1 Lesson Plan Round Decimals Age group: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 4.3 b, 4.3 c, 5.1 Virginia - Mathematics Standards of Learning (2016): 4.3.b, 5.1 Fairfax County Public Schools Program of Studies: 4.3.b.1, 4.3.c.1, 4.3.c.2, 5.1.a.1 Online resources: Wei ghi ng M at t e rs Opening Teacher present s Students pract ice Class discussion 1 3 min 1 0 min 1 2 min 1 0 min M at h Obj ect ives E xpe ri e nc e a visual model of one, one tenth, and one hundredth P rac t i c e using a balance scale Learn to round decimals De vel o p a better understanding of place value Ope ni ng 13 min
2 Display the following number line on the board: Say: I will draw a sign on the number line and each time we re going to determine whole number the sign is closest to. Place the x above the number 0.2. Ask: Which whole number is closest to the x? The closest whole number to 0.2 is 0. Place the x above the number 0.6. Ask: Which whole number is closest to the x? The closest whole number to 0.6 is 1. Place the x above the number 1.5. Ask: Which whole number is closest to the x? The distance of 1.5 from 1 and from 2 is the same, so there is not one closest whole number to 1.5. Continue asking questions of this nature until you are confident that the students can easily identify the closest whole number. Display the following number line on the board: Say: Now I will draw a sign on this new number line and this time we re going to determine to which t e nt h the sign is closer.
3 Add the 0.22 tick and place the x above it. Ask: Which tenth is closest to the x? The closest tenth to 0.22 is 0.2. Ask: Which tenth is closest to 0.79? The closest tenth to 0.79 is 0.8. Continue asking questions of this nature until you are confident that the students can easily identify the closest tenth. Say: In mathematics, rather than asking which whole number is the closest, we ask which whole number we should ro und o f f to. When we round off to 2, we mean that the closest whole number is 2. When we round off to 1, we mean that the closest whole number is 1. Ask: State a number that rounds off to the nearest tenth to 2.6. A possible response: 2.61 rounds off to 2.6. Ask: State a number that rounds off to 9, the nearest whole number. A possible response: 8.7 rounds off to 9. Ask: To which whole number should we round off 1.5? Although the distances of 1.5 from 1 and from 2 are the same, so there is no closest whole number to 1.5, but the common convention is to round off to the larger number, 2 in this case. Say: Because we are using base 10 number system, there are 10 optional digits in every place value. So 5 digits (0, 1, 2, 3, 4) round down and 5 digits (5, 6, 7, 8, 9) round up. Ask: What is the largest decimal that rounds off to 3, with two decimal digits?
4 The largest decimal (with two decimal digits) that rounds off to 3 is 3.49, because the next number (with two decimal digits) is 3.50 which rounds off to 4, according to the convention. Ask: What is the smallest decimal that rounds off to 5, with two decimal digits? The smallest decimal (with two decimal digits) that rounds off to 5 is 4.50, because 4.49 rounds down to 4, and according to the convention 4.50 round up to 5. Ask: What is the largest decimal (with two decimal digits) that rounds off to the nearest tenth to 7.4? The largest decimal (with two decimal digits) that rounds to 7.4 is 7.44, because the next decimal with two decimal digits is 7.45, which rounds off to 7.50. Ask: What is the smallest decimal (with two decimal digits) that rounds off to the nearest tenth to 9.1? The smallest decimal (with two decimal digits) that rounds off to 9.1 is 9.05. Ask: What does "round off 2.7 to the nearest whole" mean? It is asking if 2.7 is closer to 2 or 3. Ask: Round off 15.81 to the nearest tenth. What do we get? To the nearest tenth, 15.81 rounds off to 15.8. Ask: Round off 15.81 to the nearest whole. What do we get? To the nearest whole, 15.81 rounds off to 16. Ask: Round off 15.81 to the nearest ten (that is asking which is closer, 10 or 20?). What do we get? To the nearest ten, 15.81 rounds off to 20.
