Dice Activities for Algebra

RIC-6106 5.5/1004

Dice activities for division (Ages 8–10)

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Published by R.I.C. Publications® 2012 under licence to Didax Inc. Copyright© 2012 Mary Saltus, Diane Neison, Chet Delani ISBN 978-1-922116-11-6 RIC–6106

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Dice activities – Building multiplication facts and developing fluency (Ages 8–12) Dice activities – Building number sense and power (Ages 5–8) Dice activities for algebra (Ages 10–13) Dice activities for division (Ages 8–10) Dice activities for mathematical thinking (Ages 10–13) Dice activities for subtraction (Ages 6–9)

A number of pages in this book are worksheets. The publisher licenses the individual teacher who purchased this book to photocopy these pages to hand out to students in their own classes.

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Dice activities for division

Foreword

F

luency with the operation of division is a critical skill for more complex mathematical challenges.

Of the four operations, division can be the most tedious for students. It is often taught as a series of memorised procedures, making it difficult for students to wrap their minds around what is actually happening. Students are asked to practise solving division equations without a sense of the underpinnings of the operation.

Dice activities for division focuses on developing mental acuity and fluidity with the concepts of divisor, dividend, quotient and remainder. When experiencing division in a gamelike context, students readily engage in the activities and actually request opportunities to practice, or—as they would call it— ‘play the game’. Fluidity comes only with practice based upon understanding.

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With a solid group of division facts, students can more easily navigate their way through the more complex study of fractions and pre-algebra concepts. The factor and remainder activities further develop students’ understanding of how numbers work.

The partner book, Dice activities – Building multiplication facts and developing fluency, serves as a foundation for the explorations of the ideas of division presented in this text. The format should be familiar to students who have used the Building multiplication facts book, allowing them a greater opportunity for addressing the mathematical concepts involved. The common structures of the activities include graphs, charts, and tic-tac-toe. Division concepts addressed include: • • • •

division without remainders connection to the inverse operation of multiplication multiples and factors remainders

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C.Publ i cat i ons •f rr evi e wp ur p os es onl y• Dice activities foro division addresses reasoning, problem solving, and probability.

Contents

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The activities require only the use of dice and tiles or tokens—all commonly available classroom manipulatives. The activities are easily adapted to home schooling and for parents who wish to participate in the education of their children. The activities are engaging, generate a friendly competition, and provide a reason for learning division concepts.

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Teachers notes ....................................................................................................................................................................................................................... iv – viii Curriculum links .............................................................................................................................................................................................................................. viii Hundreds chart .................................................................................................................................................................................................................................... ix Division chart .......................................................................................................................................................................................................................................... x Division graph activities ................................................................................................................................................................................................... 1–13 Table completion activities ....................................................................................................................................................................................... 15–32 Chart activities: Four in a row, Square off and Cross over ................................................................................................. 33–46 Tic-tac-toe/Four grid tic-tac-toe activities ............................................................................................................................................. 47–72 Factoring activities .............................................................................................................................................................................................................. 73–80 Remainder activities .......................................................................................................................................................................................................... 81–99

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Teachers notes

Conceptualising division in three words: ‘has how many’ Attaching the term ‘has how many’ to the ÷ sign creates a vivid image of the division process. ‘Has how many’ makes sense to students in the context of their language, whereas ‘divided by’ implies a procedure or process.

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When 20 ÷ 10 becomes ‘20 has how many (sets of) 10?’ or 100 ÷ 25 becomes ‘100 has how many (sets of) 25?’ students can mentally make sense of the question and often successfully solve division problems without relying on memory, skip counting or manipulatives.

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With 27 ÷ 3 (‘27 has how many [sets of] three?’), some students may need to skip count by three to 27, or take 27 tokens and divide 27 into sets of 3 tokens each.

Conceptualising multiplication in two words: ‘of the’

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The equation 3 ÷ 5 = ? is oftentimes confusing. Students might say it is not possible. Using the term ‘has how many’ and tokens will easily clarify the confusion. Three has how many sets of 5? None. What’s left over? 3. So what is the solution? 0 remainder 3.

Reading the multiplication sign (×) as ‘of the’ enables students to make sense of what the problem is asking—for example, 5 x 3 is really asking for ‘5 of the 3s’. The term ‘of the’ invites students to mentally construct meaning from their experience rather than rely on memory.

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C.Publ i cat i ons Strategies for arriving at a solution •using f o r e i e wof the pskips. ur posesonl y• • Skip count, fir ngers to v keep track • Use the Hundreds chart (page ix) to aid in skip counting.

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• As a last resort, use the Division chart (page x). For a student with recall issues, the Division chart is a useful tool. The student can focus on the concepts of division, factors and remainders rather than struggle with recall, enabling the student to further develop number sense and a conceptual base for reducing fractions.

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Dice activities for division

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Teachers notes (cont.)

Division fact activities Objectives: • Develop fluency with division facts 2 to 12.

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• Determine a factor or multiple by skip counting.

• Explore the reciprocity of multiplication and division (for example, 2 × 3 and 6 ÷ 3).

• Develop game strategy.

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• Investigate probability concept of chance.

• Develop communication and cooperation skills by working in teams of two students.

The graph activities are introductory lessons to familiarise students with each set of division facts. The simplicity of these activities makes them a tool for diversifying learning.

Each division equation is paired with a corresponding multiplication equation to show the inverse and aid in computation. Some students may find it beneficial to stay with this activity, developing recognition and fluency, while others are ready for more challenging involvement.

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The table completion activities challenge students to fill in their chart before their opponent does. There is a table completion activity for each division fact set. Several table completion activities involve students working on a different division set from their opponent.

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In the write an equation activities, students generate a division equation in which the quotient equals the dice toss.

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With the chart activities, students choose to play one of three games: Cross over, Four in a row, or Square off.

• Cross over: Teams attempt to place their tokens so they form a continuous path zigzagging vertically, horizontally or diagonally from space to adjacent space from one side of the chart to the opposite side.

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• Four in a row: Teams attempt to line up four tokens vertically, horizontally or diagonally before the opposing team does.

• Square off: Teams attempt to arrange four tokens to form any size square: 2-by-2, 3-by-3, 4-by-4 and so on. The square can be orientated on the diagonal.

The tic-tac-toe activity is paired with a four-grid tic-tac-toe activity to provide a way to diversify while reinforcing division facts. The tic-tac-toe activity presents an opportunity for students to practise playing tic-tac-toe with each set of division facts before moving on to the more complicated four-grid tic-tac-toe.

Variations listed for each activity provide extra fun and challenge for students who are ready for it.

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Teachers notes (cont.)

Factor and remainder activities Objectives: • Explore the relationship between the concepts of factors and multiples.

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• Recognise patterns when dividing by 2, 5 and 10 (divisibility rules).

• Determine a factor or multiple by skip counting.

• Practise computing remainders.

• Develop game strategy.

• Investigate the concept of probability.

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• Recognise remainder patterns.

• Develop communication and cooperation skills by working in teams of two students.

The factor table completion activities challenge teams of students to fill in their chart before the opposing team does. Teams toss a dice to find a factor, then circle a number on their table that is a multiple of the factor. The first team to fill its chart wins. Students soon become adept at generalising divisibility rules for 2, 5 and 10.

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C.Publ i cat i ons In factor takeaway, teams arev presented dice tossed within ano octagon shape.

•f or r e i ewwithp10u r p os es nl y • Teams take turns tossing two dice, finding the product, and removing from the octagon a

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factor of that product. When all dice have been removed from the octagon, the teams total the dots on their dice to determine the winner.

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Factor two-dice switch is similar to factor takeaway. Teams toss five dice each within their designated circle. Two other dice are tossed to create a two-digit number (for example, 24). Each team removes a dice from its circle that is a factor of that two-digit number.

Next, a student switches the dice places to create a new two-digit number (42). Teams then remove a factor of this two-digit number from their circle. Teams continue tossing the two dice, creating two-digit numbers, and removing factors. The first team to remove all its dice wins. Students soon generalise that 1 is a factor of any number and 2 is a factor of any even number.

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The factor rounds – ten-dice toss activity requires students to identify multiples for each factor in a round. Each team tosses 10 dice, pairs the dice as products, and places each pair on a factor of the product. If a team can place the 10 dice on all 5 factors, it continues to the next round using the same dice numbers. In the unlikely event that the first team completes all five rounds on the chart with one toss of the 10 dice, the other team has an opportunity to do likewise. In the unlikely event that the second team succeeds in completing the chart with one ten-dice toss, the game is a tie. Actually placing the dice on the multiples gives students the opportunity to manipulate the number combinations to try to find a multiple for each factor. Before long, students realise which numbers need to be tossed to complete a round.

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Dice activities for division

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Teachers notes (cont.)

The remainder table completion activities are slightly different from the division and factor table completion activities. These tables have three columns instead of two. A designated team member tosses a dice that becomes the divisor. Each team circles a multiple in the first column that, when divided by the dice toss, will result in the largest remainder. The team records the dice toss (divisor) in the middle column and then records the remainder in the third column. After 10 tosses, the competing teams tally their remainders.

The team with the largest remainder total wins.

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In the remainder toss: write a ÷ equation activities, students generate division equations in which the dice toss equals the remainder.

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With the remainder chart activities, students choose to play one of three games: Cross over, Four in a row, or Square off.

With the remainder chart (addition/division) activity, teams toss two dice and then one more to create a dice equation involving addition—for example, (3 + 4) ÷ 5 =. The teams place a token on the remainder produced by the division equation.

With the remainder chart (multiplication/division) activity, teams toss two dice and then one more to create a dice equation involving multiplication—for example, (3 × 4) ÷ 5 =. The teams place a token on the remainder produced by the division equation.

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C.Publ i cat i ons Remainder two-dice switch is similar to factor two-dice switch.

•f or r evi ew pur posesonl y• Teams toss two dice to create a two-digit number and then switch the

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places of the dice to create a different two-digit number. Remainder two-dice switch is also similar to remainder table completion. A team tosses a third dice that becomes the divisor and records the dice toss (divisor) in the middle column.

