Pearson Assessments



Second GradeFractionsTable of ContentsContentSuggested Number of DaysPage #Part 1: Partitioning Wholes into Equal Parts Candy Bar Pictures Sort Cards for One-Half Square Fourths Eighths Guided Practice Problems #1-2Part 2: Inverse Relationship Between Number of Parts and Size of Parts Brownie Pictures Guided Practice Problem #3Part 3: Counting Fractions Greater than One Guided Practice Problem #4 Scenarios Guided Practice Problems #5-6Fraction Manipulatives Fraction Strips Fraction Circles(3 ? days)3/19-3/24(1 ? days)3/24-3/25(4 days)3/26-3/3111011131422242930314243444651 Additional Resource: Fractions (MATH_2_A_FRACTIONS 2014_RES)This Smart Board activity for fractions is also available. It includes the guided practice problems from Part 1 as well as some other activities for Parts 1, 2 and 3.TEKS 2.3The student applies mathematical process standards to recognize and represent fractional units and communicate how they are used to name parts of a whole. The student is expected to:TEKS 2.3Apartition objects into equal parts and name the parts, including halves, fourths, and eighths, using words;TEKS 2.3Bexplain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part;TEKS 2.3Cuses concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole; andTEKS 2.3Didentify examples and non-examples of halves, fourths and eighths.Vocabulary:fraction, fractional part, parts, equal, unequal, whole, fraction bar, shaded, unshaded, relationship, fair share, share, model, divide, partition, total, describes, pieces, object, represent, half, halves, one-half, two-halves, fourths, one-fourth, two-fourths, three-fourths, four-fourths, eighths, one-eighth, two-eighths, three-eighths, four-eighths, five-eighths, six-eighths, seven-eighths, eight-eighthsTeacher Background The two main concepts that second graders need to understand about fractions are:A fraction is smaller than a whole.A whole must be divided equally for its parts to be called fractions.When naming fractions, the TEKS specify that second graders use words rather than fractional notation (fraction bar symbol). Students are also expected to count fractional parts beyond a whole, such as one whole and one-fourth or five-fourths with models. Part 1: Partitioning Wholes into Equal PartsMaterials:a “candy bar” rectangle for each pair of students (page 10)a set of “one-half” sort cards for each pair of students (pages 11-12)2 large squares for the teacher (page 13) or large teacher-made paper squaresstudent copies of fourths for coloring (pages 14-17)student copies of eighths for coloring (page 18-21)concrete fractional models, i.e. fraction tiles, Fraction Towers (with fraction symbols covered with painters tape), etc.student copies of IMN Activity (MATH_2_A_2 FRACTIONS IMN 2014_RES)partner sets of Matching Cards (MATH_2_A_3 FRACTIONS 2014_RES)student copies of Guided Practice Problems #1 and #2 (pages 22-23)student copies of Fractions Practice Problems Part 1(MATH_2_A_4 FRACTIONS IP 2014_RES)37147583185Note: If you do not have enough manipulatives for your entire class, fraction strips and fraction circles are provided for halves, fourths and eighths (pages 46-53). They may be copied on tag, laminated and cut apart to create additional manipulatives for use.00Note: If you do not have enough manipulatives for your entire class, fraction strips and fraction circles are provided for halves, fourths and eighths (pages 46-53). They may be copied on tag, laminated and cut apart to create additional manipulatives for use.HalvesGive each pair of students a copy of the paper candy bar (page10). Have them cut the candy bar in half. Then, discuss what it means to “have half.” For example,How many parts did you cut the whole “candy bar” into? We cut it into two parts. Why did you cut it into two parts? Half means that you have two parts--one for me and one for you.Is there anything else that was special about the way you cut it? (If students don’t mention that the two pieces had to be equal, take a “candy bar” and cut it into unequal parts. Ask, “Is this cutting it into halves?”)So, when I cut it in half, I had to cut it into two parts of equal size. (Draw the “candy bar” on the board and show how it was cut in half. Shade one-half of it.) What did you do to make the 2 pieces equal? (Discuss.)If you pick up one of the pieces of the candy bar, what do you have? one-halfTwo pieces would be called two-halves? If I have 2 halves of the candy bar, what would I have? The whole thing or a whole. 