The purpose of this Estimation Exploration is for students to reason about the size of a complex fraction sum with large denominators. Students can see that 1 is a good estimate because one fraction is small and the other is close to 1. In the Activity Synthesis, students refine this estimate to explain why the value of the sum is a little greater than 1.
Launch
Groups of 2
Display the expression.
“¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
“Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Task Statement
¿Cuál es el valor de la suma?
Escribe una estimación que sea:
muy baja
razonable
muy alta
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
“¿Cómo saben que la suma es mayor que 1?” // “How do you know that the sum is greater than 1?” ( is short of a whole. Since 17ths are bigger than 19ths, adding makes it greater than 1.)
Activity 1
20 mins
El aderezo de la ensalada de Priya
Standards Alignment
Building On
Addressing
5.NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result , by observing that .
The purpose of this activity is for students to add and subtract fractions and estimate sums and differences of fractions, using the context of a recipe. Students may have different responses and reasoning for the estimation questions. In both cases, they can calculate and compare fractions, but they may have different thoughts about how these differences would affect the recipe or what exactly it means for the recipe to make “about cups.” In the Activity Synthesis, students discuss the reasonableness of the estimates and how to make precise calculations (MP6). When students relate their calculations to Priya's salad dressing, they reason abstractly and quantitatively (MP2).
Reading: MLR6 Three Reads. Keep books or devices closed. Display only the problem stem, without revealing the questions. “Vamos a leer este problema 3 veces” // “We are going to read this question 3 times.”
After the 1st Read: “Cuéntenle a su compañero de qué se trata la situación” // “Tell your partner what this situation is about.”
After the 2nd Read: “Hagan una lista de las cantidades. ¿Qué se puede contar o medir?” // “List the quantities. What can be counted or measured?”
Reveal the question(s).
After the 3rd Read: “¿Qué estrategias podemos usar para resolver este problema?” // “What strategies can we use to solve this problem?”
Advances: Reading, Representing
Launch
Groups of 2
“¿Qué tipo de ingredientes les gusta poner en su ensalada?” // “What kind of ingredients do you like to put in your salad?” (lettuce, cabbage, beans, seeds, beets, tomatoes, cheese)
“¿Qué tipos de aderezos le ponen a su ensalada?” // “What kinds of dressings do you put on your salad?” (homemade, Italian, ranch, tamari)
Activity
1–2 minutes: quiet think time
6–8 minutes: small-group work time
Monitor for students who:
Estimate to determine that Priya’s recipe will make about cups of dressing.
Add to determine the precise amount of dressing Priya’s recipe will make.
Activity Synthesis
“Si Priya le pide a su vecino una cucharada de aceite de oliva y la usa para preparar el aderezo, ¿ella pondrá más aceite o menos aceite del que se necesita para la receta?” // “If Priya borrows a tablespoon of olive oil from her neighbor and uses it to make dressing, will she be putting in more or less olive oil than the recipe calls for?” ( is smaller than so she will be putting in less olive oil.)
“¿Creen que 1 cucharada se acerca lo suficiente?” // “Do you think 1 tablespoon is close enough?”
Poll the class.
“¿Cómo podría cambiar el aderezo de la ensalada por la decisión de Priya de usar 1 cucharada de aceite de oliva?” // “How might Priya’s decision to use 1 tablespoon of olive oil change the salad dressing?” (It won’t make a difference because the difference is so small. It might taste more lemony or more mustardy because there is not as much oil. It might affect the consistency of the dressing a little.)
Ask previously selected students to share their estimates for the amount of salad dressing in the given order.
“¿Por qué Priya podría estimar que se preparan tazas de aderezo de ensalada con la receta?” // “Why might Priya estimate that the recipe makes cups of salad dressing?” ( is away from 1 and is close to .)
“¿Con la receta se preparan más de o menos de tazas? ¿Cómo lo saben?” // “Does the recipe make more than or less than cups? How do you know?” (More, because is more than .)
