(J Lt I Place Value Tents Materials needed: 2 colors of cardstock, BLM, scissors Prepare these ahead of time. Decide if you want students to work individually or in pairs to determine how many sets of Place Value Tents you will need. Copy and cut apart. Fold in half. 1. The thousand cards and the tens cards need to be on the same color of cardstock. 2. The hundreds and ones cards will be on the second color of cardstock. This way when numbers are built, the colors will be alternated making it easier to see if the number is correct. 3. Example: If you are building the number 3,987 - you would use \. • The 3,000 card as the base card • Place the 900 card on top of the 3,000 card leaving only the 3 on the 3,000 card visible • Place the 80 card on top of the 900 card leaving the 3 and 9 on the previous cards visible • Place the 7 card on top of the 80 card leaving the 3, 9, and 8 of the previous cards visible Students may now lift up each flap and write the number in expanded form. 3,000 + 900 + 80 + 7 Some students will try to use the ones cards in all places. This is one reason that the colors of cards are alternated. It makes it easy to check. When students use the ones in the hundred or tens place ( i .... simply explain why the 8 card can't be used for 80, etc. { ; ( , \. l 1 II I 1 " ( \ .... P0 5A Get i , \. PS7A Vtr (,lA ,-,' u I \ , '.C ;r, \ .. UL(\ ( \ ( ! I I I I, !, pi)I.?>A I v:\ J~/\ I ) " ..... f l Llll l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :, 1 , 1 G1iJi' 1":.J I~AI I GL~ \ Place Value Homework 5 Draw a picture to represent each number. Hundreds 1. 678 Tens Ones 2. 304 3. 521 Write each number in written form. 4. 801 5. 739 6. 117 _ Write each number in expanded form. 7. 807 8 456 Write the numeral for each expanded form. 9. 500 + 4 ~ ~~ _ 10. 200 + 50 _ _~ _ Place Value Homework 6 Write the value of the underlined number. 1. -20,543 2. 32,451 3. 3,065 4. 325 - --_._ .•. Write the numeral for each number word. 5. six thousand four hundred one 6. thirty-two thousand nine hundred eighty-four Write each number in expanded form. 7. 272 8. 2,704 \Nrite the number for each expanded form. 9. 300 + 30 _ ( ,;. 10. 1,000 + 20 _ _ Place Value Homework 7 Write the value of each. 1. six tens _ 2. eight hundreds 3. 4 tens 4. forty:: 5. ninety:: tens 7. 10 tens:: _ 8. 10 tens: Place Value Homework 8 Write the number in written form. 1. 507 2. 12, 865 3. 780 4. 6,803 Write the number in expanded form. ------------"- 6. 730 7. 10,325 Write the number for each expanded form. 8. 50,000 + 2,000 + 600 + 80 + 2 9. 70,000 + 900 10. 8,000 + 30 + 50 tens 6. ten:: _ _ _ fen Write the number in written form. 10. 1,197 5. 604 + _ 7 _ _ 9. 100 ones = Place Value Homework 9 Draw a picture to represent each number. Hundreds 1 .. Tens Ones -UiL JVU 2. 198 3 677 How many ones, tens, hundreds, thousands, Llnd ten thousands does each have) T Th Th T H o 4. 19,345 5. 20,536 6. 3,409 Write each number in expanded form. 7. 24,530 8. 11,702 ( \Vrite the number for each expanded form. 9. 800 ... 0 ... 7 10. 400 ... 50 ... 6 Place Value Homework 10 Write the value of each. 1. two hundreds 4. 200 =__ hundreds 3. two ten thousands 2. five tens 5. eighty =__ renS 6. sixty =__ tens Write each number in expanded form. 7. 20,906 8. 31,022 / ( \ 'Nrite the number for each expanded form. 9. 60,000 + 3,000 ... 60 10. 6,000 + 500 + 9 Place Value Homework 11 Write the value of the underlined digit. 1. 1~.463 2. 461 3. 4,9.02 4. 19,976 Write the following number in written form. 5. 2,285 6. 22,561 7. 10,005 Write the value of the followIng. 8. 8 tens 10. 70 = = _ 9. 900 tens Place Value Homework 12 Write the following as numerals. 1. thirty thousand four hundred five 2. eighty-four thousand thirty-two 3. eleven thousand nine hundred sixty 4. seventeen thousand one Write the following in expanded form. 5. 89,706 6. 19,052 7. 20,003 Write the following as numerals. 8. 10,000 + 9,000 + 400 + 2 9. 4,000 + 20 + 3 ( \.. 10. 20,000 + 800 +70 + 3 = hundreds (;L£ \ Place Value Homework 13 Write the numbers in written form. 1. 28,945 2. 246,789 3. 109,683 4. 840,083 Write the value of the underlined digit. 5. J.12,089 6. IJ.0,897 Write the number in expanded form. 7. 48,602 8. 274,921 \Nrite the number for each expanded form. 9. 50,000 + 300 t 20 + 1 to. 200,000 + 30,000 + 4,000 + 500 + 20 t 8 Place Value Homework 14 INn te the numbers in written form. 1. 690,150 2. 903,784 ~ Write the numeral for each. 3. one hundred fourteen thousand eight hundred forty-two 4. seven hundred three thousand six Write the value of the underlined digit. 6. 2611007 5. 307,242 Write the number in expanded form. 7. 365,001 8. 60,514 Write the number for each expanded form. 9. 500,000 + 2,000 + 600 + 80 10. 200,000 + 60,000 + 70 + 4 _ \. Place Value Pictures , ( ) (10 Use base ten blocks to make a picture or design on a piece of paper. I o Trace around the blocks (or cut and paste paper base ten blocks) to make a recording of your picture. l' "I! ! I I ! ! Record the value of each base ten block. Then add up all the hundreds, tens, and ones to find the total value of your picture. ~~ndYI 1:::/ 2 2. I I II tOo Exchange pictures with a partner. Use base t8n blocks to build a new picture that is the same value as your portner's picture . • . ~ •.J '" } , l Patterns for Base Ten Blocks For each set of base ten blocks, reproduce this page at least three times. On the first copy, cut out the large squares. On the second copy, cut out the squares and then cut them into strips to make tens rods. On the last copy, cut out individual units for ones squares. For durability, mount on tagboard