208661018605500278066519431000207645018605500 1 whole18383251606550012763504762500018383251689100030670506794500 one-half one-half (shaded) (unshaded)Instruct students on how this fraction is said, i.e. one-half. Throughout this unit, have students practice saying the fractions aloud.b. Defining a FractionWhat is a fraction? An equal part of a whole or any number of equal parts.Think back to the candy bar activity. When we cut the candy bar into 2 parts, what did you do? cut into two parts that were the same; made them equal (accept all reasonable responses)So, you cut the candy bar into two equal pieces. Was that important? YesWhy is that important? When you share you want it to be fair.Is there something we could do to make sure the candy bar was cut into 2 equal pieces? (Fold the candy bar in half.)It is important to know that a fraction is a whole that has been divided into equal pieces. If a whole is partitioned into 2 unequal parts, then it doesn’t represent a fraction. c. Partner PracticeEither as table groups or with partners, the students should sort the fraction pictures on pages 11-12 into those which represent one-half shaded and those which do not. Students should justify their choices to each other. Then share their decisions with the whole class. d. IMN Entry Suggestions Right Side: Give students two of the same shape found in MATH_2_A_2 FRACTIONS IMN 2014_RES. Have them draw a line through the first one to show an example of a half. Then, have them draw a line through the other shape to show two pieces that are not equal and therefore not halves. 17907008953500Left Side: Write about a time when you got one-half of something. A pre-printed statement can be found on the page 2 of MATH_2_A_2 FRACTIONS IMN 2014_RES for pasting into the IMN. 2. FourthsTeach the meaning of fourths using two copies of the square on page 13 or large teacher-made squares. Have a student come up and fold one of the squares in half. Then have them open it up. Draw a line with a marker on the fold to show two halves. Next the student volunteer or the teacher will demonstrate folding the square in half again in the opposite direction. Unfold the square. (Trace over the folds with a marker to show the four pieces. See picture below.)341947587630Step 200Step 2169545087630Step 100Step 1 150431516129000What do you notice about the square? It’s divided into four equal pieces.Question students about the number of pieces, the size of the pieces, what the pieces might be called.These pieces are called fourths. (Emphasize the “th”, and tell students that many fractions have a “th” after the number to differentiate a fourth from 4.)Each piece is one-fourth of the square.. Together count the pieces: one-fourth, two-fourths, three-fourths, four-fourths or one whole. The teacher should shade and label each fourth as the class counts out the fourths.Do you notice anything special about four-fourths? It equals one whole.Ask for a student volunteer that can fold the other square in half in a different manner than the first student. Give him or her a square. (If necessary direct the student to fold it diagonally). Draw the lines and then have the student fold it again to make fourths and trace the lines. 21526509588500Question students as to the similarities and the differences between the two squares. Why are the parts in both of these squares called fourths? There are four parts in each square. All four parts are equal in size.If students have difficulty with the equality of each piece, fold it again to show that all four pieces are the same. If they are still having difficulty, the teacher could cut apart the square that was folded diagonally and place the triangles on top of each other to prove that they are also the same size as each other. Pass out the half sheet of fourths on page 14. Students begin by coloring one-fourth of the first rectangle (whole). Have students share how they shaded one-fourth. Ask students if it matters which square they color to make one-fourth. Students should be made aware that any one of the four parts may be colored and it is still one-fourth of that rectangle. Use the pictures on the next page to demonstrate if they did not shade all of the different possibilities. Allow students time to color one-fourth on the remaining rectangles so that they show all the different ways to represent one-fourth of the rectangle.4105275143510one-fourth00one-fourth69532586360one-fourth00one-fourth401002536195one-fourth00one-fourth53340034290one-fourth00one-fourthWhat could we say about the part that is unshaded or not shaded? Three-fourths of the rectangle is unshaded.Give the students a half sheet of triangles found on page 15.Look at the triangle labeled one-fourth. How many pieces do we need to shade to show one-fourth? oneSo, shade in one of the four triangles in the picture labeled one-fourth.Now let’s look at the triangle picture labeled two-fourths. How many fourths do we need to color to show two-fourths? 