The team records the remainder in the third column. The dice are switched to create a different two-digit number. Students take turns tossing dice to create two-digit numbers and switching the digits. The teams tally their remainders, and the team with the largest remainder total wins.

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To play remainder tic-tac-toe (addition/division), teams toss two dice and then one more to create a dice equation involving addition—for example, (3 + 4) ÷ 5 =. The teams place a token on the remainder produced by the division equation.

To play remainder tic-tac-toe (multiplication/division), teams toss two dice and then one more to create a dice equation involving multiplication—for example, (3 × 4) ÷ 5 =. The teams place a token on the remainder produced by the division equation.

Variations listed for each activity provide extra fun and challenge for students who are ready for it.

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Australian Curriculum: Mathematics links

Dice activities for division includes activities which support the teaching and learning of fluency, reasoning, problem solving and communication, as well as developing understanding of concepts in Number and Algebra and Statistics and Probability.

Year 3

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Number and Algebra Number and place value • Uses multiplication and division facts for two, three, five and ten.

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Statistics and Probability Chance • Carries out chance experiments, identifies and describes outcomes and recognises the variations in results.

Data representation and interpretation • Uses tables or column graphs to collect and record data without the use of digital technologies.

• Uses data displays to compare results.

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C.Publ i cat i ons Number and Algebra or r evi ew pur posesonl y• Number• andf place value

Year 4

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Uses multiplication and division facts to 10 × 10.

Uses efficient mental strategies for division without remainder.

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Statistics and Probability Data representation and interpretation • Uses tables and column graphs to record collected data without the use of digital technologies.

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The above content descriptions have been reproduced with permission from ACARA. © Australian Curriculum: Assessment and Reporting Authority 2012

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Dice activities for division

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Hundreds chart

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or eB t 11 12 13 e 14r 15 16 17o18 19 20 s Teac he r

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0÷8=0 8÷8=1 16 ÷ 8 = 2 24 ÷ 8 = 3 32 ÷ 8 = 4 40 ÷ 8 = 5 48 ÷ 8 = 6 56 ÷ 8 = 7 64 ÷ 8 = 8 72 ÷ 8 = 9 80 ÷ 8 = 10 88 ÷ 8 = 11 96 ÷ 8 = 12

0÷7=0 7÷7=1 14 ÷ 7 = 2 21 ÷ 7 = 3 28 ÷ 7 = 4 35 ÷ 7 = 5 42 ÷ 7 = 6 49 ÷ 7 = 7 56 ÷ 7 = 8 63 ÷ 7 = 9 70 ÷ 7 = 10 77 ÷ 7 = 11 84 ÷ 7 = 12

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0 ÷ 11 = 0 11 ÷ 11 = 1 22 ÷ 11 = 2 33 ÷ 11 = 3 44 ÷ 11 = 4 55 ÷ 11 = 5 66 ÷ 11 = 6 77 ÷ 11 = 7 88 ÷ 11 = 8 99 ÷ 11 = 9 110 ÷ 11 = 10 121 ÷ 11 = 11 132 ÷ 11 = 12 0 ÷ 10 = 0 10 ÷ 10 = 1 20 ÷ 10 = 2 30 ÷ 10 = 3 40 ÷ 10 = 4 50 ÷ 10 = 5 60 ÷ 10 = 6 70 ÷ 10 = 7 80 ÷ 10 = 8 90 ÷ 10 = 9 100 ÷ 10 = 10 110 ÷ 10 = 11 120 ÷ 10 = 12

0÷9=0 9÷9=1 18 ÷ 9 = 2 27 ÷ 9 = 3 36 ÷ 9 = 4 45 ÷ 9 = 5 54 ÷ 9 = 6 63 ÷ 9 = 7 72 ÷ 9 = 8 81 ÷ 9 = 9 90 ÷ 9 = 10 99 ÷ 9 = 11 108 ÷ 9 = 12

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0÷5=0 5÷5=1 10 ÷ 5 = 2 15 ÷ 5 = 3 20 ÷ 5 = 4 25 ÷ 5 = 5 30 ÷ 2 = 6 35 ÷ 5 = 7 40 ÷ 5 = 8 45 ÷ 5 = 9 50 ÷ 5 = 10 55 ÷ 5 = 11 60 ÷ 5 = 12

0÷4=0 4÷4=1 8÷4=2 12 ÷ 4 = 3 16 ÷ 4 = 4 20 ÷ 4 = 5 24 ÷ 4 = 6 28 ÷ 4 = 7 32 ÷ 4 = 8 36 ÷ 4 = 9 40 ÷ 4 = 10 44 ÷ 4 = 11 48 ÷ 4 = 12

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0÷3=0 3÷3=1 6÷3=2 9÷3=3 12 ÷ 3 = 4 15 ÷ 3 = 5 18 ÷ 3 = 6 21 ÷ 3 = 7 24 ÷ 3 = 8 27 ÷ 3 = 9 30 ÷ 3 = 10 33 ÷ 3 = 11 36 ÷ 3 = 12

0÷6=0 6÷6=1 12 ÷ 6 = 2 18 ÷ 6 = 3 24 ÷ 6 = 4 30 ÷ 6 = 5 36 ÷ 6 = 6 42 ÷ 6 = 7 48 ÷ 6 = 8 54 ÷ 6 = 9 60 ÷ 6 = 10 66 ÷ 6 = 11 72 ÷ 6 = 12 0 ÷ 12 = 0 12 ÷ 12 = 1 24 ÷ 12 = 2 36 ÷ 12 = 3 48 ÷ 12 = 4 60 ÷ 12 = 5 72 ÷ 12 = 6 84 ÷ 12 = 7 96 ÷ 12 = 8 108 ÷ 12 = 9 120 ÷ 12 = 10 132 ÷ 12 = 11 144 ÷ 12 = 12

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0÷2=0 2÷2=1 4÷2=2 6÷2=3 8÷2=4 10 ÷ 2 = 5 12 ÷ 2 = 6 14 ÷ 2 = 7 16 ÷ 2 = 8 18 ÷ 2 = 9 20 ÷ 2 = 10 22 ÷ 2 = 11 24 ÷ 2 = 12

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0÷1=0 1÷1=1 2÷1=2 3÷1=3 4÷1=4 5÷1=5 6÷1=6 7÷1=7 8÷1=8 9÷1=9 10 ÷ 1 = 10 11 ÷ 1 = 11 12 ÷ 1 = 12

Division chart

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Division graph activities Contents

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Directions for division graph activities ................................................................. 2

÷ 3 two-dice graph ..................................................................................................................... 4 ÷ 4 two-dice graph ..................................................................................................................... 5

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÷ 2 two-dice graph ..................................................................................................................... 3

÷ 5 two-dice graph ..................................................................................................................... 6 ÷ 6 two-dice graph ..................................................................................................................... 7 ÷ 7 two-dice graph ..................................................................................................................... 8 ÷ 8 two-dice graph ..................................................................................................................... 9 ÷ 9 two-dice graph .................................................................................................................. 10

÷ 10 R two-dice graph © .

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C .Publ i cat i ons11 ÷ 11 two-dice graph 12 •f or r e v i e w p u r p o s e s o n l y• ÷ 12 two-dice graph 13 ............................................................................................................... ...............................................................................................................

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Dice activities for division

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Directions for division graph activities Objectives • Develops a working knowledge of the mathematical concepts of division.

• Practises division facts 2 to 12.

• Recognises and reinforces factors.

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• Quickly recognises all possible sum combinations on two dice.

• Practises directionality on the x and y axes.

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Variations

• First team to fill a column wins.

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The graph activities are introductory lessons to familiarise students with division facts. The simplicity of these activities makes them a tool for diversifying learning. Some students may find it beneficial to stay with the graph activities to develop recognition and fluency, while others are ready for more challenging involvement with division facts.

• First team to fill three columns wins.

• First team to fill a column stops the activity.

Teams find the total of all the numbers entered on the graph to determine the highest score.

• Toss dice 10 times. Team with the highest sum wins. Keep a record of tosses and use as a probability lesson.

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C.Pu bl i ca t i oandnfis • Team tosses two dice nds the sum.

Instead of recording the quotient, teacher •f orr evi ew pu r po setos on l y• instructs students perform another

Introduce the division graphs by demonstrating on an overhead projector or interactive whiteboard.

How to play • Toss two dice and find the sum.

calculation to the quotient and record the answer on the graph, such as:

• The first team to fill in a column wins.

– add 7, 8, 9, 10, or 11 to the quotient

Suggestions

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– halve the quotient

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– double or triple the quotient

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• The sum is the quotient of a division equation on the chart. Fill in the box above the equation with the quotient.

– add 5 to the quotient and halve the result

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• Have students use the term ‘has how many’ instead of ‘divided by’ when reading the division sign (÷).

• If students are struggling to recall division facts, suggest they skip count by the divisor until they reach the quotient (dice toss) to find the multiple (dividend) or, if necessary, refer to the Division chart (page x).

– subtract 7, 8, 9, 10, or 11 from the quotient (possible to result in a negative number) – after 5, 10 or 15 tosses, tally the answers to see which team has the highest or lowest score.

Discussion

• How do you work out a division solution if you cannot recall the division fact?

• How do the multiplication facts help with division?

• How can skip counting help in solving division problems?

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Dice activities for division

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• Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘18 has how many sets of 2?’

• Or skip count by 2s until you get to 18.

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÷ 2 two-dice graph

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• Toss two dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘27 has how many sets of 3?’

• Or skip count by 3s until you get to 27.

How to play

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16 ÷ 4

Dice activities for division

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• Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘16 has how many sets of 4?’

• Or skip count by 4s until you get to 16.

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÷ 4 two-dice graph

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• Toss two dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘35 has how many sets of 5?’

• Or skip count by 5s until you get to 35.

How to play

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÷ 5 two-dice graph

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24 ÷ 6

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• Toss two dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘24 has how many sets of 6?’

• Or skip count by 6s until you get to 24.

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÷ 6 two-dice graph

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42 ÷ 7 21 ÷ 7u84 ÷ 7

63 ÷ 7

14 ÷ 7

56 ÷ 7

ew i ev Pr

• Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘49 has how many sets of 7?’