and laminate before using. ) Unit 1 Activit) 8: Spin and Win (GLE: ~) Materials List: Ten Digit Spinner BLM, Spin and Win BLM, paper, pencil Students work \vith a partner or in groups of four using SQPL, student questionsjor purpose/iii iearmng (\ il'\\ iitlTaC\ \tr~llc~\ dCSCI'I~I1S) in this readiness activity. Students will discuss this statement that the teacher writes on the board: There is only one < 8,623. Have the number that will make this statement true: 2,863 < students turn to their partner or to their group and come up with one question they would like answered about that statement. The teacher will write the questions on the board. Next, the students will use prior knowledge about place value to answer the questions generated by the class. Next. have the students play Spin and Win to provide additional practice with large numbers. They will need the Ten Digit Spinner BLM, a pencil, and a paper clip to make a spinner. I. Place the point of a pencil through a large paper clip. 2. Place the point of the pencil on the center of the spinner. 3. Adjust the paper clip so that the end of the paper clip is on the center of the spinner. 4. "Flick" the paper clip to spin it. ( ( Have them play the game with a partner. Using the Spin and Win BLM and the Ten Digit Spinner BLM, they will try to build the largest number possible. A turn is signified by each player spinning, the Ten Digit Spinner BLM six times. After each spin the player decides where to place the digit he has spun. Once a digit is placed on the paper, it cannot be moved. After all six digits are written down, the player reads his number. The partner does the same thing. Together they must use the correct symbols «, >, =) to record the comparison of the numbers to declare the winner. Example: Spin and Win Partner 1 Partner 2 ~~~11Q < ~1~~~1 Partner ]'s Spinner Partner 2 's Spinner ( GLCJ- You will also need the Ten Digit Spinner. BLM. The first person spins and writes his digit on one of the blank spaces. Once a digit is placed in a space, it cannot be moved. The second person spins and does lhe same thing. The partners continue taking turns until there are no more empty spaces. Last. they place the correct symbol «. >. =) between the numbers determining who has won that round. Name: --------- Name: _ Winner Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 Round 8 Round 9 Round 10 The overall winner of this game was ( _ Place Value Challenge Materia!s: Place Value Mats for each player, 1 deck of card per 2 players with face cards and 10 cards removed. Aces are worth 1. Goal: To create the highest number 1. Give each player a set of place value mats. Students will play in pairs. 2. Players shuffle cards and deal them until they are gone. 3. Players take turns drawing cards. As each one draws, the player places the card in one of the place value spots on the mat. Once the card is placed, it may not be moved. The object is to get the highest number. ( 4. Play continues until all spots are filled. 5. Players record numbers and compare with <, >, or =. 6. Player with the highest number wins. Variations: Piay the same way except change to goal to create the lowest number. ( Name _ Place Value Challenge Decide which . player is Player 1 and which . plover is Plover 2. Write .. . " your name in the correct blank. Record your number and your partner's number below. Place <, >, or = in the space between the numbers. Player 1 ( Player 2 l I / ' ~ 1 ) Unit 7 Activity 1: Fractions on Grids (GLEs: ~,~, 1, ~) \laterials List: Fractions on Grids BLM, crayons. math learning log, pencil Use Fractions on Grids BLM to demonstrate fractions as part of a whole. Help students begin to understand the connection between fractions, decimals, and percents by relating them through money. Discuss the denominators that will be used to show varying amounts of money (the denominator for pennies in a dollar is I OOths, dimes in a dollar would be IOths, quarters in a dollar could be 4ths, etc.) Demonstrate for students how to color in 50¢ on the Jirst grid of the Fraction and Grids BLM. Take them through each step as you discuss the equivalent decimals, fractions, and percents for 50¢. Have the students complete the other grids on their own, stopping for class discussions when needed. (I quarter as .25 or 25/ 100, or or 25% of a dollar; 6 dimes + as .60 or 60/l00, orTo' or 60% of a do lIar; 3 quarters as .75 or75/100, or +or75% o1'a dollar, de.) Have the students create an Equivalence Table in their math learning log (\i~\v lit..:r~lc\ ;tr'!l":2-':ch''':iiLH ilJli..,). This labie wiii be used as a reference tor future activities as well as a study guide for assessments. Have students add other money amounts and their corresponding fractions and any other equivalences as the unit continues. E, xample: r Money amount . -. - $0 .75 I -J5 pennIes I 1 penny = $0.01 I > r 2 quarters = $0.50 I 1 dime = $0.10 Equivalent decimal .25 .0 I .50 =.5 Equivalent fraction 25/100 = 1/4 1/100 50/100 = 5/10 = 1/2 Equivalent percent 25% 1% 50% .10 10/ 100 = 1/l 0 10% ~.I Show 50¢ on the grid by shading in the correct number of squares. ) Write 50¢ using a decimal. What fraction of a dollar is SO~'? [s there another way to write this fraction'? What percent of a dollar is SOe'? ~how 25c on the grid by shading in the correct number of squares. Write 25¢ using a decimal. What fraction of a dollar is 25¢? ) [s there another way to write this fraction? What percent of a dollar is I 25~? ~ _ _ Show lOe on the grid by shading in the correct number of squares. l What fraction of a dollar is lOe'? -~-- Is there another way to vvrite this traction'? i I i i i I i ! ~ I I H f---1 Write lOe using a decimal. What pt:>fcent of <1 dollar is ! O¢'! I I ! i II iI ; I I i ti-l I ! I I i. ! I I I I ! i I I I II I I I Show 75¢ on the grid by shading in the correct number of squares. Write 7Se using a decimal. - - What fraction of a dollar is 75¢? _ Is there another way to write this fraction? - - What percent of a dollar is 75¢? _ Show Se on the grid by shading in the correct number of squares. Write 5e using a decimaL _ What fraction of a dollar is S¢'? ) , _ Is there another way to write this fraction? - - What percent of a dollar is 5¢,? 