Lesson 12

The purpose of this number talk is for students to develop strategies for adding decimals with a focus on composing a new whole number. Students will work on sums where a new whole number is composed throughout the lesson.

• 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.

• “¿Cómo les ayudó el valor de una de las expresiones a encontrar el valor de otra expresión?” // “How did you use the value of one of the expressions to help you find the value of a different expression?” (I knew that \(1.99 + 0.13\) is 0.1 more than \(1.99 + 0.03\).)

The purpose of this activity is for students to understand that the standard algorithm for addition can be used with decimals. Students first find the value of a sum of decimals using a strategy that makes sense to them and then see calculations organized using the standard algorithm. They recognize the importance of organizing the calculations and carefully recording any newly composed units. 

When students share their explanation of Han's calculations with a partner and revise their work after receiving feedback they critique the reasoning of others and improve their arguments (MP3).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Conversing

• Groups of 2
• “Trabajen individualmente en los primeros dos problemas” // “Work on the first two problems on your own.”

• 5–6 minutes: independent work time

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero su descripción del trabajo de Han. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your description of Han’s work with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion.
• Repeat with 2–3 different partners.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time

If students do not get the correct solution, ask, “¿Entre cuáles 2 números enteros estará la respuesta?” // “What 2 whole numbers will the answer be between?”

• “Resuelvan individualmente el último problema” // “Solve the last problem on your own.”
• 2–3 minutes: independent work time
• “¿En qué les ayudó usar el algoritmo estándar?” // “What was helpful about using the standard algorithm?” (It was helpful to line up the numbers and keep track of everything. It was also helpful to add everything in order, step by step.)
• “¿En qué se parecen usar el algoritmo estándar con números decimales y usarlo con números enteros?” // “How was the standard algorithm with decimals the same as for whole numbers?” (I add numbers with the same place value and then when I get a new unit, like the 1 here, I write it over the correct place value.)

The purpose of this activity is for students to estimate and then find sums. Students may use the standard algorithm which they just learned to find the sums or they may add by place value. The numbers here are deliberately chosen so that one number has tenths but no hundredths and the other number has hundredths. A new and important feature to adding decimals with the standard algorithm is making sure to add digits with the same place value. In practice, this means that the numbers are not always “right aligned” as they are when adding whole numbers. Students will examine an error in alignment in the next lesson.

• Groups of 2

• 8 minutes: independent work time
• 2 minutes: partner work time
• Monitor for students who use different approaches to add the numbers including using the standard algorithm or place value reasoning.

If students don’t have a strategy for determining which whole number the sum is closest to, ask, “¿La suma va a ser mayor que 8 o menor que 8?” // “Will the sum be greater or less than 8?”

• Invite students who used different strategies to add to share their work for the first problem.
• “¿En qué se parecen estas estrategias? ¿En qué son diferentes?” //  “What is the same about their strategies? What is different?” (In both of them, they had to make sure to add the same place values. They also both composed a new unit. One added on in parts, by place value, and the other used the standard algorithm.)
• “¿Cómo les ayudó la estimación a hacer sus cálculos?” //  “How did the estimate help you with your calculation?” (I saw that 4.97 was really close to 5 and that gave me the idea of adding 5 which I could do mentally and then taking away 0.03.)