
value to something because you feel in control.
Increased difficulty with completion of tasks
This allows me to build up knowledge. Starting at an entry problem allows all learners the
opportunity to progress through. Those that need more time to understand and build
knowledge of the concept are able to spend more time on the first problem, and those that
finish it quickly are able to advance to the same material but simply arranged to require more
thinking. All students are getting what they need.
It also helps me to assess where students are. Looking at how many groups successfully made it
past the initial first problem lets me know at what pace I can continue with in my unit.
Variety of instructional strategies used within a classroom
Whole class discussions allow all members of class to participate and the opportunity to all be
thinking about the same example. It gives students an opportunity to listen to how other
people solved something and gain information that they can understand and build off of.
o “Students learn by processing information, applying reasoning, hearing ideas from
others, and connecting new thinking to what they already know, all for the goal of
making sense for themselves of new concept and skills” (p.20) o Chapin, Suzanne H., Mary Catherine. O'Connor, and Nancy Canavan. Anderson.Classroom Discussions: Using Math Talk to
Help Students Learn, Grades K-6. 2nd ed. Sausalito, CA: Math Solutions Publications, 2009. Print.
“Partner Pair” problem solving allows members to build off one another’s knowledge and
support their partner’s learning. It helps them begin to ask questions of math.
Open-ended tasks allow students the opportunity to use the skills in math they already have and
apply them to new problems. They gain more skill by observing, thinking about, and learning
how other people solve the same problem.
Multiple types of expressions
Hands on building activities give kinesthetic learners the chance to think 3-dimenionally and
attack a problem from a more concrete approach.
Drawing gives visual learners the opportunity to express their thinking. Often in math it is hard
to explain what you did, and much easier to represent it as a picture.
Writing helps students reflect on what they did and how it worked. It forces them to slow down
and really think about what happened and what they are still confused about.
Verbal discussion gives students the chance to share their ideas with their peers and explain
their thoughts and questions. Working with a partner gives shy students a teammate to work
with and use to express their ideas in a smaller less intimidating setting like that of a whole
class. They can build their confidence there and then share those ideas out to the whole class.
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o One idea to help shy students is to tell them that you value their contributions and that
you want them to learn to participate and you hope they have that same goal for
themselves. Explain that you expect each of them to raise his or her hand at least once
every lesson: to ask a question, to answer a question, or even just to ask “Could you
repeat that?” (p.193) o Chapin, Suzanne H., Mary Catherine. O'Connor, and Nancy Canavan. Anderson.Classroom Discussions: Using Math Talk to
Help Students Learn, Grades K-6. 2nd ed. Sausalito, CA: Math Solutions Publications, 2009. Print.
Using Other Adults in the Room
My Mentor Teacher (MT) is in the room full time. I plan on utilizing him as a resource during my unit
plan by having him help with classroom management, work to engage students who seem un-
motivated, and helping to run stations/centers.
On the days he comes in, I will have Mr. Clark, the math specialist, help run centers and give 1:1
attention to those students who need it most based off of the formative assessments. This may be
students who are behind, but also could be students who seem to be getting bored with the material
because they understand it already.
Scaffolding and Support for Students
All IEP students go to the special education resource room for Literacy and Math.
There are not ELL students in the classroom.
Instruction is still scaffold because I am using “partner pairs” so that during most work time, students
are asked to solve the problems in partners. This allows for learning through the zone of proximal
development as well as really focuses on social interaction learning.