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SUMMATIVE MATH PROJECT

Summative Math Project

M. Catherine Theriault

St Thomas University

March 01, 2016

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Table of Contents

Annotated Bibliography: Math Anxiety 3

The "Responsive Classroom" Approach and Fifth Grade Students' Math and Science Anxiety and Self-Efficacy 3-4Causes and Reduction of Math Anxiety in PreserviceElementary Teachers 4-5Math Anxiety and Math Ability in Early Primary School Years 5-6

On the relationship between math anxiety and math achievementin early elementary school: The role of problem solving strategies 6-7Math Anxiety, Working Memory, and Math Achievement in EarlyElementary School 7-8Tips for Teaching Math to Elementary Students 8-9

NCTM Critical Reviews 10

Rationale 10Fair Shares, Matey, or Walk the Plank 10-12Building Understanding of Decimal Fractions 12-14Algebra and Art 14-15

Review of Math Manipulatives 16

Base-Ten Blocks 16-17Snap Cubes 17Number Lines 18Pattern Blocks 18-19Fraction Strips 19-20

Mathematics and Technology Products 20

Math Podcast 201st Grade Measurement Comparisons: Instructional Video 21-27Smart Notebook: Grade 3 Math Warm-ups 28

Other Areas of Interest

Interview with an Elementary Math Student 29-30Math Website Review 30-32Cross Curricular Component 32-34

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Creative Math Project 35-37

Annotated Bibliography: Math Anxiety

The phenomenon of math anxiety is widespread amongst children,

adolescents and adults alike. I have noticed that many pre-service teachers,

including my colleagues and myself, suffer from this and how it relates to the

teaching of elementary mathematics. I have chosen a mixture of annotations

focusing math anxiety as it relates to both students and educators to form the

basis of this bibliography, which can inform the reader of research based

discoveries and improvement techniques.

Griggs, M. S., Rimm-Kaufman, S. E., Merritt, E. G., & Patton, C. L. (December

01, 2013). The "Responsive Classroom" Approach and Fifth Grade

Students' Math and Science Anxiety and Self-Efficacy. School Psychology

Quarterly, 28, 4, 360-373.

This article describes a study conducted by Marissa Swaim Griggs,

Sara E. Rimm-Kaufman, Eileen G. Merritt and Christine L. Patton of

the University of Virginia. This study, focusing on fifth grade students,

examined the contribution of students’ gender, math and science

anxiety as well as schools’ use of Social and Emotional Learning

practices on students’ math and science self-efficacy. The results of

the study explored in this article suggested that gender had no effect

on math and science self-efficacy yet and for the students who self-

reported higher math and science based anxiety also reported lower

levels of self-efficacy in these subjects. Students in the study that

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attended schools using the Responsive Classroom (RC) approach

reported less negative association between anxiety and self-efficacy

than students attending schools that do not use this approach.

Students attending schools that used RC practices also reported

higher levels of self-efficacy. The results of this study suggest that

when Responsive Classroom practices are used, math and science

anxiety is reduced, thereby resulting in higher levels of self-efficacy in

these two subjects.

This article can provide insight to educators, both preservice and

experienced, on how math and science anxiety can influence students’

beliefs about their own capability to succeed in these subjects. By

using practices such as those outlined in the Responsive Classroom

approach, educators can help to reduce anxiety and create positive

learning environments that can increase student self-efficacy.

Harper, N. W., & Daane, C. J. (March 08, 1999). Causes and Reduction of Math

Anxiety in Preservice Elementary Teachers. Action in Teacher

Education, 19, 4, 29-38.

“Causes and Reduction of Math Anxiety in Preservice Elementary

Teachers” details a study that analyses the anxiety of 53 elementary

preservice teachers prior to the commencement of and after the

conclusion of their mathematics methods course. The authors discuss

the commonality of math anxiety amongst preservice teachers, stating

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that often this anxiety results in beliefs and attitudes opposite to those

described in the NCTM Standards. Factors influencing the preservice

teachers’ anxiety included the emphasis on correct answers, the fear

of making errors, timed paper and pencil tests, word problems and

confidence in mathematical competency. The authors of this article

interviewed preservice teachers before and after their methods course,

and were able to conclude that the course did reduce math anxiety.

This article is very beneficial, especially to preservice teachers.

Besides outlining that math anxiety amongst preservice teachers

opposes the views portrayed in the NCTM Standards, which could

negatively impact the future of mathematics teaching and learning, the

findings of this study examine how math anxiety develops in preservice

teachers, and enables preservice teachers to reduce math anxiety in

their future students.

