1 План урока Estimating Quotients (2-Digit Divisor) Возрастная группа: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 3.4, 4.4 d, 5.5 a Virginia - Mathematics Standards of Learning (2016): 4.2.c, 4.4.a, 4.4.d Fairfax County Public Schools Program of Studies: 3.4.a.1, 4.4.d.3, 5.5.a.4 Онлайн ресурсы: So me whe re Al o ng t he Li ne Opening Teacher present s Students pract ice Math Pract ice Closing 8 1 0 1 2 1 4 3 M at h Obj ect ives E xpe ri e nc e using a number line to indicate an estimate P rac t i c e identifying multiples of the divisor Learn to estimate quotients with a 2-digit divisor De vel o p number sense
2 Ope ni ng 8 Ask the students to answer the following question in their notebooks: What is the difference between e s t im a t ing and ro unding? When the students are done writing, share. Say: Please read what you have written about the difference between estimating and rounding. To estimate, we make a rough calculation. To round, we take a number that is definite and make it less exact. For example, we could estimate that a person is about feet tall. Or we could measure someone s height, find that he is 5 feet 10 inches tall and round up to 6 feet. When doing an estimation problem in math class, we often round first and then use the rounded numbers to find an estimated answer. For example, if we wanted to estimate the sum of 138 and 577, we might round 138 to 100 and 577 to 600, and then add 100 to 600 to find the estimate of 700. T e ac he r prese nt s M at h game : So me whe re Al o ng t he Li ne - E st i mat e Di vi si o n: 2- Di gi t Di vi so r 10 Using Presentation Mode, present Matific s episode So me whe rer Al o ng t he Li ne - E st i mat e Di vi si o n: 2- Di gi t Di vi so r to the class, using the projector. The goal of the episode is to estimate the quotient when a number is divided by a 2-digit number. Example :
3 Say: Please read the instructions. The instructions say, Estimate the value of the expression 166 divided by 16 and mark your estimate on the number line. Ask: How can we determine a good estimate? Responses may vary. A possible response: We know that 166 is close to 160, and 160 is 10 times 16. Ask: Will the q uo t i e nt of the original problem be larger or smaller than 10? How do you know? The quotient will be larger because 166 is larger than 160. Ask: How much larger than 10 will the answer be? Will it be larger than 20? How do you know? No, it will be a little over 10. One hundred sixty-six is a little over 160, so the quotient will be a little over 10. Ask a student to come to the front to highlight the portion of the number line that indicates the class s estimate. Then click. If the estimate is reasonable, the episode will give you a score. Narrow accurate estimates produce the highest scores. Click on the to proceed. If the estimate is unreasonable, the instructions will wiggle and the episode will present a rounded expression as a hint. If the estimate is too imprecise, the instructions will wiggle and the episode
4 will state, Range is too wide. The episode will present a total of three problems. St ude nt s prac t i c e M at h game : So me whe re Al o ng t he Li ne - E st i mat e Di vi si o n: 2- Di gi t Di vi so r 12 Have the students play So me whe re Al o ng t he Li ne - E st i mat e Di vi si o n: 2- Di gi t Di vi so r on their personal devices. Circulate, answering questions as necessary. M at h P rac t i c e : E st i mat i ng Quo t i e nt s Wo rkshe e t 14 Before class begins, prepare three sets of the following index cards: Divide the class into three groups. Within each group, hand each student one index card. Ask the students to estimate the quotient of the expression on their cards and then line up in their group in order from least to greatest. Once the three groups have finished, have them check for accuracy by comparing answers. The index cards should be in the same order in each group. If the index cards are not in the same order, lead a discussion where the students defend their estimates.
5 Cl o si ng 3 Say: Estimate the quotient of 325 divided by 24. How did you find your estimate? Responses will vary. A possible response: The quotient is around 13. We can round 24 up to 25 and then divide 325 by 25 to get 13. Ask: Is the actual answer when we divide 325 by 24 larger or smaller than 13? How do you know? The actual answer is larger. Twenty-five fits inside 325 13 times. Since 24 is smaller, it will fit inside 325 more times. So the quotient is larger than 13. Say: In this problem, we rounded the di vi so r to find an estimate. State an example of a division problem with a 2-digit divisor where it might make more sense to round the di vi de nd to find an estimate. Responses will vary. A possible response: In the problem 488 divided by 24, it makes sense to round 488 to 480, and then divide 480 by 24, to get an estimate of 20.