5 Say: Round off 15.81 to the nearest hundred. What do we get? To the nearest hundred, 15.81 rounds off to 0. T e ac he r prese nt s M at h game : Wei ghi ng M at t e rs - R o und De c i mal s 10 min Present Matific s episode We ighing M a t t e rs - Ro und De c im a ls to the class, using the projector. This episode allows students to practice the rounding off of decimals in the context of weight measurements. Find the weight of a cubic-cm of a certain material using a balance scale and weights of 1gr, 0.1gr and 0.01gr, and round off the answer as requested. Example : Say: Please read the instructions at the bottom of the screen. Say: First we are being asked how much a cubic cm of chalk weighs. In order to answer this question we need to place the chalk on one side of the scale and then place weights on the other side of
6 the scale until the scale is balanced. Place the chalk on the left side of the scale. Ask: What weight should we place first on the left side the 1g, 0.1g or 0.01g? We should first place the 1g weight in order to estimate whether the chalk weighs more or less than 1g. If we place the 0.1g or the 0.01g first, we might need to add several more weights later on, and the fewer the weights, the easier the problem becomes. Place the 1g weight on the right side of the scale. Ask: What can we tell about the weight of the chalk? How do you know? We can see that the chalk weighs more than 1g since the scale is still tilted to the left. Place another 1g weight on the right side of the scale. Ask: What can we tell about the weight of the chalk now? How do you know? We can see that the chalk weighs more than 2g since the scale is still tilted to the left. Place another 1g weight on the right side of the scale. Ask: What can we tell about the weight of the chalk now? How do you know? We can see that the chalk weighs less than 3g since the scale is now tilted to the right. Remove the 1g weight and place 0.1g weight on the right side of the scale. Ask: What can we tell about the weight of the chalk now? How do you know?
7 We can see that the chalk weighs more than 2.1g since the scale is still tilted to the left. Repeat this until there are 2 weights of 1g and 3 weights of 0.1g on the right side of the scale. Ask: What can we tell about the weight of the chalk now? How do you know? We can see that the chalk weighs exactly 2.3g since the scale is balanced and there are 2 weights of 1g and 3 weights of 0.1g on the right side of the scale. Say: Now we are being asked to round off the answer to the nearest gram. Ask: is 2.3 closer to 2 or 3? 2.3 is closer to 2, therefore 2.3g rounded off to the nearest gram is 2g.
8 St ude nt s prac t i c e M at h game : Wei ghi ng M at t e rs - R o und De c i mal s 12 min Have students play We ighing M a t t e rs - Ro und De c im a ls on their personal devices. Circulate among them answering their questions. Cl ass di sc ussi o n 10 min Discuss any problems the students faced while working individually. Ask the class for responses as to how they dealt with any issues their classmates brought up. Display the following problems. Have students solve the equations, and then round off the solution to the nearest ten, the nearest whole and the nearest tenth: 1. 4.21 + 3.2 = 2. 6.01 + 0.90 = 3. 12.14 + 7.2 = 4. 0.08 + 30.5 = 5. 22 + 1.91 = 6. 0.2 + 2.02 + 0.22 = Have the students work in their notebooks. When the students have finished working, review the solutions. Discuss any questions they may have.
9 1. 4.21 + 3.2 = 7.41 To the nearest ten, 7.41 rounds to 10. To the nearest whole, 7.41 rounds to 7. To the nearest tenth, 7.41 rounds to 7.4. 2. 6.01 + 0.90 = 6.91 To the nearest ten, 6.91 rounds to 10. To the nearest whole, 6.91 rounds to 7. To the nearest tenth, 6.91 rounds to 6.9. 3. 12.14 + 7.2 = 19.34 To the nearest ten, 19.34 rounds to 20. To the nearest whole, 19.34 rounds to 19. To the nearest tenth, 19.34 rounds to 19.3. 4. 0.08 + 30.5 = 30.58 To the nearest ten, 30.58 rounds to 30. To the nearest whole, 30.58 rounds to 31. To the nearest tenth, 30.58 rounds to 30.6. 5. 22 + 1.91 = 23.91 To the nearest ten, 23.91 rounds to 20. To the nearest whole, 23.91 rounds to 24. To the nearest tenth, 23.91 rounds to 23.9. 6. 0.2 + 2.02 + 0.22 = 2.44 To the nearest ten, 2.44 rounds to 0.
10 To the nearest whole, 2.44 rounds to 2. To the nearest tenth, 2.44 rounds to 2.4.