Lesson 9

In this warm-up, students observe two dot images that show the same number of dots in groups of 3 but arranged in different ways. The purpose is to elicit observations about the similarities in their structure (5 groups of 3 dots, plus 1 more group of 3 dots) and to prepare students to make sense of expressions with a similar structure in an upcoming lesson.

When students notice that there is an additional group of 3 in the equal groups diagram and the array, they are looking for and making use of structure (MP7).

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿Cómo supieron cuál era el grupo de 3 adicional de cada diagrama?” // “How do you see the extra equal group of 3 in each diagram?” (In the equal groups diagram it’s an extra group that is separate from the 5 groups of 3. In the array the extra group of 3 is the column of dots that is a different color.)

The purpose of this activity is for students to measure the side lengths of a rectangle and multiply them to find the area. Students may use the ruler to create tick marks along the sides of the rectangle to help them visualize square units or multiply the side lengths. Either strategy is fine as students work towards finding the area of rectangles with labeled side lengths.

• Groups of 2

• Display or sketch two rectangles, one with tick marks on two sides and one without.

  

  

  

  

• “¿Cómo podemos usar una regla para encontrar el área de un rectángulo que no tiene marcas en los lados?” // “How could we use a ruler to find the area of the rectangle without marks on the sides?” (We could measure to see how long each side is. The ruler would help us see the marks so we know what numbers to multiply.)
• 30 seconds: quiet think time
• Share responses.
• “Vamos a medir algunos rectángulos en centímetros para ayudarnos a calcular el área. Primero, examínenlos todos y piensen cuál tiene la mayor área” // “We are going to measure some rectangles in centimeters to help us calculate the area. First, look at all of them and predict which one has the greatest area.”
• 30 seconds: quiet think time
• “Marquen la letra del rectángulo que crean que tiene la mayor área” // “Circle the letter of the rectangle that you think has the greatest area.”
• Give each student a centimeter ruler.

• “Usen su regla para medir los rectángulos, en centímetros. Encuentren el área de cada rectángulo e incluyan las unidades” // “Use your ruler to measure the rectangles in centimeters. Find the area of each rectangle, and include the units.”
• 8–12 minutes: partner work

If students say they need to see the squares before they can multiply to find the area of the rectangle, consider asking:

• “¿Qué has ensayado hasta ahora para encontrar el área?” // “What have you tried so far to find the area?”
• “¿Podrías usar la regla para hacer marcas que te ayuden a imaginar los cuadrados?” // “Could you use the ruler to make tick marks to help you picture the squares?”

• “¿Cómo les ayuda medir con una regla a encontrar el área?” // “How does measuring with a ruler help you find the area?” (Measuring with the ruler gives the side lengths, which we can multiply.)

The purpose of this activity is for students to create a rectangle with a given area. Students use what they know about area and the structure of rectangles to decide on the side lengths of the rectangle. Students use tape (painter's or masking) to create the rectangles. They should have enough tape to create square feet within the rectangle, but should be encouraged to mark the 1 foot intervals to help them visualize the square feet inside the rectangle, if needed.

In the synthesis, each group shares strategies for creating a rectangle and how they know the area is the given number of square feet.

When students think about the structure of a rectangle and use it to create a rectangle with a given area they are looking for and making use of structure (MP7).

• Each group of 4 will need one roll of either painter's tape or masking tape.

• Groups of 4
• Give students painter's or masking tape.
• Give students access to rulers and yardsticks.
• Assign each group an area.

• “Juntos, hagan un rectángulo que tenga el área que le asignaron a su grupo” // “Work together to create a rectangle that has the area your group is assigned.”
• 7–10 minutes: small-group work time

If students don’t create a rectangle with the given area, consider asking:

• “¿Cómo construiste tu rectángulo?” // “How did you build your rectangle?”
• “¿Cómo podrías construir el rectángulo si empezaras con 1 pie cuadrado?” // “How could you build the rectangle if you started with 1 square foot?”

• Select each group to share the rectangle they created and how they know it has the given area.
• Consider asking:
  • “¿Hay otras longitudes de lado que nos den un rectángulo con un área de ___  pies cuadrados?” // “Are there any other side lengths that would give us a rectangle with an area of ___ square feet?”
  • “¿Cómo sabemos que este rectángulo tiene un área de ___ pies cuadrados?” // “How do we know this rectangle has an area of ___ square feet?”