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F ind ing Pe rime t e r o f Po l y g o ns Возрастная группа: 2nd Gr ade Mathematics Florida Standards (MAFS): 2.M D.2.5 Riverside USD Scope and Sequence: 2.M D.5 [2.4 ] , 2.M D.5 [2.5 ] , 2.M D.5 [2.7 ] , 2.M D.5 [2.9] Common Core: 2.M D.B .5 Nebraska Mathematics Standards: M A .2.3 .3 .h Georgia Standards of Excellence: M GS E 2.M D.5 Hampton City Schools Math Power Standards: 2.21S b, 2.8S a, 2.8S b Онлайн ресурсы: A l l t he W ay A r o und

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M at h Obj e c t i v e s E x pe r i e nc e finding perimeter of polygons using specific or arbitrary units P r ac t i c e measuring side lengths using measuring tools L e ar n to rotate polygons in order to measure side lengths De v e l o p strategies for finding perimeter, such as using symmetry

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Ope ni ng | 15 мин

Draw or project two or three polygons with all sides lengths provided (including units such as centimeters or inches). For the purposes of this segment of the lesson, it is not necessary for those side lengths to be accurate, but in later segments it will be necessary. A sk your students, “How far does a bug have to walk if it wants to along the outside of this shape?” As good practice, consider calling the shape out by name. Consider drawing a point at one of the vertices to represent the starting (and ending) point for the bug. Tracing the path around the shape may be a useful tool in helping your students to conceptualize perimeter. Some of your students may have answers rather quickly. Field these, making sure to ask them to explain why. Ultimately, the goal is to arrive at the point where your students understand perimeter as the total distance around an object, meaning that the perimeter is the sum of all of the side lengths for a polygon. As such, the final answer should include appropriate units. Thus, be sure to connect the distance the bug must walk with the term “perimeter.” Once this concept seems fairly clear to your students, move on. Draw or project a polygon with all but one side lengths already provided, as shown below. It is important that these side lengths are reasonably accurate, as this segment of the lesson will require some measuring.

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Ask the students once again, “How far does a bug have to walk if it wants to along the outside of this shape?” Your students should notice that one side length is missing, so this question cannot be answered. A sk the class, “How can we find the missing side length?” The simple (and correct) answer is to measure it! Place a ruler (or other appropriate measuring tool) on the projector or board, lining it up with the side without a side length. A sk the class, “What is the missing side length?” Once the correct length is found, return to the original question of finding perimeter. Again, the students should simply add the side lengths (and include units). As a challenge, consider providing polygons with more than one missing side length, and polygons where some of the missing side lengths can be determined based on traits like symmetry. Continue until your students seem largely comfortable with the general concepts of finding perimeter and measuring side lengths.

T e ac he r pr e se nt s M at h game : A l l t he W ay A r o und M e asur e P e r i me t e r s | 10 мин

Present Matific ’s episode A l l t he W ay A r o und - M e asur e P e r i me t e r s to the class, using the projector. The goal of this Copyright 2015 www.matific.com

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episode is to find the perimeter of various polygons in generic units. E x a m p le :

Each question will provide one shape and ask for the perimeter of that shape (given by name). The grid behind the shape acts as the measuring tool, with 1 unit denoted in the bottom left-center of the grid. The shape can be dragged to different places, which often makes measuring side lengths easier. Suggest to your students that they should write down the side lengths as they are measured, instead of trying to memorize them.

Some side lengths may not appear to be exactly a whole number of units. Clicking on the shape will bring up arrows surrounding the shape, as shown above. These arrows signify that the shape can be rotated clockwise or counterclockwise. Rotating the shape is another way of lining up the sides, in order to measure them more accurately. To rotate, simply click and drag the shape (with the arrows showing). In addition to finding perimeter, use this as a chance to check in Copyright 2015 www.matific.com

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with your students, asking why the shape is called by that name. For example, the scenario below calls out the red shape as a triangle. Clicking on the name on the polygon (in blue) will cause a small pop-up to show several other shapes by the same name. E x a m p le :

Encourage unique strategies, such as using symmetry to find side lengths. For example, the tringle shown above is an isosceles triangle. In its current orientation, this may not be an obvious fact, but another orientation may make this clearer. Further, this allows your students to measure one of the congruent legs and conclude that the other has the same length. Once all of the side lengths have been measured, ask the students what the perimeter is. At this point, they should remember to add all of the individual side lengths. In the example above, the side lengths are 3, 2, and 3, so the sum is 8. Note that the perimeter is 8 uni t s , which your students may forget. Use this as an opportunity to explain that the term “units” is general, but that you could be measuring in inches, Copyright 2015 www.matific.com

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meters, etc. After arriving at the correct sum (or after three incorrect attempts), the side lengths are shown, along with the sum those side lengths (the perimeter), as shown below. E x a m p le :

With the sum shown, it may be easier to find any errors the students had in finding the perimeter. For example, a common error would be omitting a side length from the sum. Comparing the student’s sum to the sum shown in the episode will help identify this error quickly.

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S t ude nt s pr ac t i c e M at h game : A l l t he W ay A r o und M e asur e P e r i me t e r s | 8 мин

Have the students play A l l t he W ay A r o und - M e asur e P e r i me t e r s on their personal devices. Circulate, answering questions. Continue to promote more efficient and creative strategies for finding perimeter, such as using symmetry. Be aware of the potential confusion between finding area and finding perimeter. Additionally, try to solidify the idea of using the general measurement of “units,” as this is occasionally difficult for students to conceptualize.

C l ass di sc ussi o n | 10 мин

Present several polygons with missing sides but known perimeters. Discuss whether or not the missing side length(s) can be found with the information given. i.e., can the side length(s) be found without measuring? Ultimately, the goal is the same as before: connecting individual side lengths with the overall perimeter. This time, however, your students will need to set up an equation with an unknown quantity. E x a m p le :

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Suppose, in the example above, you tell the class that the perimeter is 26cm. The class must arrive at the equation: 5 + 6 + 5 + _ _ = 26

For many of your students, this may not be obvious at first. Consider referencing the bug once more, asking, “How can we determine how far the bug must walk to go all the way around this polygon?” This answer should bring them back to summing the side lengths (left side of the equation). Remind them that walking all the way around is the same as walking the perimeter, which was given as 26cm (right side of the equation). This equation can be solved in several ways, so try to let your students lead the process of finding the missing value. Note: The missing side length is 10cm. Be sure to have your students include the units! Continue to other examples, including those with more than one missing side length (which can be found via symmetry or congruence, perhaps).

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