Adding to 10,000 using the standard algorithm

Students learn to add to 10,000 using the standard algorithm.

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The students can add to 10,000 using the standard algorithm with and without regrouping.

CCSS.Math.Content.4.NBT.B.4

Students will be able to add to 10,000 using the standard algorithm.

Have the students make the largest number they can with the numbers provided.

The standard algorithm is a method of adding large numbers together. Explain that with the standard algorithm you can calculate a sum in steps. Remind students of the meaning of the letters THTO. Then show the different methods in which you can add in steps using the standard algorithm, and have the students practice on their own after each different method shown. You solve the sum 4,571 + 3,126 by putting the numbers one under the other and putting the larger number on top. First add the ones values together, then the tens numbers, the hundreds numbers, and finally the thousands numbers. The answer of each intermediate sum is written underneath. Explain what you do if you cross the tens and the hundreds when adding. First you add the ones values together. The answer is larger than 10 so you write the 1 in the box above the tens numbers. Then you add the tens numbers together, and also add the 1 from the box to this. Then you add the hundreds numbers together and add the 1 from the box to that number. Finally, you add the thousands numbers together and then you have solved the sum using the standard algorithm. Also show a sum in which the tens number, hundreds number, and thousands number are crossed and ask the students to solve it. Then you explain how you solve an addition problem with multiple numbers. You then use all of the boxes to regroup.

Check whether the students can add using the standard algorithm by asking the following questions:

- Why is it useful to add using the standard algorithm?

- What do the letters T H T O stand for?

- Where do you always begin when using the standard algorithm?

- Solve these problems by putting the numbers one under another and using the standard algorithm: 1428 + 273 = and 2569 + 3756

There are 10 exercises in which the students practice adding to 10,000 using the standard algorithm. For some problems the table is already (partially) filled in, and for others they must fill it in on their own. First the students practice several two-number problems with larger numbers, and then they practice two exercises with three numbers using the standard algorithm.

Have the students drag the sums to the THTO-diagram and solve using the standard algorithm. Discuss again why it is useful to solve sums using the standard algorithm, and how you do this. Always work from right to left and use the boxes to carry over numbers for regrouping. This is also how you can solve problems with large numbers in quick steps without having to do the problem in your head.

For students that have difficulty using the standard algorithm, remind them of the meaning of T H T O and how you arrange the numbers in a THTO-diagram. Write out the intermediate sums. Note the ones values, tens numbers, hundreds numbers, and thousands numbers from the top to the bottom so it becomes obvious which numbers should be added together. Students that have already mastered using the standard algorithm can skip the instruction and may directly calculate sums using the standard algorithm without writing out intermediate sums.

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