The purpose of this True or False? is to elicit strategies and understandings students have for using place value to compare numbers and determine if an equation is true. When students share how they know an equation is true or false based on looking at the total number of tens or total number of ones on each side, they look for and make use of the base-ten structure of numbers and the properties of operations (MP7).
Launch
Display one statement.
“Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
1 minute: quiet think time.
Activity
Share and record answers and strategy.
Repeat with each statement.
Student Task Statement
Decide si cada afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cómo pueden usar lo que saben sobre decenas y unidades para explicar su respuesta a la última pregunta?” // “How can you explain your answer for the last equation using what you know about tens and ones?” (There are only 4 tens on the right.)
Activity 1
20 mins
Compartamos cintas con amigos
Standards Alignment
Building On
Addressing
2.MD.5
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
The purpose of this activity is for students to interpret and solve two-step problems involving length. Students represent and solve the problem in a way that makes sense to them.
Monitor for and select students with the following approaches to share in the Synthesis:
Represent the initial length of ribbon and the actions in the story with tape diagrams or other clearly-labeled drawings or diagrams.
Represent the initial length of ribbon and the actions in the story with base-ten diagrams or a series of equations to show subtraction. (, )
Represent the total length of ribbon that was cut off before subtracting it from the initial length of ribbon using diagrams or equations. (, )
The approaches are sequenced from more concrete to more abstract ways to represent the quantities and actions in the story problem to help students make connections between different ways to make sense of and solve a two-step problem. Some students may use a combination of different representations (for example, a tape diagram to make sense of the story and base-ten diagrams to help with the calculations). Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.
Representation: Access for Perception. Offer strips of colored paper to demonstrate the length of the ribbons, as well as the tape diagrams students create. Encourage students to cut the “ribbon” and label the parts to represent the story. Reiterate the context and connect to the idea of subtraction. Supports accessibility for: Conceptual Processing, Organization, Memory
Launch
Groups of 2
Give each group access to base-ten blocks.
“Los estudiantes de la clase de Priya están compartiendo cintas para hacer collares y pulseras para sus amigos y familiares” // “The students in Priya’s class are sharing ribbons to make necklaces and bracelets for their friends and family members.”
Activity
“Lean la historia con su compañero. Luego, decidan cómo representarla y resuelvan el problema individualmente” // “Read the story with your partner. Then decide how to represent and solve it on your own.”
“Cuando ambos hayan respondido las preguntas, comparen las respuestas para ver si están de acuerdo” // “When you have both answered the question, compare to see if you agree.”
10 minutes: partner work time
As you monitor for the approaches listed in the activity narrative, consider asking:
“¿Qué hiciste primero?” // “What did you do first?”
“¿Cómo se muestra en lo que hiciste el pedazo que Lin cortó para Noah?” // “How does your work show the piece Lin cut off for Noah?”
“¿Cómo se muestra en lo que hiciste el pedazo que Lin cortó para Jada?” // “How does your work show the piece Lin cut off for Jada?”
Student Task Statement
Lin se encuentra una cinta que mide 92 cm de largo. Ella corta un pedazo que mide 35 cm y se lo da a Noah.
Luego, Lin corta de su cinta un pedazo de 28 cm. Se lo da a Jada. ¿Cuánta cinta le queda a Lin?
Student Response
Activity Synthesis
Invite previously selected students to share in the given order. Record or display their work for all to see.
Connect students’ approaches by asking:
“¿Cómo les ayuda cada representación a entender el problema?” // “How does each representation help you understand the problem?” (In the diagrams, they used labels to show what each part means. I can see how they used Lin's length of ribbon and the parts she cut off. In the equations, I can see the same numbers, but it's a little harder to tell what each part means. I can make sense of them by looking at the other diagrams people made.)
Connect students’ approaches to the learning goal by asking:
“¿Qué diferencias hay entre este problema-historia y otros que hemos solucionado?” // “How was this story problem different from others we have solved?” (It had more steps. There were more things happening in the story. The ribbon wasn't cut just one time.)
“¿Cómo mostraron lo que debían hacer en sus diagramas o ecuaciones?” // “How did you keep track of what to do using diagrams or equations?” (I used labels to keep track of what was being subtracted in what order. I added words to my equations to help me remember what my equations were for. I reread the story to make sure my work matched what happened in the problem.)
Activity 2
15 mins
Pulseras de la amistad y regalos
Standards Alignment
Building On
Addressing
2.MD.5
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
The purpose of this activity is for students to represent and solve two-step story problems. Students begin the activity by looking at the first problem displayed, rather than in their books. At the end of the Launch, students open their books and work on the problems. In the Synthesis, students compare different ways they represent and solve the problems.
This activity uses MLR6 Three Reads. Advances: reading, listening, representing.
Launch
Groups of 2
Give students access to base-ten blocks.
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: “Andre tiene 50 pulgadas de cinta. Él corta 26 pulgadas de su cinta y se queda con lo que sobra. Ahora la cinta de Mai es 8 pulgadas más larga que la cinta de Andre” // “Andre’s ribbon is 50 inches long. He cuts off 26 inches of ribbon. Mai’s ribbon is now 8 inches longer than his ribbon.”
