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ISEE Educaton

30 March 2011

Math Expressions 4th/5th grade Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Math Expressions Math Expressions covers math fundamentals and introduces material covered in 4th and 5th grade to students through artstc expression. Drawing, dance, music, writng, and games are involved in learning the material and developing a deeper comprehension of topics. This document contains a sample schedule, day by day plan with suggested actvites and examples.

1. Sample Schedule 3:00-3:30

Students arrive and the topic of the day is introduced. The students and leaders discuss the topic and relevant questons and go over types of problems they have experienced involving the topic.

3:30-4:00

Actvity Staton 1

4:00-4:30

Actvity Staton 2

4:30-5:00

Actvity Staton 3

5:00-5:30

Actvity Staton 4

5:30-6:00

Refecton on day and student pick-up.

2. Day by Day Plan Day 1: Numbers This topic focuses on numbers themselves, what they are, how they work, and why they are useful. Questons: What is a number? What is the diference between a positve and negatve number? What do numbers represent? What do numbers help us do? What are the diferent kind of numbers you've seen? Actvites: Art staton: Students are asked to draw the largest number and smallest number they can think of and what it could represent. Next they are asked to draw a representaton of positve and negatve numbers. -Example: One student chooses the number one hundred trillion draws a picture of the night sky. They also choose 1 as the smallest number and draw themselves (because there is only Š ISEE Educaton 2011

2 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

one me!). For a representaton of positve and negatve numbers the student draws positve numbers above water and negatve numbers below water. Music staton: Students are told that a “clap” represents a positve number and an “un-clap” (pulling the hands apart without making a sound) represents a negatve number. The staton leader calls out diferent numbers or groups of numbers and the students must clap back what the numbers are. Once they understand the concept, each student gets to create their own clap patern and have the group do it. Challenge (if tme and capacity) use additon and subtracton problems to give number of claps. -Example: The group leader calls out 3 and the students clap 3 tmes. Next they call out -2 and the students do 2 un-claps. Next the leader may call 1, -2, 5 and the students do 1 clap, 2 un-claps, and 5 claps. The staton leader asks a student to start their own patern and they call out -1,-1,2, and the other students clap that patern. Contnues around the circle. Writng staton: Students play personal numbers with their leader and then write down and guess others personal numbers. Personal numbers is a game where a person chooses a few numbers that represent something about them, write the numbers and what they represent down, and then others must guess what those numbers mean. -Example: The leader shares three personal numbers 2, 1/4, and 6.30. Students guess what they mean untl the leader reveals that 2 is the number of siblings they have, they're 1/4ths Panamanian, and 6.30 is their mile tme. They then let students come up with their own and share with the group (if they want to). (From University of California, UCSD Educaton Studies) Game staton: The leader draws three lines a decimal and then three lines on the ground in chalk. Like this: ____ ____ ____ . ____ ____ ____ and ask students what they think this could represent. They go over the hundreds, tens, ones, tenths, hundredths, and thousandths places and then tell students they're going to be numbers. The leader will call out a number and then students must line themselves up behind the lines (without talking) representng the number with their bodies. Challenge: Discuss other base systems and how that could change the game and then atempt playing with that system. -Example: The staton leader calls out “ten” and one student stands in the tens place. Next the staton leader calls out “three hundred and sixty fve” and three students line up in hundreds, six in tens, and fve in ones. Next they call out “nine and three thousandths” and nine students stand in the ones place while three stand in the thousandths place. A leader can also ask something like “how can you represent eleven by only standing in the ones place” where the soluton is eleven students in the ones place. The leader could then explain that we use a base “ten” number system where whenever a place gets to 9, it overfows to the next space. They then can explain a base “seven” number system where instead of going to the next place at 9, the next place begins afer 6. (1,2,3,4,5,6,10,11,12,13,14,15,16,20...). The game can be played again with this variaton. © ISEE Educaton 2011

