Lesson 3

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for multiplying multi-digit whole numbers. These understandings help students develop fluency. The products in the number talk get increasingly more cumbersome to keep track of mentally so students can identify times when products are more easily found mentally and when the algorithm, with pencil and paper, might be preferable.

• Display one problem.
• “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 problems and work displayed.
• Repeat with each problem.

• “De los problemas que resolvieron mentalmente, ¿cuál fue el más retador? ¿Por qué creen que lo fue?” // “Which problem was the most challenging to solve mentally? Why do you think so?” (Answers vary, but students will likely mention one of the last three because there are different products to keep track of and add.)

The purpose of this activity is for students to consider the numbers when they choose a strategy to find the value of a product. Some students might choose to use the same strategy for any multiplication problem. In this activity, the numbers were chosen to encourage students to choose different strategies in order to generate discussion about why certain multiplication problems lend themselves to different strategies.

When students choose a multiplication strategy based on the factors, using the associative and commutative properties of multiplication and the distributive property, along with known facts, they make use of structure to facilitate their calculations (MP7).

• Groups of 2
• “A veces usamos distintas estrategias para resolver problemas. Elegimos una dependiendo de cuáles sean los números del problema. Sin resolver, miren los números de cada expresión y piensen en qué estrategia usarían para encontrar el valor” // “Sometimes we use different strategies to solve problems, depending on the numbers in the problem. Without solving, look at the numbers in each expression and think about the strategy you would use to find the value.”
• 1–2 minutes: quiet think time
• “Escojan 2 problemas que resolverían usando estrategias diferentes y descríbanle las estrategias a su compañero. Expliquen por qué escogieron estrategias diferentes” // “Choose 2 problems you would solve using a different strategy and describe the strategy to your partner. Explain why you chose different strategies.”
• 1–2 minutes: partner work time

• “Encuentren el valor de cada expresión. Si encuentran el valor mentalmente, escriban los pasos que siguieron en su cabeza para llegar al resultado” // “Find the value of each expression. If you find the value mentally, record the steps you used in your head to arrive at the product.”
• 5–10 minutes: independent work time
• Monitor for students who used different strategies for the same problem. For example, for \(14\times25\), some students might multiply \(14\times20\) and \(14\times5\) and some students might double 25 and halve 14 and find \(7\times50\).
• 8–10 minutes: partner work time

• Invite students to share their strategies for finding the value of \(14 \times 101\).
• “¿Pueden usar alguna estrategia mental para encontrar el valor de este producto?” // “Is there a mental strategy you can use to find the value of this product?” (Yes. I know \(14 \times 100\) is 1,400 and then I can add 14 to that.)
• Invite students to share their strategies for finding the value of \(14 \times 136\).
• “¿Cuál estrategia usaron para encontrar el valor de \(14 \times 136\)? ¿Por qué?” // “Which strategy did you use to find the value of \(14 \times 136\)? Why?” (I used the standard algorithm because I did not see a quick mental strategy for finding the value.)

The purpose of this activity is for students to try new ideas from the previous activity and practice multiplying using the standard algorithm. 

• Groups of 4

• 10 minutes: independent work time
• “Comparen sus estrategias en su grupo pequeño. ¿En cuáles problemas usaron la misma estrategia? ¿En cuáles problemas usaron estrategias diferentes?” // “Compare your strategies with your small group. Where did you use the same strategy? Where did you use a different strategy?”
• 3–5 minutes: small-group discussion

• Ask students to share their strategies for the first 3 problems.
• “¿Alguien usó una estrategia distinta al algoritmo estándar en alguno de los problemas? ¿Por qué escogieron esa estrategia?” // “Did anyone use a strategy other than the standard algorithm on any of the problems? Why did you choose that strategy?” (For \(15 \times 199\) I knew 199 is just 1 away from 200 and I could find \(15 \times 200\) in my head. I just needed to take away 15 and I could do that in my head also.)
• “¿El algoritmo estándar también funciona para resolver estos problemas?” // “Does the standard algorithm also work for these problems?” (Yes. The standard algorithm always works.)
• “¿Qué estrategia usaron para encontrar el producto \(24\times154\)? ¿Por qué?” // “What strategy did you use to find the product \(24\times154\)? Why?” (I used the standard algorithm. The numbers are complex and I could not see a good mental strategy.)