2 Point to the two-fourths triangle. Go ahead and shade in any two fourths on this triangle. Explain that the number of equal parts that are shaded defines the fraction and not the arrangement.Point to the three-fourths triangle. How many pieces should we shade in here? 3 Why? 3 pieces equal three-fourths (Repeat this process with four-fourths)Hopefully some students will shade differently than others so they can be compared and discussed. For more practice shading and labeling, the students can color the circles or squares on pages 16-17. Remind students that four-fourths really is one whole. . 3.EighthsFold a rectangle in half, in half again and in half again to show eighths as shown in the picture below. Trace the lines with a marker to make the pieces more visible to the students. Count the pieces aloud with the class while shading and labeling each eighth (one-eighth, two-eighths, three-eighths, four-eighths, five-eighths, six-eighths, seven-eighths, eight-eighths). Remember to label with words and not the numerical representation of the fraction.102235010731500Now fold a square into eighths as pictured below. Again trace the lines with a marker. Count aloud the eighths with the class and label as done with the rectangle. 21050259525000Both shapes have eight equal pieces.Can anyone tell me what this would be called? eighths Why? There are eight pieces that are equal.Are the wholes (the rectangle and the square) the same size and shape? noPoint to an eighth in the rectangle. Is this an eighth? yesPoint to an eighth in the square. Is this an eighth? yesHow can they both be eighths? Both the rectangle and the square are divided into eight equal pieces.Therefore, one piece of the square is an eighth of the square (its whole) and one piece of the rectangle is an eighth of the rectangle (its whole).Compare one-eighth from each shape.Why are the two eighths not equal in size? because their wholes are not equal in sizeIt is important to remember that when we are comparing fractions, if the wholes are not equal in size then the fractions are not equal. One-eighth is not always the same as every other one-eighth.Use the circles and/or octagons on pages 18-21 for students to color and label the pieces from one-eighth to eight-eighths. Print the pages one-sided so students may lay them next to each other and see the progression from one-eighth to eight-eighths.Give students fraction circles, fraction bars or fraction towers with labels covered by painters tape. Pre-sort the sets so students are only choosing from a few different fraction models within the same set to find the eighths. Each student’s fraction set should be from the same type, i.e., towers or circle or strips, etc.Find the whole. Find eight equal pieces that make a whole.Show me one-eighth.Show me three-eighths.Show me six-eighths, etc.For further practice with halves, fourths and eighths, the teacher may have students match the shaded fraction pictures with the fraction words (MATH_2_A_3 FRACTIONS 2014_RES).4.Guided PracticeWork Guided Practice Problem #1 with students. Read the problem together, insert speed bumps and complete Steps 1 and 2 of the 4-step process.27908244318100329565085725eight equal parts5 parts planted veg00eight equal parts5 parts planted veg140970085725parts vegNOT planted00parts vegNOT planted13716001689100In Step 3, Students label the picture with 5 parts vegetables (V) and the remaining parts with not vegetables (NV). Then they circle the squares that are not vegetables.Discuss with students the number of parts that are not planted with vegetables. Write 3 NV next to the picture. What fraction of the garden is NOT planted with vegetables? three-eighthsLook at each answer choice and put an X next to the ones that do not say three-eighths and a question mark next to the one that does say three-eighths until all answer choices have been plete Step 4. An example of the completed problem is shown on the next page.Guided Practice Problem #1557212515811500286702515811500395287517526000Kate planted her garden in eight equal parts. She planted vegetables in 5 of the parts. How much of the garden does NOT have vegetables planted?V-5905535750500VVVVNVNVNV4057650558803 NVthree-eighths003 NVthree-eighthsA.five-eighths X-3810023876000B.four-eighths XC.three-eighths ?29241753238500D.two-eighths X329565085725eight equal parts5 parts planted veg00eight equal parts5 parts planted veg140970085725parts vegNOT planted00parts vegNOT planted134302511811000320040081915Labeled the parts. Counted the parts that were not veg.00Labeled the parts. Counted the parts that were not veg.Work Guided Practice Problem #2 with students. An example of a completed problem with the strategy is shown below.Guided Practice Problem #2405765015367000213360015367000Dillon drew shapes with 4 pieces. Which picture shows fourths?9525009144000 4 not equal4143375105410008877305016500B. 4 not equal4291965154940four equal parts00four equal parts321945090170shows fourths00shows fourths1209675784220084005755245008686807239000C. 4 not equal 307657514732000447675106680008191503429000439102536195Looked for 4 equal parts00Looked for 4 equal partsD. 