3 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Day 2: Operatons This topic focuses on operatons (additon, subtracton, multplicaton, division) and how they can be applied. Questons: What are operatons? How are they related? Which operatons are opposites and which are similar? What happens when you perform operatons on decimals? What about on negatve numbers? When are operatons useful? Actvites: Art: Students draw out problems with solutons that involve diferent operatons. -Example: A student draws two chocolate chip cookies and three snicker-doodles and asks how many cookies total? They then draw a person who eats 5 of the cookies and asks how many are lef. Next they could draw 5 people at a party dividing up 30 cookies and another of a family of 5 who want 3 cookies each. Dance: First the leader teaches the students a short sequence, and plays with “adding” and “subtractng” dance moves. Once the sequence is set students know it fairly well, the leader asks the students to dance multplied or divided by diferent numbers to change speed. -Example: Leader teaches a 5 dance move sequence, and calls adding moves additon and then subtractng moves to change the choreography. Next they call out “multply by 2!” and the students dance twice as fast. Multply by ½ would be half as fast. Divide by 2 would be half as fast, whereas divide by ½ would be twice as fast. Music: Students make drums and drum out solutons to operatons. They begin with simple additon and subtracton problems, then contnue to more complex multplicaton and division problems or mult-step problems. -Example: Leader asks students to drum out “fve plus three,” the students hit their drums eight tmes. Next the leader calls out “three tmes seven” and the students respond with twenty-one drum beats. The leader then calls out “one plus six tmes fve” and the students hit the drums thirty-one tmes. The leader also calls out “negatve fve plus ten” and students will respond with fve drum beats or “thirty divided by three” for ten drum beats. Game: Students play multplicaton/division tc-tac-toe, poison, and pig. For multplicaton/division tc-tac-toe students use a pre-made board like the one below:

© ISEE Educaton 2011

4 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

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Multplicaton tc-tac-toe: The frst student chooses two factors from the botom row of numbers, places a paperclip on each, and marks the product on the game board with an x, o, or other object. The second student then moves one of the paperclips to a new factor, fnds the product, and marks the product with a diferent marker. They keep playing untl one student has marked four products in a row, column, or diagonal. The paperclips can overlap to form operatons like 3 x 3. (From University of California, UCSD Educaton Studies) Division tc-tac-toe: The divisor and quotent are both within the botom row of numbers and the paperclip must touch a divisor and quotent. In this version, the student must fnd which dividend in the box will produce the selected quotent. Otherwise, game-play is the same as in multplicaton. Poison: Two students have thirteen objects each. Students take turns removing one or two objects from their thirteen untl all of the objects have been taken. Whichever student takes in the last object loses. (From University of California, UCSD Educaton Studies) Š ISEE Educaton 2011

5 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Pig: The goal of the game is to be the frst to reach 100. Students roll a pair of dice as many tmes as they like, keeping a running total of the sum, and when they decide to stop rolling they record the total for that turn and add it to the total of the previous turn. However, if a 1 is rolled, the student's turn automatcally ends and a 0 is scored for that round. If 1s come up on both dice, the turn ends and the students total score goes to 0. (From University of California, UCSD Educaton Studies) For all of these games students will be asked to discuss strategies they used to win.

Day 3: Decimals This topic focuses on decimals, what they represent, and how to perform operatons on them Questons: What does a decimal represent? Is a decimal a number? How do you add and subtract decimals? Multply and divide them? Why are decimals useful? Actvites: Art: Students are asked to draw something that can be represented as a decimal and then add or subtract it with other drawings of “decimals”. -Example: A student draws one rock and three pebbles and says it represents 1.3. They then add two pebbles to make the total 1 rock and 5 pebbles. They then can subtract 6 pebbles to get 9 pebbles. When fnished, the leader may ask the student to write a word problem about what they drew. Writng: Students are asked to write about what diferent decimals could mean. -Example: The leader asks the students “How many things could 3.2 represent?” and the students can work alone or in pairs to come up with as many ideas as possible and then share with the group. Next the leader may ask “How would you represent a tree and three leaves as a decimal?” and discuss student answers. Dance: Students break into groups and make up a short dance and guess how many deciseconds, seconds, and minutes it is. The leader then tmes their dance and they compare their guesses with the results. -Example: Three students make up a short dance and guess it is 500 deciseconds, 50 seconds, and .8 minutes. The leader then tmes the students while they dance and gives them their actual results. The group of students then discusses why the tmes are diferent, the same, and how they came up with their original guesses. © ISEE Educaton 2011

6 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Game: Students stand in a circle and the leader gives each one of them a number. When each student has goten a number, they close their eyes and have to line up in order without seeing or talking to each other. The frst round will just include integers, while the second round will be decimals. -Example: The leader numbers fve students one through fve and they begin to play the game. The students clap out the number they are and fnd each other by listening to others claps. The next round the leader gives them the numbers 1, 1.5, 2, 2.5, 3, and the students fnd each other by clapping their ones place number and snapping their decimal.

Day 4: Fractons This topic focuses fractons, their many interpretatons, and their operatons. Questons: What does a fracton represent? What are numerators and denominators? How can you add and subtract fractons? Why are they useful? Actvites: Dance: Students are asked to dance with diferent fractons of their body. -Example: The leader calls out ½ for students to dance with. Some students start only dancing with their legs, while others use their arms, others try doing handstands and others use one arm and one leg. The leader then asks for 1/4 and students start hopping on one leg or only moving their head. Next the leader calls out 4/2 and people begin dancing in pairs. Afer the actvity students discuss what they did.

