Summative Math Project

8/12/2019 Summative Math Project

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Summative Math Project

Kayla Mutch February 24, 2014

Table of Contents

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Anderson, C., Anderson, K., Wenzel, E. (2000). Oil and water dont mix, butthey do teach fractions. Teaching Children Mathematics , 7(3), 174-178.

This article ties together math and science, which is important becausethe two subjects often have overlapping concepts. Here, the mathematicalthinking is in fractions. The lesson described consisted of visuallydemonstrating fractions to students using water and oil. Students were givenclear beakers, two cups of yellow cooking oil, and one cup of blue water. Thestudents were able to think and see in thirds, as they could visualize what 1/3,2/3, and 3/3 physically looks like. The authors included samples of student

work, so that teachers can anticipate similar responses from their ownstudents. Some students thought the water and oil would mix, to make a greencolor. Other students knew that oil and water do not mix, but did not know oil,

when mixed with water, would rise to the top of the beaker. The students werethen given time to extend their learning through group work and their ownfractions, water, and oil.

The end of the article provides further uses for oil and water whenteaching fractions. I particularly thought teaching addition and subtraction offractions through using this hands-on technique was brilliant, and am glad theauthors shared this idea. Fractions are a difficult mathematical concept forstudents to understand. The article states that according to the NationalCenter for Educational Statistics reported that only 46% of twelfth gradestudents who wrote the National Assessment of Educational Progress couldconsistently solve mathematical problems including fractions. This is alarming

and as a teacher, shows that more time and creative methods of teachingfractions need to be taken to ensure our students grasp these fundamentalskills.

Moone, G. & de Groot, C. (2006). Fraction action. Teaching Children Mathematics , 13(5), 266-271.

I thought this was a great article and supported evidence on fractionsspecified in other articles found in my research. The authors stated thatfractions are often difficult mathematical concepts for children to grasp. Theyidentify a potential reason for the problem, which I felt to be one of the most

important aspects of this article. According to Moon and de Groot, the rulesthat students learn for working with fractions go against their sense of wholenumbers. This is evident when children add numerators and denominators,and for example, believe that 1/6 is smaller than 1/12, because 6 is less than12. As a teacher, knowing that this is a significant problem when learning theconcept of fractions, it is important that I take the appropriate steps to helpstudents correct this mistake.


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The article provides an overview of a three-day lesson in grade 4. Theauthors were not in the classroom to conduct research, but rather helpstudents understand the concept of fractions through a mathematicalinvestigation. The lessons are completely realistic and replicable for anyteacher to use in his or her own classroom.

Shaughnessy, M. M. (2011). Identify fractions and decimals on a number line.Teaching Children Mathematics , 17(7), 428-434.

Shaughnessy suggests that we often ask students to show us a fractionthrough a pictorial example, more often than knowledge being demonstratedthrough a number line. She argues that a more concrete understanding offractions could be reached through showing students that fractions have aplace on a number line and repeatedly using this as a method to showfractions.

The author interviewed students in California, to investigate the nature

of the students difficulties when labeling fractions on a number line. Theprotocol included various number line tasks, asking students to label markedpoints on a number line as fractions and decimals. More students correctlylabeled number lines using decimal notations, as opposed to fractionalnotations. Also, more students appropriately labeled when the interval fromzero to one was equally divided than when the interval was unequallydivided.

The instructional implications at the end of this chapter are especiallyuseful. Identifying these errors and explaining them to students can showthem how to correctly label a number line using fractions. As a teacher,understanding mistakes students may make when working with fractions canbetter prepare you to make sense of their own reasoning. Therefore, you canfind the issue and show them the correct way.

Siebert, D. & Gaskin, N. (2006). Creating, naming, and justifying FRACTIONS.Teaching Children Mathematics , 12(8), 394-400.

This article discusses the points, as does other research in this area,that fractions are difficult for children to master, due to the complexity of therules. The tie to whole numbers is another factor that confuses children andcan prevent them from seeing fractions as a number or quantity. For example,if children are given a picture with four circles and three are shaded yellow,the authors suggest that many children would state that there are three circlesshaded out of a total of four circles, instead of seeing ! .