Krinzinger, H., Kaufmann, L., & Willmes, K. (January 01, 2009). Math Anxiety and

Math Ability in Early Primary School Years. Journal of Psychoeducational

Assessment, 27, 3, 206-225.

The goal of Krinzinger, Kaufmann and Willmes’ study as outlined in

this article was to examine the relationship between calculation ability

and math anxiety among elementary aged learners. One hundred and

forty first to third grade students with mathematical learning disabilities,

from five different schools were examined for the purpose of this study.

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The authors examined students’ calculation ability, self-reported math

evaluations and anxiety levels. Structural equation modeling was used

with the students, and revealed a strong connection between

calculation ability and math anxiety on students feelings about the

subject of mathematics as a whole. Contrary to clinical reports, which

express the correlation between ability and anxiety in adult learners

with mathematical learning disabilities, the authors found that structural

equation modeling resulted in no significant affect of math anxiety on

calculation ability, or calculation ability on math anxiety in young

learners.

This study can be advantageous for educators to read as provides

insightful information on anxiety issues for students with mathematical

learning disabilities. It is key for educators to be informed on these

issues in order to prevent subsequent issues such as depression or

psychosomatic disorders. This study is also beneficial for educators to

read as it calls attention to the need for the development of appropriate

anxiety testing instruments for young learners with these learning

disabilities.

Ramirez, G., Chang, H., Maloney, E. A., Levine, S. C., & Beilock, S. L. (January

01, 2016). On the relationship between math anxiety and math achievement

in early elementary school: The role of problem solving strategies. Journal of

Experimental Child Psychology, 141, 83-100.

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In this article, Ramirez et. al. explore the connection between

children’s self-reported math anxiety levels and their use of more

advanced mathematical problem solving strategies. The authors

hypothesized that math anxiety leads to math avoidance and disrupts

the working memory resources students use to solve math problems.

The conclusion of this study leads the authors to argue that problem

solving strategies such as decomposition, which are used most

frequently by students with high working memories, result in greater

levels of math anxiety and can detract from their overall success in the

subject.

This article urges educators to ensure that they provide students with

the tools necessary for developing a divers problem-solving repertoire

early in order to help stop math anxiety before it manifests and ensure

flexible mathematical thinking. The authors suggest that educators

involve parents in this process, in order to help stem anxiety for all

involved.

Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (January 01, 2013).

Math Anxiety, Working Memory, and Math Achievement in Early Elementary

School. Journal of Cognition and Development, 14, 2, 187-202.

Written prior to the article annotated above, “Math Anxiety, Working

Memory, and Math Achievement in Early Elementary School” written

by Ramirez, Gunderson, Levine and Beilock, discusses whether math

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anxiety at the elementary level relates to students’ math achievement.

The authors began their study of one hundred and fifty four first and

second grade students by conducting a measurement of both their

math achievement and working memory. Several days after the

measurement was conducted, the authors assessed the children’s

math anxiety. A negative correlation was found between math anxiety

and achievement for those students with high working memories, yet

not for those students with lower working memories. The authors

conclude that students with high working memories often use more

advanced mathematical problem solving strategies, which rely heavily

on working memory. When working memory is disrupted by the

negative thoughts and feelings associated with math anxiety, the

strategies that rely heavily on it are often disrupted, becoming

unsuccessful.

This article can serve as a useful resource for educators as it draws

attention to the correlation between working memory, problem solving

and math anxiety. The authors draw attention the potential for math

anxiety to snowball for those students with high working memories. If

students with high working memories, who have the highest

mathematical potential, are continuously affected by anxiety, they may

avoid math courses in the future.

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Scarpello, G. (September 01, 2010). Tips for Teaching Math to Elementary

Students. Education Digest: Essential Readings Condensed for Quick

Review, 76, 1, 59-60.

The style of this article, “Tips for Teaching Math to Elementary

Students”, varies greatly from that of the other articles annotated in this

biography. Gary Scarpello offers mathematical teaching advice to

educators based on the fact that math, unlike other subjects, can be

associated with specific anxiety and or fear. The author states that

math anxiety occurs in not only students, but also in many elementary

educators as it is rare for educators to hold a degree based in

mathematics. The root of this anxiety, for both students and teachers,

is lack of confidence, which Scarpello argues is the key to successfully

teaching math.