4 equal parts5.Independent PracticeStudents should complete Fractions Practice Problems Part 1(MATH_2_A_4 FRACTIONS IP 2014_RES) independently or with a partner.447675-76200Candy BarCandy BarCandy BarCandy BarCandy Bar00Candy BarCandy BarCandy BarCandy BarCandy Bar153035167640004105275-294640Sort Cards for One-Half00Sort Cards for One-Half40100256794500-2190751765300037528506731000375285067310004010025154940003886200164465003952875173990004114800508000042100506540500441960060960004352925114935007143755778600387223017843500-285753477260003544570318833500-30480015303500-667385262890001143000-482600FOURTHS00FOURTHS40572362346one-fourth00one-fourth1485905715one-fourth00one-fourth342265017335500-15748015557500479149135752one-fourth00one-fourth4077114146961one-fourth00one-fourth332613016446500-90170155382001148310147955FOURTHS00FOURTHS3585210122809000311150838200one-fourth00one-fourth4219575834390one-fourth00one-fourth3585683281541400145348286425500-151103647700007736862457017one-fourth00one-fourth41048972317061one-fourth00one-fourth142875564705500342900056470550042862520320three-fourthsfour-fourthsone-fourthtwo-fourthsthree-fourthsfour-fourthsone-fourthtwo-fourths00three-fourthsfour-fourthsone-fourthtwo-fourthsthree-fourthsfour-fourthsone-fourthtwo-fourths-91440042144700-19748527432000309816516954500_________________ ________________-6921530861000325056530861000_________________ ________________37909503003550057150030035500 _________________ ________________378142513335004381502286000 _________________ ________________Eighths184152533650040767008826500________________ ________________38817551498600017272019050000________________ ________________3880485303530001714518034000________________ ________________463551828800038804859715500________________ ________________37992051930400017716520574000________________ ________________39744653257550017716520383500________________ ________________3710305240665001568452476500________________ ________________276225330200039744658191500________________ ________________1430020696531500Guided Practice Problem #1Kate planted her garden in eight equal parts. She planted vegetables in 5 of the parts. How much of the garden does NOT have vegetables planted?A.five-eighthsB.four-eighthsC.three-eighthsD.two-eighthsGuided Practice Problem #2Dillon drew shapes with 4 pieces. Which picture shows fourths?9525009144000A.88773020447000B.88773021907500140970012383008969386286500C.8191503429000D.Part 2: Inverse Relationship Between Number of Parts and Size of PartsMaterials:partner or table copies of brownie pictures (page 29)student copies of IMN Activity ( FILENAME \* MERGEFORMAT MATH_2_A_5 FRACTIONS IMN 2014_RES)student copies of Fractions Practice Problems Part 2(MATH_2_A_6 FRACTIONS IP 2014_RES)1.Display the brownie pictures and/or give each table or pair a picture.If you were really hungry, would you rather have a piece of brownie from Pan A or Pan B?059055003200400173355003200400-2857500372427575565Pan B00Pan B35242537465Pan A00Pan AAre Pan A and Pan B the same size wholes or pans? YesWhy did you want a piece from Pan B? The pieces are bigger.How many pieces was Pan A cut into? eightOne brownie from Pan A is how much of the whole pan? one-eighth How many pieces was Pan B cut into? fourHow much of the whole is one piece from Pan B? one-fourthWhat can you tell about the difference between the size of the pieces of fourths and eighths from the same size whole? Eighths are smaller. Fourths are larger.Why do you think this is true? If you cut the pan into eighths you have more pieces and the sizes are smaller than if you cut it into fourths.Do you think that this is always true with other fractions? Let’s try it with some other fractions to see if we can prove this. Write this conjecture on the board: If we cut the same size whole into more pieces, the pieces will be smaller. Have students work with fraction circles, fraction bars or fraction towers to explore the concept and prove the conjecture. If they can prove it, it becomes a generalization. Have students compare two fractions at a time. Make sure that the students put the whole out along with