The purpose of this activity is for students to find the area of rectangles with one fractional side length and one whole number side length. Students begin by considering a rectangle with whole number side lengths and then look at a series of rectangles with unit fraction side length. All of the rectangles have the same whole number width to help students see how the area changes when the fractional width changes. Students should use a strategy that makes sense to them. These strategies might include counting the individual shaded parts in the diagram or thinking about moving the parts to fill in unit squares. Some students may use multiplication or division. These ideas will be brought out in future lessons. During discussion, connect the different strategies students use to calculate the areas. As they choose a strategy, students have an opportunity to use appropriate tools, whether it be expressions that represent the shaded area or physical manipulations of the diagrams, strategically (MP5).

• Ask previously selected students to share their reasoning.
• “¿En qué se parecen las estrategias? ¿En qué son diferentes?” // “What is the same about the strategies? What is different?” (They all counted the number of shaded parts, but they counted them in different ways. Some people multiplied and some people moved the parts to make whole unit squares.)
• Display image from final problem.
• “¿De qué manera la expresión  representa el área coloreada, en unidades cuadradas?” // “How does the expression represent the shaded area in square units?” (There are 6 shaded parts and each one has an area of square unit.)
• “¿De qué manera la expresión  representa el área coloreada, en unidades cuadradas?” // “How does the expression represent the shaded area in square units?” (There is a rectangle whose area is 6 square units and of the rectangle is shaded.)

The purpose of this activity is for students draw and shade rectangles with a unit fraction side length and a whole number side length. Then they find the areas of the shaded regions. The tactile experience of drawing and shading encourages students to count the number of shaded parts. Then students reason about their size or think about moving them to make full unit squares. They also consider a diagram where not all of the unit squares are shown. Students estimate how many of the unit squares are hidden. This helps to highlight that finding the total area can be done with multiplication where one factor is the area of each shaded part and the other factor is the total number of shaded parts (MP7).

If students do not draw the rectangles correctly, show them the shaded region from the previous activity with side lengths 6 units and unit and ask “¿Cómo podrías adaptar este diagrama para mostrar un rectángulo de 4 unidades por  unidad?” // “How could you adapt this diagram to show a rectangle that is 4 units by unit?”

• Display a student generated image of the unit by 4 unit rectangle.
• Ask previously selected students to describe how they drew a 4 by rectangle.
• Display image from student page of the rectangle that is partly covered.
• “¿Qué necesitan saber para encontrar el área de la región coloreada?” // “What do you need to know to determine the area of the shaded region?” (We need to know how many unit squares are under the yellow rectangle.)
• “¿Cuántos cuadrados unitarios creen que forman el rectángulo?” // “How many unit squares do you think make up the rectangle?” (6 or 7)
• “¿Cómo usaron el número de estos cuadrados unitarios para estimar el área de la región coloreada?” // “How did you use the number of these unit squares to make an estimate for the shaded region?” (I know that each shaded blue rectangle is of a square so if there are 6 or 7 of those. So, that would be or square units.)