The article is an excellent resource for elementary educators,

particularly preservice, as it outlines how to build the required

confidence, and provides tips such as always using diagnostic testing

and reminding students that while mathematics is hard work, it is

rewarding.

NCTM Article Reviews

Rationale

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The article reviews found below, while not part of a congruent theme, were

selected on the basis of providing valuable insight into mathematical subject

areas I found myself, as a preservice teacher, to be uncomfortable with. As a

young student, I struggled with fractions, decimals and algebra more than any

other concepts. In order to properly teach these concepts to my future students, I

found it essential that I properly educate myself on the associated teaching

methods. After reading and reviewing the following articles, I can now say I am

much more confident in my ability to teach these mathematical concepts.

Wilson, P. Holt., Myers, Marielle., Edgington, Cydni & Confrey, Jere. ( April

2012). Fair Shares, Matey, or Walk the Plank. Teaching Children

Mathematics, 18(8), 482–489

This article, written by P. Holt Wilson, Marrielle Myers, Cyndi Edgington

and Jere Confrey, discusses the results of using pirate themed instruction to

explore equal-size groupings with a group of young elementary students.

Findings expressed in this article are part of a larger study on the learning

trajectories for rational number reasoning, specifically how naïve understanding of

basic concepts develop into understanding of complex mathematical ideas over

time.

The theme of pirates served as a catalyst for the teachers and students

involved in this specific section of the study. Wilson et. al introduce the article by

mentioning the difficulty many students have in learning to reason about rational

numbers. These reasoning skills begin with first learning how to equipartition a

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collect or a whole. Equipartitioning refers the ability to partition a set of objects, or

a whole into parts of the same size. By learning to equipartition, students will

eventually be able use their informal knowledge of fair sharing concepts in order

to be able to eventually develop an understanding of partitive division.

Wilson et. al. argue that when children equipartition, they must

successfully coordinate a specific criteria Students must first create the correct

number. Students must create the correct amount of groups or parts, generate

groups or parts of equal size and exhaust the collection or whole. I have never

seen the success criteria for equally partitioning before, yet I find it to be quite

useful. The authors’ criteria cannot only benefit educators for the purpose of

instruction, but if thoroughly described to students, can aid in their learning as

well.

Students in the section of the authors’ study were first given a collection of

pirate coins to “fair share”. Sharing a collection of items come very naturally to

young students, as the concept is used in their daily lives. While not every student

involved was successful at equipartitioning the collection, for those that were, a

variety of strategies were used, such as “dealing” as one would do with cards as

well as recalling number facts such as doubles. Students were later given a whole

“pirate birthday cake” to equally partition. Students were given the opportunity to

partition a rectangular cake as well as a circular cake, the later proving to be

more challenging for students. Successful students use a wide range of strategies

during this activity as well, such as halving/repeated halving or a combination of

parallel and radial cuts.

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For beginning teachers such as myself, this article discusses students’

successes and struggles with equipartitioning in a way that can directly inform

teaching practices. The authors give direct advice to the reader on ways to have

students justify their partitioning strategies as well as how to navigate the criteria

given in the introduction. As this article discusses a portion of a larger study on I

found that as this article is focused on a small section of a study on learning

trajectories for rational number reasoning, a variety of useful tables and charts

are provided, including one that shows a hypothesized trajectory from

equipartitioning collections all the way to the continuity principle. As educators,

this trajectory is a great tool to ensure that we can accurately pinpoint where

student understanding is, in order to determine what needs to be done in order to

understanding the next learning objective. However, I do wish to access more

information about this study in order to ensure the validity of the proposed

learning trajectory.

D'Ambrosio, B. S., & Kastberg, S. E. (May 01, 2012). Building Understanding

of Decimal Fractions. Teaching Children Mathematics, 18, 9, 558-564.

This article begins by describing a situation where a group of preservice

teachers, such as my colleagues and myself, were unable to order numbers from

smallest to largest during a decimal ordering task. For those preservice teachers

who successfully completed the task, many were unable to justify their solution on

a decimal grid. According to the authors, this is a common issue among

elementary aged learners as well. Ambrosio and Kastberg discuss the beneficial

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use of decimal grids in the fourth and fifth grades in order to provide students with

a way of connecting symbolic representation of decimals and decimal fractions.

By shading a quantity represented by a decimal numeral or fraction, students are

able to visually see what they are representing, and from there they can easily

order and compare and connect various representations.