1 -- Show 60¢ on the grid by shading in the correct number of squares. 'I I , _ Is there another \vay to write this ['raction'? - - "Vhat percent of a dollar is 6()1;;'? _- - _ I, ,I I I I I I i , 1 I i i II I I I I i I I I !I I I I, I \Vhat fraction of a dollar is 60¢,? I 'I , I, Write 60e lIsing a decimal. I i I I I I 1 I U i--+---+-+----+-----+------,---!-----, ! , GEC Curriculum Map (,rade Level " ) ':L Subject Area Math Week If 8 Day 1f4 I "l:sson Title " GLE(s) September 30 Check Homework Set 17 Quiz 3 Subtraction facts GLEs 22, 1,2,6,12,23 I I I I fL W select and use the appropriate standard units of measure, abbreviations, I and tools to measure length and perimeter, area, capacity, weight/mass, and volume TL W read, and write place value in word, standard, and expanded form through 1,000,000 TL W read, write, and compare, and order whole numbers using place value concepts, standard notation, and models through 1,000,000 TL W model, read, write, compare, order and represent tractions with . denuminators through twelfths using region and set models TL W count money, detennine change, and solve simple word problems involving money amounts using decimal notation IL W set up, solve, and interpret elapsed time problems Pound, difference, expensive, cheapest, dozen, fraction, numeral Can students tell time and work elapsed time problems that do not cross midnight or noon? Unit 2 Activity 13: Time's Running Out GLEs 23 Materials: Student Clocks, Book PiRs on a Blanket, Demonstration Clock • Objective(s) Academ ic Vocabulary LCC Guiding Question(s) Lee Activity Resources/Materials ) Grading Period Second Six Weeks I I Bell Ringer/Released Test Bell Ringer 36 I Item I I Set/Hook/Focus I ! j-M-o-,d-e-lin-g-------- I Gu ided Practice Independent Practice - ! Evaluation I i ! ----l Closure Homework ----- - ----------j--- :'-Jotes/Comments: ------------------------1 _ _ _..J UNDERSTAi~DlNG BASIC FRACTIONAL CONCEPTS VIA FRACTION STRIP ACTIVITIES l\latcrials needed for activities: Fraction Cube~ (each cube labeled 1/16, 1/16, 1/8, 118, 1/1 , and 1/2) Strips of Paper in Five Colors Scissors i\farkers Recording Sheets ') ,\CTIVITY 1: MAKING FRACTION STRIPS ~OTE: The advantage of baving students make a sd of strips is that they physically fold each strip into a given number of EQUAL paIts and label each part with its :.:rpropri~1te fr~ction n:1111e. Through the process of mak.ing lhe strips, students eM Ji~cover or the teacher can guide shldents to constmct the following understandings: • Fractional parts of a whole arc EQUAL parts of the whole • The meaning of the boltom nwnber (denominator) in a fractional number ~ .[he meaning of the top munber (numerator) in a fractional number • There are many (in1inite) fractional names for I identified whole region (1= 1/1,2/2, .. .4/4 ....16/16... ) • There are different names for the same amount of an identified whole region (1/2 = 2/4, ..., % = 6/8, ... ) • Identify fractional amounts of an identified whole as being equal to, less than, or greater than each other • The more equal parts the same sized whole is divided into the smaller the value of each part ) Procedures: 3. Have students place the blue strip at the bottom of lheir desk or llible and label 1 Whole b. c. Have students place the red whole on top of the blue to verify that it is the same size. Have students fold the red strip so that it makes two equal pieces and cut on fold line. Guide students to name each part ~i because the whole has been divided into 2 equal parts and each part is one ofthe two equal parts ... or one of the halves (depending on vocabulary that has been developed). Follow same procedure folding, cutting, and labeling the green strip in fourths, the orange strip in eighths, and the yellow strip in sixteen1.hs. d. Have students display cut-out fractional strips one above each other with the one whole strip on the bottom, followed by halves, fourths, eighths, and sixteenths. e. Have students observe the fractional Jisplay and share observations noted. Since ';ome of the observations will represent profound understandings of fractional concepts, consider recording the statements on chart paper. As new fractional understandings \)r concepts are shared, they can be added to this chart offraction j;/cts JiscQvereJ. Th~ chart also provides a visual for those leamers whose learning is Jcpendent on visual representations knowledge, concepts, al1l1lor generalizations. Or, following d above, muve to Activity 1.. .. Students will have opportunities to make sinular observations with activities that follow. ACTIVITY 2: DIFFERENT FRACTIONAL NAMES - SAME VALUE Purpo~e: To detcmlinlt difTerent fractional n~l1nes that represent the same value or amount of a given whole stri p. To determine different fractional names that represent the same value or amOlUlt. Procedures: a. Have students place one hand on each end of the one whole strip. Have students identify this strip from end to end as the whole strip. Then, have