Возрастная группа: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 4.5 c, 4.5 d,

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1 1 План урока Ad d Decimals Tenths and Hund red ths Возрастная группа: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 4.5 c, 4.5 d, 5.5 a Virginia - Mathematics Standards of Learning (2016): 4.6.a, 4.6.b, 5.5.a, 5.5.b Fairfax County Public Schools Program of Studies: 4.5.c.1, 4.5.d.1, 4.5.d.2, 5.5.a.1, 5.5.a.3 Онлайн ресурсы: M o nst e r Sho p Opening Teacher present s Students pract ice Class discussion 1 2 мин 1 0 мин 1 0 мин 1 3 мин M at h Obj ect ives E xpe ri e nc e problem solving. P rac t i c e addition of tenths and hundredths. Learn to add decimals. De vel o p a better understanding of place value.

2 2 Ope ni ng 12 мин Display the following problems: Write the following numbers in e xpa nde d no t a t io n : = = = Have the students work in their notebooks. When they are finished writing, they should share their answers = (4 10) + (5 1) = (7 100) + (3 10) + (2 1) = (1 100) + (1 10 ) + (1 1) + (1 0.1) Say: When we look at expanded notation, we are looking at place value. Here, we are looking at the hundreds place, the tens place, the ones place and the tenths place. Today, we re going to look at another place as well. Display the following equation: = (6 10) + (8 1) + (9 0.1) + (2 0.01) Say: To make 68.9, we need 6 tens, 8 ones and 9 tenths. Ask: What is the next place value to the right of the nine? The next place value is hundredt hs. Say: So to make 68.92, we need 6 tens, 8 ones, 9 tenths and 2 hundredths. Display the following equation:

3 = (4 100) + (2 10) + (8 1) + (7 0.1) + (3 0.01) Say: To make 428, we need 4 hundreds, 2 tens and 8 ones. Ask: What are the next two place values to the right of the eight? The next two place values are t e nt hs and hundredt hs. Say: To make , we need 4 hundreds, 2 tens, 8 ones, 7 tenths, and 3 hundredths. Ask: Which place is larger, the tenths or the hundredths? How do you know? The tenths place is larger than the hundredths place. The tenths place is to the left of the hundredths place. Place values increase (times 10) as we move left. Another explanation is by comparing 1/10 and 1/100. Say: We use a base 10 number system. Place values increase times 10 as we move to the left. We need 10 hundredths to make 1 tenth, this is why the place to the left of the hundredths, is the tenths place. We need 10 tenths to make one, 10 ones to make a ten and 10 tens to make 1 hundred. Ask: When we place zeros at the end of a decimal number, do we change its value? Why or why not? Zeros to the right of a decimal point that are at the end of the number do not change its value. For example, 0.8 is the same as The number 0.80 says that there are 0 hundredths. We haven t added any hundredths to the number 0.8 so they are equal. We can compare this with 0.81, where we have added 1 hundredth to 0.8. Zeros that come in the middle of a number after the decimal point do change its value. The number 0.8 is not equal to The first, 0.8, is equal to 0 wholes and 8 tenths. The second, 0.08, is equal to 0 wholes and 8 hundredths.

4 4 T e ac he r prese nt s M at h game : M o nst e r Sho p - Add De c i mal s: Level I I 10 мин Using Preset Mode, Pesent Matific s episode M o ns t e r S ho p - A dd De c im a ls : L e v e l I I to the class, using the projector. This episode enables students to practice the addition of decimal numbers, with two decimal digits. A monster is visiting your store. Give the monster the two pieces of fruit or the vegetables it requests, and calculate the total price. Example : Say: Let s have a look at what we have in this episode. 1. On the right are vegetable and fruit boxes that contains: corn, carrots, eggplants, cabbages, oranges, red peppers, tomatoes, bananas and pineapples. 2. On the left is a price poster which tells us how much each item costs. 3. In the center is the customer's shopping list. The instructions at the bottom of the screen tell us to hand the monster the vegetables or fruit that it asked for. If the vegetable or the piece of fruit we put in the customer s hands is from the shopping list, the item will stay in the customer s hand and the price

5 5 will appear above it. Otherwise the item will return to its box. Ask: What vegetable or fruit should I give to the customer? Give the customer one of the items it requests. Say: Look at the price which appears above it. Ask: What vegetable or fruit should I give to the costumer next? Give the customer the second item. Say: Look at the price which appears above it. Pay attention to the change in the instructions at the bottom of the screen. Example : R e ad t he i nst ruc t i o ns: How much should the monster pay? Say: In order to know how much money the monster should pay, we add the prices. Ask: What is the sum of 0.12 and 0.61? In the number 0.12, 1 is the number of tenths and 2 is the number

6 6 of hundredths. In the number 0.61, 6 is the number of tenths and 1 is the number of hundredths. Now we add the numbers: 6+1 are 7 tenths and 2+1 are 3 hundredths. So the answer is Depending on the level of the class, you can give them a more advanced explanation. (Be sure that this explanation will not confuse them): In the number 0.12 there are 12 hundredths because 1 is the number of tenths which means there are ten hundredths plus 2 hundredths. In the number 0.61 there are 61 hundredths because 6 is the number of the tenths which means there are 60 hundredths plus 1 hundredth are 73 hundredths. Write 0.73 in the answering box. After we finish solving the problem, a number sentence is displayed relating the solution to an addition equation, in this case = St ude nt s prac t i c e M at h game : M o nst e r Sho p - Add De c i mal s: Level I I 10 мин Have students play M o ns t e r S ho p - A dd De c im a ls : L e v e l I I on their personal devices. Circulate, answering questions as necessary. Cl ass di sc ussi o n 13 мин Discuss any problems the students faced while working individually. Ask the class for responses as to how they dealt with any common issues their classmates brought up. Display the following equation: = 1.3

7 7 Say: Here are the three addition equations with decimals. Let s talk about them. In the third equation, why does the answer have no digit in the hundredths place? When we add 0.95 and 0.35, the number of hundredths is 10, but we only have room for one digit in the hundredths place, what should we do? We use regrouping (explain that the regrouping process is similar in decimals and in wholes). The result of the addition is The digit in the hundredths place is a zero, but there are no hundredths. Therefore, we ignore it, and write 1.3. The numbers 1.3 and 1.30 are equivalent. Display these equations with the first equation: = = = 6.78 Say: Let s use these equations to help us write down the rules for adding decimals. What steps are involved in adding decimals? Some coaching may be needed. With prompting, the students should be able to come up with a list similar to this one. 1. Write the numbers vertically, lining up the decimal points in each of the addends (this way the tenths are above the tenths, the ones above the ones, etc.). 2. Place zeros at the end of each addend as necessary so that the addends all contain the same number of decimal places. 3. Place the decimal point in the answer directly under the decimal points in the problem. 4. Add normally. Write the steps down on the board as the students develop them.

8 8 Say: Let s look at a problem. Find the mistake that was made in solving this problem. Display the following: = Ask: What is the mistake? The mistake is that the decimal points are not lined up. We are adding 0.2 to If we estimate, we can see that the answer should be more than 2. Here, the answer is less than 2. Show the right way of answering this question: Display the following problems. Have students complete them in their notebooks = = = = = = When the students are finished working, review the solutions.

9 9 Discuss any questions they may have = = = = = = 1.25