The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying within 100 and to help students develop fluency.
When students use known multiplication facts to multiply greater numbers, they look for and make use of structure (MP7).
Launch
Display the first expression.
“Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategies.
Keep expressions and work displayed.
Repeat with each expression.
Encuentra mentalmente el valor de cada expresión.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cómo usaron los hechos de multiplicación que ya conocen para encontrar algunos de los otros productos?” // “How did you use multiplication facts that you already know to find some of the other products?” (I knew that is 30, so would be 3 groups of 10 and 3 groups of 3 which is 39. Once I knew , I was able to find by doubling 39, which is 78.)
Activity 1
Standards Alignment
Building On
Addressing
3.MD.B.4
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units–-whole numbers, halves, or quarters.
The purpose of this activity is for students to generate measurement data using rulers marked with half inches and quarter inches. Students go on a walk in nature, around the school, or on the playground to measure the length of items they chose. If time is limited, this activity could also be done in the classroom.
Students may record and organize their data in the provided tables or on lined paper.
In the next activity, students will record their data on line plots. The provided blank line plots can display a range of 7 inches, if students label the tick marks in quarter inches. Also, the provided rulers are labeled 0–9 inches. So, students should measure objects up to a maximum length of 7 inches. As an alternative, students can use other measuring tools to measure longer objects, but they would still need to stay within the 7-inch range if they want to use the provided line plot labeled in quarter inches. Students could also choose to create their own line plots and thus would be free to use a different range.
MLR8 Discussion Supports. Synthesis: Revoice student ideas to demonstrate and amplify mathematical language use. For example, revoice the student statement “It lined up with one of the half thingies” as “Se alineó con una de las marcas de mitad de pulgada” // “It lined up with one of the half-inch marks,” or “We recorded it in halves” as “Lo anotamos en mitades de pulgada” // “We recorded it in half inches.” Advances: Speaking
Launch
Groups of 4
“Hoy vamos a hacer un recorrido por la escuela (o por el patio de recreo o por el salón) para medir la longitud de algunos objetos” // “Today we are going to take a walk around the school (or the playground, or the classroom) to measure the length of some objects.”
“Con su grupo, mencionen algunos objetos a los que les podemos medir su longitud durante el recorrido” // “Talk to your group about some objects whose lengths we could measure on our walk.” (sticks, leaves, pine needles, plants)
1 minute: group discussion
Share responses.
Make sure each group has a ruler that shows halves and fourths of an inch (from an earlier lesson).
If not using the table in the student book, give students blank lined paper for recording measurements.
See the Activity Narrative for ways to address the range of lengths students should gather.
Activity
“Discutan con su grupo qué objetos van a medir durante el recorrido. Deben recolectar al menos 10 medidas de longitudes” // “Discuss with your group what to measure on our walk. You’ll need to gather at least 10 length measurements.”
“Más adelante, cada grupo va a crear un diagrama de puntos con estas medidas y lo va a mostrar en un póster” // “Later, each group will create a line plot with these measurements and display it on a poster.”
2 minutes: group work time
Share responses.
“Escriban y organicen sus medidas en la tabla (o en un papel con rayas)” // “Record and organize your measurements in the table (or on lined paper).”
20 minutes: whole-class walk around the school
¿Qué objetos vas a medir? Asegúrate de medir algunos objetos en mitades de pulgada y otros en cuartos de pulgada.
Escribe las longitudes de los objetos en la tabla (o en otra hoja de papel).
objeto
longitud (pulgadas)
objeto
longitud (pulgadas)
Activity Synthesis
Invite students to share experiences measuring objects during the walk.
“Ya tenemos nuestros datos de las medidas. Hagamos un diagrama de puntos” // “Now that we have our measurement data, let’s make a line plot.”
Activity 2
Standards Alignment
Building On
Addressing
3.MD.B.4
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units–-whole numbers, halves, or quarters.
In this activity, students create a line plot using the measurement data that they generated earlier and display their group’s line plot for all to see.
Encourage students to plan their line plot using the blank line in the activity statement before creating a poster version for display in a Gallery Walk. A template for a larger line plot is provided in the blackline master. Students can join the number lines on two copies of the blackline master to create a longer number line.