students move their hands to the ends of the two Yz pieces. Ask students if the two half pieces cover the same amount of space as the one whole. To prove this have students place the whole strip over the two Yz pieces. Once the relationship is verified by all, record the relationsrup on the board in equation fonn. (1 = 2/2) Next, have students move their hands to the ends of the four l/4 pieces. Ask students if the four 1/4 pieces cover the same mnount of space as the one whole. Once again to prove this rel:1tionship, have students place the whole strip over the four 'II pieces. Once the relationship is verified by all, add to the equations recorded earlier. (l = 2/2 = 4/4) Continue this procedure until the equation reads 1=2/2 ~/4=8/8= 16/ 16. = Ask students to predict the fractional value of 1 if the whole :;trip was cut into 3 equal pieces, 20 equal pieces .....Add this information to the equation 3/3 ... 20/20 ... When clppropriate, have students verbalize the characteristics of any fractional name for one and justifY the explanation. It should make sense .... based on logical reasoning. If using the Fraction l:"acfs Discovered l:hart, alid the generalization discovered by students to the chart. Use verbiage as close to their description/explanation as possible. h. Find other fractional names for one-half using the display of Cr:lctional strips and the provided equivalency strip. Lin~ up the equivalency strip where the two one half strips meet. Observe the value of one-half and "travel up the equivalency strip" to identify amounts of other strips that equal the same amount (take up the same amount of space) as the ace-half strip. Record the equivalent values as done with the equivalent values of 1 whole. (1/2 =:: 2/4,4/8,8/16) c. Use the ~quivalency strip to iJcntify other equivalent r~lationships such as 1/4 = ..... ; % == ... ; 2/8 == ... ; 4116 = .... ; ... continue by identifying other equivalencies. FractiOlIaI concepts/understandings that students can come to "OWN" as a result of focuseJ engagement in lllis activity: Related GLE(s): _ ACTI VITY 3: COVER THE \VHOLE STRIP Purpose: To completely cover the one whole strip with other fractional parts contained in the fraction kit. Procedure: <l. Each student places the whole strip labeled "one whole" in tront ofhimJher. (Two or three students play together.) b. Stud~nts take turns rolling the fraction number cube. c. 'me fraction that appears face-up on the cube tells the player what piece to put on the whole strip. Fractional pieces may not overlap. All players must agree on the placement of fraction pieces on the whole. When a student is finished with a turn, ' he/she says, "Done" and passes the fraction cube to the next player. J. To end a rolU1J 0 f this game, the player must roll the exact fractional name for the fractional amount that is needed to cover the whole strip. G. Remove all pieces from the one whole strip and playas many rounds as time will allow. Fractional understandings that students can COllie to "O\Vi."i" as a result of focused engagement in this Jctivity: Rcbtcd OLE( s): - - - - - - - - ACTIVITY.t: UNCOVER THE WHOLE STRiP Purpose: To completely lillcover the one whole strip which has been covered with two one-ilalf pieces. Procedures: a. E::lch student completely covers the strip labeled "one whole" with two one-half pieces. b. Students take turns rolling the fraction number cube. c. The fraction that appears f::lce-up on the cube tells the player the fractional amount that must be removed from the one whole strip. Pl~yers may need to exchange equal fractional values in order to make the uncover mo ve. 1llC fractional piece that is removed must mutch the fr~ction face-up on the number cube. If 1/8 on the cube, a 1/8 piece must be removed, not two II l6ths. All players must agree on the placement of fraction pieces on the whole. When a student is ti.nished with a tum, he/she .says, '"Done" and passes the rraction eube to the next player. d. To end a round of this game, the player must roll the exact fractional name tor the fractional amount that is needed to completely uncover the one whole. e. Recover the whole with one-halves and playas many rounds as time will allow. ) Fractional understandings that students can come to "OWN" ~ a result of focused engagement in this activity: Related GLE(s): _ Uncover Options: Alter students have played the traditional game a number of times, allow them to cover the one whole in such a way thDt they think will result in their having to make the fewest value exchanges. I-fowever. students must remove the value that is face-up on the fraction cube. As the game proceeds, each stHd~r!.t keeps a record of each value exchange required. (Recording sbeet is proviJed.)After several rounds of the game, have students share initial cover options that seem to require the fewest value exchanges. Have students offer explanations for their observations. Students cover [he whole with the pieces of their choice. Students remove trOm the whole [he fractional value indicated on the fraction cube OR any \.luivaknt value. For example, if the die shows 1/8. th<.: ';fuuent coulJ remove a 1/8 pieceor two 1/16 pieces. 