“¿Cuántas tazas se preparan con la receta de Priya? ¿Cómo lo saben?” // “How many cups does Priya’s recipe make? How do you know?” (, I added , , and .)
Activity 2
15 mins
Más problemas por resolver
Standards Alignment
Building On
Addressing
5.NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result , by observing that .
The purpose of this activity is for students to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. Students work with both fractions and mixed numbers and can use strategies they have learned, such as adding on to make a whole number. When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2).
Representation: Access for Perception. Read both problems aloud. Students who both listen to and read the information will benefit from extra processing time. Supports accessibility for: Conceptual Processing, Language
Launch
Groups of 2
“Ustedes y su compañero van a escoger cada uno un problema diferente y lo van a resolver. Luego, van a discutir sus soluciones” // “You and your partner will each choose a different problem to solve, and then you will discuss your solutions.”
Activity
3–5 minutes: independent work time
3–5 minutes: partner discussion
Student Task Statement
Escoge un problema y resuélvelo.
Problema A:
Jada hornea barras de proteína para una caminata. Ella agrega taza de nueces y después decide agregar de taza más. ¿Cuántas tazas de nueces agregó en total?
Se necesitan tazas de nueces para la receta. ¿Cuántas tazas de nueces más debe agregar Jada? Explica o muestra cómo razonaste.
Problema B:
Kiran y Jada caminaron millas y tomaron un descanso. Después, caminaron de milla más antes de parar a almorzar. ¿Cuántas millas han caminado hasta el momento?
El sendero mide millas en total. ¿Cuánta distancia más caminan? Explica o muestra cómo razonaste.
Discute los problemas y las soluciones con tu compañero. ¿En qué se parecen sus estrategias? ¿En qué son diferentes?
Si es necesario, ajusta lo que escribiste.
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
“¿En qué se parecían los problemas? ¿En qué eran diferentes?” // “How were the problems the same? How were they different?” (For both problems, I had to add fractions first, and then subtract that total from another number. There were mixed numbers in both problems.)
“¿Cómo usaron fracciones equivalentes para resolver estos problemas?” // “How did you use equivalent fractions to solve these problems?” (All the fractions we worked with had different denominators, so we had to find equivalent fractions with the same denominators in order to add or subtract.)
Lesson Synthesis
“Hoy resolvimos problemas en los que fue necesario sumar y restar fracciones” // “Today we solved problems that required adding and subtracting fractions.”
Display Priya‘s salad dressing recipe.
“¿Qué estrategia usaron para encontrar cuánto aderezo de ensalada se preparaba con la receta de Priya?” // “What strategy did you use to find out how much salad dressing Priya’s recipe makes?” (The denominators for the fractions are 2, 3 and 4, so I used 12 because I know that it is a multiple of 2, 3, and 4. I put the half and the fourths together first, since I could use 4 as a common denominator, and then I used 12 to add the fourths and the third.
Display .
“¿Qué estrategia usaron para encontrar esta diferencia en el problema del aceite de oliva?” // “What strategy did you use to find this difference for the olive oil?” (I knew that 48 is and , so I used that as a common denominator. I used as a common denominator.)
“¿Cómo deciden cuál estrategia usar?” // “How do you decide which strategy to use?” (It depends on the numbers. If I know a small common multiple of the denominators, I use that. If I don’t, I can always use the product of the denominators.)
Have feedback on the curriculum?
Help us improve by sharing suggestions or reporting issues.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, . (In general, .)
Priya tiene de taza de aceite de oliva. Ella le va a pedir un poco a su vecino. ¿Cuánto aceite de oliva necesita pedirle si quiere tener suficiente para preparar su aderezo?
1 cucharada es igual a de una taza. Priya decide que solo necesita pedir 1 cucharada de aceite de oliva. ¿Estás de acuerdo? Explica o muestra cómo razonaste.
Priya dice que con su receta se preparan aproximadamente tazas de aderezo. ¿Estás de acuerdo? Explica o muestra cómo razonaste.