Place Value Activity Package - Mathematics Shed

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1Place ValueActivity PackageActivities humbly borrowed from varioussources. Where possible, sources areacknowledged with the activity.Package assembled byManuel SilvaNumeracy Project Support TeacherWinnipeg School Division2005Place Value ActivitiesWinnipeg School DivisionNumeracy Project

Place Value2 Whole number vertical computational algorithms have negative effects on thedevelopment of number sense and numerical reasoning. (Kammi, 1994, Vince Wright 2000) The standard computational algorithms for whole numbers are “harmful” for tworeasons. First, the algorithms encourage students to abandon their own operationalthinking. Second, the algorithms “unteach” place value, which has a subsequentnegative impact on the student’s number sense (Kammi & Dominick, 1998) Place Value is extremely significant in mathematical learning. Yet students tend toneither acquire an adequate understanding of place value nor apply their knowledgewhen working with computational (procedural) algorithms. (Fuson, 1990; Jones andThornton, 1989) Students associate the place-value meanings of “hundreds, tens, ones” more in termsof order in placement than in base-ten groupings (Bendarnz and Janvier 1982) A major reason for place value lapses is the linguistic complexity of our place valuesystem in English. For example, we do not name “tens” as done in some languages(e.g. “sixty” vs. “six-tens”) (Fuson, 1990; English and Halford, 1995) Students with a weak understanding of place value have a difficult time understandingdecimals.students will often assume that “more digits” implies that a number islarger. (Heibert and Wearne, 1986) Many students never master the standard long-division algorithms. Even less gain areasonable understanding of either the algorithm or the answers it produces. A majorreason a underlying this difficulty is the fact that thee standard algorithm (as usuallytaught ) asks students to ignore place value understandings (Silver et al., 1993)As teachers of early years mathematicians we cannot ignore these glaring facts from theresearch, as well, as our own classroom observations. The time is here to change the way weare teaching students to “do” math in our classrooms. We need to stop teaching verticalprocedural algorithms in our early grades (1-2) and introduce them later on once studentshave shown clear understanding of place value, part-part- whole thinking as well as flexiblestrategies with whole number computation.This package is bursting with great ideas that have been created for use by teachers in ourDivision, to assist teachers in targeting place value instruction in an engaging andmeaningful way.I would like to thank Manuel Silva for taking the time to compile all the great resourcesthat we as teachers have been creating and using.now you have them all in one place!Enjoy using these materials.kids may not remember all the math you teach them but theywill never forget your attitude!Meagan Mutchmor K-8 Mathematics ConsultantPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

3Some Thoughts on Place ValuePlace value understanding plays a key role in the primary grades. It is essential tohave a strong foundation in place value in order to achieve success in making sense ofour number system (based on the digits 0-9), counting, adding multiple-digit numbers,money and many other math skills. For this reason, it is important that place value notbe taught in isolation for a few weeks but that it be integrated all year long into the mathprogram. In fact, the National Council of Teachers of Mathematics (NCTM)recommends that all mathematics strands be taught in an integrated fashion throughoutthe year and not in isolation.When teaching place value to students, it is important to be aware of how students’developmental levels affect their understanding in place value. For example, a studentmay be able to count to 100 but may not be able to see that 23 is the same as two groupsof ten and three ones or 1 group of ten and 13 ones. They may be able to count individual items but have difficulty counting groups of objects.John Van de Walle states in his book, Elementary and Middle School Mathematics:Teaching Developmentally, that counting plays a key role in constructing base-ten ideasabout quantity and connecting these concepts to symbols and oral names for numbers.In order to develop place value concepts, activities should involve concrete models,practice using place value language orally, illustrations and symbols. The activitiesshould focus on one or more of the following three main components of place value:grouping activities, giving oral names for numbers and written symbols for the concepts.It is also necessary to help children connect place value concepts to real-world situations.Working with numbers around them at school, home and community makes learningmeaningful for the students.Jim Martland, et. al, in their book Teaching Framework in Number, outline a threelevel model for the development of base-ten arithmetical strategies.Level 1: Initial Concept of Ten. The student does not see ten as a unit ofany kind. The student focuses on the individual items that make up the ten. Studentcounts forward or backward by ones in addition or subtraction tasks involving tens. Atthis level, the student can identify numbers in the range of 1 to 10.Level 2: Intermediate Concept of Ten. Ten is seen as a unit composed often ones. The student is dependent on representations of ten such as open hands of tenfingers. The student can perform addition and subtraction tasks involving tens whenthey are presented with materials but not when presented as written number sentences.Level 3: Facile Concept of Ten. The student can solve addition andsubtraction tasks involving tens and ones without using materials or representations ofmaterials. They can solve written number sentences involving tens and ones by addingor subtracting units of tens and one.Place Value ActivitiesWinnipeg School DivisionNumeracy Project