Fractions can appear senseless to children. To me, the explanation ofthe operations was the most significant in truly explaining why fractions seemmysterious and the rules are complex. When adding or subtracting, you needto find a common denominator; but you do not when you multiply or divide.Once you have a common denominator, you only add or subtract the


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numerators. However, when we multiply, both the numerators anddenominators are multiplied. Furthermore, in regards to division, neither thenumerators nor the denominators are divided.

Siebert and Gaskin offer strategies to teach children to see fractions without whole-number lenses. Visual tools can help children create and act on

fractions. Partitioning is creating smaller, equal-sized amounts from a largeramount. Iterating means to make copies of a smaller amount and combiningthem to create a larger amount. These two skills, partitioning and iterating,are important to teach children so that they are given tools to tackle fractions.The authors suggest that it is the images, not the specific language to describethe images that should receive the most emphasis when teaching studentsabout fractions. I believe this is a very good point; we should not bog studentsdown on terms if it means it will take away from their conceptualunderstanding.

Stump, S. L. (May 2003). Designing fraction-counting books. Teaching

Children Mathematics , 9(9), 546-549.

Stump discusses her sons experience with foundational mathematicalconcepts, such as counting. She raises the point that he developed most of hisearly knowledge of fractions through a traditional route that focusedspecifically on symbol manipulation. He did not experience fractions the same

way that he experienced whole numbers; through an artistic, numerical, andsymbolic way.

This article is unique, because it addresses the way fractions have beentaught and provides a new strategy, a fraction-counting book, for teachers totry. Combined from the ideas of previous research, the activity challengesteachers to represent fractional parts in real-world settings and describethose parts in fraction language. For example, six-fourths is actually just sixobjects called fourths. Later, when students are introduced to fractions, theyhave a more contextual understanding that the numerator is the countingnumber and the denominator is what is being counted.

An interesting point made in this article is that teachers often showfraction in pies , being plural. Yet three-fourths of a pie is singular. TheEnglish convention states that the plural form is used when the quantity isgreater than one. Personally, I never considered this before and am nowgoing to be more aware of how my language dictates what students mayconsider to be expectations.

Developing fraction-counting books takes a creative spin on traditionalform of childrens literature and helps teachers and students explore thelanguage of fractions and the concept of fractional parts, before diving intothe symbolism of fractions. This is a great tool to recommend to fellowteachers!


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Roddick, C. and Silvas-Centeno, C. (2007). Understanding of fractions throughpattern blocks and fair trade. Teaching Children Mathematics , 14(3),140-145.

Roddick and Silvas-Centeno discuss the difficulties students experience

learning fractions, and how those basic issues prohibit learning in other areasof mathematics. The authors give possible reasons for the difficulties learnersexperience with fractions: the material is taught too abstractly, tooprocedurally, and outside any meaningful contexts. Also, some problems withthe understanding of fractions stem from learning fractions through rotememorization of procedures without connecting or building on the means ofoperating.

This article was interesting, as it followed two teachers that wished toaddress the flaws in students understanding of fractions. These two womenbelieved that a successful teacher should guide their students in exploringideas and concepts, so they can develop their own knowledge, along with

encouraging student-generated strategies. The teachers came together todiscuss the issue with Silvas-Centenos sixth grade math class unable to retainan understanding of fractions. The conclusion was reached that thepresentation of fractions was too abstract and focused on procedures.Therefore, it was decided that her students could benefit from a more hands-on approach. The inclusion of this point made this article interesting to me, notonly for the strategies of teaching fractions, but also because it shows thatgood teachers do need to look at their methods and reflect on how they areapproaching subjects and actively seeking ways to help their students gainunderstandings.

The teachers employed a technique of using pattern blocks, to buildthe foundation for understanding concepts and computation, and fair trade, anotion that represents equivalent fractions and gives conceptual meaning tothe procedures related to fraction operations. Furthermore, the teachers alsoincluded real-life problems to generate thinking. These techniques would beanother very helpful strategy to implement in a classroom when teachingfractions, so that the challenges surrounding the topic can be combatted.


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Using Sudoku Bulletin Boards to Teach Mathematical Reasoning

The title of this article intrigued me. I was interested by the use ofSudoku bulletin boards and its success. The author implemented theseSudoku bulletin boards as a choice assignment in the form of a tic-tac-toeinstructional strategy, where students were given opens and had to selectthree across, diagonally, or up and down. She states that the students wereimmediately interested in Sudoku puzzles.

