4th Grade Unit Area - Doral- CactusMath Corner - Home

4th Grade Unit 2 Overview and StandardsBefore You Begin This Unit.In 3rd Grade, students focused on learning the concept of area,developing a solid understanding of what area is and how it ismeasured (particularly with the use of square tiles). This unit willgive teachers the opportunity to learn what students know and need toknow about area through a variety of open-ended tasks. Teachersshould become aware of which can students recognize the row-bycolumn structure of the rectangular arrays they build and watch forstudents’ ability to connect this idea to a multiplicative relationship.You might hear students explain: “I count the number of squares inone row and repeatedly add that number (multiply) by how manyrows I have.” These concepts are critical to students’ understandingof area as a foundation to build upon in later units. For moreinformation about how to differentiate the tasks in this unit based onyour students’ understanding, read the Common Core State StandardsProgression document, pages 15-18. (see link below)Unit at aGlanceEstimatedDuration:5 days5 Lesson Unit:Day 1- OrderingRectanglesDay 2- Working withRectanglesDay 3- MissingDimensionsDay 4- RectilinearFiguresDay 5- RectilinearFiguresCCSS-M Progression Geometric MeasurementStandards Addressed in the Unit4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematicalproblems. For example, find the width of a rectangular room given the area of the flooring andthe length, by viewing the area formula as a multiplication equation with an unknown factor.Link to the CCSS Unpacking Document- Updated Sept. '14

4th Grade Unit 2 Planning DifferentiationStudents Who Struggle.BehaviorsStudents who struggle torecognize the row bycolumn structure of anarray when a grid is notprovided in the rectangle(dimensions provided).Students who strugglefinding the area of anirregular shape.ResourcesColored tilesGrid paperColoredpencil/highlighterGrid paperHow to UseAsk the student to explain how they willrepresent the dimensions using the grid paper.If the student is unsure, have him identify thelength and width of the rectangle and discusshow those measurements can be used to buildthe rectangle with color tiles. Build therectangle using color tiles and again relate thedimensions of the figure to those given onpaper. Discuss with students how to use thenumber of tiles in one row and the number ofrows in the rectangle to determine the area ofthe shape. Ask the student to draw therectangle on the grid paper and label thedimensions. Recount the tiles using the row bycolumn structure (not just counting one tile at atime).First, have students draw irregular shapes ongrid paper then solve to find the area bybreaking apart the shapes into rectangles.Highlighting each part of the irregular shapemay help students visualize how the irregularshape is composed of squares and rectangles. Ifthis proves difficult, then build the shapesusing a different color tile for each rectanglethat composes the irregular shape to helpstudents determine the dimensions needed tosolve the problem.Have students use manipulatives as much aspossible.Students who forget tomultiply to find the areaof a regular polygon.Grid paperColored tilesHave students build the area of a providedpolygon using the inch grid paper and coloredtiles. Have them identify the array beingcreated using the tiles. Next, ask the student tocreate multiplication equation that representsthe area of that polygon using what they know

about the row by column structure of the arraybuilt.After the students represent the polygon withtiles, have them draw the polygon on the gridpaper. The goal is to move the students awayfrom tiles to grid paper, then grid paper toblank paper. This progression can be madewhen teachers help students connect onestrategy (tiles) to another (grid paper).Provide students with an area of a rectangleand ask them to represent different possibledimensions of the length and width using thecolored tiles.Students who strugglewith finding dimensionsof a polygon whenprovided that area.Colored tilesGrid paperHave them take notes on grid paper as they goalong. Ask them if they notice anyconnections between the area and thedimensions.*** Another option would be to use the tileflooring in your classroom if you do not havecolored tile blocks or inch grid paper.Finding the missing sideof an irregular polygon.Colored tilesGrid paperProvide students with the irregular polygonshape and have them build the shape with thedimensions provided. Have them investigatethe missing side based off the representation ofthe task. This activity will require a lot ofsupport due to the rigor behind the concept ingeneral.Students Who Have Mastery.BehaviorsResourcesStudents who can applythe area formulas forrectangles in real worldand mathematicalproblems.Construction orgrid paperCan find area of apolygon.Multi-step WordProblemsHow to UseChallenge students to create their own"breaking apart array" problems or a differentversion of the "Designing a Storage Unit" taskand use equations to represent their strategies.Provide student with multistep word problemto solve.

Example:Jack and Jill’s mom is buying carpet to putdown in their bedrooms. Jack’s room is 12 sq.ft. by 10 sq. ft. and Jill’s room is 9 sq. ft. by 12sq. ft. If a roll of carpet contains 100 sq. ft. ofcarpet, how many rolls will their mom need tobuy?Students are to solve word problems thatinclude finding the area from providedperimeter and vice versa.Can find area of apolygonWord ProblemsExample:The area of a rectangle is 24 sq. feet. Whatcould not be the perimeter of the rectangle?Have students create more complex wordproblems involving area and perimeter.Can find area of apolygonChart paper*** For support, provide a word bank ifneeded.Example: carpet, paint, fence, wall paper, tiles,boarder and etc.