Music: Students are introduced to whole, half, and quarter beats. They then learn drum paterns based on these ideas. -Example: Afer explaining the types of beats, the leader drums out a patern and asks students to say which kinds of fractons they heard. Writng: Students write a recipe for trail mix. When they fnish they can follow the recipe and share it with their friends and family. (CHECK FOR ALLERGIES!) -Example: The leader has raisins, walnuts, and chocolate chips. One student writes that their recipe calls for ½ a cup of raisins, 1/4th cup chocolate chips, and 1/3rd cup of walnuts. They make their trail mix and then the leader asks them to determine how much trail mix they have total, and how much if they halved or doubled the recipe. Š ISEE Educaton 2011

7 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Game: Two students share a pile of patern blocks. They both begin with three yellow hexagons, each hexagon is considered one whole. On each turn, a student rolls a fracton cube with faces showing either ½, 1/3, or 1/6. These fractons represent parts of the hexagon. Afer rolling the cube a student can make 1 of 3 choices. They can get rid of a block if the student's hexagon has a block that represents the same fractonal part of the hexagon as show on the top face of the cube. The student can exchange blocks for other blocks that have the same value. The student can also skip a turn. The goal is to be the frst to lose all the blocks. -Example: A student has three hexagons and in one turn replaces a hexagon for one trapezoid, one rhombus, and one triangle. If they roll a ½ they can remove a trapezoid, 1/3 and they can remove a rhombus, and 1/6 for one triangle. 1 allows them to remove a whole hexagon. (From University of California, UCSD Educaton Studies)

Day 5: Symbols Purpose: This topic focuses on symbols, variables, and their uses. Questons: What is a symbol? Where have you seen symbols before? How can they be used? Can you add and subtract them? Multply and divide them? Actvites: Art: Students are asked to draw symbols that represent themselves and write about why. -Example: One student draws a sun with a rose and leter C inside. They write that they love the summer, roses, and their name starts with a C. Dance: Diferent variables stand for dance moves. These moves are then added and multplied and danced out. -Example: X represents jumping and swinging your arms out. Students learn X and then are asked to dance X + X. X+X = 2X so they do the move twice. They are then asked to do X tmes three, 3X, and do the move three tmes. The leader then tells them Y is reaching to the ground and asks them to dance X + Y. The students jump and swing their arms then reach towards the ground. Next the leader asks them to do 2X + 3Y. They jump twice, and reach down three tmes. © ISEE Educaton 2011

8 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Music: Diferent variables stand for the way one hits a drum. These are then subject to operatons to produce songs. -Example: The leader teaches the group that X is hitng the side of their drums and Y is a whole beat on the top of the drum. The leader then says to hit the drums as 3X + 5Y and the students hit the side of their drums three tmes, then the top 5 tmes. The students then break into groups to write their own songs with as many variables as they want. Writng: Students are asked to write about other kinds of symbols they've encountered and what they represented. -Example: A student writes about the Batman symbol and that it is projected up in the sky so Batman recognizes it. Another may write about leters or trafc signs.

Day 6: Factoring This topic focuses on factoring and its usage. Questons: How can we break down large numbers? How can this help you with other things we've learned? Actvites: Art: Students draw large chalk factoring trees and decorate them and fnd their least common multples and greatest common factors. -Example: The factoring tree of 26 and 50: 26 2

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26's prime factors: 2 x 13 50's prime factors: 2 x 5 x 5 LCM = 2 x 13 x 5 x 5 = 650 GCF = 2 Music: Students practce breaking beats into subdivisions while keeping the same tempo. -Example: One, two, one, two, becomes tri-pl-et, tri-pl-et with the leader on drums along with a metronome. Š ISEE Educaton 2011

9 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Writng: Students write a poem about a prime number. -Example: One student writes: Haiku's are prime right? Seven, fve divide with One and themselves

Game: Students roll two dice twice to get two numbers and can either use the LCM or GCF to add to their total or pass. The goal is to get to exactly 1000 frst. -Example: A student rolls a 2 and 2 for 22 and 5 and 4 for 54. 22's prime factors are 2, 11 and 54's are 2, 27. The LCM is 594 and the GCF is 2. The student chooses 594.