The authors’ analysis of preservice provides educators, both preservice

and experienced, with a variety of useful information, such as where common

student difficulties lie. Ambrosio and Kastberg examine the struggles the

preservice teachers had with using decimal grids as a tool for representing

decimal numerals. Many of these adult learners struggled because they did not

consider the relationships among the various subdivisions of a whole, such as

how tenths relate to hundredths, hundredths to thousands and so on. Others

relied heavily on procedure and struggled to understanding of pattern consistency

in regards to the relationship between adjacent decimals places or with no seeing

the additive nature of decimal places. Without a rich understanding of the

relationships between the subdivisions of a whole, the students studied were

unable to use the grid in all requested situations.

As their findings based of adult learners can be directly connected with

those of young learners, Ambrosio and Kastberg offer their readers a set of

guidelines, which I found to be the most beneficial section of this article. These

guidelines include introducing students to one grid at a time, emphasizing the

additive nature of the place value system and including a set of follow up tasks

such as those created by Fosnot and Dolk (2001). Being a preservice teacher

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who experiences math anxiety, I found this article to be very useful. “Building

Understanding of Decimal Fractions: Using Grids Can Help Students Overcome

Confusion About Place Value.” encourages teachers to reflect upon their own

understanding of decimal fractions, while providing them with helpful information

to ensure best practice methods of instruction.

Ward, R., & Muller, D. ( September 2006). ALGEBRA AND ART. Mathematics

Teaching, (198), 22-26.

In the article “Algebra and Art”, authors Robin Ward and David Ward

discuss a group of preservice teachers who set out to examine the integration of

art with algebra. Their exploration of algebra and art focused on how the

integration of art can bridge the gap between learning and playing. The

preservice teachers discussed in this article participated in an activity based on

the work of Alexander Calder that exemplified the NCTM idea that students

should see mathematics as “an exciting and creative field of study” (Principles

and standards for school mathematics 2000, p.11) Alexander Calder created the

art form of mobile construction in the 1930s, which were moving mobile

comprised of shapes suspended from rods and wires. Although these pieces

would seem to be heavier on one side, equilibrium was always maintained, which

can be explained through an algebraic formula known as the Law of Levers.

The education students discussed by the authors were first briefly

introduced to the work of Alexander Calder and were informed of algebra’s role in

his creations. In the spirit of Calder, the students completed a set of activities

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involving balancing in order to discover, through trial and error, the Law of Levers.

Once the education students discovered the Law of Levers, they created their

own Calder-like mobiles.

Although the activities done with the preservice teachers were designed to

engage middle school learners, I found this article to be very informative from the

perspective of a preservice elementary teacher. The idea that incorporating art

into mathematics makes mathematical concepts less abstract is a universal one.

Students of any age should be made to feel that mathematics is “an exciting and

creative field of study” (Principles and standards for school mathematics 2000,

p.11), which can be accomplished through the integration of art concepts. Mixing

learning with play as exemplified in this article would be just as valuable at the

elementary school level as at the middle school level. I hope to be able to

discover mathematics driven artists to share with elementary students in the

future.

Math Manipulatives Review

Base Ten Blocks

Base ten blocks are a mathematical manipulative used by students to

understand a variety of mathematical concepts. While this type of manipulative

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can be used in a variety of ways, such as skip-counting and two/ digit addition

and subtraction, they are especially useful when teaching place-value language

and concepts to elementary math students.

These three-dimensional blocks come in four different sizes, which indicate

their individual place value. The smallest blocks, known as units represent the

“one’s place”. The long, thin blocks are known as rods and represent the “ten’s

place”. The flat, square shaped blocks are known as flats, and represent the

“hundred’s place” while the large, three-dimensional cubes, known simply as

“cubes”, represent the “thousand’s place”. When teaching third grade students

base-ten concepts, I noticed many students struggling to understand how to

differentiate between how many “tens” were in a whole number in comparison to

what digit was in the “ten’s” place. Base-ten blocks gave students to chance to

both visualize and physically represent both concepts. I feel that it definitely best

practice to have this type of

manipulative in all elementary

classrooms.

Snap Cubes

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Interconnecting snap cubes, such as those pictured below are a great

mathematic manipulative. The uses for snap cubes at the elementary level are

limitless. In my professional and personal experience, I have found snap cubes to

be useful in the development of number sense, and great tools to help students

develop an understanding of patterns, adding/ subtracting as well as multiplying

and dividing. Like other manipulatives, snap cubes also support a

tactile/kinesthetic learning style. I have yet to have any professional experience at

the early elementary levels, yet I think snap cubes would be particularly useful

when teaching measurement

comparisons using non-standard units of

measure.

