how to multiply 3 and 4-digit by 3-digits, using the standard algorithm.

Transcription

1 1 U n t er r ich t splan Multiplying 4-Digit by 3-Digit numbers using the stand ard Algorithm Altersgruppe: 6t h Grade, 5 t h Grade Online-Ressourcen: M ul t i pl i c at i o n Al go ri t hm Opening Teacher present s Students pract ice Class discussion Math Worksheet Pract ice Closing 20 min 1 5 min 8 min 8 min 8 min 1 0 min M at h Obj ect ives E xpe ri e nc e problem solving with the standard algorithm of multiplication. P rac t i c e Multi - digit multiplication problems. Learn how to multiply 3 and 4-digit by 3-digits, using the standard algorithm. De vel o p algebra skills.

2 2 Ope ni ng 20 min Bring enough sticky notes, to split into small pieces (at least 5 sheets each) and distribute one to each student. Draw on the board a table like the one shown below. Now we are going to play a game: T he M at h Grand P ri x. This is a school version of the world famous race. In this case, we will have 4 races. As each race progresses, the difficulty of the race increases. The first one is the easiest, so try to take advantage of it for the final classification. The weight for each race is as follow: Race 1 (10 marks); Race 2 (20 marks); Race 3 (30 marks) and Race 4 (40 marks), which means it is possible for any of you to win the final classification. S a y : I will distribute sticky notes to all of you. Then, I will write on the board a multiplication problem for each race, one at the time. Once I say Start you have to solve the problem as fast as you can, write the answer on the back of your sticky notes, and go to the board to post it near the end line. If another student comes second, he or she has to post it below the first, and so on. There are only 5 spots available. Then, I will check if the answer is correct. If all five are correct, each of them will get marked according to the position they placed. For example, if Jose got first and his answer is correct, he will get the full 10 marks, if Maria got second and her answer is correct she will get 7 marks, third place will get 5 and fifth place will get 2 marks. The three students with the total highest score, at the end of the four races, will win T he M a t h Gra nd Prix The table with the scores is shown below: You should draw, or project, on the board a chart like the following:

3 3 Below are shown the problems for each race, you can use it or create your own, but remember as the race progresses, the difficulty of the problems increases. Let s watch the episode to practice multi -digit multiplication problems, and to see the steps involved, when use the standard algorithm to multiply a 3- or 4-digit number by 3-digit number. T e ac he r prese nt s M at h game M ul t i pl i c at i o n Al go ri t hm Di gi t by 3 - Di gi t 15 min Present Matific s episode M ult iplic a t io n A lgo rit hm Digit by 3- Digitit to the class, using the projector or interactive whiteboard, in preset mode.

4 4 This episode provides practice in solving 3- or 4 digit by 2- or 3 -digit multiplication problems. You have to find the correct product utilizing the standard algorithm. The episode begins with one multiplication problem about a 3-digit number by a 2-digit number and another regarding 4-digit number by a 2-digit number, that you have to solve as a review. Finally, there is one problem about a 4- digit number by 3-digit number, using the standard algorithm, which is the focus of this lesson. After having solved the first two problems, now we can look at 4-digit by 3-digit multiplication problems, using the standard algorithm. While you are playing this episode, imagine you are solving the multi-digit multiplication, in your notebook, using the standard algorithm. Ask: What problem do we need to solve? We have to evaluate the product of 3172 times 246.

5 5 We are going to multiply each digit below by all digits in the number above. We have to write the answer in the blank spaces, that have the question mark, by using the numeric keyboard to enter the numbers. So, a first step to solving the problem is to start with the 6 down, which is in the ones place, and multiply it by In this episode, it's possible to write anywhere on the screen. So, if you need to regroup you can demonstrate this. So, we will start multiplying, 6 times 2, which is 12. We need to write 2 in the ones place and regroup the 1 ten to the tens column. After that, we multiply 6 times 7, which is 42. We need to add the 1 we previously regrouped to obtain 43. Put 3 in the tens place, while regrouping the 4 tens to the hundreds column. Then, we multiply 6 times 1, which is 6. Add the 4 regrouped, to get 10, and put the 0 in the hundreds place, regrouping the 1 tens to the one thousands column. Finally, we multiply 6 times 3, which is 18. Adding the 1, we obtain 19, (note that 19 means 19000), and put the 9 in the one thousands place and the 1 in the ten thousands place to get the first product, which is Fo r e xample :