all the pieces they are comparing. For example, next to the whole they could build thirds and sixths. Since we don’t use the numerical representation of fractions with second graders, they must build the whole with each size fraction in order to recognize what part of the whole it represents. Some students may use fraction circles, while others use fraction bars, or fraction towers-- just make sure that the student is comparing his or her fraction pieces to other pieces from the same set so that the fractions they are comparing represent parts of the same sized-whole. For example:386715015938500Important generalizations regarding this concept are:The more fractional parts used to make a whole, the smaller the part.The fewer fractional parts, the larger the part.On sentence strips or an anchor chart have students help the teacher devise the wording to state these generalizations.152400140970Note: This thinking is contradictory to students’ whole number experiences, so students will likely need lots of discussion and exposure to strengthen their understanding. 00Note: This thinking is contradictory to students’ whole number experiences, so students will likely need lots of discussion and exposure to strengthen their understanding. Ask students to think back to when they were studying length.What did you learn about measuring length that might remind you of this? Fewer units are needed when measuring length with longer units. More units are needed when measuring length with shorter units.3.IMN Entry Suggestions:Right Side:Use the pictures of fractional parts ( FILENAME \* MERGEFORMAT MATH_2_A_5 FRACTIONS IMN 2014_RES)to label and discuss that the more parts the whole is divided into the smaller the fractional piece and the fewer parts the whole is divided into the larger the piece or part. 495300150495003590925142876Note: Have students use a different color (except yellow) for each fractions strip to number the parts and circle the name. Highlight (in yellow) the first piece of each strip to visually accent the size difference of each fractional part.00Note: Have students use a different color (except yellow) for each fractions strip to number the parts and circle the name. Highlight (in yellow) the first piece of each strip to visually accent the size difference of each fractional part.Left Side:Have students respond to the questions, “Which fraction of a candy bar would you rather have. . . . one-fourth or one-sixth? Why?” The pre-printed questions can be found on page 2 of MATH_2_A_5 FRACTIONS IMN 2014_RES.5. Guided PracticeWork Guided Practice Problem #3 (page 30) with students. An example of a completed problem with the strategy is shown below.Guided Practice Problem # 3370522516700500462915034417000181038534417000Sandy baked three cakes that are the same size. She cut the chocolate cake into 6 equal slices, the strawberry cake into 8 equal slices, and the vanilla cake into 4 equal slices. Which cake has the smallest slices?4248150179705002476501797050034677351797050072390055880001257300558800046005755588000389572555880003524250104775002476501047750027622501263650020091404572000 Chocolate 6 Strawberry 8207645017589500 Vanilla 4 The cake cut into sixths.29622753365500 The cake cut into eighths. The cake cut into fourths. smallest pieces? C = 6 pieces S = 8 pieces V = 4 pieces9144004572000Divided cakes into 4, 6 and 8 equal partsChose the cake with the smallest pieces6. Independent PracticeStudents complete Fractions Practice Problems Part 2 (MATH_2_A_6 FRACTIONS IP 2014_RES) independently or with a partner. 059055003200400173355003200400-2857500360997571755Pan B00Pan B53340081280Pan A00Pan A059055003200400173355003200400-2857500393382545085Pan B00Pan B5619756985Pan A00Pan AGuided Practice Problem # 3Sandy baked three cakes that are the same size. She cut the chocolate cake into 6 equal slices, the strawberry cake into 8 equal slices, and the vanilla cake into 4 equal slices. Which cake has the smallest slices?-23812517970500412432526543000176720510668000chocolatestrawberryvanilla The cake cut into sixths. The cake cut into eighths. The cake cut into fourths. Part 3: Counting Fractions Greater than OneTeacher Background:There are an infinite number of ways that one whole can be represented as a fraction. Students must connect what they have learned about fractions to the concept of a whole. When the number of pieces in the whole is the same as the number of parts that you are counting, the fraction is a whole. Although students will be delving into the concepts of mixed numbers and improper fractions, these terms will not be introduced.Materials:concrete fractional models, e.g. fraction tiles, Fraction Towers (with fraction