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session 2.5ASame Area, DifferentPerimeter; Same Perimeter,Different AreaMath Focus PointsVocabularyUsing tiles to find the area and perimeter of a rectanglerowcolumnsquare inchesUnderstanding that rectangles can have the same perimeterand different areas or the same area and different perimetersToday’s PlanMaterialsActivityUsing Tiles to Find theArea of Rectangles Student Activity Book, pp. 33A–33B or30 Min individuals ClassDiscussionFinding the Areaof Rectangles15 MinClassActivityFinding the Perimeterof Rectangles C14–C15, What’s the Area? Make copies.(as needed)C13, Rectangle Make 1 copy.Color tiles Students’ completed copies of Student ActivityBook, p. 33B or C15 (from Activity 1) Color tiles Student Activity Book, p. 33C or15 Min individualsSESSION FOLLOW-UPC16, Find the Area Make copies. (as needed) Student Activity Book, pp. 33D–33E orDaily PracticeC17–C18, Area and PerimeterMake copies. (as needed)Ten-Minute MathPracticing Place Value Say “seven hundred seventy-four” and ask students to writethe number. Make sure that all students can read, write, and say this number correctly.Ask students to write this number in expanded form. Then ask students to solve theseproblems mentally, if possible: What is 774 20? 774 – 50? 774 100? 774 200? 774 – 300?Write each answer on the board. Have students compare each sum or difference with774. Ask students: Which places have the same digits? Which do not? Why?If time remains, pose additional similar problems using 747.Session 2.5A Same Area, Different Perimeter; Same Perimeter, Different Area CC23INV12 TE03 U04 S2.5A.indd 236/9/11 5:54 PM

1 Activity2 Discussion3 Activity4 Session Follow-UpTeaching Note1Terminology Use this opportunity tointroduce and review the language forrows and columns, which students revisitin the multiplication and division unit asthey work with rectangular arrays.Multiplying to Find the Area Anotherway to find the area is to multiply thedimensions of the rectangle. Becausemultiplication and division are notcovered until Unit 5, most students willapproach this problem as a counting oraddition problem. Unit 5 helps studentsdevelop an understanding of thisimportant idea.NameUsing Tiles to Find theArea of Rectangles30 MinIndividualsclassYou’ve been finding the area of different shapes, and makingshapes with a particular area, using paper squares and triangles.Today we’re going to work with another unit—color tiles.Math Note2Ac tivit yShow students a color tile and explain that some people call theminch tiles because each side is one inch long. Show students the5-inch 6-inch rectangle on C13.Look at this rectangle. Turn and talk to a partner. How could youuse color tiles to find the area of this rectangle?Once students have had a chance to talk, introduce the idea ofusing tiles to find the area of the rectangle.One way to find the area is to put as many tiles as will fit in therectangle, and then count them. When using this method, therecan’t be any white space inside the rectangle, and none of the tilescan stick out from the rectangle. Let’s try it. I’m going to workrow by row. 1DatePerimeter, Angles, and AreaRectangleOnce you’ve filled the rectangle with color tiles, ask students tohelp you determine the area. Try each strategy that studentssuggest. Strategies might include counting each tile, adding thenumber of tiles in each row or column, or counting by the numberof tiles in each row or column. 2 Be sure to discuss anddemonstrate how to label your answer as square units orsquare inches.Unit 4 Session 2.5AC13 Pearson Education, Inc., or its affiliates. All Rights Reserved. 3 Resource Masters, C13INV12 BLM03 U4.indd 135/19/11 1:51 PMStudents complete Student Activity Book pages 33A and 33B orC14 and C15.Ongoing Assessment: Observing Students at WorkStudents use color tiles to find the area of rectangles. Can students use tiles to cover the area of the rectangle?Do they completely fill the rectangle, without straying outsidethe edges of the rectangle? How do students determine the area? Do they count the tilesindividually? Do they add the number of tiles in each row orcolumn? Do they count by the number of tiles in each rowor column? Do students record the area of each rectangle correctly?CC24Investigation 2INV12 TE03 U04 S2.5A.indd 24Understanding and Finding Area6/14/11 1:31 PM

1 Activity2 Discussion3 ActivityName4 Session Follow-UpDatePerimeter, Angles, and Areadifferentiation: Supporting the Range of LearnersWhat’s the Area? (page 1 of 2)Use color tiles to find the area of the rectangles.Challenge students who accurately complete theactivity to use the color tiles to make shapes with given areas. Forexample, ask students to make rectangles with areas of 14 squareinches, 9 square inches, and 20 square inches.1. Area:square inches2. Area:square inches3. Area:square inches Pearson Education 3Work with students who are counting the tilesindividually to help them find more efficient strategies for findingthe total number of tiles. For example, point out to the studentthat in the 4 3 rectangle, each row has 3 tiles in it. Then countby 3s while pointing at each column to show that the area is12 square inches.Session 2.5AUnit 433A Student Activity Book, Unit 4, p. 33A;Resource Masters, C14INV12 SE03 U4.indd 1DiscussionFinding the Area of Rectangles5/19/11 3:07 PM15 Min classNameDatePerimeter, Angles, and AreaWhat’s the Area? (page 2 of 2)Math Focus Points for DiscussionUse color tiles to find the area of the rectangles.4. Area:square inches5. Area:square inchesUsing tiles to find the area and perimeter of a rectangleGather students to discuss the problems on Student Activity Book,page 33B or C15. Have a copy of the page with the tiles arrangedon it for display during the discussion.What did you find for the area of the first rectangle? Doeseveryone agree? What about the second rectangle?We’ve talked before about shapes that had the same area, butlooked different. It seems like we’ve found another example ofthat. The area of both of these shapes is 16 square inches. Pearson Education 3Establish that both rectangles have an area of 16 square inches.33BUnit 4Session 2.5A Student Activity Book, Unit 4, p. 33B;Resource Masters, C15INV12 SE03 U4.indd 25/19/11 3:08 PMWhat if we measured the perimeter, the distance around the edge,of these shapes? Talk to a partner and make a prediction aboutthe perimeter of these two shapes. Do you think they are thesame? Or do you think that one has a greater perimeter thanthe other?Session 2.5AINV12 TE03 U04 S2.5A.indd 25Same Area, Different Perimeter; Same Perimeter, Different Area CC256/9/11 5:59 PM