4th Grade Unit 2 Planning EachInvestigation and Ten Minute MathNotes About Each InvestigationThis unit provides students with a reintroduction to the concept of area using arrays as aprimary focus of this work. Area will be also revisited later in the year with largernumbers. You may want to consider how students’ work in the first unit with multiplicationfacts can be extended as students work through Breaking Apart Arrays and Composite Shapesactivities. Connecting the representations to equations will help clearly highlight themultiplicative reasoning students use to solve these tasks. This work will also help studentsmove from using concrete manipulatives to using paper-pencil strategies (such as using gridpaper or an equation) to solve area problems.Ten Minute MathActivityNoteStandardTarget NumberStudents work on subtraction skills.4.NBT.2, 4.NBT.4Round OffStudents work on rounding and numbersense skills.4.NBT.3, 4.NBT.4What's the Value?Distance TraveledStudents work on place value skills.Students work on subtraction skills.4.NBT.1, 4.NBT.24.NBT.2, 4.NBT.4

4th Grade Unit 2 Teaching Standards forMath PracticeStandards for Mathematical Practice(behaviors of mathematically proficient students)Building the Language ofMathematicsIncreasing accountable talk is thegoal for ALL students in ourdistrict.The following activities areprovided to help ensure yourstudents are engaging inmathematical conversations thataddress SMP 3 (Construct ViableArguments) and SMP 6 (Attend toPrecision)Words you should hearstudents use inmathematicalconversations:Use tiles along with grid chartpaper to model finding area andperimeter with real word situations.Have students investigatewhich areas anddimensions would result in Have the students create aThere is a 6 foot by 4 foot bordera rectangular shape.blue print of a house oraround a garden. Sally says that sheoffice space based oncan double the area by onlyEx. 2, 4, 9, 16, and etc.teacher provided area sq. ft.doubling one of the dimensions.You can differentiate byShe also says that if she doublesHave them come up with a providing larger areas orboth the dimensions the area isspecific room details.rule and provide theirmore than double. When shetheory correct using thedoubles both dimensions how muchtiles.larger is the new gardencompared to the original garden? Isthat true for other dimensions too?Why or why not?Example of Real-world task

Building Mathematically Proficient StudentsDuring this unit, focus students’ attention on practices:MP3 Construct viable arguments and critique the reasoning of others.MP5 Use appropriate tools strategically.MP6 Attend to precision.Print the following posters and use them during your lessons.4th Grade Unit 2 Assessing StudentUnderstandingResource:Teaching Suggestion:Designing a Garden:Area/PerimeterThere are 4 sections to this performance task, so you will wantto reserve 2-3 days to complete this with your students. Also,since a rubric is not provided, you may wish to work throughthe task with your grade level team so you can determine aprocedure for scoring student work.4.MD.3 Task 1.docThe 1st assessment task may be used after Day 2 (especiallyafter Breaking Apart Arrays) to determine which students mayneed extra support in generating possible dimensions for agiven area.Example of a Real WorldTask (Previously on 4thGrade CMS Area Unitpage)There is a 6 foot by 4 foot border around a garden. Sally saysthat she can double the area by only doubling one of thedimensions. She also says that if she doubles both thedimensions the area is more than double. When she doublesboth dimensions how much larger is the new gardencompared to the original garden? Is that true for otherdimensions too? Why or why not?Howard County PublicSchool System - Grade 4Task 3 will assess students’ understanding of many ideas:-Rearranging a given area into different shapes does not affectthe amount of area-Different dimensions are required to generate different shapes-Area is found by covering or filling a shape

Exit TicketsUse afterday 2Oscar’s drawing room measures 12 feet by 16 feet. He wants to put a new carpetin the drawing room that cost 15 per square foot. How much will it cost for Oscarto carpet his drawing room?4.MD.3Use afterday 2Hector is placing molding around his 120 sq. foot bedroom. If his width is 10 sq.feet, what must be the length of his bedroom?4.MD.34th Grade Unit 2 Digital ResourcesInteractive Student ResourcesResourceSuggestion for Use:What standard(s) are addressed?Area andPerimeter PowerPointUse as a review or practice forarea and perimeter. Use afterday 3.4.MD.3 Apply the area and perimeterformulas for rectangles in real worldand mathematical problems.ComparingRectanglesUse after day 1 for comparingand ordering the area of tworectangles.4.MD.3 Apply the area and perimeterformulas for rectangles in real worldand mathematical problems.Designing a PartyUse as an enrichment activityfor day 2 or for practiceapplication after day 4.4.MD.3 Apply the area and perimeterformulas for rectangles in real worldand mathematical problems.Interactive Realworld wordproblemsUse as an enrichment activityfor day 2 or for practiceapplication after day 4.4.MD.3 Apply the area and perimeterformulas for rectangles in real worldand mathematical problems.