“¿De qué se trata esta historia?” // “What is this story about?”
1 minute: partner discussion.
Listen for and clarify any questions about the context.
2nd Read: “Andre tiene 50 pulgadas de cinta. Él corta 26 pulgadas de su cinta y se queda con lo que sobra. Ahora la cinta de Mai es 8 pulgadas más larga que la cinta de Andre” // “Andre’s ribbon is 50 inches long. He cuts off 26 inches of ribbon. Mai’s ribbon is now 8 inches longer than his ribbon.”
“¿Cuáles son todas las cosas de esta historia que podemos medir?” // “What are all the things we can measure in this story?” (the length of Andre’s ribbon at the start, the amount of ribbon Andre cuts off, the length of Andre’s ribbon after he cuts some off, the length of Mai’s ribbon)
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.
“¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?” (We can use a diagram or a drawing to show what is happening. We can use numbers in equations. We can think about it in parts. We can figure out how long Andre’s ribbon is first.)
30 seconds: quiet think time
1–2 minutes: partner discussion
Activity
“Resuelvan individualmente el primer problema. Muestren cómo pensaron. Usen dibujos, números o palabras. Después, resuelvan con su compañero el segundo problema” // “Solve the first problem on your own. Show your thinking using drawings, numbers, or words. Then work together to solve the second problem.”
5 minutes: independent work time
5 minutes: partner discussion
Monitor for students who use tape diagrams, base-ten diagrams, and equations to represent each part of the second problem.
Activity Synthesis
Invite previously identified students to share their diagrams and equations for each part of the second problem.
“¿Cómo representó _____ el problema con la cinta de Andre? ¿Cómo muestra cada representación el problema-historia?” // “How did _____ represent the problem with Andre's ribbon? How does each representation show the story problem?”
Lesson Synthesis
“Hoy resolvieron diferentes tipos de problemas-historia que tenían dos partes” // “Today, you solved different kinds of story problems that had two parts.”
“¿Cómo representaron lo que pensaron? ¿Cómo llevaron la cuenta de sus cálculos? ¿Cómo hicieron para tener presentes las longitudes que conocían y las que necesitaban descubrir?” // “How did you represent your thinking and keep track of your calculations? How did you keep up with the lengths you knew and what you needed to find out?” (I used diagrams to make sense of the story. I drew base-ten diagrams to help me solve the problem. I put a circle around my answer so I could use it for the next problem.)
“¿Qué ideas para resolver problemas-historia han aprendido de los demás?” // “What ideas for solving story problems have you learned from others?”
Student Section Summary
Aprendimos más sobre unidades estándar de longitud. Medimos usando pulgadas y pies, que son dos unidades de longitud de los Estados Unidos. Una pulgada es más fácil de usar cuando medimos cosas pequeñas. Un pie es 12 pulgadas. Resolvimos problemas-historia de 2 pasos sobre longitud. Usamos diagramas para representar “quitar una parte”. Este diagrama muestra que conocemos la longitud de la cinta y cuánto se corta. El signo “?” representa la longitud de la cinta que queda.
Han tiene un pedazo de cinta que mide 64 pulgadas de largo. Él corta 28 pulgadas para hacerle un collar a su hermana. ¿Cuánta cinta le queda?
Have feedback on the curriculum?
Help us improve by sharing suggestions or reporting issues.
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
If students complete one part of the two-step problem, but do not find the solution, consider asking:
“¿Qué has hecho hasta ahora para averiguar cuánta cinta le queda a Lin?” // “What have you done so far to find out how much ribbon Lin has now?
“¿Qué parte de la historia se muestra en lo que has hecho? ¿Qué hace falta para mostrar todas las partes de la historia?” // “What part of the story does your work show? What do you need to do to show all the parts of the story?”
Student Task Statement
Resuelve los problemas. Muestra cómo pensaste. Usa dibujos, números o palabras. Escribe las unidades.
Andre tiene 50 pulgadas de cinta. Él corta 26 pulgadas de su cinta y se queda con lo que sobra. Ahora la cinta de Mai 8 pulgadas más larga que la cinta de Andre. ¿Cuánto mide la cinta de Mai?
Han tiene 62 pulgadas de cinta. Él corta 28 pulgadas de su cinta. Se queda con lo que sobra. Clare tiene una cinta que mide 27 pulgadas. ¿Cuánto más larga es la cinta de Han que la de Clare?
Student Response
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Advancing Student Thinking
If students represent and solve the first part of each problem accurately, but clearly show they have not yet completed both steps or identified the answer to the problem, consider asking:
“¿Qué necesitas averiguar? ¿Qué sabes ya?” // “What do you need to figure out? What do you already know?”
“¿Qué pasó en la primera parte de la historia? ¿Qué descubriste? ¿Qué más tienes que hacer para resolver el problema?” // “What happened in the first part of the story? What did you figure out? What else do you need to do to solve the problem?”