clements project ii-part i, ii, iii

7/30/2019 Clements Project II-Part I, II, III

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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



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


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


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

http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf










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.



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.



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



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



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.



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?



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 <



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.



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


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


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:







pictures and words.



- Students will apply their

multiplication background

knowledge and skills during a

Halloween themed math game

played for points.



0: No effort.

4 - Video Game

Problem cont.


multi-digit word problem in an

open-ended way by working with

a partner.

[5.NF.5.a]

Anecdotal Record:







pictures and words.



5 - Video Game

Discussion

- Intro to Video

Game Project




a puzzle problem that they havesolved in a group. They will use

prompt discussion starter cards to

engage in a full class discussion



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:



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



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…



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:







pictures and words.


about how they solved it.0: No effort.

8 - Video Game

Project Discussion

- Video Game

Project Work Day




a puzzle problem that they have

solved in a group. They will use

prompt discussion starter cards to

engage in a full class discussion



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


Anecdotal Record:



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



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:







pictures and words.

http://www.sploder.com/free-platformer-game-maker.php








[5.NF.5.a]



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.



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



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


[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:









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



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.



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.



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.

clements project ii-part i, ii, iii

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