4Number Sense and Place Value DevelopmentBased on research in Young Mathematicians at Work: Constructing Number Sense, Additionand Subtraction (Fosnot and Dolk, 2001).Early Stages of Place Value DevelopmentNumber Sense: Steps and LandmarksDevelop cardinality(final number said in count is the number of objects in the set)Conservation of number (one-to-one correspondence)Subitization to 5Part/whole relationships (5 and 1 are parts of 6 because they contribute to the 6)Compensation (other ways of making the same number)Counting onPlace ValueStudent recordings of their work Sporadic drawings with no attempt to represent the quantity One-to-one correspondence in the pictures to the real object Iconic (symbols) representations to represent the quantity of the objects Symbolic representation of the quantity using one symbol (a number)Once students have developed the concepts of cardinality, one-to-one correspondence,part/whole relationships and compensation, they will begin to see the need for an organized wayto keep track of their counting, especially of larger groups of objects. They will begin toorganize their counting into groups of five or ten. After working with this concept many times,they will begin to understand that ten objects can be represented as one ten. Students need todevelop the concept that one group of ten equals ten units within that group. This is calledunitizing (using a number to count not only objects but also groups). This must be in placebefore students can understand place value. They can then start to work with the concepts ofmaking 10s (8 and 2 make 10, 7 and 3 make 10) and breaking numbers apart (26 is 20 and 6and eventually, 26 32 [20 30] [6 2]).Place Value ActivitiesWinnipeg School DivisionNumeracy Project

5SubitizingThe ability to subitize is a precursor to place value understanding.Subitizing is the ability to recognize dot arrangements in different patterns.Since children begin to learn these patterns by repetitive counting they are closelyconnected to their understanding of the particular number concept. Quantities up to 10can be known and named without the routine of counting. This can help children incounting on (from a known patterned set) or learning combinations of numbers (seeinga pattern of two known smaller patterns).Young children should begin by learning the patterns of dots up to 6. Students shouldalso associate the dot patterns to numbers,numerals, finger patterns, bead strings, etc. You can then extend this to patterns up to10 when they are ready.Subitizing is a fundamental skill in the development of number sense, supporting thedevelopment of conservation, compensation, unitizing, counting on, composing anddecomposing of numbers.For example:We want children to learn that there are 5 dots in this pattern or arrangement; five is more than four; a set of 5 objects can be separated into a set of two objects and a set of threeobjects, etc.; five counters, no matter how arranged, still retains the same numerical quantity; the associated oral name for a set of five things is “five”; the numeral corresponding to a set of five objects is “5”.More subitizing online at: www.wsd1.org/pc mathPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

6Subitize, SubitizeSubitize, Subitize,Seeing sets ofdifferent size.Sets of 3, sets of 5,It’s lots of fun tosubitize!Sets of 4 and sets of 2,Let me subitize withyou.Sets of 6 and sets of 4,Let us subitize somemore.Subitize, subitize,Seeing sets of differentsize.By Linda BoughtonPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

7Sense of Number?Place izeNumberRelationshipsCreated by Meagan MutchmorPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

8Some Activities to Further Develop Place ValueCounting Forward and BackwardCounting forward and backward helps to develop rote number patterns. Childrenshould have the opportunity to count forward and backward in multiples of 1, 2, 5,10, 3, 4 as well as from random starting points. They can count numbers in thedecades, centuries or millenniums.Number PatternsBeing able to identify number patterns on the hundred chart and addition/multiplication charts expands a child’s knowledge of number sense. Manyopportunities to explore number patterns helps students to solidify this knowledge.Counting by multiples is a counting pattern that is essential for the understandingof multiplication concepts.MoneyMoney is a great way to learn about place value and trading appropriate coins.Concepts such as fractions and decimals can also be taught through the use ofmoney.2– and 3– Digit Addition/SubtractionGood place value concepts and number sense will foster good understanding ofaddition and subtraction concepts.Place Value ActivitiesWinnipeg School DivisionNumeracy Project

