Exploring Fractions
Submitted by Terri Geffert
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Standards:
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Lesson Timeframe:
Four 20 minute sessions (1 per day)
However, tasks 1 and 4 will require extra time to finish after the initial four days.
Lesson Overview:
Students will practice math fraction vocabulary and explore fraction comparison and equivalence through activity-based experiences. The students will apply their understanding of standard mathematical concepts by creating a flag demonstrating this knowledge.
Lesson Context:
The lessons are designed to be carried out in a station format. That is, students will rotate daily through stations in small groups (5-8 students). Each small group completes one activity per day. To help prepare the students for the station activities, I set the stage as follows. On the white board at the front of the classroom, I have drawn a square divided into four parts. Each part lists a station activity. In the center of this square, I stick on a paper circle. The circle is also divided into four parts and lists the names of people in each of four groups. I rotate the circle each day until each group has completed all of the activities. The stations are located in various parts of the classroom. At each station is a plastic bin that contains all of the materials necessary to complete the station activity (worksheets, maps, visuals, etc.) as well as a folder for storing completed work.
At the beginning of the year, students and I work extensively on station expectations (low voice levels, quality work, leaving a station as clean as it was found, using the immersion language). During the second half of the year, I also use a "passport" system at stations to encourage use of the target language. Each student has a paper passport with flags of countries where Spanish is spoken. They receive stamps on the flags when either a chosen student monitor or I observe consistent use of Spanish that day.
Objectives:
Content:
Students will...
describe fractions of a whole and fractions of a group
compare fractions
explore the concept of equivalent fractions
learn the difference between the numerator and denominator Cultural:
Students will...
explore the origins of chocolate
Language: Content Obligatory
Students will...
use fraction vocabulary that includes denominators of two, three, four, etc. (up to ten) and the words "one whole"
use the phrases "es mayor que," "es menor que," and "son iguales" in comparing fractions
use the words "el numerador" and "el denominador" accurately Language: Content Compatible
Students will...
use the following phrase to claim ownership "Esta/este ___(object)_____ es mía/o." Learning Strategies / Social and Skills Development:
Students will...
work cooperatively in groups at each station
Time Frame:
Four 20 minute sessions (1 per day)
However, tasks 1 and 4 will require extra time to finish after the initial four days.
Materials Needed:
NOTE: There should be enough materials at each station for up to 8 students.
Station 1
KidPix computer software program (PowerPoint, ClarisWorks or another program which permits slide-show production could also be used.)
Disks to save student work
Large poster of fraction names
Example slide show Station 2
Dice labeled 0-5 (or regular dice on which the side with six dots has been covered with tape to read 0)
Crayons or markers of different colors
Chocolate Recording Sheets (see "Attachments") Station 3
A Brief story of chocolate http://www.mexconnect.com/mex_/mexfact/mexfactchoc.html Visual aids to illustrate the story of chocolate (some pictures listed in "References and Resources")
Mexican hot chocolate cakes (the Abuelita brand cakes are conveniently divided into 8 fractional parts and can be found in most larger supermarkets)
Blender
Measuring cups and spoons
Milk
Sugar
Medium-sized saucepan (large enough for 4 cups of liquid)
Hot plate
Drinking cups
Books or songs about chocolate (see "References and Resources") Station 4
Instructions for the task
Flag grids - one per student (See "Attachments")
Flag description pages - one per student (See "Attachments")
Crayons, markers, or colored pencils
Construction paper rectangles of various colors (for experimenting)
Flags of the World poster, or books that have examples of a variety of flags
Samples of finished flags
Description of Assessment (Performance Project):
Station 1
I am fortunate enough to have four computers in my classroom, so with a group of eight, students are paired at each computer in Station 1. In this station, students will begin a fractions slideshow that they will later present to the class. Their task is to create 4 slides, each of which illustrates a fraction. For example, to illustrate one sixth, they might draw a pizza that is divided into 6 equal pieces and has one piece highlighted. Each slide should contain a picture as well as the name of the fraction in words and numbers. Slides may represent fractions of a whole or fractions of group. The Kid Pix program allows the students to create 4 slides and then to combine them together for a slide show. Once the slide show is composed, the students may also add voice narration of the fraction names for each slide.Station 2 (adapted from the Open Court math curriculum, see "References and Resources")
In this station, students will be playing a game to practice fraction vocabulary and the phrase "Este/a ________ es mÃ∆o/a." To play, the first player rolls two dice or cubes labeled 0-5. He or she forms a fraction with the cubes, placing the smaller number on top (the numerator) and the larger number on the bottom (the denominator). He or she then says the fraction in Spanish and colors in that fraction of a chocolate bar on the Chocolate Recording Sheet - one sheet for 2 players. (In the Open Court version students color in plain circles, but in my adaptation, students color in chocolate bars.) The second player does the same.If a player colors in one-half or more of a chocolate bar, he or she writes his or her initials next to the chocolate bar and says "Este chocolate es mÃ∆o." If a chocolate bar has less than one-half colored in, either player may color on it until one-half or more is taken. If a bar already has one-half or more colored, it may no longer be colored in. Players may wish to divide their roll between two chocolate bars. For example, if a player rolls three-fourths, he or she may color in two-fourths of one bar and claim that bar, and then color in one-fourth of a second bar. A player who rolls a zero loses his or her turn.