• Or skip count by 7s until you get to 49.

How to play

w ww

8

35 ÷ 7

77 ÷ 7

28 ÷ 7

÷ 7 two-dice graph

r o e t s Bo r e p ok u S

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Teac he r

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24 ÷ 8

Dice activities for division

80 ÷ 8

32 ÷ 8

o c . che e r o t r s super

72 ÷ 8

96 ÷ 8

m . u

64 ÷ 8

16 ÷ 8

• Toss T two dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘24 has how many sets of 8?’

• Or skip count by 8s until you get to 24.

w ww

How to play

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 56 ÷ 8

ew i ev Pr

40 ÷ 8

88 ÷ 8

48 ÷ 8

÷ 8 two-dice graph

r o e t s Bo r e p ok u S

9

Teac he r

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

. te

Dice activities for division

54 ÷ 9

90 ÷ 9

o c . che e r o t r s super

m .

45 ÷ 9 72 ÷ 9u108 ÷ 9

81 ÷ 9

18 ÷ 9

63 ÷ 9

ew i ev Pr

• Toss T two dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘54 has how many sets of 9?’

• Or skip count by 9s until you get to 54.

How to play

w ww

10

36 ÷ 9

99 ÷ 9

27 ÷ 9

÷ 9 two-dice graph

r o e t s Bo r e p ok u S

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. te

÷ 10 two-dice graph Teac he r

• Toss T two t dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘60 has how many sets of 10?’

• Or skip count by 10s until you get to 60.

w ww

How to play

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

R.I.C. Publications® – www.ricpublications.com.au

o c . che e r o t r s super

Dice activities for division

60 ÷ 10 80 ÷ 10 30 ÷ 10 70 ÷ 10 120 ÷ 10 20 ÷10 100 ÷ 10 50 ÷ 10 40 ÷ 10 110 ÷ 10 90 ÷ 10

m . u

ew i ev Pr

r o e t s Bo r e p ok u S

11

Teac he r

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

. te

Dice activities for division

55 ÷ 11 88 ÷ 11

o c . che e r o t r s super

m . u121 ÷ 11 33 ÷ 11 99 ÷ 11

÷ 11 two-dice graph

22 ÷ 11 110 ÷ 11 66 ÷ 11 44 ÷ 11 132 ÷ 11 77 ÷ 11

ew i ev Pr

• Toss two dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘55 has how many sets of 11?’

• Or skip count by 11s until you get to 55.

How to play

w ww

12

r o e t s Bo r e p ok u S

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. te

÷ 12 two-dice graph Teac he r

• Toss T two t dice. d Find the sum.The sum is the quotient of a division equation on the chart.

• Fill in the box above the equation with the quotient.

Hints • Remember that ÷ means ‘has how many’. Example: ‘108 has how many sets of 12?’

• Or skip count by 12s until you get to 108.

w ww

How to play

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

R.I.C. Publications® – www.ricpublications.com.au

o c . che e r o t r s super

Dice activities for division

108 ÷ 12 96 ÷ 12 36 ÷ 12 60 ÷ 12 144 ÷ 12 84 ÷ 12 120 ÷ 12 72 ÷ 12 48 ÷ 12 132 ÷ 12 24 ÷ 12

m . u

ew i ev Pr

r o e t s Bo r e p ok u S

13

Teac he r

ew i ev Pr

r o e t s Bo r e p ok u S

w ww

. te

m . u

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s super

Table completion activities Contents

r o e t s Bo r e p ok u S

Directions for table completion activities ........................................... 16

÷ 3 table completion ........................................................................................ 18 ÷ 4 table completion ........................................................................................ 19

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Teac he r

÷ 2 table completion ........................................................................................ 17

÷ 5 table completion ........................................................................................ 20 ÷ 6 table completion ........................................................................................ 21 ÷ 7 table completion ........................................................................................ 22 ÷ 8 table completion ........................................................................................ 23 ÷ 7, ÷ 8 table completion .............................................................................. 24

÷ 9 table completion © R. I .

C.Publ i cat i ons25 ÷ 8, ÷ 9 table completion 26 •f or r e v i e w p u r p o s e s o n l y• ÷ 10 table completion 27 ........................................................................................ ..............................................................................

.....................................................................................

÷ 11 table completion ..................................................................................... 28

w ww

m . u

÷ 12 table completion ..................................................................................... 29 Mixed divisors table completion ............................................................... 30 Write-an-equation table completion ..................................................... 31

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Write-an-equation table completion (two-dice sum) .................. 32

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Dice activities for division

15

Directions for table completion activities Objectives • Develops a working knowledge of the mathematical concepts of division.

• Practises division facts 2 to 12.

• Recognises and reinforces factors.

• Quickly recognises all possible sum combinations on two dice.

r o e t s Bo r e p ok u S

Teac he r

Variations

Instead of recording the solution, the teams perform any of the variations to the solution listed below and record that computation next to the appropriate number.

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Introduce the table completion charts by demonstrating on an overhead projector or interactive whiteboard and playing against the class. Two teams with two students on a team is suggested. Teams give students an opportunity to discuss moves and strategies and provide a check on correct computation.

– Double or triple the solution.

– Halve the solution.

– Add 5 to the solution and halve the result.

How to play

• Each team tosses a dice. The higher number goes first.

– Add 7, 8, 9, 10 or 11 to the solution.

© R. I .

C.Pu–b l i cat i ons After 5, 10 or 15 tosses, tally the answers to see which team has the highest score.

•f orr evi ew pur posesonl y• • The team circles the equation on the chart

– Subtract 7, 8, 9, 10 or 11 from the solution (possible to result in a negative number).

• Taking turns, the teams toss a dice. The dice sum equals the quotient.

• The team then records the solution in the appropriate box on the chart.

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• If the quotient has already been played, the team loses a turn.

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• If a team records the wrong number, they erase it and lose a turn.

• Have students use the term ‘has how many’ instead of ‘divided by’ when reading the division sign (÷).

• If students are struggling to recall division facts, suggest they skip count by the divisor until they reach the quotient (dice toss) to find the multiple (dividend) or, if necessary, refer to the Division chart (page x).

16

• The number 1 may not be used.

• Each team (or individual) has a blank sheet of paper. One person tosses a dice. Teams race to see who can write the most division equations equaling the dice. (For example, if the toss is 6, teams will write 18 ÷ 3, 60 ÷ 10, 42 ÷ 7 and so on.) The team to write the most equations within a specified time limit of, say, one minute, wins. Or: The first team to write 5 equations, 10 equations, or 15 equations wins.

o c . che e r o t r s super

• The first team to complete its chart wins.

Suggestions

Variations: write-an-equation table completion

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whose solution is the quotient tossed.

Dice activities for division

Discussion • Is this a game of luck or skill?

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÷ 2 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘12 has how many sets of 2?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

20 ÷ 2 =

14 ÷ 2 =

10 ÷ 2 =

20 ÷ 2 =

8÷2=

18 ÷ 2 =

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

w ww 4÷2=

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16 ÷ 2 = 24 ÷ 2 = 22 ÷ 2 =

12 ÷ 2 =

m . u

© R. I .

C.Publ i cat i ons 14 ÷ 2 = 10 ÷ 2 = •f orr evi ew pur posesonl y•

o c 8 ÷ 2 =e . che r o t r s super 6÷2= 22 ÷ 2 =

12 ÷ 2 =

16 ÷ 2 =

18 ÷ 2 =

24 ÷ 2 =

6÷2=

4÷2=

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Dice activities for division

17

÷ 3 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘30 has how many sets of 3?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

30 ÷ 3 =

15 ÷ 3 =

21 ÷ 3 =

30 ÷ 3 =

6÷3=

36 ÷ 3 =

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

w ww

36 ÷ 3 = 9÷3=

24 ÷ 3 = 33 ÷ 3 =

18

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12 ÷ 3 = 33 ÷ 3 =

m . u

© R. I .

C.Publ i cat i ons 15 ÷ 3 = 21 ÷ 3 = •f orr evi ew pur posesonl y•

o c 6÷3= . che e r o t r s supe 27r ÷ 3=

12 ÷ 3 =

18 ÷ 3 =

27 ÷ 3 =

24 ÷ 3 =

18 ÷ 3 =

9÷3=

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 4 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘40 has how many sets of 4?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

40 ÷ 4 =

32 ÷ 4 =

20 ÷ 4 =

40 ÷ 4 =

8÷4=

28 ÷ 4 =

48 ÷ 4 =

w ww

12 ÷ 4 =

16 ÷ 4 =

44 ÷ 4 =

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

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24 ÷ 4 = 44 ÷ 4 =

m . u

© R. I .

C.Publ i cat i ons 32 ÷ 4 = 20 ÷ 4 = •f orr evi ew pur posesonl y•

o c 8÷4= . che e r o r s super 36t ÷4=

12 ÷ 4 =

16 ÷ 4 =

28 ÷ 4 =

24 ÷ 4 =

36 ÷ 4 =

48 ÷ 4 =

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Dice activities for division

19

÷ 5 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘45 has how many sets of 5?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

45 ÷ 5 =

30 ÷ 5 =

20 ÷ 5 =

40 ÷ 5 =

10 ÷ 5 =

20 ÷ 5 =

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

w ww

35 ÷ 5 = 50 ÷ 5 = 25 ÷ 5 = 55 ÷ 5 =

20

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15 ÷ 5 = 55 ÷ 5 =

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© R. I .

C.Publ i cat i ons 30 ÷ 5 = 60 ÷ 5 = •f orr evi ew pur posesonl y•

o c 10 ÷ 5 = . che e r o t r s supe 35r ÷ 5=

15 ÷ 5 =

50 ÷ 5 =

60 ÷ 5 =

25 ÷ 5 =

40 ÷ 5 =

45 ÷ 5 =

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 6 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘48 has how many sets of 6?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

48 ÷ 6 =

30 ÷ 6 =

72 ÷ 6 =

42 ÷ 6 =

12 ÷ 6 =

60 ÷ 6 =

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

w ww

36 ÷ 6 =

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60 ÷ 6 = 24 ÷ 6 = 54 ÷ 6 =

18 ÷ 6 =

m . u

© R. I .

