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

If students get a solution other than 8.14, consider asking:

• “¿Puedes explicar cómo encontraste el valor de la suma?” // “Can you explain how you found the value of the sum?”
• “¿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. An 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.

• Invite students who used different strategies 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. That gave me the idea of adding 5 which I could do mentally and then taking away 0.03.)