13efore the round begins, ask students to explain why they covered the whole strip as they did. Students keep a record of aJl actions made during the round. (Recording sheet is provided.) After several rounds of this option, record on the board any cover options that most consistently re4uires the fewest number of plays to completely uncover the whole. Ask students to offer explanations for result(s). ACTIVITY 5: COVER TilE \VHOLE STRIP - CONNECTING CONCEPTUAL TO ABSTRACT Playa rowld of the game of "Cover the Whole Strip" together wilh the teacher rolling the fraction cube for each turn and all students placing the same indicated fr3ctional piece on the whole strip. Once everyone's whole strip is covered, ask a stuJent to call out the name of each fractional stri p lhat has been placed on the ",.. hole strip. As the fractional names ,~re called out, the teacher rccords each tractional value on [he bo:u-d in equation form. (113 + j/16 + 14 + il16 + ~4 + 1/8 t- 118 = 1) Then the teacher asks students to help determine if there is a simpler way to rccord these amounts. Guide students to grouping same-sized fractions together, such as 2/16 + J/8 + 2/4 = 1. ) ! bve students playa round of the game according to the original directions. When the whole is completely covered, each student records the pieces covering the whole in equation form. The student then rewrites the equation in the simplest form. Students can pass equations written to another player who review :.1nd initials if he/she th..inks correct. Playas many rounds as possible having students first record all actions and then record by grouping like parts together. Instead of playing in game fonnat, have each student cover their whole in five or more ditTercnt ways and record on a recording sheet the original and simplified equation for each coverage of the whole strip. (Recording sheet is provided) Students can exchange their recording sheet with a partner to check the accuracy of the simplitied equation. If appropriate for your students, ask students to look at a covering eql4ltion such as 2/16 + 3/8 + 2/4 = 1 and work with a partner to reWlite so that each fraction uses the same sized parts. (For example, 2/16 + 6/16 + 8/16 = I or 1/8 + 3/8 + 4/8 = 1) This builds strong foundation for tinding common denominators. Fractional understandings that students can come to "OWN" engagement in this activity: ~------- Related GLE(s): -- :is a result of focused OTHER FRACTIONAL CONCEPTS TO DEVELOI) WITH FRACTION STIUPS a. Comparing Fraction.:> b. Adding and Subtracting Fractions with Like Denominators c. Adding and Subtracting Fractions with Unlike Denominators J. Multiplying Fractions ~. Dividing Fractions ) ~ ,f . ',$:1 , ~. ;y uml Namcs of Parts uscd to Cover the Whole Strip - ~umber of Parts Used 5 I EXJm pie r COVER THE \VHOLE STRIP ~...:..-- I;' liS 1/16 1/16 1/2 1 I . I , 2 - . - - i i I I .3 ! ~ ------- \ 5 \_- .~ ) Think Ahout! l. Look 3t the information you recorded in the chart. What did the parts look like when the fewest number of parts were used? Why did it take fewer of these parts to cover the one whole'? \Vb3t did the parts look like when the most parts were used? Why did it tlke more of these pans to cover the one whole? .3. Pbying this gJme, what would be the fewest number of p:lrts th:lt could be used? N WIle the parts. I. Pbying this game, what would be the most number ofp:lrts that could be useJ? Name or describe the parts. _ .~. ,[-{\)W lll~ll1Y you '1. < [[ow ylll1 ways C..in 11lJny \\aY5 em • : fuw 'luny ·,::1n3. '.\.LV5 ':.lil '1,',1) cover the whole with 2 frJctional p2rts? list the p::111S. cover [he whole with J traction:ll parts l [jst the p:lrts . COWl" [be \vh\)!e '.'.!th 1, ;::, 6, ... ;'rldi,;[j,d [':itT).' fii[ .~.' ---- . -,_.~~ ... -~--------- ~ 'J ',-J -i f ~/ RECOHDING SHEET: WRITLI\G EQUATIONS ORl\L\THEl\l-\.TIC-\.L SENTENCES 1. yvur whule strip with whatever pil:ccs you would like to usc. You must use at least three different fractional piecl:~ tv w\'er tbe one whole. " Write au c4uatiun or mathematical 3entcncc using all of th~ fractions used to eovcr/cquallhe whole. Record your mathematical :iWlClICC as EQUATION 1 in the table below. CUHf ,;. GroUlJ fntctiou3 together that have tlJe same siLe parts and rewrite the equation or mathematical sentence. Record your mathematical scutcnce as EQUATION 2 in the table bdow. -4. l{~peat the stq)S by covering your whole in five additional different ways. 1UN (Gruup fractio parts) ----- i.e. I,Lj~ I e;\,dlllplc: I 2. i -- J. EQUATION 3' t- QUATION 2 1 iunal pkccs usc) -_._----- -- ----------- -4. I :'J. I I (.I • L ~ ---~---- I • 11' "pprupriale for yow' stlld~nts, usk students to work with partners or in a group of 3 to rev,Tite each E,QUA nON 2 using parts that arc the .J,uu..: for e~ch fraction. For example, 'ATite all fractions in halves or fourths or eighths or si;x.teenths. Record the fractions \vith like pms in til\: EQUATION 3 column. The thinking required to 'ATite tht;;se equations is the same thinking requird to add or subtract fractions with LJi diL,: J<::llllIlliIldtors. ..• + ..."• - + ( :'=P..ACTiON SUNDAES \. ) I J . ,-,er~ s 1" ,) eel/CiOUS \Voy to helD ~tudenL$ ii:,uo{i<:e fractional peru :')( G g,-oup i 'MHATYOU NEED .. ~r<\ction SUndJ€ S ~ reprodlAcible ~ Pattern for each page 93) construction paper In ~tud~:lt "ice cream" co!ors ,~ 1,:2 Cream Flavor Color Combinations i,r"produclble page 91) .. t.ipe WHAT TO DO Student in5tf"Uctions i Teacher Notes , • Cut out the sundae dish and set ;t aside. 