C.Publ i cat i ons 30 ÷ 6 = 66 ÷ 6 = •f orr evi ew pur posesonl y•

o c 12 ÷ 6 = . che e r o r s super 36t ÷6= 54 ÷ 6 =

18 ÷ 6 =

72 ÷ 6 =

66 ÷ 6 =

24 ÷ 6 =

42 ÷ 6 =

48 ÷ 6 =

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Dice activities for division

21

÷ 7 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘49 has how many sets of 7?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

49 ÷ 7

35 ÷ 7

70 ÷ 7

56 ÷ 7

42 ÷ 7

84 ÷ 7

w ww

28 ÷ 7

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

63 ÷ 7 35 ÷ 7 21 ÷ 7 56 ÷ 7

22

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14 ÷ 7

m . u

© R. I .

C.Publ i cat i ons 84 ÷ 7 77 ÷ 7 •f orr evi ew pur posesonl y•

o c 42 ÷ 7 . che e r o t r s supe63 r ÷7

28 ÷ 7

70 ÷ 7

77 ÷ 7

21 ÷ 7

14 ÷ 7

49 ÷ 7

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 8 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘56 has how many sets of 8?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

56 ÷ 8

96 ÷ 8

40 ÷ 8

32 ÷ 8

88 ÷ 8

24 ÷ 8

48 ÷ 8

w ww

48 ÷ 8

16 ÷ 8

72 ÷ 8

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

. te

96 ÷ 8 80 ÷ 8

m . u

© R. I .

C.Publ i cat i ons 24 ÷ 8 88 ÷ 8 •f orr evi ew pur posesonl y•

o c 56 ÷ 8 . che e r o t÷ 8 r s super 16

32 ÷ 8

40 ÷ 8

64 ÷ 8

80 ÷ 8

72 ÷ 8

64 ÷ 8

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Dice activities for division

23

÷ 7, ÷ 8 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘49 has how many sets of 7?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

49 ÷ 7

56 ÷ 7

80 ÷ 8

42 ÷ 7

40 ÷ 8

88 ÷ 8

w ww

48 ÷ 8

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

64 ÷ 8 35 ÷ 7 21 ÷ 7 56 ÷ 8

24

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14 ÷ 7

m . u

© R. I .

C.Publ i cat i ons 84 ÷ 7 24 ÷ 8 •f orr evi ew pur posesonl y•

o c 96 ÷ 8 . che e r o t r s supe70 r ÷7

28 ÷ 7

32 ÷ 8

77 ÷ 7

63 ÷ 7

16 ÷ 8

72 ÷ 8

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 9 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘54 has how many sets of 9?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

54 ÷ 9

45 ÷ 9

90 ÷ 9

63 ÷ 9

81 ÷ 9

108 ÷ 9

72 ÷ 9

w ww

36 ÷ 9

45 ÷ 9

18 ÷ 9

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

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27 ÷ 9 63 ÷ 9

m . u

© R. I .

C.Publ i cat i ons 108 ÷ 9 99 ÷ 9 •f orr evi ew pur posesonl y•

o c 54 ÷ 9 . che e r o t÷ 9 r s super 72

36 ÷ 9

90 ÷ 9

99 ÷ 9

27 ÷ 9

18 ÷ 9

81 ÷ 9

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Dice activities for division

25

÷ 8, ÷ 9 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘54 has how many sets of 9?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

54 ÷ 9

45 ÷ 9

40 ÷ 8

32 ÷ 8

9÷9

24 ÷ 8

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

w ww

48 ÷ 8 16 ÷ 8 45 ÷ 9 27 ÷ 9

26

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8÷8

m . u

© R. I .

C.Publ i cat i ons 24 ÷ 8 9÷9 •f orr evi ew pur posesonl y•

o c 18 ÷ 9 . che e r o t r s supe r 54 ÷9 36 ÷ 9

32 ÷ 8

16 ÷ 8

36 ÷ 9

40 ÷ 8

18 ÷ 9

48 ÷ 8

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 10 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘40 has how many sets of 10?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

40 ÷ 10

50 ÷ 10

70 ÷ 10

80 ÷ 10

50 ÷ 10

120 ÷ 10

90 ÷ 10

w ww

40 ÷ 10

30 ÷ 10

20 ÷ 10

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

. te

100 ÷ 10 60 ÷ 10

m . u

© R. I .

C.Publ i cat i ons 120 ÷ 10 110 ÷ 10 •f orr evi ew pur posesonl y•

o c 60 ÷ 10 . che e r o t÷ 10 r s super 90

80 ÷ 10

70 ÷ 10

110 ÷ 10

30 ÷ 10

20 ÷ 10

100 ÷ 10

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Dice activities for division

27

÷ 11 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘44 has how many sets of 11?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

44 ÷ 11

55 ÷ 11

77 ÷ 11

88 ÷ 11

55 ÷ 11

132 ÷ 11

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

w ww

99 ÷ 11 22 ÷ 11

110 ÷ 11 66 ÷ 11

28

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44 ÷ 11 33 ÷ 11

m . u

© R. I .

C.Publ i cat i ons 132 ÷ 11 77 ÷ 11 •f orr evi ew pur posesonl y•

o c 66 ÷ 11 . che e r o t r s supe r 99 ÷ 11

88 ÷ 11

121 ÷ 11

121 ÷ 11

22 ÷ 11

33 ÷ 11

110 ÷ 11

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 12 table completion How to play • Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• Remember that ÷ means ‘has how many’. Example: ‘96 has how many sets of 12?’

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Equation

Team: Quotient

Equation

96 ÷ 12

60 ÷ 12

144 ÷ 12

84 ÷ 12

24 ÷ 12

120 ÷ 12

72 ÷ 12

w ww

36 ÷ 12

120 ÷ 12

108 ÷ 12

ew i ev Pr

Teac he r

• Each team tosses a dice.

• Higher number goes first.

Quotient

. te

48 ÷ 12

108 ÷ 12

m . u

© R. I .

C.Publ i cat i ons 60 ÷ 12 132 ÷ 12 •f orr evi ew pur posesonl y•

o c 24 ÷ 12 . che e r o t÷ 12 r s super 72

36 ÷ 12

144 ÷ 12

132 ÷ 12

48 ÷ 12

84 ÷ 12

96 ÷ 12

R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

29

Mixed divisors table completion • Each team tosses a dice.

• Higher number goes first.

Equation

• Toss two dice. Find the sum.The sum equals the quotient.

• Circle the equation on the chart whose solution is the sum of the dice.

Record the quotient next to the equation.

• If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e Team: p ok u SQuotient Equation Quotient

48 ÷ 8

28 ÷ 7

63 ÷ 9

110 ÷ 11

48 ÷ 12

72 ÷ 9

56 ÷ 8

84 ÷ 7

ew i ev Pr

Teac he r

Team:

How to play

24 ÷ 12

35 ÷ 7

45 ÷ 9

132 ÷ 12

56 ÷ 8

w ww

36 ÷ 12

72 ÷ 6 54 ÷ 6 72 ÷ 9 28 ÷ 4

30

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35 ÷ 5

m . u

© R. I .

C.Publ i c t i ons 36 ÷a 12 •f orr evi ew pur p o÷s sonl y• 100 ÷ 10 63 7e 22 ÷ 11

o c . che 48 ÷ 6 r e o r super 49s ÷t 7 72 ÷ 12

96 ÷ 12

54 ÷ 9

45 ÷ 5

132 ÷ 12

56 ÷ 7

72 ÷ 8

54 ÷ 9

56 ÷ 7

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

Write-an-equation table completion How to play • Toss a dice. Circle the toss on the chart.The dice value equals the quotient.

• Write a division equation whose solution is the number tossed.

(Remember that ÷ means ‘has how many’.) Record the equation in the appropriate box.

• Teams may not repeat an equation that appears on either chart. If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Team:

Write an equation ÷

=

Dice toss 3

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Teac he r

• Each team tosses a dice.

• Higher number goes first.

Write an equation ÷

=

Dice toss 4 2

=

1

÷

=

5

÷

=

5

÷

=

3

=

2

÷

=

6

=

4

÷

=

2

÷

÷ . t e ÷ ÷

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÷

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C.Publ i cat i ons ÷ = 6 ÷ = •f orr evi ew pur posesonl y•

o c ÷ . = ch=e 5 e r o st ÷ s = r 3u = per

6 4

÷

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÷

=

1

÷

=

2

÷

=

3

÷

=

4

÷

=

5

R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

31

Write-an-equation table completion Two-dice sum How to play • Toss two dice and find the sum. Circle the sum on the chart.The sum equals the quotient.

• Write a division equation whose solution is the sum. (Remember that ÷ means ‘has how many’.) Record the equation in the appropriate box.

• Teams may not repeat an equation that appears on either chart. If no quotient is available, lose a turn.

• First team to complete its table wins.

r o e t s Bo r e p ok u S

Team:

Team:

÷

=

Dice toss 7

÷

=

11

÷

=

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Teac he r

• Each team tosses a dice.

• Higher number goes first.

=

Dice toss 4

÷

=

5

9

÷

=

9

=

2

÷

=

6

=

8

÷

=

÷

o c = 5 ÷ = . c e her r o t s÷ uper = 3s =

2

÷

=

6

÷

=

12

÷

=

12

÷

=

3

÷

=

4

÷

=

10

Write an equation

Write an equation ÷

÷ ÷ ÷

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Dice activities for division

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C.Publ i cat i ons ÷ = 10 ÷ = 11 •f orr evi ew pur posesonl y•

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Chart activities: Four in a row, Square off and Cross over Contents

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Directions for the chart activities ............................................................ 34

÷ 2 game chart ..................................................................................................... 36

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Teac he r

Student directions for Four in a row, Square off and Cross over .................................................................................................... 35

÷ 3 game chart ..................................................................................................... 37 ÷ 4 game chart ..................................................................................................... 38 ÷ 5 game chart ..................................................................................................... 39 ÷ 6 game chart ..................................................................................................... 40

÷ 7 game chart .................................................................................. 41

÷ 8 game chart .................................................................................. 42 © R. I .

