Lesson 8

The purpose of this Number Talk is to elicit and connect strategies and understandings students have for multiplication of whole numbers and mixed numbers. These understandings help students develop fluency through reasoning about the distributive property.

• 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.

• “¿En qué se parecen las estrategias que usaron para los 2 primeros problemas y las que usaron para los 2 últimos problemas?” // “How were your strategies for the first 2 problems the same as your strategies for the last 2 problems?” (I decomposed the 15 into 10 and 5 and I also decomposed 2 and \(\frac13\) in the third problem. I also used what I knew about problem 1 to help with problem 2 and used problem 3 to help with problem 4.)

The purpose of this activity is for students to choose from activities that offer practice multiplying multi-digit numbers, with and without composing. 

• Greatest Product
• Number Puzzles Stage 2

• Gather materials from: 
  • Greatest Product
  • Number Puzzles Stage 2

• “Hoy vamos a escoger juegos de los que ya conocemos” // “Today we are going to choose from games we have already learned.”
• Display the choices in the student book.
• “Piensen qué les gustaría hacer primero” // “Think about what you would like to do first.”
• 30 seconds: quiet think time

• Invite students to work at the game of their choice.
• 10 minutes: partner work time
• “Escojan qué les gustaría hacer ahora” // “Choose what you would like to do next.”
• 10 minutes: partner work time

• See lesson synthesis.

The purpose of this activity is for students to make products of a 2-digit number and a 3-digit number using 5 given digits with a goal of getting as close as they can to a given target number. This builds on their work from the previous activity and lesson where they tried to make the largest possible product. It is not important that students select the best possible products and the activity synthesis focuses on the strategies that they use. Fundamental to these strategies will be understanding place value and making estimates of products of a 2-digit number and a 3-digit number (MP7).

• Groups of 2.
• “Van a escoger un número de 3 dígitos y uno de 2 dígitos para acercarse lo que más puedan a un producto objetivo” // “You are going to choose a 3-digit and a 2-digit number to get as close as possible to a target product.”

• 5 minutes: independent work time
• 3 minutes: partner discussion time
• Monitor for students who change their product after finding the value and comparing to the target number.

• Invite selected students to share how they changed their reasoning about where to put each digit.
• “Cuando su número objetivo era 50,000, ¿qué dígito escogieron para poner en la posición de las centenas?” // “When your target number was 50,000 what did you choose for the hundreds place?” (I chose a 9 because I thought I could use the 5 or 6 in the tens of the other number and get pretty close to 50,000.)
• “Cuando su número objetivo era 20,000, ¿qué dígito escogieron para poner en la posición de las centenas?” // “When your target number was 20,000 what did you choose for the hundreds place?”(I used the 6 because I thought with the 3 in the tens of the other number that would give me 18,000 which is pretty close.)