Buckley articulates the need for clarity and simplicity when teachingprimary aged students thinking and logical skills. Modeling a constructivistteaching style, she guides inquiry-based lessons to facilitate discussions andindependent thinking. Sudoku puzzles allow students to develop logic andreasoning skills independently.

To set students up for success, Buckley introduced students to a Sudokumade from a 2x2 grid of four basic colors. By eliminating numbers and onlyfocusing on colors, this allows for students to begin from basics. I thought this

was interesting. All too often, we tie Math to numbers, when in actualitydeveloping logic and reasoning skills builds beyond numbers. Colors couldmore likely be processed simply for students as opposed to numbers. Ithought this was a creative way to introduce Sudoku bulletin boards to youngstudents.

Buckley emphasizes the importance of considering how to explainSudoku to students so that the instruction is clear, but fostering their ability tothink autonomously. After administering puzzles to the students, those familiar

with Sudoku quickly finished; peers helped students unfamiliar with theconcept of the puzzles. It was interesting that Buckley discusses that students

who were helping their peers had them model behaviours to aid in theirsolving of puzzles, such as using their finger to guide them or holding a fingeron a specific place to mark it.

In no time at all (209) students had completed all prepared colored2x2 Sudoku, Buckley created a more difficult 4x4 grid, using four letters (M-A-T-H). Students found these too easy and exhausted them quickly. It was fromthis that Buckley created the Sudoku bulletin board.

Initially, Buckley states some students were confused. She did notdetect any correlation between age and gender. Through strategy teaching tosmall groups of students experiencing difficulty, she allowed them to beeased back into the responsibilities of the puzzle. Incorporating differentiationinto the Sudoku bulletin board was something I felt was needed andappreciated that Buckley included it. Those who are experienced can begiven puzzles that challenge their abilities, but students who are lesscomfortable are given the option to complete the puzzles. All students weregiven the choice to complete the puzzle independently or with a partner.


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What was interesting was to hear students verbalize their thinkingduring their solving. Buckley discusses the various strategies that the studentsemployed, such as beginning at the top and going across, attempting to focuson a singular color at a time, using visual numbers that could be possiblesolutions, etc.

Buckley discusses that the success in completing the Sudoku has beenmixed with the second and third grade students, however their reasoning andpersistence impressed her. In my opinion, I do not believe at this age that it isimportant if the answers are necessarily correct, as long as students arebeginning to explore their problem-solving and reasoning skills. I thoughtthis article was an interesting idea to use in a classroom. Buckley accentuatedhow this task appealed to gifted students and students who weremathematically advanced. With this in mind, I would be eager to use this as anenrichment project. I would not overwhelm students struggling to grasp basicmathematical concepts, yet as Buckley did, teach the strategies and skills andallow it to be an option or an activity outside of classroom instruction.

Reference

Buckely, C. (2008). Using Sudoku bulletin boards to teach mathematicalreasoning. Teaching Children Mathematics , 15(4), 208-211.


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Identify Fractions and Decimals on a Number Line

We often ask students to show us a fraction through a pictorial example.

They give us a shaded piece of a pizza or a chocolate bar. What we do notoften ask students is where fractions fall on a number line. A more concreteand flexible understanding of fractions could be achieved through showingstudents that fractions have a place on a number line. Shaughnessy says thatrather than giving your students a fraction and asking them to place it on anumber line, have them use the fractional notation to label points on thenumber line. This requires the student to strategize. One way includesdetermining the number of parts of equal distance from 0 to the target, thenmarking the number line.

To investigate the nature of the students difficulties when labelingfractions on a number line, the author interviewed students in California. The

protocol included various number line tasks, asking students to label markedpoints on a number line as fractions and decimals. More students correctlylabeled number lines using decimal notations, as opposed to fractionalnotations. Also, more students appropriately labeled when the interval fromzero to one was equally divided than when the interval was unequallydivided.