C.Publ i cat i ons ÷ 9 game chart .................................................................................. 43 •f or vchart i ew pur posesonl y• ÷r 10e game ................................................................................

44 ÷ 11 game chart ................................................................................ 45

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÷ 12 game chart ................................................................................ 46

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Dice activities for division

33

Directions for the chart activities – Four in a row, Square off, Cross over Objectives • Develops a working knowledge of the mathematical concepts of division.

• Practises division facts 2 to 12.

• Recognises and reinforces factors.

• Analyses opponent’s possible moves to develop a blocking strategy.

r o e t s Bo r e p ok u S

• Identifies the role of luck versus skill in an activity using dice.

Introduce the Four in a row, Square off and Cross over activities by demonstrating on an overhead projector or interactive whiteboard and playing against the class. Two teams with two students on a team is suggested. Teams give students an opportunity to discuss moves and strategies and provide a check on correct computation.

Square off

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Teac he r

• Develops communication and cooperation skills by working in teams of two students.

• Is this more a game of luck or skill?

• Is there more of an opportunity in Square off than in Four in a row or Cross over to play defensively—that is, to prevent the opposing team from forming a square? Why? • What strategies have you and your teammate learned from each other?

© R. I .

C.Pu bl i ca t i o n sgames with a • Would you prefer to play these partner or without? Why? •f orr evi ew pCross ur p osesonl y• over

How to play See next page.

• Is this more a game of luck or skill?

Four in a row

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• This activity is similar to the games Othello and Pente, in which defence is important. How does the toss of the dice influence strategy? Is this activity more a game of defence or offence?

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• Which of the three activities—Square off, Four in a row, or Cross over—offers more opportunities to block the other team? Why?

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Discussion

• Do you play more offensively or defensively?

Why? Is one strategy more effective? What happens if you and your opponent both play defensively?

o c . che e r o t r s super

• Does this activity involve more luck or skill?

• Keep a record of each dice toss. Which combinations were tossed the most? The least?

34

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

Directions for Four in a row How to play • Each team tosses a dice. The higher number goes first.

• Taking turns, the teams toss two dice and find the sum. The sum is the quotient of a division equation on the chart. Place a token on the quotient.

• The object of the game is to line up four tokens, vertically, horizontally or diagonally before the opposing team does.

r o e t s Bo r e p okfor Square off Directions u S

How to play

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Teac he r

• First team to line up four tokens wins.

• Each team tosses a dice. The higher number goes first.

• Taking turns, teams toss two dice and find the sum. The sum is the quotient of a division equation on the chart. Place a token on the quotient.

• The object of the game is to place four tokens on the chart so that they form any size square, 2-by-2, 3-by-3, 4-by-4 and so on. The square can be oriented on the diagonal.

© R. I .

C.Publ i cat i ons •f orr evi ew pur po sesonl y• Directions for Cross over

• The first team to form three squares wins.

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How to play • Each team tosses a dice. The higher number goes first.

• Taking turns, teams toss two dice and find the sum. The sum is the quotient of a division equation on the chart. Place a token on the quotient.

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• The object of the game is to place your tokens so they form a continuous path zigzagging vertically, horizontally or diagonally from space to adjacent space from one side of the chart to the other. If the quotient is taken, lose a turn.

• The first team to form a continuous path across the chart wins.

Variation: • Start play in either the outside right or outside left column of the chart. If no box in either column contains the quotient of your team’s first dice toss, lose a turn.

• If the opposing team does place a token on an outside column box, your team must place a token in a box on the opposite outside column.

• You may not place a token on an occupied box.

• The first team to reach the opposite side wins.

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Dice activities for division

35

÷ 2 game chart How to play

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18 ÷ 2

20 ÷ 2

22 ÷ 2

10 ÷ 2

16 ÷ 2

8÷2

14 ÷ 2

4÷2

24 ÷ 2

14 ÷ 2

6÷2

8÷2

14 ÷ 2

16 ÷ 2

18 ÷ 2

14 ÷ 2

22 ÷ 2

20 ÷ 2

12 ÷ 2

10 ÷ 2

20 ÷ 2

16 ÷ 2

12 ÷ 2

18 ÷ 2

© R. I .

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10 ÷ 2

6÷2

6÷2

. t 8 ÷e 2

14 ÷ 2

20 ÷ 2

16 ÷ 2

8÷2

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22 ÷ 2

36

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘18 has how many sets of 2?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

12 ÷ 2

o 8÷2 c . che e r o r st super 12 ÷ 2

18 ÷ 2

10 ÷ 2

14 ÷ 2

16 ÷ 2

4÷2

12 ÷ 2

24 ÷ 2

20 ÷ 2

24 ÷ 2

10 ÷ 2

14 ÷ 2

18 ÷ 2

6÷2

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 3 game chart How to play

r o e t s Bo r e p ok u S

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘27 has how many sets of 3?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

27 ÷ 3

30 ÷ 3

33 ÷ 3

15 ÷ 3

24 ÷ 3

12 ÷ 3

18 ÷ 3

6÷3

36 ÷ 3

21 ÷ 3

9÷3

12 ÷ 3

21 ÷ 3

24 ÷ 3

9÷3

27 ÷ 3

21 ÷ 3

6÷3

30 ÷ 3

33 ÷ 3

15 ÷ 3

12 ÷ 3

21 ÷ 3

18 ÷ 3

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30 ÷ 3

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C.Publ i cat i ons •f orr evi ew pur posesonl y• 27 ÷ 3

18 ÷ 3

. t e÷ 3 18 ÷ 3 27 ÷ 3 15 ÷ 3 21 o 24 ÷ 3 12 ÷3 c . che e r o r st super

36 ÷ 3

21 ÷ 3

33 ÷ 3

9÷3

6÷3

18 ÷ 3

24 ÷ 3

30 ÷ 3

24 ÷ 3

12 ÷ 3

36 ÷ 3

15 ÷ 3

21 ÷ 3

27 ÷ 3

9÷3

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Dice activities for division

37

÷ 4 game chart How to play

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28 ÷ 4

40 ÷ 4

48 ÷ 4

20 ÷ 4

24 ÷ 4

12 ÷ 4

16 ÷ 4

8÷4

36 ÷ 4

32 ÷ 4

48 ÷ 4

16 ÷ 4

28 ÷ 4

24 ÷ 4

44 ÷ 4

28 ÷ 4

20 ÷ 4

8÷4

36 ÷ 4

16 ÷ 4

40 ÷ 4

24 ÷ 4

28 ÷ 4

32 ÷ 4

© R. I .

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w ww

20 ÷ 4

48 ÷ 4

32 ÷ 4

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40 ÷ 4

32 ÷ 4

20 ÷ 4

12 ÷ 4

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28 ÷ 4

38

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘28 has how many sets of 4?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

36 ÷ 4

o 20 ÷ 4 c . che e r o r st super 44 ÷ 4

36 ÷ 4

40 ÷ 4

8÷4

24 ÷ 4

28 ÷ 4

16 ÷ 4

44 ÷ 4

40 ÷ 4

36 ÷ 4

16 ÷ 4

24 ÷ 4

28 ÷ 4

32 ÷ 4

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 5 game chart How to play

r o e t s Bo r e p ok u S

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘35 has how many sets of 5?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

35 ÷ 5

50 ÷ 5

55 ÷ 5

25 ÷ 5

30 ÷ 5

15 ÷ 5

20 ÷ 5

10 ÷ 5

45 ÷ 5

40 ÷ 5

60 ÷ 5

20 ÷ 5

45 ÷ 5

35 ÷ 5

30 ÷ 5

50 ÷ 5

10 ÷ 5

25 ÷ 5

40 ÷ 5

50 ÷ 5

20 ÷ 5

25 ÷ 5

30 ÷ 5

35 ÷ 5

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20 ÷ 5

60 ÷ 5

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© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 40 ÷ 5

45 ÷ 5

. t e÷ 5 55 ÷ 5 45 ÷ 5 50 ÷ 5 35 o 35 ÷ 5 15 ÷5 c . che e r o r st super

30 ÷ 5

40 ÷ 5

10 ÷ 5

30 ÷ 5

35 ÷ 5

20 ÷ 5

15 ÷ 5

50 ÷ 5

25 ÷ 5

55 ÷ 5

45 ÷ 5

25 ÷ 5

35 ÷ 5

60 ÷ 5

40 ÷ 5

R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

39

÷ 6 game chart How to play

r o e t s Bo r e p ok u S

36 ÷ 6

12 ÷ 6

54 ÷ 6

24 ÷ 6

66 ÷ 6

18 ÷ 6

42 ÷ 6

60 ÷ 6

48 ÷ 6

30 ÷ 6

72 ÷ 6

42 ÷ 6

54 ÷ 6

36 ÷ 6

66 ÷ 6

48 ÷ 6

30 ÷ 6

12 ÷ 6

60 ÷ 6

24 ÷ 6

60 ÷ 6

36 ÷ 6

42 ÷ 6

48 ÷ 6

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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24 ÷ 6

72 ÷ 6

30 ÷ 6

. t 54 ÷e 6

48 ÷ 6

12 ÷ 6

24 ÷ 6

18 ÷ 6

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42 ÷ 6

40

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘36 has how many sets of 6?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

18 ÷ 6

o 30 ÷ 6 c . che e r o r st super 42 ÷ 6

54 ÷ 6

60 ÷ 6

42 ÷ 6

36 ÷ 6

42 ÷ 6

24 ÷ 6

66 ÷ 6

60 ÷ 6

54 ÷ 6

30 ÷ 6

36 ÷ 6

72 ÷ 6

48 ÷ 6

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 7 game chart How to play

r o e t s Bo r e p ok u S

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘35 has how many sets of 7?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