symbols covered with painters tape), fraction strips or circles (p. 46-53) etc.What Makes a WholeGive each student or pair of students one set of fraction pieces (bars, circles, towers, strips etc.).Have students place the whole in front of them on the table. With the students, build a whole using the halves. Have them place the halves on top of the solid whole.74295062230001428750913447500Count the halves together . . . one-half, two halves.What do you notice when you have two halves? Two halves make one whole.Are the two halves together the same size as the whole? Yes.Are the halves the same size as each other? Yes. Repeat the process with thirds. Have students build the whole with thirds on top of the solid whole.30854647605395001047750175260002314575742950035909257429500156083059283600018288007524750003085464760539500As done above, count out the thirds until you reach a whole . . . one-third, two-thirds, three-thirds.How many thirds are needed to make one whole? 3Three-thirds equals one whole.Repeat the process with fourths. Have students build the whole with fourths.840740793750085725013843000953135679132500How many fourths equal a whole? Four-fourths equals one whole.Let’s review what we have learned. Two halves make a whole.Three thirds make a whole.Four fourths make a whole. Do you see a pattern? Explain.How many fifths do you think are needed to make a whole?Let students predict and then prove with the fraction manipulatives.How many eighths do you think are needed to make a whole?Let the students predict and then prove with the fraction manipulatives.Is there a conclusion we can draw from this experience? (Through questioning, lead the students to come to the understanding that: When you have all the pieces the whole is divided into, it makes one whole!)More Than a WholeDisplay five halves with fraction pieces... 25241251143000032956501238250018288001047750011430001314450034290010477500Have students do the same. Then ask students to put the pieces together to form as many wholes as they can.296227517145000498157520002500426720018097500384810018097500254444516764000How many wholes could you make with 5 halves? 2Did you use all your halves? noHow many halves were left over? 1So what can you tell me about five-halves?(5 halves is the same as 2 wholes and one-half or 2 wholes and one-half is the same as 5 halvesRepeat this with varying amounts of halves, fourths and eighths. Make sure to do multiple examples.Guided Practice Problem # 4 (p. 42)Read the problem together and insert the speed bumps. Susan baked pies for her party. She cut the pies into eighths. The number of slices that were eaten are shown below. Show 2 ways to write how many slices were eaten.Main Idea: 2 ways to show how many eighths were eaten.First let’s label the picture eighths, since the slices represent eighths.14001758572500328021625400eighths0eighthsThe bullets below the picture have guiding questions to help us find the answer.Let’s read the first bullet together. How many eighths are there? Now count the number of slices.How many did we count? 14Let’s write that number next to the question and then write that information in the detail section.The next guiding question asks, “How many eighths make a whole pie?”What do we know about the number of eighths you need to make a whole? Eight eighths make a whole. How do you know? because the pie was cut into 8 slices and if you put the 8 slices back together you get a whole pie. That is important information so let’s write that in the details as well (see below).355282512446014 slices eaten8 eighths = 1 whole14 slices eaten8 eighths = 1 whole324239080644121920069852 ways to show how many eighths were eaten.02 ways to show how many eighths were eaten.1377523297815The next bullet asks us to group the eighths to show a whole pie. (Have students count out a group of eight and circle them.742315-75758001340485120015003310001-635eighths0eighthsDo we have a enough slices to make a whole pie? yes Can we make another whole pie? no Why not? We don’t have eight more slices.So, how many whole pies do we have? 1Let’s write that number next to the question, “How many whole pies can you make?”Point to the remaining slices of pie. Count them out and number them together.How many eighths do we have left? 6Do we have enough information to write the number of eighths 2 ways? yesWhat is one way to write it? one whole and six-eighthsAnd another way? fourteen-eighths59753520955000000025666702367280eighths0eighths= 1 whole7842256635755520897851206522118872027940113757295260354429705305270533 179324013462066An example of a completed problem is below.Guided Practice Problem #4Susan baked pies for her party. She cut the pies into eighths. The number of slices that were eaten are shown below.632033133350001191260191198511209232518961102229730701936750333759835191008044786765254762055000025666702367280eighths0eighths= 1 whole1821815895356j66j6?How many eighths are there? ________14______?How many eighths make a whole pie? ____8______?Group the eighths to show a whole pie.?How many whole pies can you make? ____1________?How many eighths are left? _______6_______?Write 2 ways to show how many eighths were eaten.1. __________________________________________2.