Play continues until all of the chocolate bars on the sheet have been colored in. The player who has more chocolate bars is the winner. As students become more proficient at the game, the rules may be altered so that equivalent fractions can be used. For example, if a student rolls 1/2, and that fraction is not available to color in, the student may instead color in 2/4.
Station 3
In this station, students will be working with the teacher or an adult volunteer to make Mexican hot chocolate. Teachers can find a brief history of chocolate at the website: http://www.mexconnect.com/mex_/mexfact/mexfactchoc.html. This website tells the story of Hernán Cortés being served chocolate by Moctezuma and about how chocolate came to be popular in the old world. As background information for this station, teachers should retell the story to the whole class beforehand according to the skill level of their students. A carving of Moctezuma greeting Cortés can be found at http://www.aoc.gov/cc/art/rotunda/frieze/cortez.cfm?displaylargeimages=1.English Instructions - for the helper
The chocolate should be precut for safety reasons, but keep at least one cake whole to show the fractional parts of the cake. Work together with students to measure 4 cups of milk into the saucepan to heat on the hot plate; and 1/8 of the chocolate cake and 4 teaspoons of sugar to place in the blender. When the milk is warm, add the milk to the blender and mix until well-blended. Serve the chocolate. While waiting for the milk to heat and while students are drinking the chocolate, read El libro de contar de los chocolates marca M & M or sing "El Chocolate". See "References and Resources" section for citations and contact information.Español
Modo de empleo
Mezcla en la licuadora una tablilla de Abuelita, un litro de leche hirviendo y azucar al gusto
SÃ∆rvelo caliente
Pon 4 tazas de leche en la tazuela.
Usa el hornillo para calentar la leche.
Pon 1/8 del circulo de chocolate y 4 cucharitas de azucar en la licuadora.
Cuando la leche esté caliente, ponla en la licuadoray mésclala con los otros ingredientes hasta que estén bien mescladas.
SÃ∆rvelo caliente.
Station 4 (Adapted from a lesson by Ann McCoy (See" References and Resources")
In this station, students will be designing a flag that incorporates fractions. Their fraction flags must meet the following criteria.
1. Necesitas usar 4 colores, ni más ni menos.
2. Debes planear tu diseño en una matriz de 16 rectángulos.
3. Color 1 debe cubrir 1/2 de la bandera.
Color 2 debe cubrir 1/4 de la bandera.
Color 3 debe cubrir 1/8 de la bandera.
Color 4 debe cubrir 1/8 de la bandera4. Necesitas describir tu bandera cuando termines
In explaining this station, the teacher should use the finished examples to show various ways to meet the criteria (ie: 1/4 of the flag may be a block of the flag or smaller rectangles dispersed throughout the flag).
Students can first experiment with the construction paper rectangles on a grid. When they are satisfied with an arrangement, they can use crayons, markers, or colored pencils to create the final product.
When students finish their flag, they should fill out a description of the flag and post the items for classroom display.
Assessment:
Station 1
Teachers and students can use the holistic rubric in the Attachments to evaluate the slide shows.Station 2
Teachers should examine completed game recording sheets to check for understanding and on-task behavior.Station 3
The teacher or adult at this station can check for understanding as he/she montors the activity by observation and using question prompts.Station 4
Teachers and students may evaluate the flags produced in station 4 by using the criteria specified in the station instructions.
References and Resources:
Station 2 was adapted from a game in the Open Court math curriculum, now published by SRA/McGraw Hill.
http://www.mcgrawhill.ca/school/about+us/imprints+offered/sra/math/index.phpStation 4 was adapted from a lesson by Ann McCoy, Clinton Middle School, (660) 885-3353, ann@clinton.k12.mo.us (http://www.successlink.org/great/g1043.html).
McGrath, B. Más matemáticas con los chocolates de "M&M's". Watertown, MA: Charlesbridge Publishing. http://www.charlesbridge.com ISBN 1570914818
McGrath, B. El libro de contar de los chocolates marca "M&M's". Watertown, MA: Charlesbridge Publishing. http://www.charlesbridge.com ISBN 0881069035
Orozco, José Luis. "De colores" (Vol. 9) cassette/cd. Song is "El Chocolate." Arcoiris Records. http://www.joseluisorozco.com/Vol09.htm ISBN 1574170090
Rand McNally and Company. (1998). Picture Atlas of the World. Rand McNally & Co; USA.
A brief history of chocolate - http://www.mexconnect.com/mex_/mexfact/mexfactchoc.html
A painting of Cortés - http://encarta.msn.com/media_461536998_761561161_-1_1/Hernán_Cortés.html
Pictures of the cacao seed pod - http://www.pbase.com/selvin/image/55891904
click the "Next" button twice to see a close up and the opened pod.
Attachments:
NOTE: some attachments are in PDF form (get Acrobat Reader)Station 1: Rubric for Slide Show (rubric-sides.doc)
Station 2: Chocolate Recording Sheet
Station 4: Flag Grid
Station 4: Flag Description Worksheet (flag-description.doc)