The purpose of this Warm-up is to elicit students’ knowledge about 1 year as a measure of time and the ways it can be represented. The reasoning and conversations here will be helpful as students solve problems that involve time in years later in the lesson.
Launch
Display: “1 año” // “1 year”
“¿Qué saben sobre 1 año?” // “What do you know about 1 year?”
“¿Qué se mide con un año?” // “What does a year measure?” (time)
“¿Qué aspectos del tiempo se relacionan con un año?” // “What are some aspects of time that are related to a year?” (seasons, months, weeks, days)
Activity 1
Standards Alignment
Building On
Addressing
4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
In this activity, students use what they learned about multiplication of multi-digit numbers and unit conversion to solve problems involving measurements. Students may choose to represent the situations in a number of ways—concretely or visually (by drawing diagrams) or abstractly (by writing expressions and equations). While some problems can be reasoned additively, students may opt to reason multiplicatively for practical reasons.
Regardless of their chosen representations and reasoning strategy, students reason quantitatively and abstractly when they interpret and solve the questions about different units of time (MP2).
This activity uses MLR7 Compare and Connect. Advances: representing, conversing
Action and Expression: Develop Expression and Communication. Provide access to a variety of tools, including colored pencils, grid paper, base-ten blocks, and a visual display that students can use as a reference showing a variety of strategies from throughout the section. Supports accessibility for: Conceptual Processing, Organization, Memory
Launch
Groups of 2–4
Give each group tools for creating a visual display.
“Hoy vamos a resolver problemas de medidas” // “Today we’ll solve some problems that involve measurements.”
“Antes de comenzar a resolver los problemas, hagamos una estimación” // “Before we solve any problem, let’s do some estimation.”
Read the first problem as a class.
“Estimen: ¿Aproximadamente cuántos días tiene la bebé elefante?” // “Estimate: About how many days old is the baby elephant?”
1 minute: quiet think time
Display the following ranges and poll the class on their estimate. (Alternatively, post each range in a different part of the classroom and ask students to stand by the range that reflects their estimate.)
280 to 299
300 to 349
350 to 400
Select a student who selected each range to explain their estimate. Then ask students if they’d revise their estimate.
Activity
“En silencio, resuelvan los dos primeros problemas durante unos minutos. Luego, discutan sus respuestas con su grupo y trabajen juntos en el último problema” // “Take a few quiet minutes to solve the first two problems. Then, discuss your responses with your group and work on the last problem together.”
5 minutes: independent work time
5 minutes: group work time
Monitor for the different representations and strategies used to solve the problems.
Assign one problem to each group.
MLR7 Compare and Connect
“Creen una presentación visual para mostrar cómo resolvieron el problema que le fue asignado a su grupo. Organicen su trabajo para que los demás puedan entenderlo” // “Create a visual display to show how you solved the problem assigned to your group. Organize your work so that it can be followed by others.”
3 minutes: group work time
5 minutes: gallery walk
Prompt students to make note of the different strategies they see and any solutions that they question.
Activity Synthesis
“Podemos resolver la mayoría de los problemas usando multiplicación. ¿En qué se parecen las soluciones y las estrategias de multiplicación que vieron? ¿En qué son diferentes?” // “Most of the problems can be solved by multiplication. What is the same between the solutions and multiplication strategies that you saw? What’s different?”
30 seconds quiet think time
1 minute: partner discussion
Record students’ responses, or display students’ diagrams and representations.
“¿Qué estrategias conocen para multiplicar un número de varios dígitos por un número de un dígito (48 por 7 o 366 por 3)?” // “What are some common strategies for multiplying a multi-digit number by a one-digit number (48 and 7, or 366 and 3)?”
“¿Cuáles estrategias vieron para multiplicar 2 números de dos dígitos (12 por 31)?” // “What are some strategies you saw for multiplying 2 two-digit numbers (12 and 31)?”
Activity 2
Standards Alignment
Building On
Addressing
4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
This activity offers students more practice with using multiplication to solve contextual problems (MP2), including situations in which at least one factor is four digits long, and to generate a new problem according to some parameters.
Launch
Groups of 2–4
Activity
6–7 minutes: independent work time
2–3 minutes: group discussion
Monitor for and select different ways students represented the situations and solved the problems.
La familia de Lin reúne 2,074 monedas de cinco centavos. ¿A cuántos centavos equivale esa cantidad?
Si la familia de Lin ahorra 2,074 monedas de cinco centavos cada año durante 4 años, ¿cuántas monedas de cinco centavos tendrán?
Inventa una situación en la que haya un problema que se pueda resolver encontrando el valor de . Resuelve el problema. Explica o muestra cómo razonaste.
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
“En la síntesis de la lección, vamos a comparar distintas estrategias” // "In the Lesson Synthesis, let's compare some different strategies."
Lesson Synthesis
“Hoy usamos lo que hemos aprendido sobre la multiplicación para resolver problemas de medidas” // “Today we used what we have learned about multiplication to solve problems involving measurement.”
Invite selected students to share their responses to the problems in the last activity. As each student shares, ask if others in the class solved it the same way and if they approached it differently.
Prompt students to explain what their numerical solutions represent in each situation.
“¿Cómo hicieron para saber si sus soluciones eran correctas?” // “How would you know if your solutions were correct?” (I used another strategy to see if I got the same answer. I estimated first so that I had an idea how big or small the answer would be. I checked with my groupmates.)
Consider asking: “Cuando tuvieron que multiplicar números, ¿en qué método se apoyaron más? ¿Qué hizo que escogieran ese método?” // “When you had to multiply numbers, which method did you rely on the most? What made you choose that method?”
Student Section Summary
Aprendimos a multiplicar factores en casos en los que el producto es mayor que 100. Para esto, usamos distintas representaciones y estrategias.
Al trabajar con factores de varios dígitos, es útil descomponerlos de acuerdo a su valor posicional antes de multiplicarlos. Por ejemplo, para encontrar el valor de , podemos descomponer primero el 5,342 en su forma desarrollada: . Luego, podemos usar un diagrama o un algoritmo que nos ayude a multiplicar.
Tanto en el diagrama como en el algoritmo, el 20,000, el 1,200, el 160 y el 8 se llaman los “productos parciales”. Estos son los resultados de multiplicar por 4 cada parte en la que se descompuso 5,342.
Podemos hacer lo mismo para multiplicar un número de dos dígitos por otro número de dos dígitos.
Por ejemplo, estas son dos formas de encontrar el valor de . El 31 se descompone en y el 15 se descompone en .
multiply. 31 times 15. 7 rows. First row: 31. Second row: multiplication symbol, 15. Horizontal line. Third row: 5. Fourth row: 1 hundred fifty. Fifth row: 10. Sixth row: plus 3 hundred. Horizontal line. Seventh row: four hundred sixty 5.
Standards Alignment
Building On
Addressing
Building Toward
4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