Four common reasoning for incorrectly labeling a number line aresummarized. The first is using unconventional notation. Labeling a markedpoint on a number line requires an understanding of the conventions offractions. The representation the student may use to convey their answer maynot be the standard convention. An example of this may be a student using

10/8 when they meant 8/10. Secondly, is redefining the unit. When given anumber line in which the shown distance is not the unit distance, they mayredefine the unit distance on the number line and treat the entire distanceshown as the unit distance, rather than the distance between zero and one.Such as labeling 8/20 on the number line, reasoning that there should be tentick marks from 0-1, and ten tick marks from 1-2. Thirdly, a two-count strategythat focuses on tick-marks rather than distances was also reported. Thisoccurs when the denominator becomes the number of tick marks and thesecond count, the numerator, is the number of tick marks from zero to thetarget point. Finally, a one-count strategy that focuses on tick-marks ratherthan distances may be seen when the number of tick marks from zero thelargest point become the denominator.

Meghan Shaughnessy is a postdoctoral research fellow at the Universityof Michigans School of Education. She designs and studies innovativeprofessional development materials for practicing teachers and teachesmethods courses. Her research focuses on the teaching and learning ofrational numbers. From a critical perspective, I felt that this investigation

would need to be repeated several more times before these four commonerrors can be truly narrowed down. The author only conducted the


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investigation in an urban city school in Northern California, using studentsonly in grade 5, However, the information is a red flag for teachers to beaware of in their teaching.

The instructional implications at the end of this chapter are especiallyuseful. Identifying these errors and explaining them to students can show

them how to correctly label a number line using fractions. As a teacher,understanding mistakes students may make when working with fractions canbetter prepare you to make sense of their own reasoning. Therefore, you canfind the issue and show them the correct way. Students flexibility can beincreased when given a variety of number lines, ones that are equally dividedand ones that are unequally divided, as well as being asked to label numberlines using fractions or decimals.

Reference

Shaughnessy, M. M. (March 01, 2011). Identify fractions and decimals on a

number line. Teaching Children Mathematics , 17(7), 428-434.


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Mathematical Adventures with Harry Potter

The unique concept of this article is what caught my eye. Harry Potter was an extremely popular series when I was in elementary and middle school,and still is. The idea of turning math, a subject children often find abstract anddifficult, into an adventure integrated with language arts was appealing to me.

I thought this article was great in the sense that it was very practical andprovided teachable ideas. The authors provide a basic summary of the storyline to Harry Potter and the Philosophers Stone , the first novel in the series, sothat an unfamiliar audience can be aware of the plot. The authors recommendthis mathematical adventure could be geared toward grades 3-6. Then, theyprovide three areas in which a teacher could incorporate the story into math.

Firstly, the article states that students could develop graphing skills by

applying what they are reading in Harry Potter and interpreting it as data,rather than just part of the story. For example, the article suggests keepingtrack of house points Gryffindor gains or loses. These are subtle aspects of theoverall storyline, but help students build their abilities in being able to readliterature, internalize it, and transfer their knowledge into data, then graph it.The authors provide questions regarding the title of the graph and the x and yaxis, in which students should be able to answer after completing their graph.I liked this example, because it is not something that remains static throughoutthe story it is constantly being changed. I think it keeps students reallyattentive to the details, building their literacy skills, as well as allowing themto put fun into making graphs. This graphing idea is very transferable and is

not solely bound to the Harry Potter novel series; it could be adapted to anybook involving change.The second suggestion for this mathematical adventure is a game

based upon Harrys favorite wizarding sport Quidditch! The rules of thegame are explained and then transferred into a game involving partners andtwo dice. This game focuses on probability. Depending on the sum of the roll,you either can win the game by catching the Golden Snitch (2 or 12), lose aturn by being hit by a Bludger (3, 5, 9, or 11), keeps their turn by dodging theBludger (4, 8, 6, or 10), or gains ten points by scoring a Quaffle (7). Studentskeep track of their game and are then asked to discuss questions, such as:Which events happened most often? Is there an equal chance of catching the

Golden Snitch, dodging the Bludger, being hit by a Bludger, or scoring aQuaffle? This game is not set in stone and can be adapted by the teacher andclass; Quidditch-inspired games could be very versatile.

