Virginia - Mathematics Standards of Learning (2009): 5.5 a, 6.7 Virginia - Mathematics Standards of Learning (2016): 5.5.a, 5.5.b,

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1 1 U n t er r ich t splan Estimate Division with Decimals Two Decimal Places Altersgruppe: 6t h Grade, 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 5.5 a, 6.7 Virginia - Mathematics Standards of Learning (2016): 5.5.a, 5.5.b, 6.5.c Fairfax County Public Schools Program of Studies: 5.5.a.4, 5.5.a.5, 6.7.a.1, 6.7.a.2 Online-Ressourcen: A B al l park E st i mat e Opening Teacher present s Students pract ice Math Pract ice Closing M at h Obj ect ives E xpe ri e nc e so l vi ng estimation problems. P rac t i c e estimating division with decimals. Learn that there are different degrees of accuracy in estimation. De vel o p the concept of estimation.

2 2 Ope ni ng 8 Display the following problems: = = Ask: Without solving the problem, estimate the value of the expression How did you detere your estimate? A possible response: The value is approximately 6, because 30 is close to, and above, 28.9 and 30 divided by 5 is 6. So, will be just under 6. Ask: What is your estimate for the value of the expression ? How did you arrive at that estimate? A possible response: the value is close to 11, because 77 is close to, and below, and 77 divided by 7 is 11. So, is just over 11. Show the following problem: = Ask: Is the value of the expression larger or smaller than 20? How do you know? The value is smaller than 20, because 180 is close to, and above, and 9 is close to, but less than 9.3 Therefore, is 20. Now, if we increase the dividend and decreased the divisor, we get a larger solution. So, the value is smaller than 20. Emphasize that the quotient is higher if the divisor is smaller, and vice versa. Explain that the closer the estimate is to the exact answer, or the narrower the range,the more accurate the estimate.

3 3 T e ac he r prese nt s M at h game : A B al l park E st i mat e - Di vi si o n: T wo De c i mal P l ac e s 12 Using Preset mode, on the projector, present Matific s episode A Ba allpa arkr k Es t im a t e - Div is io n: T w o De c im a l Pla c e s to the class. This episode allows students to practice the estimation of quotients, using whole numbers and decimals (two decimal places). Estimate each quotient by marking a range on a number line. The narrower the range, the higher your score. Display, for the class, the second question, in the presentation mode. Example : Say: Please read the instructions at the bottom of the screen. Students read the instructions. Ask: Let s estimate the value of the expression How do we know? A possible response: the value of the expression is approximately 7.5, because is approximately the middle between 49 and

4 4 56, and 49 divided by 7 is 7, as well as 56 divided by 7 is 8. So the quotient is approximately the middle of 7 and 8. Ask: Is the value of the expression closer to 7 or 8? Answers may vary, but students should be encouraged to recognize is closer to 56 than to 49, so the value of the expression is closer to 8. Now we mark our estimate on the number line. Example : Show students the third question, in the presentation mode. Example :

5 5 Say: Please read the instructions at the bottom of the screen. Students can read the instruction. Say: Let s estimate the value of the expression A possible response: We will use upper and lower limits. Consider that 6 is close to, and less than, 6.31, and 7 is close to, and greater than, Division by 0.2 is like multiplying by 5, so the lower limit is 5 x 6, which is 30, and the upper limit is 5 x 7, which is 35. Therefore, the value of the expression is between 30 and 35. Ask: Is the value of the expression closer to 30 or to 35? Answers may vary, but students should be encouraged to recognize that 6.31 is closer to 6 than to 7, so the value of the expression is closer to 30.

6 6 St ude nt s prac t i c e M at h game : A B al l park E st i mat e - Di vi si o n: T wo De c i mal P l ac e s 12 Have students play A Ba llpa rk Es t im a t e - Div is io n: T w o De c im a l Pla c e s on their personal devices. Circulate answering questions. Ask students, especially the stronger ones, not to settle for less than excellent accuracy. M at h P rac t i c e : E st i mat i ng Di vi si o n Wo rkshe e t 10 Discuss any challenges students faced while working individually. Ask the class for responses relating to how they dealt with common issues encountered by their classmates. Display the following problems: = = = = Have students work in pairs. Ask them to arrange the quotients from smallest to greatest. After pairs have worked for a few utes, provide time to share. Ask: What is your estimate for every quotient? How did you detere your estimate? The value of is between 24 and 25,because 75 is close to,

7 7 but above, 74.25, and 75 3 is 25. Therefore, 72 is close to, and below, 74.25, so 72 3 is 24. The value of is just under 20, and 1.5 is close to, and below, 1.6, therefore, is 20. So, if we increase the divisor we decreased the quotient and 2 is above 1.6, we detere 30 2 is 15. So, the range is from 15 to 20. The value of is just over 34, because 8.5 is close to, and below, Division by a quarter is like multiplying by 4, with 4 times 8.5 equalling 34. The value of is just over 10,since 150 is close to, and below, Consider is 10, and 165 is above , therefore is 11. So, the range is between 10 and 11. The correct sequence, from smallest to largest, is: Cl o si ng 3 Say: State each step needed to decide which value is lower: or is bigger than 9.1 and 3.1 is bigger than 3, therefore is lower than , because the quotient is higher when the divisor is smaller, and the quotient is higher when the dividend is higher.