9Show with base 10 blocks [younger groups can use 10 frames]The number just before is .10 more than this number is .Write in expanded notation .This number is odd/even .10 less than this number is .The number just after is .Write out in words .3 other ways to make this number are:This number is a multiple of .25 more than this number is .Start at today’s number and count by 5’s ten times.Created by Meagan MutchmorPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

10More Number of the DayRoll dice to determine three digits(for example 562:)The greatest number you can make byrearranging them is 652. The smallest number you can make is 256. Add the digits together.(5 6 2 13). Multiply them (5x6x2 60). Count up in tens(562, 572, 582, 592, 602 and so on). Count down in tens(562, 552, 542 and so on). Count up in hundreds(562, 662, 762, 862, 962, 1062 etc.). Count down in hundreds(562, 462, 362, 262, 162, 62). Subtract the numbers (5-6-2 -3). Divide it by tens(562, 56.2, 5.62, 0.562, 0.0562 and so on). Multiply by ten(562, 5,620, 56,200, 562,000 and so on). Created by Meagan MutchmorPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

11Number of the Day ChartShow/draw using materials,money, blocks etc.Base ten sforrepresentingthe numberNumber of theDay inNumeral form35Create apicturestoryWords: Thirty fiveShow on ten frames or drawanother representation, digiblocks, bean sticks, bundles ofstraws, etc.Note : this is just a starter of ideas to use. You can change any of the boxes to suit yourstudents and grade level.Place Value ActivitiesWinnipeg School DivisionCreated by Meagan MutchmorExpanded NotationNumeracy Project

12Flip and Fold Use Flip and Fold cards to help your students learn their number relationshipsas well as learn to “Bridge to Ten” Create cards on construction paper and then mac-tac or laminate to protectthem. Different Flip and Fold cards can be made to go with your thematic units, usestickers or copied pictures to make more variety. These cards can be a great take home game that students create on their own.Use potato prints as a art activity or bingo dabbers. Parents could also makethem at a parent function and then use them with their children.Source: Meagan Mutchmor, Math Consultant, WSDPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

13Go 10Materials: 3-4 players1 deck of cards, minus the face cardsAce 11.2.3.Deal out all the cards. The game is played like Fish, exceptthat each player is trying to make 10.Each pair of cards that makes 10 is placed face up in front ofthe player who makes it.The winner is the player with the most pairs when no more10s can be formed.LeftoversMaterials: 2 players1 deck of cards, no face cards25 bingo chips1.2.3.4.5.Place Value ActivitiesOne player deals half the cards to each player.Both players turn over their top two cards.Each player determines how close the total of their cards is toten.The player whose total is closest to ten gets a chip. Ties areboth rewarded a chip.The game is over when the chips are gone. The winner is theperson with the most chips.Winnipeg School DivisionNumeracy Project

14Making TensMaterials: 2 players5 or more regular dice10 bingo chips, or any other counter1.2.3.4.One player rolls all the dice and makes groups of ten with thenumbers rolled. The total points left over after making tensis remembered by the player.The second player takes a turn.The player with the least leftover points wins the round andtakes one bingo chip.The game is over when the chips are gone. The winner is theperson with the most chips.Knock KnockMaterials: 2-4 players1 deck of cards10 counters1.2.3.4.5.6.7.Place Value ActivitiesAces are worth 1; face cards are worth 10.Each player is dealt 4 cards, and the remaining cards becomethe draw pile.The players take turns taking the top card from the draw pile,and discarding one of the cards in their hand.They are trying to make the greatest possible total value.When one player thinks he/she has the largest total, he/shesays Knock, Knock. Everyone else has one more turn.Players then add their totals. The winner takes one counter.The game is over when counters are used up.Winnipeg School DivisionNumeracy Project

