This Warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved. Students observe images that show three ways of making a T shape, using sticky notes, a context they will see in the first activity.
This prompt gives students opportunities to look for structure (MP7)—specifically, the number and orientation of the sticky notes of which each T shape is composed—and make use of it to solve problems later.
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 compañero 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
“Las tres T están hechas con el mismo número de notas adhesivas. ¿Tienen todas las T el mismo ancho y el mismo alto?” // “All three Ts are made of the same number of sticky notes. Do the Ts have the same width and the same height?” (No)
“¿Por qué ocurre esto?” // “Why might that be?” (The sticky notes have a longer side and a shorter side, and are not all oriented the same way.)
Activity 1
Standards Alignment
Building On
Addressing
4.NF.B.3.d
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
This optional activity prompts students to analyze a design problem that involves fractional measurements. Students determine which of the three designs from the Warm-up would fit on a folder that is 9 inches wide and 12 inches tall. To do so, they find the heights and widths of each design using addition, subtraction, multiplication, or a combination of operations.
Representation: Internalize Comprehension. Activate or supply background knowledge. Invite students to discuss the skills and the concepts they have learned during this unit. Record their answers with examples or pictures on a display. Encourage students to reference the display as they approach their tasks today. Supports accessibility for: Conceptual Processing, Organization, Memory
Launch
Groups of 2–4
Read the task together as a class.
“¿De qué piensan que se trata el problema? ¿Qué preguntas necesitan responder antes de comenzar a trabajar en el problema?” // “What do you think the problem is asking? What questions do you need answered before working on it?”
1 minute: group discussion
Share responses. Clarify any confusion before students begin the task.
Activity
“Trabajen de forma individual durante unos 8 a 10 minutos. Después, discutan con su grupo cómo pensaron” // “Work independently on the task for about 8–10 minutes. Then discuss your thinking with your group.”
10 minutes: independent work time
5 minutes: group discussion
Tyler hace una figura en forma de T con notas adhesivas pequeñas para decorar una carpeta.
El lado más largo de la nota adhesiva mide pulgadas. El lado más corto mide pulgadas. La carpeta mide 9 pulgadas de ancho y 12 pulgadas de alto.
Tyler podría organizar las notas adhesivas de estas 3 maneras:
¿La carpeta tiene el alto y el ancho suficientes para que quepan sus diseños? Si es así, ¿cuál o cuáles diseños cabrían? Muestra tu razonamiento.
Student Response
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Advancing Student Thinking
Activity Synthesis
Invite a group to share their responses and their reasoning on each design. Display their reasoning, or record it for all to see.
Ask others if they agree and if they approached it the same way.
Explain to students that they will now verify their responses. Assign one design for each group to verify.
Give 12 small sticky notes to each group. Ask students to use the sticky notes to create the design.
Next, give each group an inch ruler, and ask them to measure to see if their design is less than 9 inches wide and less than 12 inches tall.
Activity 2
Standards Alignment
Building On
Addressing
4.NF.B.3.d
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.For example, express as , and add .
In this optional activity, students interpret and solve problems involving fractional measurements and operations of fractions in the context of distances on a map. First, students examine the measurements on the map and use them to answer questions. Next, they interpret given expressions and consider what the expressions might represent in the situation. Finally, they write a new problem, based on the given quantities and information. The work here prompts students to reason quantitatively and abstractly (MP2).
This activity uses MLR6 Three Reads. Advances: reading, listening, representing.
Launch
Groups of 2
MLR6 Three Reads
Display only the problem stem, without revealing the question(s).
“Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
1st Read: “Jada y Noah están de excursión en un parque. Este es un mapa de los senderos. Se muestra la longitud de cada sendero” // “Jada and Noah are hiking at a park. Here is a map of the trails. The length of each trail is shown.”
“¿De qué se trata esta situación?” // “What is this situation about?”
1 minute: partner discussion
Listen for and clarify any questions about the context.
2nd Read: “Jada y Noah están de excursión en un parque. Este es un mapa de los senderos. Se muestra la longitud de cada sendero” // “Jada and Noah are hiking at a park. Here is a map of the trails. The length of each trail is shown.” (Display the trail map.)
“Mencionen las cantidades. ¿Qué podemos contar o medir en esta situación?” // “Name the quantities. What can we count or measure in this situation?”
30 seconds: quiet think time
2 minutes: partner discussion
Share and record all quantities.
Reveal the question(s).
3rd Read: Read the entire problem, including question(s) aloud.
“¿Qué estrategias podemos usar para resolver este problema?” // “What are some strategies we can use to solve this problem?”
30 seconds: quiet think time
1–2 minutes: partner discussion
Activity
“Trabajen individualmente durante 10 minutos. Después, discutan sus respuestas y terminen el último problema con su compañero” // “Work independently on the task for 10 minutes. Then discuss your responses and complete the last problem with your partner.”
10 minutes: independent work time
3–4 minutes: group work time
Jada y Noah están de excursión en un parque. Este es un mapa de los senderos. Se muestra la longitud de cada sendero.