The final suggestion involves measurement, and incorporates sciencebased on Harrys Potions class with Professor Snape. The authors suggestgrouping students into threes and fours, administering measuring cups,

water, and a mystery substance (preferably crystalized juice mix, for safetyconcerns). Using their scientific exploration skills, students can investigate


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what they believe the mystery substance is and experiment with mixingproportions of the two substances together to find the best recipe. The recipecould then be adjusted to be served to the entire class. By practicing theirmeasuring skills, students are developing their sense of fractions, along withdiscovery-based learning. Similarly, this exploration could be adapted and

made into a creative project or science/math centre.My greatest concern with this article revolves around the content of

Harry Potter , as it may be on a banned-list in some schools due to the subjectof magic. However, the ideas put forth in this article could provide anyteacher with great stepping-stones to creating their own mathematicaladventure with another novel character. The topics are extremely flexible andcould be customized for a book of class interest. The authors had very greatideas and demonstrated creativity in doing so. As teachers, it is important toconsider that meaningful learning often takes place when children do notrealize they are learning at all. By making lessons engaging and tailored totheir interests, it is more likely to reach the students and have them take

something away!

Reference

Wagner, M. M., & Lachance, A. (2004). Mathematical adventures with HarryPotter. Teaching Children Mathematics , 10(5), pp. 274-277.


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MirasMiras are a core tool that can be used to teach symmetry. To reach its

full potential, each student should be given a mira to use, so they can explorethe concept of symmetry at their own pace. Miras are wonderful because they

visually show students what symmetry is. When I was a volunteer in a grade 4math class, students created symmetrical masks using miras. First, thestudents were allowed to draw one half of their mask however they wanted.Then, using the mira, they made their mask symmetrical. To introducesymmetry to kindergarten students, the grade 4 students used buddyteaching. Here, each partner colored half of the mask. Although the colorsmay not have been the same, the mask was symmetrical. The kindergartenstudents were amazed with the miras and practiced symmetry with theirbuddy after their masks were finished. This was a great way to integrate artinto math!


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Pattern BlocksColored pattern blocks are great manipulatives that can be used across

elementary grade levels. Beginning in kindergarten, they can be used toteach basic 2-dimensional shapes and colors. Following on, students can be

introduced to more complex shapes, such as a hexagon, rhombus, ortrapezoid. Concepts learned from these shapes can be built on when teachingstudents about 3-dimensional shapes. Outside of geometric thinking, studentscan use these blocks to build patterns and explore their algebraic thinking,even at a young age! Students can create patterns and sort the blocks byshapes and colors. The fantastic aspect of these manipulatives is that they areuniversal. All shapes are assigned to their own color. So it allows students toassociate orange to square, for example.

In my own teaching, I have used these blocks to show students howthey can create simple and complex patterns, and how to identify the core of apattern. It helps them to be able to have a tactile representation in front of

them, rather than a pattern always be drawn on paper.


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DiceDice make wonderful mathematical manipulatives because students are

familiar with them. A great tool does not need to have a single purpose, butthe ability to reinforce numerous concepts. Furthermore, children often

associate a die with games, which are fun! Engagement is a fundamentalcomponent of learning and sometimes students need to learn without beingtold they are learning.

Dice can be used to teach addition, subtraction, probability, place value, and basic counting skills. They also can help students learn numbersense. They are inexpensive tools that every elementary classroom shouldhave plenty of. With SMART Board technology and the copious amount ofresources available online, you can use activities in class that only requireinteractive die as well.

In my internship, dice were used in games to learn about the missingaddend, as well as help solidify the concepts of making doubles. In a game

called Doubles, in pairs, students were each given pre-made cards of all theeven numbers from 2-12, along with a die and bingo markers. The studentshad to roll the die and double the number that number. Then, they were to puttheir bingo marker over the number on their card. This game was lateradapted to Doubles + 1, with all the odd numbers from 3-13. The studentsreally enjoyed this game and were practicing their doubles without trulyrealizing it!


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This SMART Board activity allows students to build on their regroupingskills, place value, and adding two digit numbers. Through infinite cloning ofthe base ten blocks, students can add given numbers and show them in the

workspace provided. By modeling, students can see that you have workspaceto represent the numbers and regroup. Then, you present your number in the

given tens and ones columns. I used this activity as a warm-up in myinternship classroom with grade 2. This activity could also be modified fromthis technologically based version, into a physical system, so students couldshow regrouping with the actual base ten blocks.


