E xpe rii e nc e step-by-step guidance with long division

Transcription

1 1 План урока Long Division Algorithm with 4 Digit Divid end Возрастная группа: 5 t h Grade, 6t h Grade Virginia - Mathematics Standards of Learning (2009): 4.4 c, 5.4 Virginia - Mathematics Standards of Learning (2016): 4.4.c Fairfax County Public Schools Program of Studies: 4.4.c.1, 4.4.c.2, 5.4.a.8 Онлайн ресурсы: Di vi de be f o re Lo ng Opening Teacher present s Students pract ice Class discussion Math Worksheet Pract ice Closing M at h Obj ect ives E xpe rii e nc e step-by-step guidance with long division P rac t i c e division facts Learn the long division algorithm De vel o p number sense Ope ni ng 6

2 2 Say: Let s review some vocabulary. What is the answer to an addition problem called? What is the answer to a subtraction problem called? A multiplication problem? A division problem? The sum is the answer to an addition problem. The di f f e renc e is the answer to a subtraction problem. The pro duc t is the answer to a multiplication problem. The q uo t i e nt is the answer to a division problem. Say: Today, we are going to look at some division problems. Before we do, let s look at a little more vocabulary. Write on the board: Ask: In this division problem, what is the dividend and what is the divisor? Thirty-six is the dividend, and 4 is the divisor. Say: State a word problem where we might divide 36 by 4 to find the answer. Responses will vary. A possible response: A teacher has 36 desks and wants to put them in rows of 4 desks each. How many rows will she need? Say: Today we will look at problems where the dividend is a 4-digit number. We will use our previous knowledge of division to solve these more difficult problems.

3 3 T e ac he r prese nt s M at h game : Di vi de be f o re Lo ng Di gi t by 1- Di gi t 10 Using Preset Mode, present Matific s episode Di vi de be f o re Lo ng Di gi t by 1- Di gi t to the class, using the projector. The goal of the episode is to practice the long division algorithm for quotients of 4-digit numbers by 1-digit numbers. Ask: What problem are we being asked to solve? We are trying to solve 1044 divided by 9. Say: Look at the problem at the top of the episode. There is a box with a question mark in it. What do we ask ourselves in order to fill in that box?

4 4 We ask ourselves: What is 10 divided by 9? Say: Yes. Imagine we did not remember how to start this problem. We could click on the question mark on the monster s belly to get a reminder. Click on the on the monster s belly. Ask: What does the monster say? The monster says, How many times does 9 go into 10? Say: We know that 9 goes into 10 once. So let s type in 1 in the quotient. Click on the under the 10. to enter 1. The episode will present another Ask: What belongs in this question mark? Why? We enter a 9 in that space because we multiply the 1 in the quotient with the 9 in the divisor to get 9. Click on the to enter 9. The episode will present another. Ask: What belongs in this question mark? Why? Here, we enter a 1 because we subtract the 9 from the 10 to get 1. Click on the to enter 1. The episode will present an arrow to show that the next step is to drop the 4. Click on the. Continue to ask the students for the steps required in the long division. Remind them that if they are stuck on a step, they can click on the on the monster s belly to get a hint. If an incorrect answer is entered, the incorrect number will be highlighted brown, the other

5 5 numbers involved will be highlighted, and the monster will give a hint. When the long division is complete, click on the to enter the quotient and then click. The episode will present a total of three problems. The second two have remainders. St ude nt s prac t i c e M at h game : Di vi de be f o re Lo ng Di gi t by 1- Di gi t 12 Have the students play Di vi de be f o re Lo ng Di gi t by 1- Di gi t and Di vi de be f o re Lo ng Di gi t by 2- Di gi t on their personal devices. Circulate, answering questions as necessary. Cl ass di sc ussi o n 8 Display the following incorrect division problems: Say: There is a mistake in each of these problems. Find them. What is the mistake in the problem on the left? The mistake in this problem is that the first digit of the quotient

6 6 is too small. The first digit should be a 9, not an 8. When we subtract, if the difference is equal to or greater than the divisor, the digit in the quotient is too small. Here, when we subtract 24 from 27, we get 3, which is equal to the divisor. Then we are forced to put a 2-digit number (11) into the divisor, which is wrong. The answer should be 916 remainder 1. (There is no way that the quotient should be larger than the dividend, since we divided by a whole number.) Ask: What is the mistake in the problem in the middle? The answer should be 309, not 39. There is a zero missing from the quotient. We cannot bring down both the 7 and the 2 without placing a 0 in the quotient. Ask: What is the mistake in the problem on the right? The answer should be 214 remainder 6. As we write each digit in the quotient, we should make sure that we place it in the correct spot. Since we are asking ourselves, How many times does 12 go into 25?, we should place our answer of 2 over the 5 in 25, not over the 2. Then we will know when we are done, and we will not make the mistake of affixing a 0 to the end of the quotient.

7 7 M at h Wo rkshe e t P rac t i c e : Di vi si o n by 1- Di gi t N umbe r - Up t o 10,000 6 If students no longer need the step-by-step treatment of the long division algorithm provided in the episode, they can continue to practice long division with the following worksheets: Di viv i si o n by 1- Di gi t N umbe r - Up t o 10,000 and Di vi si o n by 2- Di gi t N umbe r - Up t o 10,000.

8 8 Cl o si ng 5 Distribute a small piece of paper with the following problems: Collect papers, to review later.