Students learn to subtract to 10,000 using the standard algorithm.
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The students can subtract to 10,000 using the standard algorithm with and without regrouping.
Students will be able to subtract to 10,000 using the standard algorithm.
Play the sound clips and have the students drag the numbers to the correct location.
The standard algorithm is a method that can be used to subtract large numbers. Explain that by subtracting using the standard algorithm you can solve a difference in steps. Remind students of the meaning of the letters THTO and then show in steps how you approach a subtraction problem using the standard algorithm. Have the students practice on their own with the assignments after each instruction. You see the difference 3798 - 56 in the THTO-diagram, with the numbers one under another. You always calculate working from right to left. First you subtract the ones values from one another. Then the tens, hundreds, and thousands numbers. With this problem there are no numbers that need to be regrouped so you don't have to borrow. Then explain the difference 3464 - 247. You first subtract the ones values. This is impossible so you must borrow from the tens numbers. You cross out the 6 and write in the box above the tens values what is left over (5). Then you add the 1 from the tens to the ones values and write it above the ones column. Now you can subtract the ones numbers. Then you subtract the tens numbers from one another, using the number you wrote above that is left over after you borrowed. Then you subtract the hundreds numbers and thousands numbers from one another and you have solved the problem using the standard algorithm. Ask the students to solve the difference 7124 - 3657. For this you must borrow from the tens numbers, the hundreds numbers and the thousands numbers and so you must use all of the spaces above the columns.
Check whether the students can subtract using the standard algorithm by asking the following questions:
- Why is it useful to subtract using the standard algorithm?
- What do the letters T H T O mean?
- Where do you always start when calculating with the standard algorithm?
- Solve these problems by putting the numbers one under another and using the standard algorithm: 3,458 - 129 = and 7,863 - 2,376 =.
There are 10 exercises in which students practice subtracting to 10,000 using the standard algorithm, both with and without borrowing. For some of the problems the THTO-diagram has been filled in already, and for others the students must fill in the diagram on their own.
Have the students drag the differences to the THTO-diagram and solve using the standard algorithm. Discuss once again why it is useful to calculate using the standard algorithm and how you do this. Always work from right to left and borrow from the next column if you don't have enough to subtract This is how you can solve problems with large numbers in quick steps without having to solve them in your head.
For the students that have difficulty with using the standard algorithm, remind them of the meaning of T H T O and how you put numbers in a THTO-diagram. Write out the intermediate steps. You may label the ones values, tens numbers, hundreds numbers and thousands numbers from top to bottom so that it is obvious which numbers you are subtracting from each other. Students that have already mastered the standard algorithm can skip the instruction and may calculate problems using the standard algorithm directly without writing out the intermediate problems.
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