The purpose of this Warm-up is for students to describe the rectangles in the representation of a quilt, which will be useful when students divide strips of paper into unit fraction sized pieces in a later activity. While students may notice and wonder many things about this image, the variety of lengths and colors of fabric strips is the important discussion point.
Launch
Groups of 2
Display the image.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
¿Qué observas? ¿Qué te preguntas?
Student Response
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Advancing Student Thinking
Activity Synthesis
“Estas imágenes muestran mujeres de Gee's Bend, Alabama, que han hecho colchas por generaciones. ¿Cómo describirían la colcha en la que ellas están trabajando?” // “These pictures show women from Gee's Bend, Alabama, who have been making quilts for generations. How would you describe the quilt they are working on?” (It is colorful. There are rectangles. There are different colored pieces of fabric.)
Consider showing students examples of abstract or improvised quilts by Gee’s Bend Quiltmakers from the website of Souls Grown Deep.
Activity 1
Standards Alignment
Building On
Addressing
5.NF.B.7.b
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that because .
The purpose of this activity is for students to solve problems about dividing a whole number by a unit fraction in a way that makes sense to them. The context of quilt making is used so students can visualize a strip of paper that is a whole number length being cut into fractional sized pieces. As students describe how the problems are similar and different, listen for the authentic language they use to describe division. The paper strip, or tape, is a helpful diagram to use when dividing a whole number by a unit fraction because students recognize important relationships between the divisor, dividend, and quotient (MP7). For example, if the length of the strip stays the same, but the size of the pieces gets smaller, then the number of pieces will get bigger.
This activity uses MLR2 Collect and Display. Advances: Conversing, Reading, Writing.
Launch
Groups of 2
Refer to the picture from the Warm-up.
“Si la tira de tela azul que está bajo el mentón de la mujer mide 1 metro de largo, ¿aproximadamente qué tan larga es la tira gris corta que está al lado?” // “If the blue strip of fabric under the woman’s chin is 1 meter long, about how long is the short gray strip next to it?” ( meter)
Activity
1–2 minutes: independent think time
8–10 minutes: partner work time
MLR2 Collect and Display
Circulate to listen for and collect the language students use to describe what was the same and different about the strategies they used to determine the number of pieces of paper for each color. Listen for:
The size of the pieces changed.
The pieces were shorter.
There were more pieces.
I made more cuts.
Record students’ words and phrases on a visual display and update it throughout the lesson.
Estos son diagramas de tiras de papel de diferentes colores. Cada tira mide 2 pies de largo.
La tira roja se va a cortar en pedazos que miden pie de largo. ¿Cuántos pedazos habrá?
La tira verde se va a cortar en pedazos que miden de pie de largo. ¿Cuántos pedazos habrá?
La tira amarilla se va a cortar en pedazos que miden de pie de largo. ¿Cuántos pedazos habrá?
¿En qué se parecen estos problemas? ¿En qué son diferentes?
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Qué otras palabras o frases importantes deberíamos incluir en nuestra presentación?” // “Are there any other words or phrases that are important to include on our display?”
As students share responses, update the display by adding (or replacing) language, diagrams, or annotations.
Remind students to borrow language from the display as needed.
Display:
“¿Cómo representan estas ecuaciones los problemas sobre las tiras de papel?” // “How do these equations represent the problems about the paper strips?” (The 2 is for 2 feet of paper, and the fractions show the size of the pieces that the paper is being cut into. The 4, 6, and 8 are the number of pieces of each color of paper.)
Activity 2
Standards Alignment
Building On
Addressing
5.NF.B.7.b
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that because .
The purpose of this activity is for students to represent division of a whole number by a unit fraction with diagrams and equations. The context is the same as the previous activity so students can use a tape diagram to solve the problem, if they choose. In the previous activity, students recognized that when the length of paper stays the same and the size of the pieces gets smaller, there are more pieces of paper. In this activity, students will consider what happens when the length of the paper changes, but the size of the pieces stays the same.
Representation: Access for Perception. Provide access to strips of paper for students to cut and fold. Ask students to identify correspondences between the number of pieces/folds and the fraction they represent. Supports accessibility for: Conceptual Processing, Memory
Launch
Groups of 2
Activity
1–2 minutes: independent think time
6–8 minutes: partner work time
Monitor for students who:
Determine that Kiran will have 12 pieces of paper.
Can explain how the equation represents the yellow strip of paper being cut into -foot strips.
Describe the equation as representing a 3 foot strip of paper being cut into 18 pieces that are each of a foot long.
Kiran tiene una tira de papel amarillo que mide 2 pies de largo. Él corta la tira en pedazos que miden de pie de largo.
¿Cuántos pedazos tiene Kiran? Explica o muestra cómo razonaste.
Escribe una ecuación de división que represente la situación.
Describe de qué manera la ecuación representa una tira de papel que mide 3 pies de largo y que se corta en pedazos de igual tamaño.
Student Response
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Advancing Student Thinking
If students write an equation other than , consider asking:
“¿De qué manera tu ecuación representa la situación?” // “How does your equation represent the situation?”
Show them and ask, “¿De qué manera esta expresión representa la situación?” // “How does this expression represent the situation?”
Activity Synthesis
Ask previously identified students to share their solutions.
Display:
“¿Cómo se representa la tira de papel amarillo en esta ecuación?” // “How does this equation represent the yellow strip of paper?” (The strip of paper is 2 feet long and it is cut into pieces that are of a foot long, so there will be 12 pieces.)
Display:
“¿De qué manera esta ecuación representa una tira diferente que se corta en pedazos de igual tamaño?” // “How does this equation represent a different strip of paper being cut into equal sized pieces?” (A 3 foot piece of paper is cut into pieces that are of a foot long, so there are 18 pieces.)
“¿Por qué en ambas ecuaciones el cociente es más grande que el dividendo?” // “Why is the quotient larger than the dividend in both of these equations?” (You are cutting a whole number length into fractional sized pieces, so there will be more pieces than when you started.)
Lesson Synthesis
“Hoy resolvimos problemas en los que había que cortar tiras de papel en pedazos pequeños. Escribimos ecuaciones para representar la división de un número entero entre una fracción unitaria” // "Today, we solved problems about cutting strips of paper into small pieces. We wrote equations to represent dividing a whole number by a unit fraction.”
Display:
“Estas son algunas de las ecuaciones que discutimos hoy. ¿Por qué el cociente se hace más grande en cada ecuación?” // “These are some of the equations we discussed today. Why is the quotient getting larger in each equation?” (The size of the pieces are getting smaller, so there will be more pieces.)
Display .
“Esta es otra ecuación que discutimos. En esta ecuación, el tamaño de las partes es el mismo que en la ecuación de arriba. ¿Por qué el cociente es más grande que cuando se divide 2 entre ?” // “Here is another equation we discussed. In this equation, the size of the pieces is the same as the equation above it. Why is the quotient larger than when 2 is divided by ?” ( The number being divided into the same-size pieces is greater, so there will be more pieces.)
“En la siguiente lección, vamos a aprender más sobre las relaciones que hay entre los números de las ecuaciones de división que tienen fracciones unitarias” // “We are going to learn more about the relationships between the numbers in division equations with unit fractions in the next lesson.”
Standards Alignment
Building On
Addressing
Building Toward
5.NF.B.7.b
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that because .
