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The purpose of this Warm-up is to elicit the idea that letters can be used to represent an unknown quantity in a tape diagram and an equation, which will be useful when students represent unknown quantities in word problems later in the lesson. While students may notice and wonder many things about these images, the fact that a letter can be used to represent an unknown in the same way as a question mark, line, or box is the important discussion point.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
¿Qué observas? ¿Qué te preguntas?
The purpose of this activity is for students to match tape diagrams, equations, and descriptions of situations, and to explain the connection to model with mathematics (MP4). The situations share the same context and numbers. Students consider how different unknown quantities are reflected in the diagrams, depending on what's happening in the situations.
When students relate the quantities and relationships in situations to the equations and diagrams that represent them, they reason quantitatively and abstractly (MP2).
Part A
Part B
En este problema, cada situación tiene una cantidad desconocida. En los diagramas y en las ecuaciones cada cantidad desconocida está representada por la letra n.
Parte A
Empareja cada diagrama con una situación. Prepárate para explicar cómo razonaste.
Parte B
Empareja cada ecuación con una de las situaciones de la parte A.
Previously, students matched diagrams and equations to situations with an unknown quantity. Here they generate such equations, using a letter for the unknown quantity, solve problems, and explain how they know their answers make sense. Students should be encouraged to solve, using any strategy that feels comfortable to them. If not yet addressed, mention that any letter can be used for the unknown quantity in their equation. Make the point also that the same letter can represent different unknown quantities in different equations.
While this activity is focused on independent practice, encourage students to discuss the problem with a partner if needed. Though the task asks students to write an equation first, students may complete the task in any order that makes sense to them.
Students reason abstractly and quantitatively when they write an equation that represents the situation (MP2). They also practice making sense of a problem and its solution in terms of the context (MP1).
Kiran va a preparar un juego de mancala. Tiene un tarro con 122 piedras.
Él toma 3 piedras del tarro para poner dentro de cada uno de los 6 hoyos que están en su lado del tablero.
¿Cuántas piedras hay ahora en el tarro?
“En las últimas lecciones, hemos representado situaciones con ecuaciones que tienen un símbolo o una letra que representa una cantidad desconocida. También hemos usado diagramas para ayudarnos a resolver problemas” // “During the last few lessons, we have represented situations with equations that have a symbol or a letter for an unknown quantity. We also have used diagrams to help us solve problems.”
“¿En qué tienen que pensar para representar y resolver problemas?” // “What do you have to think about to represent and solve problems?” (l can draw a diagram first so that I can imagine the situation, and then I can write the equation more easily. I can write the equation first so I see how the numbers are related. It helps me to round numbers and think about what number should be close to the answer first.)