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February 08, 2014

Let's see what you know. Do you know the names of thesecoins? Click the black circle to see if you arecorrect.

nickel

dime

quarter

"loonie"$1 coin

"toonie"$2 coin

penny

penny

penny

penny

penny

dime

dime

dime

dime

dime

nickel

nickel nickel

nickel

quarter

quarter

quarter

quarter

"Loonie"

"Loonie"

"Loonie"

"Toonie"

"Toonie"

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After introducing grade 2 students to money, together, we played theseactivities based on Canadian money. First, students had to guess the names ofthe coins, and then checked their answers by clicking on the black circles.Secondly, students took turns working together to fill the game board. By

clicking the spinner, a coin is chosen. You then have to match the coin to itsname on the game board. The goal is to fill the entire board with coins.Thirdly, the last slide shows an interactive multiple choice activity about thenames of coins and their descriptions. This allows students to begin to makeconnections about the appearances of coins and how to recognize them.

This SMART Board file has been adapted from the original version,found from SMART Exchange:(http://exchange.smarttech.com/details.html?id=c113e811-932d-4c1a-8a2a-b3b7464ded47 ).


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February 08, 2014

Which is Bigger?

Using the first set, roll the three times. Thefirst roll is the hundreds, the second is tens, andthe third is ones. Drag the appropriate base-tenblocks into the place value chart.

Do the same for the second set.

Which number in the place value charts is thelargest?

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones


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This SMART Board activity is an interactive way for students to practiceplace value. We used this activity in my internship class as a model, and thenthe students were given their own physical versions to play with as a mathcenter with a partner. Firstly, you roll the dice three times and place eachnumber in the hundreds, tens, or ones column, respectively. The base ten

blocks are infinitely cloned, so the students can build their three-digitnumber. Then repeat, filling in the second chart. It is then up to the student touse their knowledge of place value to determine which number is bigger. Thisgame could be adapted to figure out which number is smaller, as well.


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Web Links

Dinosaur Dentist: http://ictgames.com/dinosaurDentist/index.html This game helps students utilize doubles as a mental math strategy to

solve problems that are near doubles. You begin by clicking the top of the

dinosaurs head. The addition sentence is presented on the left. Consideringthe closest double, in this case, 10 + 10, you remove one of the dinosaursblack teeth, making number of teeth in his mouth 10 + 9, in this case. Then,you are given three options and must select the correct answer. If the correctanswer is selected, the dinosaur does a boogie. If the incorrect answer isselected, the dinosaur cries in pain.

Students benefit from this game because it allows them to visualizetheir mental math strategy of using doubles, and identify these additionsentences. Plus, the sound effects and humor of the game keep studentsengaged and they find it fun. In my internship, students would beg to play thisgame!


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iXL: http://ca.ixl.com

iXL is a wonderful mathematical website. It is broken down into gradesand into a list of all of the skills students learn in the specific grade! Theseskills are organized into categories, which can be aligned with each

provincial curriculum. iXL allows students to log in and then keeps track oftheir progress. Therefore, teachers can view the students work. Students loveusing iXL because it makes math fun. I have worked in grades 2 and 4 mathclasses in which the teachers used iXL as math centers.

ABCya: http://www.abcya.com

ABCya is a great website that is all game-based. This website includesgames that appeal to all subjects, including math. Games are categorized bygrade and are tailored to the age-groups corresponding to those grades. All

games are easy to use in a safe online-environment and are child-friendly, as well as parent-friendly. This website would make a great recommendation forstudents to play at home. There are also apps available through ABCya todownload.

Music and Videos

What Makes Ten? http://safeshare.tv/w/NacGOnRJjI

I showed this video to grade 2 students during my internship and they

went wild over it. This video reinforces the mental math strategy of makingten. It first shows students the different combinations that make ten, then asksthem to fill in the missing addend. We did this as a class, danced around, andshouted the missing addend and used our fingers to represent the number.The kids begged to do it almost every day and loved it. Since it wassomething we could physically jump around and dance to, while listening andsinging, students were committing their combinations that make ten tomemory, while having fun!


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>"$&.8*&9 9*$0 % ?$='&"$

This was my interview with an 11-year-old student about math. Iconducted this interview to show what real students think about math, whatthey struggle with, and what they think about teaching practices and whatthey want in a math teacher. This was an eye-opening experience, because itmade me reflect as a teacher (I was not this students teacher), and my ownteaching philosophy and practices. Math is oftentimes a difficult subject forstudents to feel confident in and master. If we can pinpoint the areas ofstruggle, we can increase our students success.

