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Co mp aring Pe rime t e rs Возрастная группа: 2nd Gr ade , 3 r d Gr ade Texas - TEKS: G3 .7 .GM .B , G4 .5 .A R .C Mathematics Florida Standards (MAFS): 2.M D.1.4 , 2.M D.2.5 , 3 .M D.4 .8, 3 .OA .4 .8 Riverside USD Scope and Sequence: 2.M D.4 [2.3 ] , 2.M D.5 [2.4 ] , 2.M D.5 [2.5 ] , 2.M D.5 [2.7 ] , 2.M D.5 [2.9] , 3 .M D.8 [3 .4 ] , 3 .M D.8 [3 .9] , 3 .OA .8 [3 .12] Oklahoma Academic Standards Mathematics: 2.GM .2.2, 3 .A .2.1, 3 .GM .2.1, 3 .N .2.8 Common Core: 2.M D.A .4 , 2.M D.B .5 , 3 .M D.D.8, 3 .OA .D.8 Virginia: 3 .10a, 3 .9d Alaska: 3 .M D.10, 3 .M D.D, 4 .M D.3 Fairfax County Public Schools Program of Studies: 3 .10.a.1, 3 .9.d.1, 3 .9.d.2 Nebraska Mathematics Standards: M A .2.3 .3 .d, M A .2.3 .3 .e , M A .2.3 .3 .h, M A .3 .2.2.b, M A .3 .2.3 .a, M A .3 .3 .3 .a, M A .3 .3 .3 .h South Carolina: 2.M DA .4 , 3 .A T O.8, 3 .M DA .6 Indiana: 3 .M .7 , 4 .M .4 Georgia Standards of Excellence: M GS E 2.M D.4 , M GS E 2.M D.5 , M GS E 3 .M D.8, M GS E 3 .OA .8 Minnesota: 2.3 .2.1, 2.3 .2.2, 3 .3 .2.2, 3 .3 .2.3 Hampton City Schools Math Power Standards: 2.21S b, 2.8S a, 2.8S b, 3 .4 S f , 3 .4 S g Онлайн ресурсы: A l l t he W ay A r o und

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ЦЕ Л И : P r ac t i c e finding perimeter using arbitrary units L e ar n to compare the perimeters of two polygons De v e l o p a more conceptual understanding of perimeter, including what it means for one polygon to have a larger perimeter than another

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Ope ni ng | 10 мин

Review perimeter by drawing or projecting polygons with all side lengths provided, then asking the students to find the perimeter of the shapes shown. It is important to discuss the different ways that students arrived at their answers, in order to develop and strengthen strategies. Additionally, ask the students the names of the polygons shown (pentagon, rectangle, etc.). Then, provide pairs of polygons with side lengths. Ask the students, “Which shape has the longer perimeter?” Then ask, “How much longer? And how do you know?” Some students may have guessed based on the size of the shapes or the numbers that were used for side lengths. The most important point is that they can verify their hunches or guesses using the values provided. Be sure to remind them that you can first find the individual perimeters, then compare those whole number values. Further strategies can be discussed during the episode presentation or class discussion. Students may also have questions about other strategies while working on their own devices.

T e ac he r pr e se nt s A l l t he W ay A r o und: C o mpar e P e r i me t e r s | 15 мин

Present Matific ’s episode A l l t he W ay A r o und - C o mpar e P e r i me t e r s to the class, using the projector. The goal of this episode is to compare the perimeters of various polygons, with the added element of identifying the correct polygons from the three given. Copyright 2015 www.matiﬁc.com

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This episode alternates between finding the perimeter of just one polygon and comparing the perimeters of two polygons. E x a m p le :

Have the students identify which of the three shapes is named in the question. If they do not come to a consensus, click on the name on the polygon (in blue). A small pop-up will provide several other shapes by the same name. E x a m p le :

Once the correct shape is chosen, ask the students what the perimeter is, in general. Then, ask the students how to find the perimeter of the chosen shape. Show the students that you can move and rotate the shape. Move the shape as needed in order to measure Copyright 2015 www.matiﬁc.com

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the side lengths in arbitrary “units.”

Some side lengths may not appear to be exactly a whole number of units. E x a m p le :

As the sides are measured, have the students keep track of the individual lengths. Finally, ask the class how to find the perimeter of the figure. Other questions will involve a comparison between the perimeters of two of the shapes shown. E x a m p le :

The individual perimeters can be found as in the previous question. However, the key will be to ask, “How can we compare these perimeters?” Be sure to note the order of comparison, as well as relative vocabulary, such as “longer.” Note that it is possible for both shapes to have the same Copyright 2015 www.matiﬁc.com

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perimeter.

The episode will present a total of six questions.

S t ude nt s pl ay A l l t he W ay A r o und: C o mpar e P e r i me t e r s | 12 мин

Have the students play A l l t he W ay A r o und - C o mpar 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 and for comparing the perimeters of polygons. Be aware of the order of subtraction, reminding students that it would not make sense to say one perimeter is “negative two units longer” than another perimeter, if such phrasing is suggested. Be aware of the potential confusion between finding area and finding perimeter.

C l ass di sc ussi o n | 10 мин

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Ask the students if they discovered or developed any notable strategies for finding or comparing perimeters. Walk through some examples of any strategies that are particularly useful or which did not get covered already. Present several polygons with several sides of the same length, then ask the class to compare the perimeters. E x a m p le :

Notice that both polygons have side lengths of 4 and 6.

It is likely that many students will treat such an example no differently than the others, which is obviously still correct, but work to hint at some powerful strategies of comparison, such as equal side lengths “canceling” each other out in the final comparison. Be sure the students understand that this is not a trick, but rather the result of summing the same values. For an extra challenge, you can ask the students to make the same type of comparisons between shapes that do not have common side lengths. Again, it is imperative that the students have a firm sense of why this works. Work on some comparative perimeter examples that involve reallife scenarios. For example, draw two polygons with some (or all) side lengths given, including units. Propose to the class a scenario, such as: Suppose we are building a short fence around two gardens. How Copyright 2015 www.matiﬁc.com

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much more fencing is needed for the second garden? E x a m p le :

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