Although I have yet to incorporate

STEM standards into my everyday

teaching, I think that the use of snap

cubes would be an excellent place to

begin. Students adore snap cubes, not

because they believe they help them understand math concepts, but because

they love building with them. Combining students love of building with Math

curricula and STEM standards can only result in a very engaging lesson, and

thereby reflect best practice methods

Number Lines

I think that individual number lines are an essential mathematic

manipulative for every elementary classroom. Number lines are a great tool to

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help students begin to understand the relationships between numbers. Counting

and numeration concepts can be learned through the use of number lines, as

students can follow the line to count or add. Number lines also promote

mathematical problem solving and

reasoning skills as well as help students

understand the concepts of odd/even and

greater than/less than. In the upper grades,

number lines also help students understand

fraction and whole number concepts. When

teaching third-grade students, I found

number lines to be particularly useful when teaching estimation, which was a

relatively new concept for my students. Number lines are a great resource for

visual learners, but are beneficial to every student in the classroom therefore

showing the use of number lines as a tool of best practice.

Pattern Blocks

Pattern blocks are geometrically shaped math manipulatives, which come

in the forms of squares, triangles, hexagons, parallelograms and trapezoids.

These colorful shapes not only engage children, but help them better understand

concepts in the areas of number, geometry and patterns, and proportional

reasoning. In the lower elementary grades, through the use of pattern blocks,

students can recreate and translate pattern sequences and become familiar with

geometric terminology. In the upper elementary grades, pattern blocks would be a

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great way to aid students in

understanding area formulas for

shapes such as triangles, rectangles

and parallelograms. Pattern Blocks

can also be used in replace of

counters, to help students grasps

addition and subtraction concepts, or used in an array in order to help develop

multiplication and division concepts.

Fraction Strips

Fractions are often a very difficult concept for young learners to grasp,

therefore it is essential that teachers use manipulatives such as fraction strips in

the classroom. Visualizing parts of a whole is very difficult without a concrete

example. Fraction strips show the various ways to divide a whole, thereby

allowing students to not only partition off an object or number, but to compare

fractional relationships and to compare/ order as well. In a classroom setting, I

think a large magnetic set of fraction strips would be great to have, yet I feel that it

is key for each student to have a

set of handmade fraction strips at

their desks. I also think it is

important to used fraction strips

that are colour-coded, in order to

minimize confusion for students.

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Mathematics & Technology Products

Math Podcast

For my first internship, I taught 3rd grade French Immersion. During my

experience, I was able to gain insight into common problem areas for students in

relation to mathematical concepts. Many of the insights I gained stemmed from a

conference between the school numeracy lead, my co-operating teacher, and

myself. In this meeting, we reviewed the results from the key stage outcomes

assessment from the year prior. Nearly all of the third grade students assessed at

the end of 2015 could not answer; “How many tens are in ?” correctly.

In order to avoid similar results in 2016, we focused a great deal of time and

energy on differentiating place value concepts and how many ones, tens and

hundreds were in a given number.

Below I have included a link to a podcast I created, which describes the

methods I found effective in guiding my students towards this key skills outcome.

To access this link, please click the image on the right.

Instruction Video: Grade 1 Measurement Comparison Lesson

A mandatory component of my Math Methods course was the creation of a

peer-teaching lesson. For my peer-teaching lesson, I used outcomes from the 1st

Grade New Brunswick curriculum to create a lesson on comparing

measurements. By clicking the image below, you can gain access to the

instructional video I have created based on this lesson.

Although I have not yet had the opportunity to use this

lesson in a first grade classroom, I think that my

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http://vocaroo.com/i/s0NoWYrJI89i


incorporation of language arts, physical movement and a game-like design will

engage young learners.

To access an online copy of the Smart Notebook file used in this lesson, please go to:

file:///Users/Cat/Pictures/Measurement-Building%20on%20Comparison%20Lesson%20by%20Catherine%20Theriault.html

To access the website used to access e-book resource, please go to:

https://www.getepic.com/app/account_select

The lesson plan referred to in this video can be found below.