35 ÷ 7

70 ÷ 7

56 ÷ 7

21 ÷ 7

63 ÷ 7

28 ÷ 7

42 ÷ 7

14 ÷ 7

49 ÷ 7

35 ÷ 7

63 ÷ 7

28 ÷ 7

84 ÷ 7

56 ÷ 7

42 ÷ 7

63 ÷ 7

49 ÷ 7

70 ÷ 7

21 ÷ 7

49 ÷ 7

84 ÷ 7

49 ÷ 7

56 ÷ 7

42 ÷ 7

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77 ÷ 7

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© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 35 ÷ 7

56 ÷ 7

. t e÷ 7 63 ÷ 7 35 ÷ 7 28 ÷ 7 42 o 70 ÷ 7 14 ÷7 c . che e r o r st super

77 ÷ 7

49 ÷ 7

77 ÷ 7

28 ÷ 7

42 ÷ 7

14 ÷ 7

63 ÷ 7

49 ÷ 7

28 ÷ 7

35 ÷ 7

56 ÷ 7

70 ÷ 7

49 ÷ 7

84 ÷ 7

70 ÷ 7

R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

41

÷ 8 game chart How to play

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32 ÷ 8

80 ÷ 8

56 ÷ 8

24 ÷ 8

88 ÷ 8

16 ÷ 8

80 ÷ 8

16 ÷ 8

40 ÷ 8

80 ÷ 8

72 ÷ 8

64 ÷ 8

56 ÷ 8

32 ÷ 8

88 ÷ 8

48 ÷ 8

40 ÷ 8

72 ÷ 8

80 ÷ 8

24 ÷ 8

32 ÷ 8

64 ÷ 8

40 ÷ 8

48 ÷ 8

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C.Publ i cat i ons •f orr evi ew pur posesonl y•

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24 ÷ 8

72 ÷ 8

40 ÷ 8

. t 48 ÷e 8

80 ÷ 8

32 ÷ 8

96 ÷ 8

16 ÷ 8

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56 ÷ 8

42

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘32 has how many sets of 8?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

56 ÷ 8

o 96 ÷ 8 c . che e r o r st super 64 ÷ 8

96 ÷ 8

56 ÷ 8

72 ÷ 8

48 ÷ 8

56 ÷ 8

64 ÷ 8

88 ÷ 8

64 ÷ 8

56 ÷ 8

40 ÷ 8

32 ÷ 8

72 ÷ 8

48 ÷ 8

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 9 game chart How to play

81 ÷ 9

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘81 has how many sets of 9?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

63 ÷ 9

54 ÷ 9

27 ÷ 9

99 ÷ 9

18 ÷ 9

45 ÷ 9

108 ÷ 9 45 ÷ 9

90 ÷ 9

72 ÷ 9

81 ÷ 9

54 ÷ 9

36 ÷ 9

54 ÷ 9

45 ÷ 9

36 ÷ 9

72 ÷ 9

90 ÷ 9 108 ÷ 9

36 ÷ 9

63 ÷ 9

54 ÷ 9

63 ÷ 9

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18 ÷ 9

72 ÷ 9

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© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 99 ÷ 9

81 ÷ 9

. t e÷ 9 63 ÷ 9 27 ÷ 9 90 ÷ 9 72 o 63 ÷ 9 81 ÷9 c . che e r o r st super

99 ÷ 9

90 ÷ 9

36 ÷ 9

45 ÷ 9

54 ÷ 9

81 ÷ 9 108 ÷ 9 63 ÷ 9

27 ÷ 9

18 ÷ 9

63 ÷ 9

90 ÷ 9

36 ÷ 9

45 ÷ 9

R.I.C. Publications® – www.ricpublications.com.au

72 ÷ 9

Dice activities for division

43

÷ 10 game chart How to play

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘100 has how many sets of 10?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

100 ÷ 10 70 ÷ 10 120 ÷ 10 50 ÷ 10 80 ÷ 10 60 ÷ 10 30 ÷ 10

80 ÷ 10 20 ÷ 10 90 ÷ 10 110 ÷ 10 40 ÷ 10 100 ÷ 10 70 ÷ 10

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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50 ÷ 10 90 ÷ 10 70 ÷ 10 30 ÷ 10 90 ÷ 10 60 ÷ 10 120 ÷ 10

40 ÷ 10 60 ÷ 10 80 ÷ 10 100 ÷ 10 70 ÷ 10 50 ÷ 10 80 ÷ 10

110 ÷ 10

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50 ÷ 10 60 ÷ 10 20 ÷ 10 70 ÷ 10 40 ÷ 10

70 ÷ 10 40 ÷ 10 80 ÷ 10 120 ÷ 10 60 ÷ 10 30 ÷ 10 100 ÷ 10

20 ÷ 10 100 ÷ 10 90 ÷ 10 70 ÷ 10 40 ÷ 10 110 ÷ 10 50 ÷ 10

44

Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

÷ 11 game chart How to play

r o e t s Bo r e p ok u S

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘110 has how many sets of 11?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

110 ÷ 11 77 ÷ 11 132 ÷ 11 55 ÷ 11 88 ÷ 11 66 ÷ 11 33 ÷ 11

88 ÷ 11 22 ÷ 11 99 ÷ 11 121 ÷ 11 44 ÷ 11 110 ÷ 11 77 ÷ 11

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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55 ÷ 11 99 ÷ 11 77 ÷ 11 33 ÷ 11 99 ÷ 11 66 ÷ 11 132 ÷ 11

44 ÷ 11 66 ÷ 11 88 ÷ 11 110 ÷ 11 77 ÷ 11 55 ÷ 11 88 ÷ 11

. te÷ 11 55 ÷ 11 66 ÷ 11 22 ÷ 11 77o 121 ÷ 11 99 ÷ 11 c . che e r o r st super

44 ÷ 11

77 ÷ 11 44 ÷ 11 88 ÷ 11 132 ÷ 11 66 ÷ 11 33 ÷ 11 110 ÷ 11

22 ÷ 11 110 ÷ 11 99 ÷ 11 77 ÷ 11 44 ÷ 11 121 ÷ 11 55 ÷ 11

R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

45

÷ 12 game chart How to play

r o e t s Bo r e p ok u S

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Teac he r

• Use this chart for Four in a row, Square off and Cross over.

• Each team tosses a dice. Higher number goes first.

• Toss two dice and find the sum.The sum is the quotient of a division equation on the chart.

• Remember that ÷ means ‘has how many’. Example: ‘120 has how many sets of 12?’

• Place a token on the equation. If the equation is not available, lose a turn.

• First team to place tokens according to the rules of the game being played wins.

120 ÷ 12 84 ÷ 12 144 ÷ 12 60 ÷ 12 96 ÷ 12 72 ÷ 12 36 ÷ 12

96 ÷ 12 24 ÷ 12 108 ÷ 12 132 ÷ 12 48 ÷ 12 120 ÷ 12 84 ÷ 12

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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60 ÷ 12 108 ÷ 12 84 ÷ 12 36 ÷ 12 108 ÷ 12 72 ÷ 12 144 ÷ 12

48 ÷ 12 72 ÷ 12 96 ÷ 12 120 ÷ 12 84 ÷ 12 60 ÷ 12 96 ÷ 12

. t12 132 ÷ 12 108 ÷e

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60 ÷ 12 72 ÷ 12 24 ÷ 12 84 ÷ 12 48 ÷ 12

84 ÷ 12 48 ÷ 12 96 ÷ 12 144 ÷ 12 72 ÷ 12 36 ÷ 12 120 ÷ 12

24 ÷ 12 120 ÷ 12 108 ÷ 12 84 ÷ 12 48 ÷ 12 132 ÷ 12 60 ÷ 12

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Dice activities for division

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Tic-tac-toe/ Four-grid tic-tac-toe activities Contents

r o e t s Bo r e p ok u S

Directions for tic-tac-toe/ four-grid tic-tac-toe activities .................................................. 48–49

Two dice ÷ 2 four-grid tic-tac-toe ................................................. 51

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Two dice ÷ 2 tic-tac-toe .................................................................. 50

Two dice ÷ 3 tic-tac-toe .................................................................. 52

Two dice ÷ 3 four-grid tic-tac-toe ................................................. 53 Two dice ÷ 4 tic-tac-toe .................................................................. 54

Two dice ÷ 4 four-grid tic-tac-toe ................................................. 55 Two dice ÷ 5 tic-tac-toe .................................................................. 56

Two dice ÷ 5 four-grid tic-tac-toe ................................................. 57 © R. I .

C.Publ i cat i ons Two dice ÷ 6 tic-tac-toe ................................................................... 58 •f or r e w tic-tac-toe pur p osesonl y• Two dicev ÷i 6e four-grid .................................................

59 Two dice ÷ 7 tic-tac-toe .................................................................. 60

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Two dice ÷ 7 four-grid tic-tac-toe ................................................. 61 Two dice ÷ 8 tic-tac-toe .................................................................. 62

Two dice ÷ 8 four-grid tic-tac-toe ................................................. 63

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Two dice ÷ 9 tic-tac-toe .................................................................. 64

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Two dice ÷ 9 four-grid tic-tac-toe ................................................. 65 Two dice ÷ 10 tic-tac-toe ............................................................... 66

Two dice ÷ 10 four-grid tic-tac-toe .............................................. 67 Two dice ÷ 11 tic-tac-toe ............................................................... 68

Two dice ÷ 11 four-grid tic-tac-toe .............................................. 69 Two dice ÷ 12 tic-tac-toe ............................................................... 70 Two dice ÷ 12 four-grid tic-tac-toe .............................................. 71

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Dice activities for division

47

Directions for tic-tac-toe/four-grid tic-tac-toe Objectives • Develops a working wo knowledge of the mathematical concepts of division.

• Practises division facts 2 to 12.

• Recognises and reinforces factors.

• Analyses opponent’s possible moves in order to develop a strategy to block opponent.

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• Identifies the role of luck versus skill in an activity using dice.

The tic-tac-toe activities provide a challenging and playful variation of a familiar game form to use in mastering division facts. Each tic-tac-toe activity is paired with a four-grid tic-tac-toe activity, providing a way to diversify learning while reinforcing division facts. The tic-tac-toe activity presents an opportunity for students to practise playing tic-tac-toe with each set of division facts before moving on to the more complicated fourgrid tic-tac-toe.