Day 7: Graphs This topic introduces types of graphs, what they represent, and how to make them. Questons: What is a graph? What can it show? What diferent graphs have you seen? What can graphs represent? Actvites: Art: Students create Venn diagrams with drawings as the insides. -Example: Two circles in the Venn diagram could be blue and red. On the blue side they draw the ocean, a blue bird, and eyes, on the red side they draw an apple and lips, in the middle they draw an American fag and a striped shirt. Dance: Students dance on a giant chalk coordinate plane. The leader asks them to dance to diferent points and later draw lines of their own dance. -Example: The leader calls out (1,2) and all the students move to that space, next they call out (-5,-3) and the students move there. Afer this the students write down their own path for a coordinate dance and follow it along with music.

Š ISEE Educaton 2011

10 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Music: Students learn a song with diferent kinds of beats and then make bar graphs representng how many of each beat occurred. -Example:

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Writng: Students make pie charts about who they are and write about why they created diferent slices of the pie. -Example: One student creates a pie chart that is equally split between “friendly,” “outgoing,” and “smart.” The student says they are friendly because they always help people in need, they are out going because they like making new friends, and smart because they love to read.

Day 8: Estmaton This topic focuses on number sense, estmaton, and making predictons. Questons: What is estmaton? Why do we do it? How is it useful? Can we and should we estmate everything? Actvites: Art: Students are asked to draw something someone would have to estmate -Example: One student draws fans in a football stadium and writes that you cant count all the fans but could estmate how many their are. © ISEE Educaton 2011

11 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

Music: A student makes up a drum beat and it must be replicated around the circle. Leader comments on how its easier when the beat is simpler. -Example: The inital drum beats is four quarter beats on the top, two whole notes on each side, a drum roll, and hitng both hands on the top of the drum. As the students replicate it around the circle it becomes more and more simple and distorted. The next inital drum beat is just hitng the drum twice and it is much easier to replicate. The leader then starts a discussion about how simpler beats (and numbers) are easier and faster to work with. Writng: Students write about a tme they had to estmate. -Example: A student writes about a tme when they went shopping and that they had to estmate how much money they spent to determine how much more they could buy. Game: Students are given beans, rice, and a container and have to estmate how many scoops of beans it takes to fll the container and how many scoops of rice it takes to fll the container. -Example: Three students estmate that it will take 10 scoops of beans and 15 scoops of rice to fll the same container. Afer they do the test they realize that it takes 9 scoops of beans and an equal 9 scoops of rice to fll the same space. When asked to explain why they answer that is because the measurement of a scoop was the same for both beans and rice. (From University of California, UCSD Educaton Studies)

Day 9: Probability This topic introduces probability and its efects. Questons: What does probability mean? How does it efect you? Actvites: Art: Students do collaboratve drawings and stories. -Example: A group of four students passes around two pieces of paper, one with a drawing and one with a story writen on it. They make predictons about what the other students will draw or write and contribute accordingly. Dance: Students mirror each others dances by predictng what the leader will do. -Example: A group of four students stands in a circle while one leads. The leader starts moving to the lef with their hand and then quickly moves right. While students could follow to the lef the movement to the right did not seem as probable. They talk about how moves that were similar were easier to follow where unexpected ones were more difcult. Writng: Students write about a tme probability has efected them. Š ISEE Educaton 2011

12 Author: Acacia Overoye


Project Name: Math Expressions Document Number / Version Number: 1.0

-Example: One student writes about playing Go-Fish and that the probability of getng the card one needs decreases with the more of that card they have. Game: Students have a coin and an object on a number line. With each fip of the coin the object moves right or lef depending on heads or tails and the students predict where the object will be afer 10 fips, 25 fips, 50 fips, 100 fips. -Example: A group of students agrees that afer 10 fips the coin will be 5 spaces to the lef, 25 fips 10 spaces to the lef, 50 fips, 20 spaces to the lef, and 100 fips 25 spaces to the lef. Afer doing the experiment they realize that with more fips, the object stayed closer to the center. Since the coin toss is random, the more tmes you do it the closer to 50/50 it becomes.

3. Tips –

Let students have tme to refect and discuss what they are experiencing. Its okay if parts of actvites are skipped because of lively discussion.

Encourage sharing, but don't require it. If a student seems shy or unwilling to share one day respect their comfort zone.

Be quiet. Wait for students to give responses before jumping in with your ideas. Sometmes it just takes a litle tme to hear some answers.

Do some problems! Make sure you understand how to do any and all types of problems implied by this program. Can you fnd the GCF and LCM? How do fractons, decimals, and negatve numbers work?

Be actve. As a group leader you should always be partcipatng in the actvites – drawing, dancing, writng, drumming, or playing with the students.

© ISEE Educaton 2011

13 Author: Acacia Overoye


Math Expressions Pilot Curriculum