2. Cut out the ice cream pattern. Trace the pattern as many times as you like on different colors of construction paper. Use the Ice Cream Flavor Color Combinations list for ideas. Each color wili be a scoop of a different ice cream "flavor" for your sundae. Cut out the shapes. ( ) Adjust the moth leyel of this aai.,iry to students' skill leyel with (ractions. Students who are new to fraaions may need instructions as specific as "Put six scoops o( Ice cream on your sundae. One hai( of the scoops must be chocolate, and one hal( must be 'Ianilla," Higher-level students can tackle problems such as "Put on odd number of scoops of ice cream on your sundae. Use five (lavors o( ice cream. Each f7avor must represent a different (raction o( the whole number o( scoops." ]. Tape the scoops of ice cream to your sundae dish. Tope me backs of the scoops o( ice cream, overlapping them in (ront .J ;( = • ,au EMS • • Ila; • • + GLC~ + ~. Describe )'OUt· sundae in fractions. How many scoops of ice t:ream does it have in <:til? T"~t number will be the denominato" of your' fractions. How many scoops of ea"h flavor does your !Sunciae navel Those numbers will be the numerators of your fractions. list all the fractions on your sundae dish. Then top off your sundae with a red construction· "aper cherryl Refer to the photo on page 90 to see how to label the sundae dishes. TIPS FOR A SUCCESS;-UL PROJECT .. Get students reallY excited about this project by inYlting them to creat~ their own wacky ice creJ.m flavors and add the c.olor COr:1bJn3t10m to their li~ts. V-IANT TO KEEP GOING? ( '" .. ) ". Cut out lots of sundae dishes and scoops of ice cream. Hang up a lis:: of "flayors" and ~et up all "ice cream parlor" in your classroom. Swdents can take turns serYlng one another. Or invite students from another class to VISit )'eur Ice cream parlor and let them o.-d~r ~undaf:?s b)' the fracticl\! • Create a monster sundae on a bulletin board in your classroorT'. Have StudenLS contrtbute flavors untl! you have reached 3 certain number of scoops, such as 100. Ther. work together to figwrc cut all of r.he fractIons that make up the whole sundae. Check your work l;Jy adding up all of the numeratOrs to make sure the total is the same number as the dE;nominator. PossIble Ice Cream Flavor CombiIlatlOns: :.; ~ra v.bern~ '-" "j r- nl-. ~aC'er '. 'Wllh red Jots ChocoJ:He ch'r .- ,,;,'hlre paper WI rh hrown dms Cookie ~lnJ...'gh = white ?ape;- \"1t~ tan chHn.ks :\11:11choc:o!:H~ :"ll:; ". :,'Te~n paper 'Nlth hfown (j;;LS Fudge Ripp!e = while Darer '.\"llh brown stnfXs Bubble Gum '-" PInk paper wilh blue dots V:ln:lla'-- v-:hliC ~per ~. ---...._-_...._~!'ft1lI_.._----.~~----"""'-- ere ~_IrIIii ZC'c, ,.I'I_ _~tml!D'lt' ........._ '"tme::"~l!fzDt w'· ( ) 1 I j I () j "') '-. ' I f 1 \ IJ 4\ '" / ~ .,t:I- ) \ '~ l ( ) \ \ • A Unit 2 Activity 9: Organizing Your :\'loney (GLEs: 1, ID :V1atcrials List: Organizing Your :V1oncy BLM, colored pencils, index cards with money amounts un them, box, learning log notebook In this activity, have students create a graphic organizer in their math learning log (\ iel\ lil~_r~lc~ ,tIJk'cC\ ,J"",,~rjilll(1I1") connecting fractions to decimals to percents as it relates to a dollar bill. They will need this graphic organizer as a reference to help study for future tests. Have them complete the grid dollars on Organizing Your Money BLM. They will use this dollar to display ~ of the dollar, .10 of the dollar, 10% of the dollar by shading in the corresponding spaces on the grid dollar. 1lave them do the same fort, .25,25%; 1f2, .50, 50%; J/" .75, 75%; 100/1 00, 1 \\-hole, 100%. The pro{essor know-ii-ali (\je\,-Jjl':-,!::I~:~_~tJ":llCh:_-,Il:_~idI'j l1Ji\2lh) strategy can be lIsed to check fJf understanding. r\ ~hiid is chosen to come to the front of the class. They will pull a money amount card from a box and read it. (The amount could be written as a decimal, with words, or using a cent sign.) Alter the student reads the amount, the class will ask him a variety of questions. For instance: Can you rewrite your money amount in another form? What fraction of a dollar is that amount'? What percent of a dollar do you have? Can you describe your amount in coins'? Name: \ ~~~~~---~. } $1 00 I~, ae h Sh ad e In . 10c square stan d s for $ 01 I Frauion r,ae h square stan ds for $ 01 $1 00 ~- ~T ~. ) P<.:rc<.:nt D<.:<.:imal Sh aelO d . 25i - I I I L hactlOn $1.00 ! i I I I i I I I~i- I i Perc<.:nl Decimal Each , square stands for $.01 I IT~ I i ! i i i I I 1-r~IClillll ! I ! i I I I I I i I I I i I Shade in SO¢ ---rr I-Tl ! I J---Lj I t i I I I I I I I I I i i I I I I I I ! ..J Name: --------r $1 00 :a~ ~ Fra~tion y au ~an Sh ad em . 75¢ . h square san t d s for,$01 I I [)~cimal I'~rc~nl choose your own amount for the next ones. .Shadem. E~a~ h square s tan d s ~or $ 01 $1 "-- 00 I - 1 I ) - Fraction no $1 I I I ! I I i I I [:ach square stan ds for $ 01 i ! ! I I i I i I i Percent Decimal I I· ra~tion I I I I I i I i I Sh aem d . I I I I ! I I i I I I [)e~lmal I i I I I I I i i I Percent I I I : I I I Money Foldable Look at the foldable basic directions. Follow the direction for the layered book. After you have created a layered book using two pieces ofconstruction paper and using a hotdog fold, staple a whole sheet of construction paper on the back. This will give you 5 layers. Put the dollar on the top layer. Cut the next layer in half and glue the half dollar on each part. You may label the parts like the sample or have students put different ways to write the m.oney amount on differentparts. You decide. Cut the next layer in 4ths and put the quarters. Label each piece however you want. Cut the next layer in lOths. Glue the dim.es on and label. The final layers is cut into 20ths. This layer is labeled only. ) Once the book is complete, you could have students lift up the flaps and draw different coins to make the amount on the flap. t-:-tj --------·----·--L~;-L Foldables Basics TN by Dinah Zlke Foldables are 3-dimensionaJ, interactive graphic organizers that can help your students to organize, remember, review, and learn many kinds of infonnation. They