Suggestions

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• Develops communication and cooperation skills by working in teams of two students.

• Have students use the term ‘has how many’ instead of ‘divided by’ when reading the division sign (÷).

• If students are struggling to recall division facts, suggest they skip count by the divisor until they reach the quotient (dice toss) to find the multiple (dividend) or, if necessary, refer to the Division chart (page x).

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Discussion

• Does the team/individual who goes first have an advantage?

How to play: tic-tac-toe

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Variations Introduce the tic-tac-toe activity by • Team places a token on every box where the demonstrating on an overhead projector or solution appears. interactive whiteboard and playing against the class.

• Team replaces opponent’s token with its own As with the other activities, two teams with two for a solution. students on a team is suggested.

• Each team chooses a colour token and tosses a dice. The higher number goes first.

• Is this a game of luck or skill?

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• Taking turns, teams toss two dice and find the sum. If the sum is the quotient of a division equation on the chart, the team places a token on the equation. If the team cannot place a token on an equation, it loses its turn.

• Is there a fair chance of each solution being tossed?

• Teams attempt to place their tokens in continuous alignment vertically, horizontally or diagonally as in tic-tac-toe.

• The first team to form a tic-tac-toe wins that game.

• The team winning 2 out of 3 games is the winner.

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Dice activities for division

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How to play: four-grid tic-tac-toe • Taking turns, teams toss two dice and find the sum. The sum is the quotient of a division equation on the chart.

• The team locates the equation on any of the four tic-tac-toe grids and places a token on only one of the equations.

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• With each toss of the dice, the teams attempt to place their tokens in continuous alignment vertically, horizontally or diagonally to win as many tic-tac-toe games as possible.

• If the equations already have tokens on them, the team loses a turn.

• When no more plays are possible, the teams count their tic-tac-toe wins. The team with the most, wins.

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Variations

4÷2

20 ÷ 2

10 ÷ 2

6÷2

20 ÷ 2

12 ÷ 2

16 ÷ 2

14 ÷ 2

8÷2

14 ÷ 2

16 ÷ 2

10 ÷ 2

• Opposing teams agree to use the same strategy at the same time to see what happens.

18 ÷ 2

12 ÷ 2

24 ÷ 2

18 ÷ 2

8÷2

14 ÷ 2

12 ÷ 2

14 ÷ 2

16 ÷ 2

20 ÷ 2

18 ÷ 2

22 ÷ 2

10 ÷ 2

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Discussion

• What was your strategy in trying to win? Were you playing offensively or defensively? Did you work on one quadrant at a time, or did you look at all four quadrants simultaneously?

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• Team places a token on every division equation in all four tic-tac-toe grids in which the quotient is the solution.

8÷2

18 ÷ 2

10 ÷ 2

8÷2

20 ÷ 2

14 ÷ 2

22 ÷ 2

6÷2

14 ÷ 2

16 ÷ 2

12 ÷ 2

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• Which strategy works better: trying to get the most three tokens in a row or trying to block your opponent?

• Discuss what would happen if both teams agreed to use the same strategy. Try this out.

• Discuss what might happen if two teams agreed to each use a different strategy and let the opposing team know its strategy. Try this out.

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Dice activities for division

49

Two dice ÷ 2 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘8 has how many sets of 2?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

8÷2

6÷2

16 ÷ 2

14 ÷ 2

18 ÷ 2

22 ÷ 2

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10 ÷ 2

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12 ÷ 2

Dice activities for division

20 ÷ 2

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Two dice ÷ 2 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘4 has how many sets of 2?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

4÷2

20 ÷ 2

10 ÷ 2

6÷2

20 ÷ 2

12 ÷ 2

16 ÷ 2

14 ÷ 2

8÷2

14 ÷ 2

16 ÷ 2

10 ÷ 2

18 ÷ 2

12 ÷ 2

24 ÷ 2

18 ÷ 2

8÷2

14 ÷ 2

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12 ÷ 2

20 ÷ 2

22 ÷ 2

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10 ÷ 2

18 ÷ 2

8÷2

20 ÷ 2

14 ÷ 2

22 ÷ 2

10 ÷ 2

6÷2

14 ÷ 2

16 ÷ 2

12 ÷ 2

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Dice activities for division

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Two dice ÷ 3 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘12 has how many sets of 3?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

12 ÷ 3

9÷3

24 ÷ 3

21 ÷ 3

27 ÷ 3

33 ÷ 3

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15 ÷ 3

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18 ÷ 3

Dice activities for division

30 ÷ 3

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Two dice ÷ 3 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘6 has how many sets of 3?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

6÷3

30 ÷ 3

12 ÷ 3

15 ÷ 3

33 ÷ 3

9÷3

27 ÷ 3

21 ÷ 3

15 ÷ 3

21 ÷ 3

18 ÷ 3

12 ÷ 3

24 ÷ 3

18 ÷ 3

36 ÷ 3

27 ÷ 3

30 ÷ 3

24 ÷ 3

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15 ÷ 3

30 ÷ 3

21 ÷ 3

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21 ÷ 3

27 ÷ 3

18 ÷ 3

12 ÷ 3

24 ÷ 3

33 ÷ 3

12 ÷ 3

9÷3

21 ÷ 3

15 ÷ 3

18 ÷ 3

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Dice activities for division

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Two dice ÷ 4 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘12 has how many sets of 4?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

12 ÷ 4

36 ÷ 4

32 ÷ 4

24 ÷ 4

28 ÷ 4

44 ÷ 4

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16 ÷ 4

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20 ÷ 4

Dice activities for division

40 ÷ 4

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Two dice ÷ 4 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘8 has how many sets of 4?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

8÷4

40 ÷ 4

20 ÷ 4

12 ÷ 4

44 ÷ 4

24 ÷ 4

32 ÷ 4

28 ÷ 4

16 ÷ 4

28 ÷ 4

32 ÷ 4

20 ÷ 4

36 ÷ 4

24 ÷ 4

48 ÷ 4

36 ÷ 4

16 ÷ 4

40 ÷ 4

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24 ÷ 4

40 ÷ 4

28 ÷ 4

. t28 e÷ 4 32 ÷ 4 16 ÷ 4 c 36o ÷4 . che e r o r st super

20 ÷ 4

36 ÷ 4

16 ÷ 4

40 ÷ 4

24 ÷ 4

44 ÷ 4

20 ÷ 4

12 ÷ 4

28 ÷ 4

32 ÷ 4

28 ÷ 4

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Dice activities for division

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Two dice ÷ 5 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘45 has how many sets of 5?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

45 ÷ 5

35 ÷ 5

15 ÷ 5

30 ÷ 5

25 ÷ 5

55 ÷ 5

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50 ÷ 5

56

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20 ÷ 5

Dice activities for division

40 ÷ 5

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Two dice ÷ 5 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘10 has how many sets of 5?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

10 ÷ 5

50 ÷ 5

20 ÷ 5

15 ÷ 5

55 ÷ 5

25 ÷ 5

45 ÷ 5

35 ÷ 5

30 ÷ 5

35 ÷ 5

30 ÷ 5

20 ÷ 5

40 ÷ 5

25 ÷ 5

60 ÷ 5

45 ÷ 5

50 ÷ 5

40 ÷ 5

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25 ÷ 5

50 ÷ 5

35 ÷ 5

. t35 e÷ 5 40 ÷ 5 30 ÷ 5 c 45o ÷5 . che e r o r st super

20 ÷ 5

45 ÷ 5

30 ÷ 5

50 ÷ 5

40 ÷ 5

55 ÷ 5

20 ÷ 5

15 ÷ 5

35 ÷ 5

25 ÷ 5

35 ÷ 5

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Dice activities for division

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Two dice ÷ 6 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘54 has how many sets of 6?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

54 ÷ 6

42 ÷ 6

18 ÷ 6

36 ÷ 6

30 ÷ 6

66 ÷ 6

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60 ÷ 6

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24 ÷ 6

Dice activities for division

48 ÷ 6

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Two dice ÷ 6 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘12 has how many sets of 6?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

12 ÷ 6

60 ÷ 6

24 ÷ 6

24 ÷ 6

66 ÷ 6

30 ÷ 6

66 ÷ 6

42 ÷ 6

18 ÷ 6

42 ÷ 6

36 ÷ 6

24 ÷ 6

48 ÷ 6

30 ÷ 6

72 ÷ 6

54 ÷ 6

60 ÷ 6

48 ÷ 6

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30 ÷ 6

60 ÷ 6

36 ÷ 6

. t42 e÷ 6 48 ÷ 6 36 ÷ 6 c 54o ÷6 . che e r o r st super

30 ÷ 6

54 ÷ 6

36 ÷ 6

60 ÷ 6

48 ÷ 6

42 ÷ 6

42 ÷ 6

54 ÷ 6

42 ÷ 6

24 ÷ 6

18 ÷ 6

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Dice activities for division

59

Two dice ÷ 7 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘56 has how many sets of 7?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

56 ÷ 7

42 ÷ 7

21 ÷ 7

28 ÷ 7

35 ÷ 7

77 ÷ 7

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70 ÷ 7

60

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49 ÷ 7

Dice activities for division

63 ÷ 7

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Two dice ÷ 7 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘56 has how many sets of 7?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

56 ÷ 7

70 ÷ 7

28 ÷ 7

21 ÷ 7

77 ÷ 7

35 ÷ 7

63 ÷ 7

42 ÷ 7

21 ÷ 7

42 ÷ 7

49 ÷ 7

28 ÷ 7

49 ÷ 7

35 ÷ 7

84 ÷ 7

56 ÷ 7

63 ÷ 7

70 ÷ 7

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70 ÷ 7

63 ÷ 7

49 ÷ 7

. t42 e÷ 7 49 ÷ 7 49 ÷ 7 c 56o ÷7 . che e r o r st super

70 ÷ 7

56 ÷ 7

35 ÷ 7

77 ÷ 7

63 ÷ 7

35 ÷ 7

28 ÷ 7

14 ÷ 7

42 ÷ 7

49 ÷ 7

28 ÷ 7

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Dice activities for division