As students visit others’ data displays, they consider how the line plots are alike and how they are different, as well as why different scales might have been chosen for different objects measured.
Representation: Access for Perception. Synthesis: Use gestures during the explanation of the line plot to emphasize important aspects of the line plot. Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 4
“Examinen los datos que recolectaron con su grupo. ¿Qué necesitan saber para hacer un diagrama de puntos que represente los datos?” // “Look at the data your group collected. What do you need to know to make a line plot that represents the data?” (The longest and shortest measurements. Whether the lengths are whole numbers or include halves and fourths of an inch.)
1 minute: group discussion
Share responses.
Give each group 2 copies of the blackline master, scissors, glue or tape, and tools for creating a visual display.
Activity
“Con su grupo, hagan un diagrama de puntos que represente sus datos. Más adelante van a compartir su diagrama de puntos con el resto de la clase” // “Work with your group to create a line plot that represents your data. You will share your line plot with the class later.”
“Pueden usar la recta numérica que está en blanco, en su página, para planear cómo van a hacer su diagrama de puntos antes de crear el diagrama final que van a presentar” // “You can use the blank number line on your page to plan your line plot before creating a final one to display.”
Consider asking:
“¿Cómo planean hacer la escala del diagrama de puntos para que pueda mostrar todas sus medidas?” // “How do you plan to make the scale for the line plot so that it can show all your measurements?”
“¿Qué información o qué marcas pueden incluir para ayudar a los demás a entender su diagrama de puntos?” // “What information or labels could be included to help others understand your line plot?”
Demonstrate how to join and tape (or glue) the 2 copies of the blackline master to make a large line plot.
“Después de que completen la versión final de su diagrama de puntos, péguenlo con cinta (o con pegamento) en un póster” // “After you complete your final line plot, tape (or glue) your line plot on a poster.”
12–15 minutes: group work time
Activity Synthesis
Ask students to display their posters.
MLR7 Compare and Connect
“Cuando vayan a ver los pósteres con su grupo, piensen en qué se parecen y en qué son diferentes los diagramas de puntos. Prepárense para compartir sus observaciones” // “As you visit the posters with your group, think about how the line plots are alike and how they are different. Be prepared to share your observations.”
5 minute: Gallery Walk
See Lesson Synthesis.
Lesson Synthesis
Discuss students' observations from the gallery walk.
“¿En qué se parecen los diagramas de puntos?” // “How are the line plots alike?” (They all show lengths in inches and at least 10 Xs. They all show at least one stack of Xs that is taller.)
“¿En qué son diferentes?” // “How are they different?” (They represent lengths of different objects. Some line plots show more or fewer Xs than others. The numbers on the ends of the lines are different. The locations of Xs and how they are spread out are different. On some line plots, each space represents inch. On others, it represents inch.)
“¿Por qué los diagramas de puntos tenían escalas diferentes?” // “Why did the line plots have different scales?” (The scale depends on the data the group collected. Some types of objects are usually longer than others. For example, twigs are usually longer than leaves. Some data include only lengths in half inches. Others include quarters of an inch.)
Consider asking: “¿Qué aprendieron sobre los diagramas de puntos en las últimas lecciones?” // “What did you learn about line plots in the past few lessons?” (They are used to show measurements, including fractions of an inch. We can choose the scale of the line plot based on the measurements. We can get some information about the data more easily from a line plot than from a list.)
Student Section Summary
Aprendimos a medir longitudes usando reglas que estaban marcadas con mitades y con cuartos de pulgada.
También aprendimos a hacer diagramas de puntos para mostrar medidas en mitades de pulgada o en cuartos de pulgada.
Standards Alignment
Building On
Addressing
3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that , one knows ) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Hagan un diagrama de puntos que represente los datos de las medidas que recolectaron. Más adelante, van a mostrar y a compartir su diagrama de puntos con la clase.
Pueden usar esta recta numérica que está en blanco para hacer un borrador. Piensen en:
cómo escribir los números que corresponden debajo de cada marca para que puedan incluir todas las medidas
incluir detalles que ayuden a los demás a entender los datos que recolectaron
