Lesson 1

This warm-up prompts students to carefully analyze and compare the area of different figures. In making comparisons, students have a reason to use language precisely (MP6) as they describe the area of different figures. It also enables the teacher to hear the terminologies students know and how they talk about characteristics of shapes that help them find different areas.

For all warm-up routines, consider establishing a small, discreet hand signal that students can display to indicate they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or a different subtle signal. This is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

Math Community

• After the warm-up, ask students to reflect on both individual and group actions while considering the questions, “¿Qué ven y qué escuchan cuando hacemos matemáticas juntos como una comunidad matemática? ¿Qué estoy haciendo yo? ¿Qué están haciendo ustedes?” //  “What does it look and sound like to do math together as a mathematical community? What am I doing? What are you doing?”
• Record and display their responses under the “Doing Math” header. Students might mention things such as: we talked to each other and to the teacher, we had quiet time to think, we shared our ideas, we thought about the math ideas and words we knew, you were writing down our answers, you were waiting until we gave the answers.

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Cómo podemos encontrar el área de cada figura?” // “How could we determine the area of each figure?” (We can use multiplication for most of them or count the units in one of them.)
• Consider saying: “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to find the area of a rectangle by tiling and to recall that the area can also be found by multiplying the side lengths. Students use inch tiles to build rectangles with a given side length and find the area of those rectangles. They work together to compare and explain the strategies used to find the area of rectangles and make connections between strategies. Students observe how the area of rectangles with a given width varies as the length changes and make predictions about what areas are possible with the given widths (MP7).

• Each group of 2 needs at least 36 tiles.

• Display the rectangle in the book.
• “Examinen el rectángulo que ven en su página y descríbanselo a un compañero” // “Look at the rectangle on your page and describe it to a partner.” (It has 6 units. There are 2 rows and 3 columns.)
• Give each group 10 tiles.
• “Construyan todos los rectángulos que puedan usando 10 fichas. Descríbanselos a un compañero” // “Build all the rectangles you can using all 10 tiles. Describe them to a partner.”
• 2 minutes: partner discussion
• “¿Quién tiene un rectángulo que mide 2 fichas de ancho?, ¿o uno que mide 5 fichas de ancho?, ¿o uno que mide 10 fichas de ancho?” // “Who has a rectangle that is 2 tiles wide, 5 tiles wide, 10 tiles wide?”
• Draw each rectangle as students share their responses.

• Give students more inch tiles.
• “Ahora construyan cinco rectángulos diferentes, que midan 2 fichas de ancho. Anoten el área de cada rectángulo en la tabla” // “Now build five different rectangles that are each 2 tiles wide. Record the area of each rectangle in the table.”
• “Repitan esto con rectángulos que midan 3 y 4 fichas de ancho” // “Repeat with rectangles that are each 3 tiles and 4 tiles wide.”
• 5–7 minutes: partner work time
• Monitor for students who:
  • build one row or column and repeat the same number of tiles over again to build the area
  • skip-count or multiply to determine the area of each rectangle
  • combine skip-counting with another counting strategy

Students may count tiles by 1 to determine the area of the rectangles they build. Consider asking, “¿Ves grupos de fichas que te sirvan para contar?” // “Do you see groups of tiles that could help you count?”

• Collect predictions for areas of rectangles with a width of 2. (18, 14, 20, 30)
• Para rectángulos que miden 2 fichas de ancho, ¿cómo podemos saber si nuestras predicciones sobre el área son verdaderas sin construir cada rectángulo?” // “For rectangles that are 2 tiles wide, how can we tell if our area predictions are true without building each rectangle?” (Each area is an even number. It is what we say when counting by 2 or multiplying by 2.)
• “¿Cómo podemos comprobar nuestras predicciones para rectángulos que miden 3 o 4 fichas de ancho?” // “How can we check our predictions for rectangles that are 3 or 4 tiles wide?” (The predictions are numbers we get when we multiply a number by 3 or 4.)

The purpose of this activity is for students to explore the idea of multiples through an area context. Students learn that a multiple of a number is the result of multiplying any whole number by another whole number. As students build and find the area of rectangles given one side length, they see that every area is a multiple of each of the side lengths of a rectangle.

• Each group of 2 needs at least 36 tiles from the previous activity.

• Groups of 2
• Give each group inch tiles and access to grid paper.
• “Estoy pensando en un rectángulo que mide 2 fichas de ancho. ¿Cuál podría ser el área de mi rectángulo?” // “I am thinking of a rectangle that is 2 tiles wide. What could be the area of my rectangle?”
• 1 minute: partner discussion
• Share and record responses.
• “¿Cómo sabemos que todas estas áreas son posibles?” // “How do we know all of these are possible areas?” (We can multiply another number by 2 to get those numbers.)

• “En esta actividad vamos a pensar en cuál podría ser el área del rectángulo si solo supiéramos una de las longitudes de sus lados. Respondan estas preguntas con su pareja” // “In this activity, we are going to think about what the area of a rectangle could be if we only knew one side length. Work with your partner to answer these questions.”
• 5–7 minutes: partner work time
• Monitor for students who notice that areas you can build are a result of multiplying 3 by another possible side length.

• Display a set of student-generated areas that are less than 30 square units.
• “¿Qué notaron sobre las áreas que encontraron?” // “What did you notice about the areas you found?”
• Ask students to explain why the rectangle couldn’t have an area of 28 square units.
• “En las últimas dos preguntas, ¿cómo supieron si un rectángulo que mide 3 unidades de ancho podía tener esa área?” // “For the last two questions, how did you know whether a rectangle with a width of 3 units could have that area?”
• “Podemos tener un área de 12 unidades cuadradas cuando el ancho del rectángulo es 3 unidades. Esto es porque 12 es un múltiplo de 3” // “We can have an area of 12 square units when the width of the rectangle is 3 units. That is because 12 is a multiple of 3.”
• “Un múltiplo de un número es el resultado de multiplicar ese número por un número entero” // “A multiple of a number is the result of multiplying a number by a whole number.”
• “Revisen su trabajo y discutan con su compañero: ¿Qué números son múltiplos de 3?” // “Look back at your work and discuss with your partner: Which numbers are multiples of 3?” (3, 6, 9, 12, 15, 18, 21, 24, 27, and 30)
• “¿Qué números no son múltiplos de 3?” //  “Which numbers are not multiples of 3?” (29, 28, 26, 25, 23, 22, 20, 19, 17, 16, 14, 13, 11, 10, 8, 7, 5, 4, 2, 1)
• 2 minutes: partner discussion