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The purpose of this True or False is for students to demonstrate strategies and understandings they have for interpreting a fraction as division of the numerator by the denominator and vice versa. These strategies help students deepen their understanding of the relationship between division and fractions where the unknown is the numerator, denominator, or the value of the quotient.
1 minute: quiet think time
En cada caso, decide si la afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.
En el caso en el que cada persona recibe más de 1 libra de arándanos, ¿cuántas libras recibe?
En el caso en el que cada persona recibe menos de 1 libra de arándanos, ¿cuántas libras recibe?
(Haz una pausa después de responder las 2 preguntas).
The purpose of this activity is for students to explain why for any whole numbers and when is not 0. Students may use words, equations, or diagrams to explain why this is true. In order to see a wide variety of interpretations, students take a Gallery Walk to observe their classmates’ work. Then they discuss how words and diagrams help show the equation for different values of and .
Constructing an argument that works for any pair of numbers requires thinking carefully about the meaning of the dividend, , and the divisor, . Students may use diagrams or situations to help communicate their thinking but will need to explain why these make sense for any numbers and (MP3).
This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.
MLR7 Compare and Connect
¿Qué números pueden reemplazar los signos de interrogación en cada ecuación? Explica tu razonamiento.
(Haz una pausa para escuchar las instrucciones del profesor).
Display and read: “¿Qué saben sobre la relación entre la división y las fracciones?” // “What do you know about the relationship between division and fractions?” (Both can represent fair sharing situations. A fraction can mean division. For example, can mean 3 people shared 2 things equally and each person gets of the thing.)
If not mentioned by students, ask, “¿Cómo podemos representar la relación que hay entre la división y las fracciones?” // “How can we represent the relationship between division and fractions?” (We can use diagrams, situations, and equations to represent the relationship.)
Aprendimos que hay una relación entre la división y las fracciones.
Podemos ver esta relación en diagramas, situaciones y ecuaciones.
Ejemplo: Este diagrama representa 2 sándwiches que se comparten equitativamente entre 5 personas. Cada persona recibe de un sándwich. La ecuación también representa la situación.