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19 www.movingwithmath.com Conceptual Understanding 40 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Adding Fractions When you add two fractions with the same denominator, look for a pattern. Julio made a large pizza and cut it into 6 parts of equal size. Julio ate of the pizza. His friend ate of the pizza. How much did they eat all together? Use fraction circles to add problems 1–6. Find 2 different ways to break each fraction apart. 1. + ______ 2. +_______ 3. +______ 4. +_______ + + 7. 8. Pattern: To add fractions with common denominators, ________________ ________________ ______+ ______ ______+ ______ + = ? + = ______ the 5. + = ________ 6. + = ________ 9. What is the pattern for adding 2 fractions that have the same denominator? ©MathTeachersPress, Inc. Assessment 68 The area of a rectangular rug is 15 square feet. Each square is one square foot in the grid below. Draw a rectangle with an area of 15 square feet. Find the perimeter, in feet, of the rectangle you drew. Objective1: To show anumberwithblocks, as apicture and in expandednotation. ELL Materials: Base tenblocks,PlaceValueMats (orMasters 1 and2 taped together),6-sideddice Vocabulary: expandednotation Multi-Digit Numeration Todevelop students’understandingofmulti-digit numeration, facilitatepracticewith the following activities: 1. Writingnumerals fromblocks. Display a setofones, tens, andhundredsblocks.Atfirst donotuse tenormoreof anyonekindofblock.Ask the students todescribewhat they see.Askhow theywould recordwhat they see.Repeatwith adifferent setofblocks. When students are able to correctly record thenumeral, display a setofblocks thathas10ormoreonesblocks so that studentsmust exchange10ones for1 tenbefore recording.Thendisplay a setofblocks thathas10ormore tensblocks so that studentsmust exchange10 tens for 1hundredblockbefore recording.Finally,display a setof blocks thathas10ormoreonesblocks and10ormore tens blocks.This activityprovides readiness for the regrouping in addition and subtraction. 2. Buildingblocks fromnumerals. Write a3-digitnumeralon theboard.Ask students to explainwhat eachdigit in thenumeralmeans.Ask how to read thisnumber.Then ask them tobuild the numberwithbase tenblocks. Include examples inwhich zeromustbeused as aplaceholder.This activity canbe practiced inpairswithonepersonwriting anumeral and theotherperson saying andbuilding thenumber withbase tenblocks. 3. Buildingblocks andwritingnumerals fromoral presentation. Say a3-digitnumeralout loud (e.g.,265).Students shouldbuild thenumberwithbase tenblocks and then record thenumeral. Include examples inwhich zeromust beused asaplaceholder. 4. Drawingpicturesofnumerals. Useyourblocks tobuild537.Place theblocksonyour PlaceValueMat.Read thenumberaloud.Drawapicture of theblocks. To show studentshowtodrawapicture,use a small square for eachhundred, a straight line for each ten and adot for eachone as shownbelow. 5. Expandednotation.Explainthat expandednotation meanswriting anumber as a sumof thevaluesof itsdigits. 473 =4hundreds+7 tens+3ones= aaaasssssssd =400+70+3 Repeat the activitywithothernumbers, including numbers thatneed touse zero as aplaceholder.Examples: 320 =3hundreds+2 tens+0ones= aaass =300+20+0 705 =7hundreds+0 tens+5ones= aaaaaaadf =700+0+5 Direct attention to the topof thepage.Have students useblocks to show thenumber342,draw apictureof the number ( aaassssf ) andwrite thenumber in expanded form.Have students complete thepageon theirown. Chisel to 0 Usebase tenblocks in apile:20 tens and30ones.Eachplayer startswith a hundredflat.Aplayer tosses a6-sided die and removes thenumber tossedout ofherhundredflat.For example, if a3were thrown, the playerwouldhave exchange thehundredflat for10 tens first, then exchangeoneof the tens for10ones so that the 3ones couldbe removed.Thewinner is thefirstplayer to toss the exactnumber to reach exactly0blocks inherpile. Journal Prompt (Masteravailable in theAssessment section.) Draw apictureof thenumber156.Then write thenumber in expandednotation.Whichdigit has the leastvalue?Howdoyouknow? 2 ©MathTeachersPress,Inc.,Reproductionbyanymeansisstrictlyprohibited. ExpandedNotation Anumbercanbeshowninmanyways. 342 withblocks 342 withpictures Buildblocks.Drawpictures.Writeeachnumberinexpandednotation. Writethenumber. 5. 900+50+1=__________ 7. 600+10+9=__________ 6. 400+20+7=__________ 8. 300+90=__________ 1. 214 Hundreds Tens Ones _______+_______+_______ 2. 176 Hundreds Tens Ones _______+_______+_______ 3. 503 Hundreds Tens Ones _______+_______+_______ 4. 460 Hundreds Tens Ones _______+_______+_______ Anumbercanbewritteninexpandedformusingplacevalue. 3hundreds+4tens+2ones 300 + 40 + 2 342= 200 10 4 100 70 6 500 0 3 400 60 0 951 619 427 390 Lesson 2, 4ETeacherManual 2 Conceptual Understanding Conceptual Understanding Items prompt students to explain and draw a picture of what they are learning. These items prepare students for next generation assessments. Sum It Up! Students reflect and generalize upon what they have learned. Teachers lead discussions to develop student understanding of central ideas. Journal Prompt Journal Prompts require students to explain and show the thinking that must be done to successfully answer the question. 9. What is the pattern for adding 2 fractions that have the same denominator? Journal Prompt (Master available in the Assessment section.) Draw a picture of the number 156. Then write the number in expanded notation. Which digit has the least value? How do you know? Journal Prompt Question: Answer: Lesson from Teacher Manual Student Book Page