Measurement: Building on Direct Comparison to Understand OrderingGrade: 1Subject: MathLesson Duration: 45 minutesDate: February 9th, 2016

Standards & OutcomesNew Brunswick Curricular Outcomes:GCO: Shape & Space (SS): Use direct or indirect measurement to solve problemsSCO: SS1: Demonstrate an understanding of measurement as a process of comparing

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https://www.getepic.com/app/account_select

https://www.youtube.com/watch?v=xkGs30hqTx0&feature=youtu.be


By identifying attributes that can be compared Ordering objects Making statements of comparison

NCTM Pre-K – 2 ExpectationsIn pre-K through grade 2 all students should:

Recognize the attributes of length, volume, weight, area, and time; Compare and order objects according to these attributes; Understand how to measure using nonstandard and standard units; Select an appropriate unit and tool for the attribute being measured.

Lesson RationaleTo activate students’ prior knowledge of direct comparison of two objects based on a single attribute such as length, mass and volume in order to develop understanding of measurement as a process of comparing.Contextual Resources

Lesson plan based on information gathered from:Elementary and Middle School Mathematics: Teaching Developmentally by Van de Walle, Karp, Bay-Williams, McGarvey, & Folk, p. 369-372

Necessary Materials Too Tall Tina by Donna Marie Pitino (accessed

through the GetEpic website) SmartNotebook Presentation (Math Peer Teaching) SmartBoard 7 Ziploc baggies filled with yarn of various lengths

(designed for 7 groups of three with a class size of 21)

Broom Handle 2 packs of sticky notes Recording Sheets (See Appendices) Limbo Rock Youtube Clip

https://www.youtube.com/watch?v=7nb2IgMgw54

ProcedureLesson Preparation:

Prior to beginning the lesson, ensure that the Smart Notebook file entitled “Measurement Lesson 1” as well as the getepic.com’s ebook version of Too Tall Tina is open on the SmartBoard

Introduction/Hook (10-12 minutes): Gather students at the front of the class, surrounding the SmartBoard. Before reading

the book to students, ask students to “Pay extra close attention to the coloured boxes at the bottom of some of the pages”. Open up the getepic.com link (click the globe icon

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https://www.youtube.com/watch?v=7nb2IgMgw54


at the corner of the book image on page 2 of the Notebook file) and begin to read Too Tall Tina to the class. *see differentiation notes

After the book is read ask students “ At the bottom of some of the pages in Too Tall Tina, there were coloured boxes with words in them, can anyone remember what some of these words are?” Allow students to raise their hands to share with the class which words they remember seeing.

After a sufficient wait time is given (depending on whether or not any students can recall some of the words they saw), go to page 3 of the Notebook file.

Tell students that; “We are going to do a variety of activities based on the measurement comparisons we’ve seen in Too Tall Tina, and hand out recording sheets. (See Appendices) Remind students not to write on their sheets until instructed.

ActivitiesTall, Taller and Tallest (5-7 minutes):

Tell students that; “Tall, taller and tallest is the 1st measurement comparison we see in Too Tall Tina.” Instruct (and guide) students to order themselves from tall to tallest. Have students write a sentence stating who is the tallest in the class on their recording sheet.

Short, Shorter and Shortest (5-8 minutes): Tell students that; “Short, shorter and shortest is the 2nd measurement comparison we

see in Too Tall Tina.” Place students in predetermined groups of 3 (based on mathematical skill level) and give each group a baggie filled with multi-length pieces of yarn. Have students order the pieces of yarn from short to shortest.

Low, Lower and Lowest (5-8 minutes): Tell students that; “Low, lower and lowest is the 3rd measurement comparison we see

in Too Tall Tina” Grab the broom handle and explain to students that the class will play limbo in order to see who can go low, lower and lowest. Choose two students to hold the broomstick and demonstrate to the class how to play. After demonstration is given, click the link on page 7 of the Notebook file to open the limbo song Youtube clip.

Students will alternate holding the broom handle as they play. After the limbo game is finished, instruct students to write a sentence on their recording sheet about whom in the class could go the lowest.

High, Higher and Highest (5-8 minutes): Tell students that; “High, higher and highest is the 4th measurement comparison we

see in Too Tall Tina.” Have students return to their desks and hand a sticky note out to each. Instruct students to write their names on their sticky notes. Once students have finished, line students up facing an unobstructed classroom wall. Have students one at a time, jump as high as they can with the sticky part of their note facing the wall, placing the note as high as possible. Once each student has had a turn, instruct students to write a sentence on their recording sheet about who in the class could jump the highest. Collect the sticky notes for later use.