1 Activity2 DiscussionName3 Activity4 Session Follow-UpGive students time to talk, and then collect predictions.DatePerimeter, Angles, and AreaFind the AreaStudents might say:Each rectangle has a perimeter of 12 inches. Find the area.1. Area:square inches“I think if they have the same area, theywill have the same perimeter too.”square inches3. Area:square inches“I think the longer one will have a greaterperimeter because it’s so much longer.”Now let’s find the perimeter of the two rectangles. There are twoways we can do this. Pearson Education 32. Area:Session 2.5AUnit 433C Student Activity Book, Unit 4, p. 33C;Resource Masters, C16INV12 SE03 U4.indd 35/19/11 3:08 PMShow students the completed sheet, with tiles on it. Then draw asketch of the rectangles on the board and label each dimension.Demonstrate finding the perimeter of each rectangle by countingthe sides of the actual tiles. Then demonstrate finding theperimeter of each rectangle by adding the dimensions.4 in.8 in.2 in.8 2 8 2 204 in.4 4 4 4 16Remind students that the rectangles had the same area, but havedifferent perimeters.Ac tivit yFinding the Perimeterof Rectangles15 Min individualsWe’ve been looking at two rectangles with the same area, andtalking about the perimeter of those shapes. We found out thatrectangles that have the same area don’t necessarily have the sameperimeter. Now we’re going to look at the opposite situation.Direct attention to Find the Area (Student Activity Book page 33Cor C16).CC26Investigation 2INV12 TE03 U04 S2.5A.indd 26Understanding and Finding Area6/9/11 6:01 PM

Each of the rectangles on this sheet has a perimeter of 12 inches.If you filled each rectangle with tiles and counted the edges, youwould get 12. Or, if you added each of the 4 numbers togetherlike we did earlier, you would get 12. Or, if you used a ruler, youwould find that the perimeter of each rectangle is 12 inches. Yourjob is to figure out the area of each of these rectangles.See the Ongoing Assessment and Differentiation suggestions onpages CC24 and CC25 for support in observing and supportingstudents while they work. When they have finished, call themback for a brief discussion. Reach a consensus on the area ofeach rectangle.What did you find for the area of the first rectangle? (9 squareinches) Does everyone agree? What about the second rectangle?(8 square inches) The third one? (5 square inches)Each of these rectangles has a perimeter of 12 inches, but eachrectangle has a different area. Does this surprise you? Why orwhy not?2 DiscussionName4 Session Follow-UpDatePerimeter, Angles, and AreaDaily PracticeArea and Perimeter (page 1 of 2)1. Each rectangle has an area of 20 squareunits. Find the perimeter of each rectangle.Perimeter:unitsPerimeter:note Students find the areaand perimeter of rectangles.110–111, 114–115units2. Each rectangle has an area of 18 square units.Find the perimeter of each rectangle.unitsPerimeter:Perimeter:units3. What do you notice about the perimeter of shapes that have thesame area?33DUnit 4Session 2.5A Student Activity Book, Unit 4, p. 33D;Resource Masters, C17INV12 SE03 U4.indd 46/8/11 12:58 PMNameDatePerimeter, Angles, and AreaDiscuss students’ ideas, but keep in mind that the reason this istrue is quite complicated for third graders to think about andexplain. Students might mention how what they are counting isdifferent: when they are finding area, they are counting whole tiles;when they are finding perimeter, they are counting the sides oredges of the color tiles. When finding perimeter, sometimes one tileis counted more than once (e.g., corner tiles). In other words,perimeter is a one-dimensional or linear measure, while area is ameasure of two-dimensional space.Daily PracticeArea and Perimeter (page 2 of 2)4. Each rectangle has a perimeter of 16 units.Find the area of each rectangle.Area:square unitsArea:square units5. Each rectangle has a perimeter of 14 units.Find the area of each rectangle.Area:square unitsArea:square units6. What do you notice about the area of shapes that have thesame perimeter? Pearson Education 3SESSION FOLLOW-UPSession 2.5ADaily PracticeSession 2.5AUnit 433E Student Activity Book, Unit 4, p. 33E;Resource Masters, C18INV12 SE03 U4.indd 5Daily Practice: For reinforcement of this unit’scontent, have students complete Student Activity Bookpages 33D–33E or C17–C18.INV12 TE03 U04 S2.5A.indd 273 Activity Pearson Education 31 ActivitySame Area, Different Perimeter; Same Perimeter, Different Area6/8/11 12:55 PMCC276/9/11 6:02 PM

Apr 03, 2017 · Same Area, Different Perimeter; Same Perimeter, Different Area Math Focus Points Using tiles to find the area and perimeter of a rectangle Understanding that rectangles can have the same perimeter and different areas or the same area and different perimeters vocabulary session 2.5A same Area, different Perimeter; same Perimeter, different Area cc23

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