encourage students to use their creativity in a kinesthetic learning environment while reinforcing important thinking and communication skills. Listed below are a few basic Foldables instructions. On the other side you'll find some of the most versatile Poldables designs. ,---_'>-.._. -"-/ Valley Fold A valley fold has sides that rise up from the center fold. Hamburger Fold Fold a rectangular sheet of paper in half along the long side. Shutter Fold Hotdog Fold Fold a rectangular sheet of paper in half along thG short side. Find the midpoint on a piece of paper, then fold each side in to meet that point. Mountain Fold A mountain fold has sides that slope down from the center fold. Taco Fold Fold the comer of a sheet of paper over to create a triangle. Trim any :ss. Bu rrito Fold A burrito fold rolls the page up without creating a crease ;n the paper. C~LE 1 N Foldables Basics by Dinah Zlke -) Matchbook Fold a sheet of paper in half like a hamburger but leave one side one inch longer than the other. Fold that one-inch tab up over the short side tQ create an envelope-like fold. Cut in half or in thirds (depending on the paper size) to create --1\ multiple Matchbooks. '-----------' Vocabulary Book Fold a sheet 01' notebook paper in naIf like a hotdog. On one side, cut every third line to create tabs. You can adjust the ')_ number of lines depending on the paper and the desired size of the tabs. Label the tabs with vocabulary words ;md write the definitions undemeath. o o Folded Table or Chart Fold a sheet of paper in half (for two columns), then in half again (for four columns). Do the same in the other direction for the desired number of rows. or simply make one fold .llong the top for column headings. H=m ~ ...acm"'4n/l,.4cGraw· 11111 Pocket Book I I , Fold a large sheet of paper in half like a hamburger. . up, then &Id ~ ./' Open it .0_ one of 11 _ the long sides up to fonn a , tab of about two inches. Refold so that the newly fonned pockets are on the inside. Use glue.or staples to secure the outer edges. Students can place index cards or quarter sheets of paper inside the labeled pockets. Layered-Look Book Stack two or more sheets of paper so that the top edge~ are one inch apart. Bring the bottom edges up and align the sheets so that all of the layers (or tabs) are the same distance apart. Fold and crease well to form the Layered-Look Book. Use glue or staples to hold the sheets together. Students can label the tabS and record mformauon illside the _ _ _~ Layered-Look Book. f 1 I 1 T M-35 ') 200 1 ,~!,M,S EduI':3tion F~ljr:rJJtion j 'I THe UNITED STATES OP AMERICA '7 ) llnit -I Activit}' 6: Understanding Multiplication II (GLEs: !!,.!..IJ Materials List: graph paper or base J 0 blocks, pencil. paper Lxtend Activity 3 to 3-digit by I-digit and 2-digit by 2-digit multiplication problems. Instead of dot arrays. students should draw rectangles vr use base 10 blocks. as shown below, 10 show the problems. Make sure the rectangles arc broken along place value lines f()r both numbers. Repeat this activity several times with various multiplication problems. Notice the use of the distributive property: II >: 52 = (10 + I) x (50 + 2) = I Ox50 + I Ox2 + I x50 + I x2 = 572. (This will take two to three days 01" practice.) I,'or example, II 52 \vould be represented as: < 2 50 10 \ 10 x 50 ~ i \. 572 ( 10 x2 Activity II: Real-World Scenarios (GLEs: 13,!.:!, 12.) Materials List: paper, pencil, Real-World Scenarios BLM Have the students write number sentences or equations for each situation Scenarios I3LM and solve using algebraic thinking. 011 the Real- World Name: Date: - - - - - "\.' I. The t'ourth graders have earned some "free" time. They want to play games. There are 7 groups of ehildrcn with 4 children in each group. How many children are going to play games'? J Ms. Smith's class is going to play kick ball. They will need two teams. If there are 24 ehildrcn in the room. how many children will be on each team? 3. Mr. Thompson's class 01'27 students wants to have relay races. If they put 9 people on each team, how many teams will they have? ~. Mrs. Clark has put her class into groups of 5 to bring treats for the 5 parties they will have this year. I-low many students are in Mrs. Clark's class? 5. Challenge Question---Activities have been planned for the party. Each activity \vililast twelve minutes. There are three activities. If they begin their party at 2: 10 and eat for 30 minutes. will they have enough time for all the activities to ue completed by 3: 15? Date Name ) -----------~ I. I'he fourth graders have earned some "free" time. They want to play games. There arc 7 groups of children with 4 children in each group. How many children are going to play games? 'x-l==n 7 X -I 28 There are 28 children playing games. == 2. Ms. Smith's class is going to play kick ball. They will need two teams. [1' there are 24 children in the room, how many children will be on each team'? .2 x n == J -I -'- 2 },-I or 2-1 -'- 2 = n == 12 Thf!re will be 12 chi/eire n on each team. 3. Mr. Thompson's class 01'27 students wants to have relay races. If they put 9 people on each team, how many teams will they have? f) or n = 27 or 27;- 9 },7 ) 4. -7- 9=J .= n They will have 3 teams. Mrs. Clark has put her class into groups of 5 to bring treats for the 5 parties they will have this year. How many students are in Mrs. Clark's class? 5 or 5 ~ n 5 x 5 = 25 there are 25 students in Airs. Clark '5 class. 