6 6 Now, let s multiply the 4, which is in the tens place, for each of the digits in the number above. So, 4 times 2 is 8. However, in this case, we do not just write the 8 in the ones place, remember the 4 digit is in the tens place, so it is actually a 40. Because it is 40, we can put a 0 below the 2 in the ones place or just leave this place blank. So, we write the 8 in the tens place. After that, we multiply 4 times 7, which is 28, so we write the 8 in the hundreds place and regroup the 2 tens to the hundreds column. Then, we multiply 4 times 1, which is 4. Add the 2, that we previously regrouped, to obtain 6, and put it in the one thousands place. Finally, we multiply 4 times 3, which is 12 (note that 12 means ). We put the 2 in the tens thousands place and the 1 in the hundred thousands place to get the second product, which is Fo r e xample : Ask: Are we done? No, we are not done, we need to multiply the 2 down. Excellent!. Let s multiply the 2, which is in the hundreds place,

7 7 for each of the digits in the number above. So, 2 times 2 is 4. However, in this case, we do not just write the 4 in the ones or tens place, remember the 2 digit is in the hundreds place, which means it is actually a 200. Because it is 200, we can put two 0 s below, one in the ones place and the second one in the tens place, or just leave these places blank. So, we write the 4 in the hundreds place. Then, we multiply 2 times 7, which is 14. We write the 4 in the one thousands place and regroup the 1 tens to the hundreds column. After that, we multiply 2 times 1, which is 2. Add the 1, we previously regrouped, to obtain 3, we put it in the tens thousands place. Finally, we multiply 2 times 3, which is 6 (note that 6 means ), put the 6 in the hundred thousands place to get the third product, which is Fo r e xample : Finally, we need to add the products up: 2 plus 0 plus 0 is 2. 3 plus 8 plus 0 is 11, we put 1 in the tens place and regroup the 1 tens to the hundreds column.

8 8 0 plus 8 plus 4 plus the 1, that we previously regrouped, is 13. We put 3 in the hundreds place and regroup the 1 tens to the one thousands column. 9 plus 6 plus 4 plus the 1, that we previously regrouped, is 20. We put 0 in the one thousands place and regroup the 2 tens to the tens hundreds column. 1 plus 2 plus 3 plus the regrouped 2 is 8. we write it in the tens thousands place. To finish we add 1 plus 6, and get 7, and write it in the hundred thousands place. Fo r e xample : Ask: What is the final product of 3172 x 246? The final product is Click on to continue to the next problem. A new multiplication problem appears.

9 9 Continue solving problems, asking students for the steps required to multiply 4-digit by 3-digit, using the standard algorithm. If the answer is correct, the episode will proceed to the next problem and the answer will turn green. If the answer is incorrect, the answer will turn pink. The episode will present a total of three problems. St ude nt s prac t i c e M at h game M ul t i pl i c at i o n Al go ri t hm Di gi t by 3 - Di gi t 8 min Have students play Matific s episode M ult iplic a t io n A lgo rit hm Digit it by y 3- Digitit on their personal devices. Circulate, answering questions as necessary. Encourage students to play the game M ult iplic a t io n A lgo rit hm Digit by 1 - Digit, if you think they need more guidance on how multiply 2- to 4 digit by 1-digit number. If you don't have time for more practice, assign this episode as homework.

10 10 Cl ass di sc ussi o n 8 min Bring to the class a plastic bottle, and ask the students to sit in a circle on the floor. Display the following solved multiplication problem, on the board. I will put a bottle in the middle of the circle, and I will rotate it randomly. The student pointed out by the bottle will have to explain the first step involved in solving this multiplication problem. Then, I will repeat the process until all the steps have being explained.

11 11 M at h Wo rkshe e t P rac t i c e M ul t i pl i c at i o n - 2- Di gi t B y 3 - Di gi t 8 min Have your students work on the worksheet M ult iplic a t io n - 2- Digit By 3- Digit on their personal devices, in order to help them build their skills on solving 2-digit by 3-digit multiplication problems, using strategies of multiplication. Circulate among students, answering questions. Cl o si ng 10 min Print the attached handout. Pass out a copy to each student and keep them working independently. They have to solve the following 3- or 4-digit number by 3-digit number, using the standard algorithm for multiplication. Ask students to write their names on the sheet. When the students are done, collect their sheets to review later.

12 12 Print a ble H a ndo ut : M ult iplic a t io n pro ble m s 1. Help Danny solve the following multi - digit multiplication problems.