Adding by Place-Vertically

Transcription

1 Adding by Place-Vertically Objective: The purpose of this lesson is to prepare students to use the U.S. Standard Algorithm for Addition by practicing adding by place vertically. Vocabulary: addition, sum, vertical Materials: Number Cards, Adding by Place Vertically Recording Sheet-1 per student Introduction: Put the following problems on the board horizontally and vertically = Have students turn and talk to a partner and discuss how they would solve. Ask for a volunteer who might have added by place to help you solve. Have student explain aloud how they would add this addition situation by place for you as you record horizontally = = = = =375 Ask students if they can add vertically in the same manner. If we add our hundreds, we get 300, next we add our tens, which is 60, and then we add which is 15. When we add we get If we are going to add efficiently which method of adding by place would you choose adding by place horizontally or adding by place vertically? We call adding by place vertically an algorithm. Algorithms show a clear sequence of steps that can be used to solve a certain kind of problem. Activity: Students will choose six number cards and create two 3-digit numbers that they will then practice adding by place vertically on the recording sheet

2 Name: Date: Adding by Place Vertically

3 The US Standard Conventional Algorithm Focus: I can learn and apply the US Algorithm for Addition. Vocabulary: algorithm Materials: I Have, Who Has? Game Cards (1 set of cards per 4 students) Practicing the US Standard Algorithm page (1 per student) Teacher s Note: The US Algorithm for addition, sometimes called the carrying algorithm shows a clear and concise sequence of steps that can be used to solve problems. The power of the algorithm for quick calculation lies largely in the fact that they require the user to carry out a series of mostly single digit calculations. They were designed so that the user could rely on a small set of known combinations and the repetition of a small sequence of steps to solve any problem. The algorithm is a strategy that student will likely see others use. This algorithm was invented because, when you understand it, it can be used very efficiently for adding numbers of any size. Even if students don t use this strategy, it s good to be exposed to the Algorithm. Students should have at least one or two strategies that are clear, that they understand and that they can use efficiently. The US Algorithm can be added to your anchor chart of efficient strategies for addition. Students should determine whether or not this is a strategy that works for them. Introduction: Students will play I Have, Who Has? a game that reinforces addition combinations. Cut out the cards, shuffle them, and pass out set of cards per group of 4 students. Each student should get 4 cards. The student with the card that says, Begin here will begin by asking..? The purpose of the game is to reinforce the facts students need to know to add quickly. Tell students they will be examining an addition strategy many people use, the US Algorithm for Addition. Write the following problem on the board: =. Tell students that in this strategy each place value is added separately and that instead of starting with the largest place value we start with the smallest place value. The people who invented this algorithm wanted to add only a small set of combinations (facts). To make the connection between students current understanding and this new shortcut method, first add the numbers vertically by place. Ask students to help you add by place and record Add 7 and 6 and get 13. Record the 3 below the 7 and 6 and carry the 10 to the tens place. You represent the 10 with a one. The one represents adding one more ten in the tens place. Add the 1 ten to the 8 tens and the 3 tens to get 12 tens. The result is 12 tens and 3 ones, which gives you 123.

4 Work addition problems together with students completing them on a white board and discussing how the US Standard Algorithm works. Have students explain to a partner when working the problems what they are doing. For example: Students should say, I added 5 and 9, it made 14. I wrote a 4 in the ones place under the 5 and 9 and carried the ten to the tens place. Then, I added 1 ten, 7 tens and 4 tens, it made 12 tens. If I add 12 tens and 4 ones I get 124. Extend the addition problems to 3 digits plus 2 digits and then 3 digit plus 3 digit. Be sure to stress reasonableness. Does the answer make sense? If you are adding 125 and 80, and the answer you get is around 100, does this make sense? Investigation: Students work in pairs on the attached problems to practice using the US Standard Algorithm for Addition. Look for: Do students understand the re-grouping? Do they understand they are moving a group of 10s or 100s? Can students use the algorithm quickly and efficiently for addition? Are students looking at their answer and determining if it is reasonable? Discussion: Discuss problem #5. Have students explain the regrouping process to the hundreds place. Make a comparison to adding by place vertically. Day 2: Practicing the US Standard Algorithm for Addition. Give students two and three digit addition problems to practice.

5 I Have, Who Has? Game Cards I have 16 I have 14. I have 9. I have 10. BEGIN HERE: ? 8 + 2? 4 + 3? I have 7. I have 18. I have 13. I have 5? 9 + 9? 7 + 6? 2 + 3? 8 + 3? I have 11. I have 15. I have 17. I have ? 8 + 9? 4 + 8? 4 + 4? I have 8. I have 6. I have 5. I have ? 3 + 2? 1 + 3? 9 + 7?

6 Name: Date: Practicing the US Standard Algorithm-Addition Solve the following problems using the US Standard Algorithm for Addition. Check your work using your most efficient strategy