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This Warm-up prompts students to compare four different shaded regions in order to introduce the new type of region that will be considered in this lesson, namely regions where neither side length is a unit fraction. It gives students a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about regions with fractional side lengths. During the discussion, focus on Diagram A, which has a rectangular region where both sides are non-unit fractions.
¿Cuáles 3 van juntas?
¿De qué manera cada expresión representa el área de la región coloreada? Explica o muestra tu razonamiento.
The purpose of this activity is for students to observe and use the structure of diagrams to find areas of shaded regions with non-unit fraction side lengths. Students build on what they learned in the previous activity, solidifying their understanding of why the numerator of a product of two fractions is the product of the numerators and the denominator of a product of fractions is the product of the denominators.
Action and Expression: Internalize Executive Functions. Invite students to verbalize their strategy for writing multiplication expressions to represent the area of the shaded rectangle in each figure before they begin. Students can speak quietly to themselves, or share with a partner.
Supports accessibility for: Organization, Conceptual Processing, Language
Completa la tabla.
Display Diagram A from the last activity.
Display .
“Podemos multiplicar los numeradores para encontrar el numerador del producto. ¿De qué manera el diagrama representa ?” // “We can multiply the numerators to find the numerator in the product. How does the diagram represent ?” (The shaded pieces are a 2 by 3 array and there are 6 of them.)
“Podemos multiplicar los denominadores para encontrar el denominador del producto. ¿De qué manera el diagrama representa ?” // “We can multiply the denominators to find the denominator in the product. How does the diagram represent ?” (The unit square is a 4 by 5 array so there are 20 pieces in the whole unit square.)
“¿De qué manera el diagrama representa ?” // “How does the diagram represent ?” (There are 6 pieces shaded and they are each of the unit square.)