Addition to 1,000 using standard algorithm with regrouping

General

Students learn to add numbers to 1,000 using the standard algorithm crossing tens and hundreds.

Common core standard(s)

4.NBT.B.4

Relevance

Explain to students that the standard algorithm helps them to add larger numbers quicker and easier. You can use this to add larger numbers together.

Introduction

Ask students to create the given numbers by dragging blocks. Have students name how many hundreds, tens, and ones are needed to create the given numbers.

Development

Introduce students to the term "standard algorithm". Explain that it is a method to use when adding (and subtracting). Using the standard algorithm you can add more easily. Show students the addition problem written in the place value chart showing H(hundreds), T(tens), and O(ones). Show students step by step how to use the standard algorithm adding 267 + 125. Write the problem in the place value chart. Start by explaining that when you use the standard algorithm, you add from right to left. First you add the ones together. 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. Show the totals of each step and then that all the numbers together are the total. That's using the standard algorithm with regrouping. Ask students to practice using the standard algorithm in which they must regroup the tens number. Then explain how to use the standard algorithm on the problem 285 + 172 where you must regroup tens. First add the ones together. The total is not greater than ten, so you don't need to regroup. Then add the tens together, and as 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 hundreds. Next add the hundreds together and also add the number from the box. Show the totals of each step and then that all numbers together are the total. Have students practice three different math problems using the standard algorithm.

Check that students are able to add numbers to 1,000 using the standard algorithm with regrouping by asking the following questions:
- Why is it useful to be able to use the standard algorithm?
- What do the letters H, T, and O stand for?
- Where do you start adding when using the standard algorithm?
- Solve the following problems using the standard algorithm: 438 + 471 = ?, and 276 + 346 = ?

Guided practice

Students are given addition problems to solve using the standard algorithm. They are given problems in which they must regroup tens, and regroup hundreds. They must also some a problem with three hundreds numbers.

Closing

Ask students to come up with numbers and to drag them to the place value chart. Ensure that they create problems that involve regrouping tens, regrouping hundreds, and problems with three numbers and then solve them as a class. Refresh why it is important to be able to add using the standard algorithm, and that you add from right to left. Remind students to use the little boxes at the top to show when they regroup numbers, and that tens go high, ones stay low. You can easily add larger numbers this way.

Teaching tips

Students who have difficulty with this learning goal can work 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 addition problems of the ones, tens, hundreds separately and then to write those totals together to make it extra clear which numbers are being added together. They can also be supported by working on regrouping, and remembering that when a total is greater than 10 that they regroup and that the tens go high, the ones stay low. This can be shown using MAB blocks or other manipulatives (that you make 10 and that it carries to the next place value.