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Lesson Plan Title: Computational EstimationTopic to Teach: Variation of Estimation MethodsCurriculum Standards Addressed: Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate sums. (Page 43, 3.5)Lesson Goals and Learning objectives: The students will be able to estimate the sum of a problem through one of various methods: Front-end with adjustment, Grouping to nice numbers, Clustering, Rounding and Using the Range. Students’ Needs: This is a third grade class where all the students know how to add, subtract, multiply and divide simple numbers. The first two sections of this chapter, the different types of algorithms used for any of these problems, is a review for them. This section on estimation is completely new however. They have learned how to calculate the exact answers to addition, subtraction, multiplication and division problems, but this section will teach them simpler and quicker ways to reach an answer, through estimation.Materials: Jar of gumballs, pennies, marbles, etc.White-board/smart board for teacherWhite board markersWorksheets (for stations)Lesson:Before Phase: For example, to get them to understand what estimation actually is, I will hold up a jar of marbles and ask the class to look at it and guess how many marbles are in the jar. This will teach the students that estimation doesn’t give exact numbers; it gives an answer somewhere near the exact number. I will explain that estimated numbers are rounded numbers. I will also explain that estimating numbers is easier than finding the exact number. By informing this class that estimation can be fun and sometimes easier, I’m hoping this will catch their attention for the lesson I’m about to teach. I will then go through each method and explain step by step on the board for the whole class. I will begin with the first method: Front-end with adjustment. In this method, it is important that they understand the concept of adding the first digit of each number, also known as the front-end digit. For example, in the problem 423 338 + 561_ the front-end digits would be 4, 3 and 5 (highlighted in yellow). After adding 4+3+5 we get 12. Because of the place value of these numbers (hundreds place) 12 is actually turned into 1200. The next step is to round the numbers to numbers that are easy to add. We would round the remaining 23 (highlighted in green) to 20, and the 38 and 61 (highlighted in blue) to approximately 100. After adding these sums, 1200 + 20 +100 the adjusted estimate is equal to 1320. After completing this first lesson, I will move onto the second estimation method: Grouping to nice numbers. The strategy used to obtain the adjustment in this method is to “nicely” fit together numbers in groups. For example: 23 39 32 64+49_ In this problem, I would show that 23+32+49 (highlighted in yellow) around about 100, by just looking at them. It’s easier to determine this if you look at 23 being rounded to 20, 32 being rounded to 30 and 49 being rounded to 50. Therefore, adding 50+30+20 we get 100. The same process is used to add 39 (rounded to 40) and 64 (rounded to 60) (these numbers are highlighted in green). To get a final estimation, we add 100+100 and get a sum of 200. The third method is referred to as clustering. In this method I will teach the students the concept of averaging numbers into a common value. In the following example, the numbers seem to cluster around 6000. 6200 5842 6512 5512+6319_ The “average” of all these numbers estimates to be 6000. Then I will explain that the 6000 must be multiplied by the number of values, which in this case is 5. 6000 x 5 =30,000. The fourth method I will explain to them, called rounding, makes the numbers a lot easier to handle. 4724 5000 (Round 4724 to 5000)+3192 +3000 (Round 3192 to 3000) 8000 (Add the rounded numbers)This method can also be used for subtraction. The only difference is subtracting the rounded numbers, rather than adding them. Rounding is a very simple, easy method of estimating a sum of a problem. The fifth and final method I will teach in this lesson plan is known as Using the range. It is important for the class to understand what range an answer falls. The range can be determined by finding a low and high estimate and reporting that the answer falls in that interval. An example of this method follows:ProblemLow EstimateHigh Estimate 378 300 400+524 +500 +600 800 1000From this example, we can conclude that the range is from 800 to 1000. They will copy these notes in their notebooks and it will give the students the basic knowledge on how to estimate large numbers.During Phase: Before I break the class into groups, I will be sure to answer any questions the students may have. I’m hoping that before they break into groups that they have at least some understanding of the estimation methods. I’m not looking for the students to have all five methods memorized already; I’m looking to see that they recognize what to do when they see problems on the worksheets. Then I will break the class into groups and assign each group a different method to practice. I’m hoping to circulate the room as the groups try and figure out each method together and practice problems at each station. My goal is for them to use their notes, and each other, to try their best at completing the four problem worksheets. If one student doesn’t understand, I’m looking to see if the groups can work together to help that individual figure it out. After groups feel pretty confident at their first station, they will move onto the next and practice that. These five different stations include: 1.) Front-end with adjustment 2.) Grouping to nice numbers 3.) Clustering 4.)Rounding and 5.) Using the range. Each station will have a worksheet with problems for them to practice the method over and over (together). Worksheets will contain addition and subtraction problems, seeing as how the methods are the same. I’m allowing more time for this lesson than usual math lessons because I know this may be more advanced than their used to. I think if I give them enough time they will be able to complete the work appropriately. After Phase: To wrap up the lesson I will bring the class back together and ask them their opinions on which method they prefer, which one was easy or which one was hard. I will make a discussion out of the various five methods they just learned. I will conclude by asking if any of them have questions of any parts they don’t understand so I can clear their confusion. If any students are confused, I will try having the other classmates teach the method on the board. Often times other students learn better when fellow class members explain it to them. Like we do in math today, groups will have the opportunity to go up to the white board and teach their preferred method to any students who are confused. Assessment:Observe: I’m looking to see that they understand there are multiple ways to estimate the sum of large numbers and that they don’t need to memorize all of them. It’s important that they choose their preferred method because it’ll be easier to remember.Ask: I will ask them if they have any questions for me, and if they do I will be sure to answer them at my best ability. I will be sure to reinforce the fact that estimation can be used in other subject areas other than math.Differentiated Instruction: In order to make sure all students understand the concept of estimation I will teach all five methods from section 3-5. For example, I will teach the Front-end adjustment, Grouping to nice numbers, Clustering, Rounding and Using the range. This way it gives everybody a preferable method of learning. It offers a variety of ways for students to pick their favorite. Some students may catch on to the rounding method immediately, while others prefer the grouping or clustering methods. It all depends on their preference. Possible connections to other subjects: Estimation plays a very important role in not only math but also subjects like science. Estimation comes in handy for measuring liquids or materials in any type of science lab. The same goes for history. Estimation can also be used when describing a certain time period. For example, remembering the exact dates for every war or battle that has taken place is nearly impossible. It is possible however to estimate the time that an important event took place. Rather than knowing the exact year World War II took place, you can refer to it as taking place in the late 1930’s and early 1940’s. (Worksheets follow below)Worksheets:METHOD 1: Front-end adjustmentComplete the following problems, together as a group:3.) 100 381 +741756 812 +3284.) 627 227 +327941 111 +423METHOD 2: Grouping to nice numbersComplete the following problems, together as a group:2.) 45 52 87 +2639 23 44 +894.) 82 25 74 +31 12 62 34 87 +09METHOD 3: ClusteringComplete the following problems, together as a group:2.3.) 8112 J 7599 8487 +7814 2698 3255 2501+34602.4.) 6352 5514 5889 +6221 1463 981 1002 +955METHOD 4: RoundingComplete the worksheet, together as a group:3.) 8862 3200 9145 +5499 4569+78413.) 56 1543 6578 +9999 8126 6664+2347METHOD 5: Using the RangeComplete the worksheet, together as a group: 548+74314696352 +657 56324+8541230024 7859 4136 +97856 ................
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