The purpose of this activity is for students to see that there are different types of square units that can be used to measure area and that an area with the same number of square units can be larger or smaller, depending on the unit that is used. To facilitate comparison, one partner works on inch grid paper and one works on centimeter grid paper. In the Activity Synthesis, students are introduced to square inches and square centimeters.

• “¿Qué estamos midiendo cuando medimos el área?” // “What are we measuring when we measure area?”
• “Si hay la misma cantidad de cuadrados, ¿cómo influye cambiar el tamaño de los cuadrados en el área que ellos cubren?” // “If there are the same amount of squares, how does changing the size of the squares affect the area that the squares cover?”

• “¿En qué se parecen los rectángulos? ¿En qué son diferentes?” // “How are the rectangles the same? How are they different?” (The rectangles have the same number of squares, but they do not have the same area because they do not cover the same amount of space.)
• Give students rulers.
• “Con su pareja, investiguen los cuadrados de las dos cuadrículas. Prepárense para compartir lo que encuentren” // “Work with your partner to investigate the squares on both grids. Be prepared to share what you find.” (On the grid with the large squares, each side is 1 inch. On the grid with the small squares, each side is 1 centimeter.)
• “Estos son 2 tipos de cuadrados que podemos usar para medir el área. La pulgada cuadrada tiene una longitud de lado de una pulgada. El centímetro cuadrado tiene una longitud de lado de 1 centímetro” // “These are 2 types of squares we can use to measure area. The square inch has a side length of 1 inch. The square centimeter has a side length of 1 centimeter.”
• “La cuadrícula 1 es papel cuadriculado de pulgadas. Los cuadrados del papel cuadriculado de pulgadas tienen una longitud de lado de 1 pulgada. La cuadrícula 2 es papel cuadriculado de centímetros. Los cuadrados del papel cuadriculado de centímetros tienen una longitud de lado de 1 centímetro” // “Grid 1 is inch grid paper. Inch grid paper has squares with side lengths of 1 inch. Grid 2 is centimeter grid paper. Centimeter grid paper has squares with side lengths of 1 centimeter.”

The purpose of this activity is for students to estimate, and then find, the area of a square, using different standard units of area (square inches and square centimeters). Students discuss why using square inches and square centimeters give different measurements for the same area.

To measure the area of the square, students trace the square or cut it out, place the traced or cut square on the grids from the previous activity, and determine the number of squares covered on each grid. The measurement in square centimeters is not exactly 25 square centimeters because the square is 2 inches by 2 inches. The main idea is that it takes more of a smaller unit than a larger unit to cover the same area. When students reference units in their area measurements, they are attending to precision in language (MP6).

This activity uses MLR2 Collect and Display. Advances: conversing, reading, writing.

• “¿Qué otras palabras o frases deberíamos incluir en nuestra presentación?” // “Are there any other words or phrases that are important to include on our display?”
• As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
• Remind students to borrow language from the display as needed.
• “Cuando medimos con unidades cuadradas diferentes, ¿cómo cambió la medición del área del cuadrado?” // “How did measuring with different square units affect the measurement of the area of the square?” (It took more of the smaller squares to tile the same area. It took fewer of the larger squares to tile the same area.)