Long, Longer and Longest (5-8 minutes)

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Tell students that; “Long, longer and longest is the 5th measurement comparison we see in Too Tall Tina. In groups of 3, let's see whose hair is long, longer and longest!” Help the class organize themselves (as an entire group) from whose hair is long to longest. Have students write a sentence on their recording sheet about whose hair is longest.

Far, Farther and Farthest (5-8 minutes) Tell students that; “Far, farther and farthest is the 6th measurement comparison we

see in Too Tall Tina. Using our limbo stick as a starting line and sticky notes to mark our places, let's see who can jump far, farther and farthest! Line students up aligned with the broom handle on floor. Have students jump as far as they can, one at a time, using the sticky notes from the High, Higher and Highest activity to mark students places. Have students write a sentence on their recording sheets about who jumped the farthest.

Wrap-up (3-5 minutes) Allow students who have not yet finished to finish up their sentences (punctuation,

capital letters etc.) and instruct those who have finished to add illustrations to their work.

Using Popsicle sticks*, have students each share something they have learned from the lesson.

*See Assessment

Differentiation/Special Consideration For students with learning disabilities, such as dyslexia, all instructions are given orally. For students with autism, all instructions will also be displayed on the board, and can

be printed and given to the students prior to the lesson. Students with autism can also be asked to help change the slides, allowing them to feel as if they have more control.

For other students who tend to fall behind, the combination of oral and verbal instructions should also help.

For students with ADD/ADHD the lesson is tailored to be very hands on and kinaesthetic.

For students struggle with motor skill issues, peers and support staff can help to guide them through the lesson.

For students with hearing impairments, a microphone system will be used, as well as written instructions.

For students with visual impairments, a closed circuit TV can be used to read instructions when required. Support staff/educator/peers can help guide them through the physical components of the lesson.

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Gifted students will be encouraged to explore other measurement comparison options and record them on their sheets. If students are capable, they can be introduced to standard units of measure and instructed to use measuring tape/rulers to order and compare.

*Student groupings will be predetermined based on ability level.Assessment

Anecdotal notes will be taken throughout the course of the lesson to monitor student understanding and participation.

Recording sheets will be collected and considered a method of formative assessment for the unit

Post Lesson Notes and Reflections Record what went well during the lesson and what could be improved upon for future

lessons Review anecdotal notes, and compared them to other notes taken during other

lessons.

Appendix

Measurement and Ordering: Recording Sheet

Name:

Date:

Example: Miss Theriault has the shortest straw.

Tall, Taller and Tallest

Low, Lower and Lowest

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High, Higher and Highest

Long, Longer and Longest

Far, Farther and Farthest

References

Van de Walle, K., Folk, S., Karp. K., Bay-Williams, J., & McGarvey, L.M. (2015).

(4th Canadian ed). Elementary and middle school mathematics: Teaching

developmentally. Toronto, ON: Pearson.

Pitino, D. M., & Woodruff, L. (2005). Too-Tall Tina. New York: Kane Press.

Smart Notebook File: Grade 3 Math Warm-Ups

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The following selection of Math warm-ups was inspired by my

first internship in 3rd grade French Immersion. I based the warm-ups

on curricular concepts that had been covered in the class between

September and December. Often, I found my students struggled to

get into “Math Mode”, as Math began immediately after recess.

Warm-ups, lasting approximately 5 minutes, are a great way to

engage learners and to provide an opportunity to brush up on

concepts.

To gain online access to this file, please click on the image below:

Other Areas of Interest

Interview with an Elementary Math Student

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For this component, I was able to interview my step-daughter about her

experiences in Math. Bella is currently in first grade and is quite shy. I originally

intended to videotape our conversation, yet that proved to be a bit too

overwhelming for her. Using the Smart Recorder software, I was able to audio

record our conversation. Although I had a list of predetermined prompt questions,

I allowed the conversation to flow naturally, which I allowed me an insight into the

mind of a young student. In the interview, Bella talks about her likes and dislikes,

as well as some of the concepts she has learned this year.

To access the interview, please click the image below.

Math Website Review

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https://www.youtube.com/watch?v=_uW2PIExg7M


Below I have comprised a list of electronic math resources, which I feel,

can spark student interest and promote mathematics engagement. Although

these resources can be

useful for a variety of

different grade levels, I

have examined the

following through the lens of

a 3rd grade teacher, as that

is the level in which I have

the most experience.

ABCya!

http://www.abcya.com/third_grade_computers.htm

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http://www.abcya.com/third_grade_computers.htm


ABCya! is a resource free for both

parents and educators. This website provides

a variety of different mathematic, language

arts, strategy and skills games for children.