5. Challenge Question---Activities have been planned for the party. Each activity will last twelve minutes. There are three activities. If they begin their party at 2: I 0 and cat for 30 minutes before they begin the activities, will they have enough time for all the activities to be completed by 3: IS? ::10\- 30 minutes = 2:-10 I': minutes or J games == 36 2:-10 36 minutes == 3.16 r They 1-Fill begin playing games at 2:-10. They will need 36 more minules to play the games. There is not enough time/or all the aclivities as planned !3onlls----Ask .I'll/dents jur possihle solutions 10 have enough time fiJr their party. (Start or end t!arfier'less time jur eating/fewer aClivitieslless time jur each activity, elc.) 6 ) GALLON MAN .' 1 G-AT4T40N~ (Or Woman) Help students develop an understanding of standard liquid measurement by constructing "GALLON MAN." I1's easy, it's fun, and students will create a concrete model for use as a resource mtil they master the concept. Materials Needed small paper plates 4 sheets colored paper SCIssors Procedure 1. Use the paper plate for the head of the figure. ) 2. Use 1 whole sheet of paper for the body. Write 1 gallon on the page. 3. Use a different color sheet of paper to create the quart. Fold the page into four equal parts and cut apart. Glue the 1/4 pieces to the body as arms and legs. 4. Use a different color sheet of paper to create the pint. Fold the page into ~ equal parts and cut apart. Glue two 1/8 pieces to the unattached end of the arms and legs. 5. Use a different color sheet of paper to create the cup. Fold the page into sixteen equal parts and cut apart. Glue two 1/16 pieces to each of the unattached end of the arms and legs. Discussion 1. Ask students if they see any patterns in creating "Gallon Man (or woman)." \) 2. Ask students conversion questions (i.e. number of cups needed to make a pint, quart or gallon). 3. Have students develop questions they could ask someone who is looking at their creation. 4. Use everyday containers (measuring cup, pint milk carton, gallon orange juice bottle) to prove the model's measurements are correct. 5. At a later date, have students visualize "Gallon Man (or woman)" and orally, or on paper, create the model from memory. 6. Students may want to name their model. Have students write a short story about uGalIon Man (or woman)." 7. Let students work in groups to develop measurements larger than one gallon (i.e. number of quarts, pints, or cups in 3 gallons). () -.... ",-.L. "-"/ Gallon Man You need: 4 pieces of construction paper 1 paper plate for a head * 1 sheet for body = gallon • 1 sheet for quarts Means where to glue. . A \d ~ Anns (1 hotdog fold) Q .L r ~ Top part of legs (I hamburger fold) Make sure you fold hotdog style first, then hamburger. -... Cut along the line. .-... • "-.;. '-......J Gallon Man .1P.'tPt't!1 g Arms (2 hotdog folds) Bottom part of 1 sheet for pints ~~ 1 1 I I I 1 , , ,, I I Legs (I hamburger fold) legs and anns, two pieces per part. 1 I 1 sheet for cups ~'9~ Fingers(3 hotdog folds) g Four pieces per part. ~'¥:WifJEq '.-., \..i~ P I I I 1 1 1 I , I I I , I I Toes( 1 hamburger fold) '-...,..: v Gallon Man cups ~' p. ~: ~~-M quart ~ ~. cups J LAYERED LOOK BOOK 1. Stack tvvo sheets of paper (8 1/2" x 11"), and place the back sheet on e Inch higher than the front sheet. 2. Bring the bottom of both sheets upward and align ihe edges so that all of the layers or tabs are the same distance apart. I;' 3. VVhen all tabs are an equal distance apart, fold the papers and crease well. 4, Open the papers and glue them together along the valley/center fold. I / 1 7 "\ ) ) What is the perimeter of the figures below? 6 ft. 1. 4 ft. 4 ft . Perimeter = • 6 ft. 4 in. 2. Perimeter = 4 in. Find the area and perimeter of the figures below. 3. 5m 10 m Area = Perimeter = Unit I Activity 18: Explain the Rule (GLEs: ..., 14, ) m rvlaterials List: Explain the Rule BLM, calculator, pencils \Vrite these open-ended number sequences on the board. • • • 2,7, 12, 17, _ _, ' Rule: ---------------8,16,32,64, _ _, _ _, _ Rule: ---------------203,195,187,179, , _ _, _ Rule: ---------------- Have students tind the next three numbers in the pattern, describe the rule (function), and then th th name the 5 and 6 number in the pattern. Have students determine if the numbers are increasing (adding or multi plying) or decreasing {subtracting or dividing). Have the students work in pairs to complete the Explain the Rule BLM. When they have completed this activity, have students generate their own open-ended number sequence for a ~artner to S~lv. e by usi~the calculator. First, have them choose a startin~ number. Th~n th.e y put In "the rule . ([~ 5, or ~ 3, or [J 4. or 6, etc.). Next, have them wnte down the tlrst tour numbers of their number sequence. Their partner tries to discover the rule and writes down the )-th an d 6th num b er 'In the pattern. GJ ) Name: ') / Date: Complete these tables and state the rule. ~ I 17 12 7 2 I I I Rule: l:S 74 70 2~ ~8 • ~ Rule: 12 96 I Rule: CHALLENGE 1_62'5_0_0-----'-_12_'~_-0_0_;_2_,5_0_0 Rule: 500 ------'-1__ _-----' _ ----- A. lfthe numbers in the pattern increase, what operations could be used? B. If the numbers in the pattern decrease, what operations could be used? Name: Date: _ ~~~ _ ~ ") Rule: Add 5 (2 + n = 7 n = 5) 1~8 I 74 Rule: Subtract 4 Rule: I 70 CZ8 - L~~ I n",,74 Multiply by 2 ( 12 x n n = 62 I 58 I 54 I = 4) 24 n = 2) ) CHALLENGE 62,500 12,500 [ 2500 f5_O_O_----'-_ Rule: Divide by 5 (62,500 -:-- n = 12,500 n = 5) 1_0_0~~_2_0~~_4 _ ____' :\. If the numbers in the pattern increase, what operations could be used? .1ddition or ,\[ultiplication B. If the numbers in the pattern decrease, what operations could be used?

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