15In Between GameMaterials: 3 students12, 20 or 30-sided die for each student30 bingo chips1.2.3.4.5.6.Each student rolls a die without the other students seeing thenumber rolled.Each student, in turn, tries to predict whether they have thelowest, highest or in between number.After hearing all the predictions, they may change theirprediction.Students show their number.Each student who was correct receives a bingo chip.The winner is the first child to get 10 chips.Race to 10/100/1 000Materials: 2-4 players1 000, 100 or 10 place value mats6, 20, or 30-sided diceBase ten materials – units (1), longs (10), flats (100) andblocks (1 000)1.2.Students roll die and the highest number goes first.Students play in turn by rolling the die and taking theappropriate amount of units, longs, flats, etc.e.g. a roll of 19 1 long (10) and 9 units (1s)3.4.Students continue and make appropriate exchanges asneeded.The winner is the first to reach the targeted number: 10, 100or 1 000.Variations: Start with 10, 100 or 1 000 and subtract the roll.Grades 4 may race to 10 000 or use decimalnumbers.Place Value ActivitiesWinnipeg School DivisionNumeracy Project

16Guess My NumberMaterials: Hundred Chart pocket chart or an overhead of a Hundred Chart1.Pick a secret number from the hundred chart and don’t tell thestudents what it is.Have students ask you questions to try and guess what thenumber is? Sample questions include: is it more than/lessthan, odd/even, a multiple of , end in , have tens/units,etc.Cross off numbers on the overhead chart or flip them on thepocket chart as they are eliminated by student questions.Use a tally to keep track of how many guesses it takes theclass before they identify the secret number. Next time youplay, try to beat that number of guesses.2.3.4.Extensions: Students may play the game in partners or small groups. Use hundred charts in the various centuries.What’s Your Number?Materials: 3 diceRecording sheet1.2.3.4.5. Place Value ActivitiesRoll the 3 dice.Arrange all three in order to make 6 different numbers.e.g. 3 2 6326, 263, 632,362, 236, 623.Record your numbers as in the example above.Order your numbers from least to greatest.Show your numbers usingpicturesstandard notationexpanded formWinnipeg School DivisionNumeracy Project

17NameDateWhat’s Your Number?Record your 3 numbers from the dice.Make 6 different numerals using them.Order the 6 numerals from least to greatest., , , , , .Draw a picture to show 1 of these numerals.Write the numeral using standard notation.Write the numeral in expanded form.Place Value ActivitiesWinnipeg School DivisionNumeracy Project

18Hidden Number GameMaterials: Whole class/small group/individualOverhead projectorBase ten blocksMagic cloth1.Show the students part of an equation while part ofthe equation is hidden.6 2. orStudents determine the answer.Variation: Show students part of an equation.e.g. 11 ? My number is 45. What is my hidden number?Place Value ActivitiesWinnipeg School DivisionNumeracy Project

19Five Tower GameMaterials: 2 playersUnifix cubes2 dice1 copy of the Recording Sheet per student1.2.3.4.5.6.7.Roll the dice and take that many cubes.Snap them into a tower.Take turns doing this with your partner until you each have 5towers.Each player snaps his/her own 5 towers together into a train.Compare your tower with your partner’s. Whose is longest?How much longer?Each partner now breaks his/her own train into tens andones.Record your results on the recording page.Source: A Collection of Math Lessons by Marilyn BurnsPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

20NameDateFive Tower GameMy train is cubes long.My partner’s train is cubes long.Whose train is longer?How much longer is it?I have tens and ones in my train.Total cubesMy train is cubes long.My partner’s train is cubes long.Whose train is longer?How much longer is it?I have tens and ones in my train.Total cubesPlace Value ActivitiesWinnipeg School DivisionNumeracy Project

21Number Pattern Detectives*Use of a vertical number line provides a powerful visual representation of place valuenumber patterns which facilitates numerical understanding.Materials: Chart paper-sized graph paper cut into strip (vertical number line),2 or 3 columns across or adding machine tapeOverhead projectorBase 10 blocks—tens and onesPermanent black marker1.2.3.4.5.6.7.Show students the vertical number line that you have prepared.Divide students into pairs and number each student as 1 or 2.Have a pair of students come up to the overhead and have partner 1add 1 cube to the overhead. Partner 2 records the number on thevertical number line, either starting at the

Meagan Mutchmor K-8 Mathematics Consultant Place Value . Place Value Activities Winnipeg School Division Numeracy Project 3 Some Thoughts on Place Value Place value understanding plays a key role in the primary grades. It is essential to have a strong foundation in place value in order to achieve success in making sense of .

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