___________________________________________45926241096060506730011239514 slices eaten8 eighths = 1 whole14 slices eaten8 eighths = 1 whole27336751701802 ways to show how many eighths were eaten02 ways to show how many eighths were eaten27909083705000481053976504Counted eighths.Labeled slices.Grouped whole.Counted eighths.Labeled slices.Grouped whole.c.ScenariosDisplay Scenario #1 on page 43. Sixteen-eighths are needed for Scenario #1. Jorge had two boards that were the same size. He cut each board into eight equal parts. He used ten of the pieces. What are two ways to write the amount Jorge used?Together the teacher and students place two whole fraction strips or bars to represent the two boards. If he cuts the first board into eight equal parts, how can we show this? Put eight eighths on the first whole. Repeat this process for the second board.The teacher labels the eighths below the fraction pieces/strips. 1 2 3 4 5 6 7 8 eighth eighths eighths eighths eighths eighths eighths eighths 1 2 3 4 5 6 7 8 eighth eighths eighths eighths eighths eighths eighths eighthsHow many pieces did Jorge use? 10Let’s count out the ten pieces. What were our pieces cut into? eighthsSo how many eighths did Jorge use? ten-eighthsJorge used ten-eighths.How many eighths are in a whole? 8We have eight, let’s count out the rest together, nine, ten.Remove the six pieces from the last whole. 1 2 3 4 5 6 7 8 eighth eighths eighths eighths eighths eighths eighths eighths 1 2 3 4 5 6 7 8 eighth eighths eighths eighths eighths eighths eighths eighthsWe have ten eighths. How many eighths make a whole? 8How many wholes do we have? 1How many more eighths do we have? 2 eighthsSo the two ways to write the amount of wood Jorge used is ten-eighths or one whole and two-eighths.Display Scenario #2 on page 43.Jesse had three sandwiches. He cut each sandwich into fourths. Jesse and his friends ate eleven-fourths of the sandwiches. What is another way to write the amount of sandwiches that were eaten?Display three wholes with fraction pieces. (Have students mirror your actions.) Now have students find the fractional pieces that are partitioned into fourths. Together count out one-fourth, two-fourths, three-fourths and four-fourths for the first whole. Repeat this for the second whole. (Place the four fourths on top of each whole.) On the first whole the teacher should label the pieces 1 fourth, 2 fourths, 3 fourths, 4 fourths. Do the same on the second and third wholes.)542925040640fourths0fourths 1 2 3 4 5429250152400fourths0fourths 1 2 3 4542925081915fourths0fourths 1 2 3 4Jesse and his friends ate eleven-fourths of the sandwiches. How many fourths make up our whole? fourHow many fourths do we have in the first sandwich? FourIn the second sandwich, there are four more. How many pieces is 4 + 4? 8They ate eleven-fourths of the sandwiches, so we can count out the rest on the third sandwich. Count together nine, ten, eleven.Remove the extra piece from the last whole. 558165079375fourths0fourths 1 2 3 4 5638800123190fourths0fourths 1 2 3 4 552450079375fourths0fourths 1 2 3 4We have eleven-fourths. How many fourths make a whole? 4How many wholes do we have? 2So the two ways to write the amount of sandwiches Jesse and his friends ate are eleven-fourths or two wholes and three-fourths.d.Guided PracticeWork Guided Practice Problem # 5 (p. 44) with the students. Read the problem together, insert speed bumps and complete the 4-step process. At this time you may want to discuss that labeling each fourth separately is a lot of writing. Therefore, we are going to number the pieces and label the shapes with the name of the fraction it is divided into.Guided Practice Problem #55855335140335001416685-83820004491990-3873500265112513335000Kari has two pizzas. She cuts each pizza into four equal pieces. Kari and her friends eat seven pieces of the pizza. What is another way to write seven-fourths? 