Teaching Complex Math Computation – Addition (3/4)
To the teacher or parent: These blogs outline ways that I learned to help teachers for several decades. Maybe it can help you or one of your colleagues.
To read the previous part click on the link below.
Teaching the Regrouping Operation
Say to the student(s), “Now we are going to work problems where we have to use regrouping. Here is the rule about regrouping. Listen. If the bottom number of the subtraction problem is greater than the top number of the subtraction problem, we need to regroup.
Listen again. If the bottom number of the subtraction problem is greater than the top number of the subtraction problem, we need to regroup. Touch the first problem on your exercise sheet. My turn to read the problem. Listen.”
Say to the student(s), “Now we are going to learn how to subtract large numbers when we regroup.” Touch the top number in the problem. Say to the student(s), “Read this number for me. Ready.” Signal.
The students read(s), “Four hundred and fifty-eight.”
Say to the student(s), “Good work.” Touch the bottom number and say to the students, “Now read this number. Ready.” Signal.
The student(s) read(s), “Three hundred and sixty-eight.”
Say to the student(s), “Good job. Now we are going to subtract 368 from 458.” Touch the ones column and say to the student(s), “Here’s a rule. When we subtract numbers that are larger than nine, we always start in the ones column on the right. Listen again. When we subtract numbers that are larger than nine, we always start in the ones column on the right. What column do we always start with? Ready.” Signal.
The student(s) say(s), “We start with the ones column on the right.”
Say to the student(s), “My turn to read the numbers in the ones column. Listen. This problem says ‘eight minus eight’. Read the problem with me. Ready.” Signal.
The student(s) and the teacher read, “Eight minus eight.”
Say to the student(s), “Your turn to read the problem starting in the ones column. Ready.” Signal.
The student(s) read(s), “Eight minus eight.”
Say to the student(s), “How much is eight minus eight? Ready.” Signal.
Student(s) respond(s), “Zero.”
Say to the student(s), “Correct. I will write a zero in the ones column. Now we have to work in the tens column.” Point to the six at the bottom of the tens column. Say to the student(s), “What is the number at the bottom of the tens column? Ready.” Signal.
The student(s) respond(s), “Six.”
Say to the student(s), “That’s correct.” Touch the top number in the tens column and say to the student(s), “And what is the number at the top of the tens column? Ready.” Signal.
The student(s) respond(s), “Five.”
Say to the student(s), “Remember the rule. When the number at the bottom of the column is larger than the number at the top of the column, we have to regroup. What do we have to do? Ready.” Signal.
The student(s) answer(s), “Regroup.”
Say to the student(s), “Good work. To regroup, we borrow ten from the hundreds column. What do we do? Ready.”
The student(s) answer(s), “Borrow ten from the hundreds column.”
Say to the student(s), “To borrow ten from the four in the hundreds column, we cross the four and write a three above it. Then we add the ten to the tens column by writing a one in front of the five to make it fifteen. Listen again. To borrow ten from the four in the hundreds column, we cross the four and write a three above it. Then we add the ten to the tens column by writing a one in front of the five to make it fifteen. What do we do first? Ready.” Signal.
The student(s) answer(s), “We cross out the four in the hundreds column.”
Say to the student(s), “Correct. And what number do I write above the hundreds column? Ready.” Signal.
The student(s) answer(s), “Three.”
Say to the student(s), “Right. I have written the three above the number four in the hundreds column. What do we do next? Ready.” Signal.
The student(s) respond(s), “We write a one in front of the five in the tens column to make it fifteen.”
Say to the student(s), “Now the top number in the tens column is fifteen. Is fifteen a bigger number than six? Ready.” Signal.
The student(s) answer(s), “Yes.”
Say to the student(s), “So can I subtract six from fifteen? Ready.” Signal.
The student(s) reply(ies), “Nine.”
Say to the student(s), “I will write the nine in the answer below the tens column. Now look at the hundreds column. What numbers do I subtract? Ready.” Signal.
The student(s) reply(ies), “You subtract three minus three.”
Say to the student(s), “How much is three minus three? Ready.” Signal.
The student(s) respond(s), “Zero.”
Say to the student(s), “So how much is 458 minus 368? Ready.” Signal.
The student(s) say(s), “Ninety.”
Say to the student(s), “That’s the answer. Now let’s see if we can do the next problem. Read the top number in the next problem. Ready.” Signal.
Repeat the presentation for the first five questions, then give the student(s) a chance to complete the worksheet exercise on their own.
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