Addition & Subtraction to 1,000 using standard algorithm

General

Students learn to add and subtract numbers to 1,000 using the standard algorithm, with and without regrouping.

Common core standard(s)

4.NBT.B.4

Relevance

The standard algorithm allows you to add and subtract larger numbers easily, and particularly with numbers that are difficult to solve in your head.

Introduction

Ask students to create the given numbers by dragging the blocks on the board. Name the hundreds, tens, and ones that are required to create the numbers. They play the audio fragments and ask students to drag the named numbers to the correct squares on the place value chart to form the spoken number.

Development

Explain that by using the standard algorithm, you make addition and subtraction of large numbers easier. There are two ways of adding and subtracting using the standard algorithm: with and without regrouping numbers. After each instructional segment, the students practice that which has just been explained. Repeat the explanation of the place value chart with hundreds H, tens T, and ones O. Explain that you write the numbers one below the other and always start on the right when calculating, working your way to the left. The larger number goes at the top and you write the results of the problem directly below, in the same place value column. Then show students step by step how to add using the standard algorithm. Start by adding the ones, then the tens, and finally adding the hundreds. Then show students an example of adding with regrouping. Remind students that if the total is greater than 10 you must regroup the number, by splitting it into tens and ones. The tens go high, the ones down low, which means that the tens go up to the little box above the tens column on the place value chart. Then add the tens together, remembering to also add the tens from the box at the top. Then add the hundreds. Then explain how to solve a subtraction problem using the standard algorithm. First subtract the ones, then the tens, and finally the hundreds. If the number on the bottom is greater than the ones number on the top it means that you need to borrow ten from the tens column. You do so by crossing out the number and writing 1 less in the little box. You then add the ten to your ones number. You then subtract the regrouped number in the ones column. Next you subtract the tens, and remember to subtract using the number in the little box, not the number you crossed out. Then subtract the hundreds. Ask students if they can determine which answer belongs in the yellow boxes. Then repeat but show how to borrow from the hundreds column. If your bottom tens number is greater than the top number, you borrow from the hundreds.

Check that students are able to add and subtract numbers to 1,000 using the standard algorithm by asking the following questions:
- Why is it useful to be able to use the standard algorithm?
- Where do you borrow from if your bottom ones number is greater than the top? Where do you borrow if the bottom tens number is greater than the top?
- What do you do when adding if your total is greater than 10 from the ones and tens columns?
- Where do you start calculating when using the standard algorithm?
- Solve the following problems using the standard algorithm: 534 + 127 = ? and 465 - 218 = ?

Guided practice

Students are given 10 exercises in which they practice addition and subtraction problems in which they must regroup tens and hundreds.

Closing

Ask students to come up with problems on their own by dragging numbers to the place value chart. Make sure that different kinds of problems are produced. Discuss why it is useful to be able to use the standard algorithm and remind students to always start on the right. When adding using the standard algorithm, when your total is greater than 10, your tens go high, the ones down low, and you add to the next column. When subtracting using the standard algorithm, when the bottom number is greater than the top number you borrow 10 from the column to the left. You use this to solve larger problems that are difficult to do in your head.

Teaching tips

To support students who have difficulty with the standard algorithm, start by working on their knowledge of the place value chart (HTO) and how to correctly write a number into the place value chart. You can choose to write the subtraction/addition problems of the ones, tens, hundreds separately and then to write those differences together to make it extra clear which numbers are being subtracted/added. For students who have difficulty understanding the borrowing(or regrouping), they can be supported by making use of MAB blocks to physically move blocks from the tens column to the ones column.