The purpose of this activity is for students to add and subtract multi-digit numbers through the hundred-thousands place. To find the value of some differences, students will decompose more than one unit.

The last question includes problems with a missing addend and a missing subtrahend. Besides making use of the structure of the standard algorithm (MP7), students will need to rely on what they know about the relationship between addition and subtraction to find the missing numbers.

• “How can you tell if your answers are correct? How can you check them?” (One way to check the result of subtraction is by adding it back to the number being subtracted. One way to check the result of addition is by subtracting one addend from the sum. Another way of checking is by performing the calculations with the numbers written in expanded form.)

In this activity, students analyze addition and subtraction calculations, identify errors, and explain what makes certain ways of calculating problematic. This activity gives students opportunities to construct logical arguments and critique the reasoning of others (MP3).

• “How did you find Lin’s errors?”
• “How can solving the subtraction problem help you to find all of Lin’s errors?”

• Select 2–3 students to share their responses and reasoning.
• Record responses as students share.
• “What are some errors that are commonly done when subtracting two numbers using the standard algorithm?” (Subtracting without lining up the numbers by place value. Using the notation of regrouping without decomposing a unit. Crossing out digits without including them in the regrouping. Subtracting from left to right without decomposing units.)
• “What ideas do you have for avoiding those errors?” (Use grid paper to line up the digits by place value. Decompose the unit before regrouping. Check answers using addition.)