While there are grade level options, I have

found from experience that they are not

always accurate therefore I recommend parents and educators to first explore the

game options prior to letting students play to ensure appropriate fit.

The only negative aspect about this resource is that not every available game

possesses the same educational merit, therefore it is important the adults monitor

which games are being played, especially during instructional hours.

Math Playground

http://

www.mathplayground.com/games.html

Although I have yet to use this resource with students, based on a brief

exploration, I am confident this resource could be well used by students. I

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http://www.mathplayground.com/games.html




particularly like the puzzle pic addition and subtraction games. I also find they

have a variety of engaging fraction making and comparing activities.

The only negative aspect of this resource is that while it provides a

plethora of money counting and change making games, two concepts which

students struggle with, the examples given are American. As we do not use 1-

dollar bills and pennies are not used in Canada, I would hesitate to use the

games with Canadian students.

Learning Games for Kids

http://www.learninggamesforkids.com/math_games.html

In comparison

to the other resources I

have examined thus

far, Learning Games for Kids appears to be

slightly less user-

friendly. Once I

became acclimated to

the resource, I was

able to discover many math vocabulary games, which I found the other resources

I examined to be lacking in. Although I would not encourage students to use this

website independently, as some of the jargon is a bit complex, the math

vocabulary games appear to be something that could be used as a part of whole

class instruction. I particularly liked the Number Sense LetterFall and the Matchit

Geometry Terms games, and can see ways in which they could compliment a

lesson.

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http://www.learninggamesforkids.com/math_games.html


Cross Curricular Component: Science Observation Journal

During the first semester of the

B.Ed program at St Thomas University,

students in the elementary cohort were

required to complete a nature

observation journal, in order to learn

how to use this type of project with

future students. I have included

examples of my observation journal to showcase the cross-curricula math

components that be explored through the compilation of daily observations.

Observing elements such as weather, animal sightings, precipitation, litter,

growth and decay on a daily basis

can provide students with a variety of

learning opportunities. From a

science perspective, students can

develop inquiry, observation and

classification skills as well as

develop an understanding of the

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scientific process. From a mathematical standpoint, observation journals such as

this teach students about data collection and analysis as well as measuring and

graphing. Visual Arts outcomes can also be reached through this type of project

based learning.

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Creative Math Project: Mathematical Snakes and Ladders

In October 2015, my colleague Nadia El-Khoury and I collaborated to re-

invent the traditional game of “Snakes and Ladders” to incorporate elementary

math concepts. I have seen first hand how effective math games can be in

regards to learning, long-term memory as well as the understanding of new

concepts. This board game was designed to encourage students to practice

numeracy, addition and subtraction, pattern and shape recognition as well as

problem solving skills all while having fun. The game can be played with 2-3

players and targeted to Grade 2 students, yet can be played by students in

grades 1-3, depending on ability level.

This game is comprised of:

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1 game board

3 game pieces (1 per player)

1 die

50 game cards

Instructions

It is suggested that teachers read these aloud to students, prior to their first

experience with the game

1. All players must place their game pieces on the space labeled START

2. The youngest player rolls the die first. The die contains 6 possible options; roll

again, star, circle, square, triangle or diamond. The star icon represents

addition problems, the circle represents subtraction problems, the square

represents pattern sequences, the triangle represents mystery card and the

diamond represents word problems.

3. If the player rolls “Roll Again” they must roll again, if they get anything else

they must move their game piece to the nearest card that is labeled with the

same shape. Example: If a player rolls a star, they must move to the nearest

“Star” space.

4. After moving to the matching space, the player must then pick up the

corresponding card. Example: If the player rolled a circle and moved to the

circle space, they would need to pick up the card with the circle in the upper

right corner. After picking up the corresponding card, the player must either do

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as the card says (for the cards marked with a triangle) or answer the

corresponding question. If they answer the question correctly, they may stay

at their new space, but if they answer incorrectly, they must go back to the

space they were at before.

5. If players land on a space with either a snake or a ladder, they must go up or

down from that space even if they answer the corresponding question

incorrectly.

6. Players will continue to alternate rolling the die, moving to the corresponding

space and picking/answering the corresponding questions.

7. The first player to land on FINISH wins!

Some images of the original game design can be seen below.

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SUMMATIVE MATH PROJECT 37

SUMMATIVE MATH PROJECT 38

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