Q) Do you like math? Why or why not? A) Nope, because it is hard. I think that sometimes teachers make it hard tolike math.

Q) If you could make up the best teacher on earth, how would he or sheteach math? A) He or she would be nice and not strict and never give any tests.

Q) Why dont you like math tests ? A) Because they are hard.

Q) What is your favorite part about math class? A) Getting to use the SMART board because it is bright and we get to playgames on it.

Q) Would you like math more if you played a lot of games? A) Yeah.

Q) What grade did you enjoy math the most? Why? A) Grade 1, because there werent tests and it was a lot of games.

Q) Of all the topics you have learned so far, what has been the hardest foryou?

A) Measurement and geometry.

Q) What was your favorite topic that you learned about so far? Why?

A) Patterns. I didnt find it hard. I like to make patterns.

Q) Do you think you would like math more if you got to pick a project andshow what you know, rather than doing a test?

A) Yes. As long as it isnt a test or an assessment, I would like it a lot more.

Q) Do you like to do math with a buddy or alone? Why?


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A) A smart buddy. But sometimes when you partner with a smart buddy theydont let you talk. They just say to copy off their work and I dont get to doanything.

Q) What kind of homework does your teacher give you?

A) She gives us a lot of worksheets and if you dont get them done you getdetention.

Q) If you had trouble with your math homework, do you think you couldget help at home?

A) Yeah.


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Dear Math Diary,

Today I found this resource on Pinterest. This is a fun way to introduceadding to students, so they can visually see adding, and it allows them tokinesthetically do addition. This activity is made from a piece of Bristol board,two Styrofoam cups, paper-towel tubes, and a basket underneath which is

where the answer is, and uses marbles. I would use this activity in K-1. I likethis idea because it is interactive and would probably engage students in theiraddition. I would have students count their marbles, record the number, count

the next set of marbles, record the number, then count the number in thebasket and record it as the answer. This develops addition awareness andcounting skills. Marbles available would have to be limited so the students donot get carried away into facts beyond their ability, but they should bechallenged.


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Dear Math Diary,

Today, I found an activity called, I Have, Who Has? make great warm-ups to get students thinking in mathematical terms. This version teachesstudents time. The first player is chosen by their card, which says I have thefirst card. Who has 12:00? Then the players must all look at the top of theircards, which has a clock. The person whose clock shows 12:00 goes next, bysaying I have 12:00. Who has 3:30? This continues until the game is finishedand all players have gone. I like this idea, because it presents students with

reading time from an analog clock, as well as reading written time. I wouldlike to use this someday if the need arose. I found this resource on Pinterest.


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Dear Math Diary,

Today I found an activity called, The Fractions of Me. On six strips ofequally cut paper, students write on thing that makes up who they are, andlabels the strip correctly. For example, 1/6: I am a daughter. Once thestudents write 6/6 strips of paper, they can create construction paper versions

of themselves. In the centre, as the body, the students can transfer what they wrote from their strips of paper onto a stationary page. This activity crosses with Language Arts.

I would like to use this activity with a math class, because it furthers thefoundational understandings of fractions being parts of a whole. The numberof strips could be adapted, depending on grade, level of readiness, ordifferentiation. This activity allows students to think critically and plan, as wellas reflect on themselves as a person.


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Students will continue to develop their depth of understanding of 3-Dobjects. Grade 2 students need many varied opportunities to manipulate 3-Dobjects. Activities in which they describe, compare, and build 3-D objects,and discuss their observations help to develop essential geometric skills. It isthrough such activities that students will learn the names of 3-D objects andbegin to recognize their characteristics.

This book is about identifying basic shapes throughout the story.During this book, the reader is asked to build the shape of a tent (using themanipulatives provided). This book and activity were designed to beimplemented early in the school year, as a review of basic shapes with theintroduction to 3D shapes. Another potential Math assignment could be tointroduce this book at the beginning of a lesson, then have the students maketheir own books about shapes.

The back of the book includes instructions and the materials needed tocomplete the math assignment, suggested within the book. The manipulativesare the jelly candies posed with the toothpicks to make and show how tocreate 3D objects, and such as the tent. The lesson could be taken further byasking the students to build other 3D shapes, as well as using it to form alesson on vertices, faces, and correctly identifying shapes.

Summative Math Project

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Transcript of Summative Math Project