The purpose of this activity is for students to understand that the standard algorithm for subtraction can be used with decimals. Students first find the value of a difference of decimals using a strategy that makes sense to them and then see calculations organized using the standard algorithm. When students calculate using a strategy of their choice, they may or may not show decomposition of a whole into 10 tenths. The standard algorithm explicitly shows this decomposition. 

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.

• “Solve the last problem on your own.”
• 2-3 minutes: independent work time
• “How is the standard algorithm for subtraction the same as the standard algorithm for addition?” (I work from right to left. I line up all of the place values and make sure the digits I am subtracting have the same place value.)
• “How is the standard algorithm for subtraction different from the standard algorithm for addition?” (Sometimes I need to decompose a unit. I need to decompose a whole into 10 tenths. With addition, I sometimes need to compose a new unit.)

The purpose of this activity is for students to estimate and then find differences. Students just learned the standard algorithm for subtraction can be used with decimals in the previous activity and may use it here. All students should be encouraged to find the differences in a way that makes sense to them. Any subtraction strategy they use will require close attention to place value and this is the focus of the Activity Synthesis. 

• Invite students to share their strategies for finding the difference .
• “How are the strategies the same? How are they different?” (They both broke up 4.3 into pieces and then subtracted each piece. Some students used the standard algorithm and some subtracted by place value. The standard algorithm works in one way. There are different ways to subtract 4.3 by place value.)
• Invite students to share their estimate for .
• “How did you know that the value would be close to 6?” (16.14 is just a little more than 16 and 9.8 is almost 10. So, I used whole number subtraction to estimate, .)
• “Did the estimate help you with the calculation?” (Yes, I used the standard algorithm and got an answer that was just a little more than 6 and that agreed with my estimate. Yes, the estimate made me think of subtracting 10 which I could do in my head. Then adding back 0.2 which I could also do in my head.)

The purpose of this activity is for students to analyze a common error when using the standard algorithm to subtract decimals. This activity is recommended if students need additional practice with the standard algorithm when the two numbers do not have the same number of decimal places. The standard addition algorithm requires students to subtract digits with the same place value. In the given example the two numbers are “right aligned” as when subtracting whole numbers. This alignment leads to the error of subtracting hundredths from tenths, tenths from ones, and so on as if these digits had the same place value.

When students identify and correct Elena's error they construct viable arguments and critique the reasoning of others (MP3).

• Display Andre’s solution and explanation.
• “Why do you think Andre wrote 71.40 instead of 72.4?” (It helps him keep the place values and decimals in line so he doesn’t mix up the places when he is subtracting. 71.40 is equivalent to 71.4.)
• Display Elena’s solution.
• “How can you see without finding the difference that Elena’s answer is not correct?” (Taking 71 away from 622 is a lot less than 615. so the answer should be around 550.)