Lesson 11

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for subtracting fractions with unlike denominators. These understandings help students develop fluency and will be helpful later in this lesson when they will need to be able to subtract fractions with unlike denominators.

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• Display first two differences.
• “¿Cómo se relacionan las diferencias?” // “How are the differences related?” (\(\frac{1}{6}\) and \(\frac{1}{2}\) are \(\frac{2}{3}\) so I can take away \(\frac{1}{6}\) and that gives me \(\frac{1}{2}\) or I can take away \(\frac{1}{2}\) and that gives me \(\frac{1}{6}\).)

The purpose of this activity is for students to practice subtracting fractions with unlike denominators. The structure of this activity is identical to the first activity in the previous lesson except that students are calculating differences instead of sums. Monitor for students who:

• try to make one fraction in each pair as large as they can and the other fraction as small as they can
• find a common denominator for all 4 differences in order to add them together

While playing the game, students may find that they have a smaller fraction as the minuend and a larger fraction as the subtrahend. There are several ways students could navigate this situation, one of which is to switch the order of the fractions.

• Each group of 2 needs a paper clip.

• Groups of 2
• “Tómense un minuto para leer las instrucciones de ‘La mayor diferencia’” // “Take a minute to read over the directions for Greatest Difference.”
• 1 minute: quiet think time
• “Jueguen ‘La mayor diferencia’ con su compañero” // “Play Greatest Difference with your partner.”

• 10–12 minutes: partner work time

• “¿Qué estrategias les ayudaron mientras jugaban ‘La mayor diferencia’?” // “What strategies were helpful as you played Greatest Difference?” (I tried to make the first fraction in each pair as large as possible and the second fraction in each pair as small as possible.)
• “¿Cuál es la mayor diferencia posible entre las fracciones de este juego? ¿Cómo lo saben?” // “What is the biggest difference possible between fractions in this game? How do you know?” (\(\frac{6}{1} - \frac{1}{6}\) since \(\frac{6}{1}\) is the biggest number and \(\frac{1}{6}\) is the smallest.)
• “¿Alguien obtuvo la fracción \(\frac{6}{1} - \frac{1}{6}\)?” // “Did anyone get \(\frac{6}{1} - \frac{1}{6}\) as one of their fractions?” (Answers vary.)

The purpose of this activity is for students to practice subtracting fractions with unlike denominators. This activity has the same structure as the previous activity except that students are looking for the smallest difference rather than the largest difference and this time they are given all of the numbers at once rather than spinning them one at a time. Some strategies to monitor for include:

• trying to get differences that are 0 using equivalent fractions
• trying to make all of the fractions as small as possible, that is using a similar strategy to the sum game when they tried to get the smallest possible sum

While playing the game, students may find that they have a smaller fraction as the minuend and a larger fraction as the subtrahend. There are several ways students could navigate this situation, one of which is to switch the order of the fractions.

• Groups of 2
• “Ahora veamos cuál es la diferencia más cercana a 0 que pueden formar a partir de un grupo de números dado” // “Now, let’s see how close you can get to a difference of 0 using a given set of numbers.”

• 5 minutes: independent work time
• “Comparen su total con el de su compañero para ver cuál es más cercano a 0. Descríbanle su estrategia a su compañero” // “Compare your total with your partner to see who is closest to 0. Describe your strategy to your partner.”
• 10 minutes: partner discussion

• “¿Qué estrategias les ayudaron mientras intentaban encontrar la menor diferencia?” // “What strategies were helpful as you tried to find the smallest difference?” (I tried to choose equivalent fractions so that I could get a difference of 0. I tried to choose small fractions so then the difference would also be small.)
• “¿Alguien escogió números que hicieron que la segunda fracción fuera mayor que la primera?” // “Did anyone choose numbers that made the second fraction larger than the first?” (Yes.)
• “¿Qué hicieron en ese caso?” // “What did you do?” (I switched the order of the fractions so that I could subtract.)
• “¿Alguien logró obtener un total de 0?” // “Was anyone able to get a total of 0?” (No. I could get some equivalent fractions with sixths, or fourths, thirds, or halves but there was nothing I could do with fifths. If I put the 5 in the numerator I can’t make an equivalent fraction.)