319087550800003714755080000Main Idea: another way write seven-fourthsDetails/Known: 2 pizzas in fourths 7 pieces eatenStrategy: With the students divide each pizza into four equal pieces. (Students should not spend time making it perfect, an approximation is allowable when drawing free-hand. Just remind students that a fraction is always equal parts, but when we draw it, we do the best we can.)638175111125003695700635000Count and label the four fourths in each pizza.5362575137160200236982401276351001624840167005001652270150495003719830419100025514302476520022762254381510014705985381000063817514541500369189017018000264985592075300321590023495 400 43412490635400457023001397030031352550175260fourths00fourths428942553975 fourths00 fourthsTeacher and students count out and shade in seven pieces of the pizzas.241490520104102002160337526650954004552196086995200238576251536701001069851001200977515087603003583882517691103003350520016516354004-276225156972040041933575476252002124777513061954004352425137604530033814445112395005210810121412070075210810487045620062440055048704550051249680553720200245720048704510011 wholethree-fourthsHow many whole pizzas were eaten? 1How many more fourths were eaten? 3How do we say seven-fourths in another way? one whole and three-fourthsIs this the only way to shade the model to show seven-fourths? Discuss. How/Why: Counted and labeled seven-fourths. Seven-fourths is equal to one whole and three-fourths.Work Guided Practice Problem #6 (p. 45) together. An example of a completed problem is shown below.Guided Practice Problem #6309562514097000160020017145000Nate drew these three same-size rectangles. Which answer shows two ways to write the shaded part?4933950160655200259912251758954 004 53911501663703 003 25241251320802 002 36766501168404 004 30289501320803 003 1933575711201 001 11430001320804 004 01606552 002 5238751263653 003 -6000751473201 001 -647705022855 005 -133355022856 006 -381005022857 007 323855022858 008 -800105118106 006 -6800855118105 005 10629905118108 008 4438655118107 007 430530057151 001 -6667551054000-6267455295907 007 -11506205295906 006 -17506955295905 005 -76205295908 008 44481751346201 eighth 001 eighth 19335751346208 eighths = 1 whole 008 eighths = 1 whole -6000751346208 eighths = 1 whole 008 eighths = 1 whole (8+8 =16) 16 + 1 = 17 eighthsA.two wholes and one-half or eighteen-eighths-7620026479500B.one whole and one-eighths or seventeen-eighthsC. two wholes and one-eighth or seventeen-eighthsD.one whole and one-eighths or eighteen-eighths26193751600200028194001600201 whole = eight-eighths whole = eight-eighths001 whole = eight-eighths whole = eight-eighths Write shaded part 2 ways6750058890000 2 wholes and six-eighths Counted and labeled shaded parts twenty-two eighths3. Independent PracticeThe students complete, either independently or with a partner, the Fraction Practice Problems Part 3 (MATH_2_A_7 FRACTIONS IP 2014_RES).4.Mixed PracticeThe student should complete, independently, the Mixed Practice Fraction Problems(MATH_2_A_8 FRACTIONS MIXED PRACT 2014_RES).Guided Practice Problem #4Susan baked pies for her party. She cut the pies into eighths. The number of slices that were eaten are shown below. Show 2 ways to write how many slices were eaten?29527549530How many eighths are there? ___________________How many eighths make a whole pie? ______________Group the eighths to show a whole pie.How many whole pies can you make? _______________How many eighths are left? _________________Show 2 ways to write how many eighths were eaten. ___________________________________________________________________________________Scenario #1Jorge had two boards that were the same size. He cut each board into eight equal parts. He used ten of the pieces. What are two ways to write the amount Jorge used?Scenario #2Jesse had three sandwiches. He cut each sandwich into fourths. Jesse and his friends ate eleven-fourths of the sandwiches. What is another way to write the amount of sandwiches that were eaten?Guided Practice Problem #5Kari has two pizzas. She cuts each pizza into four equal pieces. Kari and her friends eat seven pieces of the pizza. What is another way to write seven-fourths? 304800018288000666758763000Guided Practice Problem #6Nate drew these three same-size rectangles. Which answer shows two ways to write the shaded part?A.two wholes and six-halves or twenty-one eighthsB.one whole and six-eighths or twenty-two eighthsC. two wholes and six-eighths or twenty-two eighthsD.one whole and six-eighths or twenty-one eighthsFraction Strips-8365793857160-8365792159000-7776452159000Fraction Circles28397201526300-33337520129500-1264596382259200-43875846348650033744981656410034658304636135003509401522251500-338292523666900349881024477300-336550108585003524777554857200-237490556514000351741419464600-234950175895003366351577779700-218440587819500353980123623100-2476522669500 ................
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