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The purpose of this Number Talk is for students to demonstrate the strategies and understandings they have for multiplying whole numbers by fractions. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to solve problems involving multiplication of a whole number by a fraction.
Encuentra mentalmente el valor de cada expresión.
Info Gap Picking Fruit Cards, Spanish
This activity, which features an Information Gap routine (also Info Gap routine), gives students an opportunity to solve problems about data represented on line plots. In both sets of cards, there is a partially complete line plot and some unknown data.
This activity uses MLR4 Information Gap.
For the first set of cards, the Problem Card has the unknown data and the Data Card has a partially complete line plot. Monitor for students who request:
For the second set of cards, the Problem Card has the partially complete line plot and the Data Card has information to determine the unknown data. Here students likely will need to communicate with each other as the information about the most common weight is vital to solve the problem, but the student with the Problem Card may not think to ask about this.
The Info Gap routine allows students to refine the language they use to ask increasingly more precise questions until they get the information they need (MP6).
MLR4 Information Gap
Tu profesor te dará una tarjeta de problema o una tarjeta de datos. No se la muestres ni se la leas a tu compañero.
Haz una pausa aquí para que tu profesor pueda revisar tu trabajo. Pídele al profesor un nuevo grupo de tarjetas. Intercambia roles con tu compañero y repite la actividad.
Optional
The purpose of this optional activity is for students to answer questions about a line plot, using the same context as in the previous activity. Students relate repeated addition of the same fraction to multiplication which they studied in a previous unit. They also address a question about the sum of all of the data. Because there is a lot of data, there are many viable strategies to answer this question and the Activity Synthesis focuses on sharing these strategies.
When students solve problems about the apricot weights, using the line plot, they reason abstractly and quantitatively (MP2).
Este diagrama de puntos muestra los pesos de los albaricoques que recolectó Mai.
“Hemos sumado, restado y multiplicado fracciones para resolver problemas sobre diagramas de puntos” // “We have added, subtracted, and multiplied fractions to solve problems about line plots.”
“¿Cómo usamos estas operaciones para resolver problemas sobre diagramas de puntos?” // “In what ways did we use these operations to help us solve problems about line plots?” (Line plots have a lot of different data and the data had fractions, so when we answered questions about the data, we had to add, subtract, or multiply.)
“¿Cuál fue su problema favorito sobre diagramas de puntos?” // “Which was your favorite problem about line plots?” (The eggs because I thought the picture was really interesting.)
Aprendimos a sumar y a restar fracciones.
Aprendimos cómo sumar y restar fracciones que tienen el mismo denominador.
Ejemplo:
Sumamos los décimos. Hay 11 décimos, entonces .
También aprendimos cómo sumar y restar fracciones que tienen denominadores diferentes.
Ejemplo:
Encontramos un denominador común, así podemos sumar partes del mismo tamaño.
Una forma de encontrar un denominador común es usar el producto de los dos denominadores. Este siempre es un múltiplo común.
Al usar 48 como denominador, encontramos que . Esto quiere decir que .
También podemos usar un denominador común más pequeño.
Como 24 es un múltiplo de 6 y de 8, podemos reescribir como , que es .