Addition to 1,000 via simplification

General

Students learn that you can use a simplified addition problem to use as a first step to solving a more difficult addition problem. If you know the total of an addition problem without the hundreds, you can quickly determine the answer with hundreds.

Common core standard(s)

2.NBT.B.7

Relevance

It is important to learn this, to make calculating large numbers quicker and easier.

Introduction

Start by creating numbers with the three given digits. You can make 6 numbers with the given digits. Ask students to try to find all 6 in groups. Then ask which created number is the greatest, and which is the least. Next, give them a pop quiz with addition problems to 100 with and without regrouping.

Development

Show students a set of addition problems in which simplification is shown. Ask students if they notice anything about the set of addition problems. They should notice that the answers all have hundreds added to them. They can also notice that the addition problems are linked- that they are part of the same set. Tell the students that they can solve an addition problem with hundreds easier if they first solve the addition problem without the hundreds. You can use that as your first step. If you know that 10+3 = 13, then you know that 110+3=113 without needing to recalculate the entire problem. Show the set of addition problems on the interactive whiteboard. Emphasize that students don't need to add the second problem because they already know the answer from the first step. You add 100 to the addend, so you add 100 to the total. Check that students have understood by doing a few addition problems together, first with visual support, and then without the visual support. Show the addition problems as pairs and ask students how much is being added to the addend, and how much should be added to the total. You can imagine the MAB-blocks being added in your head. You can also give the students MAB blocks to work with on their desks.

Check that students understand addition to 1,000 using simplification by asking the following questions:
- 46+2=18, 146+2= ?
- 4+9=13, 304+9= 313. How do you know this?
- 28+13=41, Which addition problem can you now easily solve?

Guided practice

Students first practice with addition problems in which 100 is added to the first step. Then students are given addition problems with random amounts of hundreds added.

Closing

Repeat why it is important to learn how to simplify while adding to 1,000. It helps you solve large addition problems easily and quickly. If you can solve the problem without the hundreds then you will also be able to solve the problem with hundreds. Check that students have understood by asking students to solve an addition problem with visual support, as well as a few without visual support.

Teaching tips

Make the method of simplification visual for students by having them work with MAB blocks or with money. Give them a 20 dollar bill and a 10 dollar bill. They know that 20+10=30. If you give them a 100 dollar bill, then they get 110=20=130. And if they get a second hundred dollar bill it is 210+20=230. And if they get yet another hundred dollar bill it is 310+20=330. Repeat this with different amounts. Make sure to point out that they do not need to recalculate the addition problem with hundreds, because they already know what the total should be by having the total of the first step.