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There is a popular story that Gauss, Mathematician extraordinaire, had a lazy teacher. So - call educator wanted to keep kids busy so they could take a nap; he asked class to add numbers 1 to 100. Gauss approaches with his answer: 5050. So soon? The teacher suspected cheat, but no. Manual addition was for suckers, and Gauss found a formula to sidestep the problem: Let share a few explanations of this result and really understand it intuitively. For these examples, well add 1 to 10, and then see how it applies for 1 to 100.

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The purpose of this task is to show students that rectangle can be partitioned into unit squares, and that there are a number of reasonable ways to count resulting squares. The third part encourages students to count by fives, as called for by 2. Nbt. 2, and make connection between equal - size groupsA and area of rectangle representations for multiplication, which will be developed in third grade. Counting by numbers other than five is not called for by standards, but would be a nice additional outcome. Inviting students to make their own rectangle with a grid of size of their choosing. To learn about world cultures as well as mathematics, one can take the opportunity to explore game boards with this kind of shape. In particular, Snakes and Ladders is a game which has been played around the world. See Wikipedia page on Snakes and Ladders for more information. Students could make their own game with different - sized rectangular boards and different ways to navigate them, reinforcing the fact that there are different ways to count and all ways give the same answer. Playing such games can develop skills in estimation, relationship between multiplication and division, and probability, setting the ground for a wide range of later work. Investigating which numbers can be represented as total number of squares in some grid. Even at this grade level, some students may take interest in numbers which can only be made by grid with side length One. Students need to experience partitioning rectangles themselves to understand the area. If students have not yet done this, then they should partitioningA themselves. However, if students are already proficient at partitioningA and understand that squares taken together constitute larger rectangle, then they can start with the pre - partitionedA rectangle.

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Mode is the most frequently - occurring value in the set of values. Mode is interesting as it can be used for any type of data, not just numbers. In this example, assume that you have bought a pack of 100 balloons, pack is made up of 5 different colours,. You count each colour and find that you have: 18 Red, 12 Blue, 24 Orange, 25 Purple, 21 Green Mode of our sample of balloons isA Purple as there are more Purple balloons than any other colour balloon. To find the number of days in each month: 7 months have 31 days, 4 months have a total of 30 days and only 1 month has a total of 28 days. 1 33445, for example, are the two most frequently occurring numbers. This is known as bimodal set. Data sets with more than two modes are referred to as multi - modal data sets. If the data set contains only unique numbers, then calculating mode is more problematic. It is usually perfectly acceptable to say there is no mode, but if a mode has to be found, then the usual way is to create number ranges and then count one with the most points in it. For example, from a set of data showing the speed of passing cars, we see that out of 10 cars record speeds are: 40 34 42 38 41 50 48 49 33 47. These numbers are all unique, there is no mode. In order to find Mode we build categories on an even scale: 30 - 32A | 33 - 35 | 36 - 38A | 39 - 41A | 42 - 44 | 45 - 47A | 48 - 50 Then we work out how many values fall into each category, how many times number between 30 and 32 occurs, etc. 30 - 32 = 0 33 - 35 = 2 36 - 38 = 1 39 - 41 = 2 42 - 44 = 1 45 - 47 = 1 48 - 50 = 3 categorys with most values is 48 - 50 with 3 values. We can take mid value of category to estimate Mode at 49. This method of calculating Mode is not ideal because mode may change depending on categories you define.

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1 adding up numbers quickly can be useful for estimation. Notice that the formula expands to this: let's say you want to add numbers from 1 to 1000: suppose you get 1 additional visitor to your site each day - how many total visitors will you have after 1000 days? Since thousand square = 1 million, we get million / 2 + 1000 / 2 = 500 500. 2 this concept of adding numbers 1 to N shows up in other places, like figuring out the probability of birthday paradox. Having firm grasp of this formula will help your understanding in many areas. 3 Most importantly, this example shows there are many ways to understand formula. Maybe you like pairing method, maybe you prefer rectangle technique, or maybe there is another explanation that works for you. Dont give up when you dont understand try to find another explanation that work. Happy math. By way, there are more details about the history of this story and techniques Gauss may have used.

First, you need to create some range names, and then apply array formula to find cells that sum to target value, Please do with following step by step: 1. Select number list and define this list range Name - Range1 into the Name Box, and press the Enter key To finish range Name define, see screenshot: 2. After defining range name for number list, then you need to create two further range names in the Name Manager Box, Please click Formulas > Name Manager, in Name Manager dialog Box, click New button, see screenshots: 3. In pop out New Name dialog, Enter Name List1 into Name field, and type this formula = rowindirect, and press Shift + Ctrl + Enter keys together, then drag fill handle down To cell B8, last Number of list, and you can see numbers whose total amount is 480 are mark as X in column B, see screenshot: IF you are confuse with above method, Excel contains Solver Add - in feature, by using this Add - in, you can also identify numbers which total amount equals give Value. 1. First, you need to activate this Solver Add - in, Please Go To File > Options, in Excel Options dialog Box, click Add - Ins from leave pane, and then click Solver Add - in from Inactive Application Add - Ins section, see screenshot: 2. Then click the Go button to Enter Add - Ins dialog, check the Solver Add - in option, and click OK to install this Add - in successfully. 3. After activating Solver Add - in, then you need to enter this formula into cell B9: = SUMPRODUCT, and press the Enter key, see screenshot: 4. Then click Data > Solver To Go To Solver Parameter dialog Box, In dialog, please do the following operations: click the button to select cell B10 where your formula is from the Set Objective section; then in the To section, select Value Of, and enter your target Value 480 as you need; under by Changing Variable Cells section, please click button To select cell range B2: B9 where will mark your corresponding numbers. 5. And then click the Add button To Go To Add Constraint dialog Box, click button to select cell range B2: B9, and select bin from the drop down list, see screenshot: 6. Click OK to go back to Solver Parameter dialog, then click the Solve button, Some minutes later, Solver Results dialog Box pops out, and you can see a combination of cells which equal give Sum 480 are mark as 1. In Solver Results dialog, please select Keep Solver Solution option, and click OK to exit dialog. See screenshot: first two methods are all complex for most of our Excel users, Here, I can create VBA code to solve this job quickly and easily. To get the correct result, you must sort the number list into descending order first. And then do the following steps: 2.

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