Map. Magnolia Hills Park, Trail Map. Red, Blue, Orange, Green Trails. Red, has points C, D, E, and B. From B to C, sixty five hundredths mile. From C to D fourteen hundredths mile. From D to E forty one hundredths mile. From E to B two tenths mile. Red, total fourteen tenths miles. On the left of the red trail is the Blue trail, has points C and D. Blue, total one and 2 one hundredths miles. top right of red trail is Orange trail. It has points E to F. Orange, total, twenty four hundredths mile. Bottom right of red trail is Green trail. It has points, B to A. Green, total, six hundredths mile.
Jada y Noah caminan por el sendero anaranjado del punto F al punto E. Dan toda la vuelta por el sendero rojo hasta regresar al punto E. Después, caminan desde el punto E de regreso al punto F.
¿Cuántas millas caminaron? Muestra tu razonamiento.
Estas son dos expresiones que representan algunas situaciones de la caminata. ¿Qué pregunta se podría responder con la ayuda de cada expresión? Escribe la pregunta y la respuesta.
Usa las distancias que hay en el mapa para escribir una nueva pregunta y encuentra su respuesta. Después, intercambia la pregunta con la de un compañero y responde su pregunta.
Student Response
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Advancing Student Thinking
Activity Synthesis
Invite 2–3 students to share their responses to the last two problems.
Activity 3
Standards Alignment
Building On
Addressing
4.NF.B.3.c
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.For example, express as , and add .
In this optional activity, students hone the skills they have learned in this unit: multiplying a fraction by a whole number, adding and subtracting fractions with the same denominator (including mixed numbers), and adding tenths and hundredths. Students are each given a fractional expression. They evaluate the expression, find a classmate whose expression is different but has the same value (verifying that this is indeed the case), and write a new expression that also has the same value. (See Student Responses for the matched expressions.)
In addition to evaluating expressions, students who have Cards J, K, and L also will need to think about fractions that are equivalent to the value of their expression in order to find their matches. For instance, a student may reason that the value of Card K is or , but the match—Card 2—shows . Consider using these expressions to differentiate for students who could use an extra challenge.
Launch
Give one card from the blackline master to each student.
Tell students that they are to find the value of the expression, and then find a classmate whose expression has the same value.
“Si su expresión está marcada con una letra, entonces su pareja es alguien que tiene una expresión marcada con un número, y viceversa” // “If your expression is labeled with a letter, your match is someone whose expression is labeled with a number. And vice versa.”
“Cuando encuentren a su pareja, completen el resto de la actividad como se indica en el enunciado” // “Once you’ve found your match, complete the rest of the task as directed in the Task Statement.”
Activity
7–8 minutes: independent work time on the first problem and then matching time
7–8 minutes: partner work time
Give each group tools for creating a display. Ask them to show that their two expressions are a match, and that their new expressions also have the same value.
Tu profesor te va a dar una tarjeta que tiene una expresión.
Encuentra el valor de la expresión.
Busca un compañero que tenga una tarjeta con el mismo valor que encontraste. Demuéstrale a tu compañero que el valor es el mismo.
Juntos, encuentren al menos 2 características que sus expresiones tengan en común, diferentes al hecho de que tienen el mismo valor.
Escriban otra expresión que tenga el mismo valor, pero en la que se use una operación diferente.
Student Response
Activity Synthesis
Ask students to display their work around the room.
“Caminen por el salón durante unos minutos y examinen el trabajo de al menos otras 3 parejas” // “Take a few minutes to walk around and look at the work of at least 3 other groups.”
“Mientras estudian el trabajo de otros, presten atención a cosas parecidas y también diferentes del trabajo de ustedes” // “As you study others’ work, pay attention to how the work is like and unlike yours.”
6–7 minutes: Gallery Walk
“¿En qué se parecen los cálculos que vieron? ¿En qué se diferencian?” // “What is the same about the calculations that you saw? What is different?”
1 minute: quiet think time
Discuss responses.
Lesson Synthesis
“En las últimas lecciones, resolvimos diversos problemas en los que había fracciones y operaciones de fracciones. Vimos problemas sobre situaciones y también problemas que no eran sobre situaciones” // “In the past few lessons, we solved a variety of problems that involve fractions and operations of fractions. We saw problems about situations and those that are not about situations.”
“¿Qué estrategias les ayudaron a comenzar a resolver problemas que tuvieran fracciones?” // “What were some helpful ways to get started when solving problems with fractions?” (Make sense of the problem and what it is asking. Read any word descriptions carefully and more than one time. Make sense of the quantities.)
“¿Qué estrategias les ayudaron a evitar errores comunes?” // “What were some helpful ways to prevent making common errors?” (Check the numbers, including numerators and denominators, carefully. Think about what the numbers mean in the situation.)
“¿Cómo supieron si sus respuestas tenían sentido?” // “How did you know if your answers make sense?” (Check to see if the result makes sense in the situation. Discuss with a partner. Work backward from the solution toward the problem.)
Standards Alignment
Building On
Addressing
Building Toward
4.NF.B.3.d
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
