GRADE 5 SUPPLEMENT - Math Learning Center

GRADE 5 SUPPLEMENT

Set D1 Measurement: Area & Perimeter

Includes Activity 1: Measuring Area Activity 2: Measuring Perimeter Activity 3: The Ladybugs' Garden Activity 4: Hexarights Independent Worksheet 1: Area & Perimeter Review Independent Worksheet 2: Measuring Rectangles

D1.1 D1.5 D1.9 D1.15 D1.23 D1.27

Skills & Concepts H determine area by finding the total number of same-sized units of area that cover a shape

without gaps or overlaps

H select appropriate units, strategies, and tools for solving problems that involve estimating or measuring perimeter and/or area

H find the areas of complex shapes by dividing those figures into basic shapes (e.g., rectangles, squares)

H understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas

H measure necessary attributes of shapes to use perimeter and area formulas to solve problems

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Bridges in Mathematics Grade 5 Supplement Set D1 Measurement: Area & Perimeter

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Set D1 Measurement: Area & Perimeter

Set D1 H Activity 1

ACTIVITY

Measuring Area

Overview Students review the term area and work together to generate a formula for determining the area of rectangles and squares. In the process, they have an opportunity to see and handle a square inch and a square foot. Then they apply the information as they work in pairs to find the area of various items around the classroom.

Skills & Concepts H determine area by finding the total number of same-

sized units of area that cover a shape without gaps or overlaps H select appropriate units, strategies, and tools for solving problems that involve estimating or measuring perimeter and/or area H measure necessary attributes of shapes to use perimeter and area formulas to solve problems

You'll need H Measuring Area (page D1.4, run a class set) H one 12" ? 12" piece of red construction paper H 10" ? 18" blue construction paper (1 piece for every 4

students) H square inch tile (class set) H rulers (class set) H yardsticks and measuring tapes H masking tape H calculators (optional, class set) H Student Math Journals H Word Resource Cards (area, dimension)

Instructions for Measuring Area

1. Post the Word Resource Card for area on the board. Ask students to pair-share what they know about this term. After a minute or two, invite volunteers to share their ideas with the class. As the discussion unfolds, review the following concepts: ? areaisameasureofhowmuchsurfacesomethingtakesup. ? areaismeasuredinsquareunitssuchassquareinches,squarefeet,orsquaremiles.

area

2.Holdupasingletileandaskstudentstoreportitsareainsquareinches.Ifnecessary,haveavolunteer measure the dimensions of the tile and work with the class to establish the fact that it's exactly 1 squareinch.Usealoopofmaskingtapetofastenthetiletotheboard.Workwithclassinputtolabelits dimensions and area.

3.Distributesetsoftile.Askstudentstoworkingroupsoffourtobuildasquarewithanareaofexactly 144squareinches.Afterthey'vehadafewminutestowork,havethemshareandcomparetheirresults.

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Bridges in Mathematics Grade 5 Supplement ? D1.1

Set D1 Measurement: Area & Perimeter

Activity 1 Measuring Area (cont.)

Students We thought it was going to be really big, but it's not so big after all. We knew it was going to be a 12" ? 12" square because 12 ? 12 is 144. We each made 3 rows of 12 and put them together. It went pretty fast for us.

4.Askeachgrouptomeasurethedimensionsofthesquarethey'vejustbuiltwiththeinchsideoftheir ruler.Whatcantheytellyouaboutthesquarenow?Asvolunteerssharewiththeclass,pressthemto explain their thinking.

Alex It's 12 inches on both sides.

Teacher What is the area of your square, and how do you know?

Students It's 144 square inches because that's what you told us to do. It's 144 square inches because we used 144 tiles, and each tile is 1 square inch. You can see a 10 ? 10 square inside the 12 ? 12. Then just add 12 on the top and bottom, and 10 on both sides. It makes 144 in all. It's 12 rows of 12. If you just multiply 12 ? 12, you get 144.

5. Show students the 12" ? 12"squareofredconstructionpaperyou'veprepared.Askavolunteertocomparethepapertothetilesquareathisorhertable.Afterconfirmingthatthetwoarethesamesize,fastenthepapersquaretotheboard.Workwithclassinputtolabelitsdimensionsandarea.Explainthatbecause it is 12"or1footoneachside,it'scalledasquarefoot,andrecordthisinformationontheboard.

12"

12" 144 square inches

1" 1"

1 square inch 1 sq. in. 1 in2

1 square foot 1 sq. ft. 1 ft2

6. Give each group a 10" ? 18"pieceofblueconstructionpaper.Askthemtofindtheareaofthisrectangle,usingtheirrulersand/orthetiletohelp.Challengethemtofindamoreefficientmethodthancover-

ing the entire rectangle with tile. Have them each record the answer, along with any computations they made,intheirjournals.

7. When they've had a few minutes to work, ask students to share their answers and explain how they found the area of the rectangle. Record their strategies at the board.

D1.2 ? Bridges in Mathematics Grade 5 Supplement

? The Math Learning Center

Set D1 Measurement: Area & Perimeter

Activity 1 Measuring Area (cont.)

18" 10"

It's 10 tiles along the side and 18 along the top. 10 rows of 18 is 180.

If you count by 10's it's 180.

10" x 18" = 180 sq. in.

8.Chancesare,somestudentswillhavecomparedthepaperrectangletothetilesquareattheirtableto findthesidelengths,andthenusedsomekindofcountingstrategytofindthearea.Othersmayhave donethesamebutmultipliedthedimensionstofindthearea.Stillothersmayhavemeasuredthedimensionswiththeirrulersandmultiplied.Ifthethirdstrategydoesn'tcomefromthestudents,tapeone of the 10" ? 18" pieces of paper to the board and model it yourself.

9. Post the Word Resource Card for dimensionontheboard.Explainthattofindtheareaofasquareor a rectangle, we measure its dimensions and multiply the 2 numbers. Press students to explain how and why this works, and then work with input from the class to write the general formula: area = length ? width or A = lw.

dimension

3 5

10.Explainthatinaminute,studentswillbeworkinginpairstomeasuretheareaofsomethings aroundtheclassroom.Askthemtolookaround.Cantheyspotanythingthey'dmeasureinsquare inches?Whataboutthecalendargridpocketchartorthewhiteboard?Wouldtheyfindtheareaofthese insquareinchesorsquarefeet?

Students I'd use square inches to find out the area of small stuff like my math journal or probably my desk. I'd maybe use square feet instead of square inches to get the area of the calendar chart. I'd definitely use square feet to measure the area of the rug or the whole room.

11.GivestudentseachacopyoftheMeasuringAreaworksheet.Examinethecharttogetherandexplain thetasksasneeded.Makesuretheyknowwheretofindtheyardsticksandmeasuringtapesasthey need them. Then ask them to work in pairs to complete the sheet.

Note Advise students to work to the nearest inch in measuring the dimensions of the items listed on the worksheet.

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Bridges in Mathematics Grade 5 Supplement ? D1.3

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