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Two dice ÷ 8 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘56 has how many sets of 8?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

56 ÷ 8

48 ÷ 8

64 ÷ 8

32 ÷ 8

40 ÷ 8

88 ÷ 8

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80 ÷ 8

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24 ÷ 8

Dice activities for division

72 ÷ 8

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Two dice ÷ 8 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘16 has how many sets of 8?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

16 ÷ 8

80 ÷ 8

72 ÷ 8

88 ÷ 8

56 ÷ 8

40 ÷ 8

88 ÷ 8

48 ÷ 8

56 ÷ 8

72 ÷ 8

32 ÷ 8

64 ÷ 8

32 ÷ 8

40 ÷ 8

64 ÷ 8

56 ÷ 8

80 ÷ 8

48 ÷ 8

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56 ÷ 8

80 ÷ 8

24 ÷ 8

. t32 e÷ 8 48 ÷ 8 56 ÷ 8 c 64o ÷8 . che e r o r st super

96 ÷ 8

64 ÷ 8

72 ÷ 8

40 ÷ 8

48 ÷ 8

80 ÷ 8

40 ÷ 8

56 ÷ 8

32 ÷ 8

24 ÷ 8

72 ÷ 8

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Dice activities for division

63

Two dice ÷ 9 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘54 has how many sets of 9?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

54 ÷ 9

45 ÷ 9

63 ÷ 9

36 ÷ 9

81 ÷ 9

99 ÷ 9

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90 ÷ 9

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27 ÷ 9

Dice activities for division

72 ÷ 9

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Two dice ÷ 9 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘18 has how many sets of 9?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

18 ÷ 9

90 ÷ 9

81 ÷ 9

99 ÷ 9

63 ÷ 9

45 ÷ 9

99 ÷ 9

54 ÷ 9

63 ÷ 9

81 ÷ 9

36 ÷ 9

72 ÷ 9

36 ÷ 9

45 ÷ 9

72 ÷ 9

63 ÷ 9

90 ÷ 9

54 ÷ 9

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81 ÷ 9

90 ÷ 9

27 ÷ 9

. t36 e÷ 9 54 ÷ 9 63 ÷ 9 c 81o ÷9 . che e r o r st super

108 ÷ 9

72 ÷ 9

63 ÷ 9

45 ÷ 9

63 ÷ 9

90 ÷ 9

45 ÷ 9

54 ÷ 9

36 ÷ 9

27 ÷ 9

72 ÷ 9

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Dice activities for division

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Two dice ÷ 10 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘50 has how many sets of 10?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

50 ÷ 10

60 ÷ 10

90 ÷ 10

80 ÷ 10

70 ÷ 10

110 ÷ 10

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100 ÷ 10

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30 ÷ 10

Dice activities for division

40 ÷ 10

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Two dice ÷ 10 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘20 has how many sets of 10?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

20 ÷ 10 100 ÷ 10 40 ÷ 10

30 ÷ 10 110 ÷ 0 50 ÷ 10

90 ÷ 10 70 ÷ 10 60 ÷ 10

70 ÷ 10 60 ÷ 10 80 ÷ 10

80 ÷ 10 50 ÷ 10 120 ÷ 10

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40 ÷ 10 80 ÷ 10 110 ÷ 10

70 ÷ 10 40 ÷ 10 30 ÷ 10

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Two dice ÷ 11 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘33 has how many sets of 11?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

33 ÷ 11

99 ÷ 11

88 ÷ 11

66 ÷ 11

77 ÷ 11

121 ÷ 11

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55 ÷ 11

Dice activities for division

110 ÷ 11

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Two dice ÷ 11 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘22 has how many sets of 11?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

22 ÷ 11 110 ÷ 11 44 ÷ 11

33 ÷ 11 121 ÷ 11 55 ÷ 11

99 ÷ 11 77 ÷ 11 66 ÷ 11

77 ÷ 11 66 ÷ 11 44 ÷ 11

88 ÷ 11 55 ÷ 11 132 ÷ 11

99 ÷ 11 110 ÷ 11 88 ÷ 11

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110 ÷ 11 88 ÷ 11 77 ÷ 11

121 ÷ 11 44 ÷ 11 77 ÷ 11

77 ÷ 11 55 ÷ 11 33 ÷ 11

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Two dice ÷ 12 tic-tac-toe How to play • Toss two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation.

• Remember that ÷ means ‘has how many’. Example: ‘132 has how many sets of 12?’

• If the equation is not available, lose a turn.

• First team to place three tokens in a row wins.

• Play 3 games.Team winning 2 out of 3 games wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

132 ÷ 12

108 ÷ 12

96 ÷ 12

84 ÷ 12

72 ÷ 12

36 ÷ 12

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Two dice ÷ 12 four-grid tic-tac-toe How to play • Toss T two dice. Find the sum.The sum is the quotient of a division equation on the chart. Place a token on that equation on any of the four tic-tac-toe grids.

• Remember that ÷ means ‘has how many’. Example: ‘24 has how many sets of 12?’

• If the equation is not available, lose a turn.

• Team with the most ‘three tokens in a row’ wins.

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• Each team chooses a coloured token.

• Toss a dice. Higher number goes first.

24 ÷ 12 120 ÷ 12 48 ÷ 12

36 ÷ 12 132 ÷ 12 60 ÷ 12

108 ÷ 12 84 ÷ 12 72 ÷ 12

84 ÷ 12 72 ÷ 12 48 ÷ 12

96 ÷ 12 60 ÷ 12 144 ÷ 12

108 ÷ 12 120 ÷ 12 96 ÷ 12

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120 ÷ 12 108 ÷ 12 72 ÷ 12

120 ÷ 12 96 ÷ 12 84 ÷ 12

132 ÷ 12 48 ÷ 12 84 ÷ 12

84 ÷ 12 60 ÷ 12 33 ÷ 12

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Factoring activities Contents

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Directions for factoring activities ............................................................................ 74

Factor takeaway ........................................................................................................................... 77

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Student directions for factor takeaway, factor two-dice switch and factor rounds .......................................... 75–76

Factor takeaway two-dice sum ................................................................................... 78 Factor two-dice switch ....................................................................................................... 79 Factor rounds – ten-dice toss ..................................................................................... 80

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Directions for factoring activities Objectives • Develops De elo s automaticity a in recognising factors of a whole number, • Practises division facts 2 to 12.

• Practises using divisibility rules for 2, 5 and 10.

• Analyses the properties of a number to determine a factor.

Factor takeaway

Introduce the factor activities by demonstrating on an overhead projector or interactive whiteboard.

Factor two-dice switch

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Factor takeaway, factor two-dice switch, and factor rounds engage students in identifying factors of whole numbers. These activities develop automaticity in applying basic divisibility rules and reinforce the relationship between multiplication and division.

Materials • Teams share a chart

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• 10 dice to be placed inside the octagon • 2 dice for teams to toss

Materials • Chart for each team • 5 dice for each team

• 2 dice to create a two-digit number © R .

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P u b l i cat i ons • How can you tell if a number is a factor of Factor rounds – ten-dice toss another number?

Materials • f o r r e v i e w p u r posesonl y• • Are there any whole numbers that are

Getting started – questions to ask:

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• Are there any whole numbers that have no factors?

• Are there any numbers that are factors of half of all the whole numbers?

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• How can you quickly tell if 2 is a factor of a number?

• Chart for each team • 10 dice • Tokens

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factors of every whole number?

How to play: factor takeaway, factor two-dice switch and factor rounds – ten-dice toss

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• How can you quickly tell if 5 is a factor of a number?

See next pages.

• How can you quickly tell if 10 is a factor of a number?

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Directions for factor takeaway How to play • Each team tosses a dice. Higher number goes first.

• Team 1 tosses 10 dice inside the octagon. Team 1 then tosses 2 other dice, places one in each box at the top of the chart, and finds the product of the two dice.

• Team 1 removes a dice from the octagon that is a factor of the two-dice product. If no factor is available, the team loses a turn.

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• Team 2 tosses two dice, replaces the two dice in the boxes at the top of the chart, and finds the product of the two dice.

• Team 2 removes a dice from the octagon that is a factor of the two-dice product.

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• Play continues with the teams taking turns until all dice have been removed from the octagon.

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• When the octagon is empty, the teams total the dots on their dice and record the total for Round 1 on the score chart.

• Teams play four rounds, alternating who goes first. After four rounds, teams total their scores. Team with the higher total wins. (Variation: Team with the lower total wins.)

• Factor takeaway two-dice sum: Same directions as above except teams toss 4 dice (2 red and 2 green), place in the appropriate boxes at the top of the chart, and perform the calculations.

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How to play

• Each team tosses a dice. Higher number becomes Team 1 and goes first.

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• Each team tosses 5 dice within its circle.

• Team 1 tosses two dice and places a dice on each of the two boxes at the top of the chart to create a two-digit number. (Example: The team tosses a 4 and a 2; the number in the box is 42.)

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• Both teams remove from their circle a dice whose value is a factor of the two-digit number.

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• Team 1 then switches the dice in the boxes so that the tens dice is now the ones dice and the ones dice is the tens dice. (The new number is 24.)

• Both teams remove from their circle a dice that is a factor of the reversed two-digit number.

• Team 2 tosses the two dice and places the dice in the boxes at the top of the chart to create a new twodigit number. (Example: 36) • Both remove from their circles a dice that is a factor of the two-digit number.

• Team 2 switches the dice in the boxes, creating a new number. (63) • If possible, the two teams remove a factor of the new number from their circle.

• The two teams continue taking turns tossing the dice and switching dice places to generate two-digit numbers. First team to remove all the dice from its circle wins that game.

• The team winning 2 out of 3 rounds wins. (Variation: Teams remove as many dice as possible with each turn.)

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Directions for factor rounds – ten-dice toss How to play • Each team tosses a dice. Higher number goes first.

• Team 1 tosses 10 dice and arranges the dice in pairs, keeping in mind the product of the two dice paired.

• Team 1 places the dice pairs on a factor of its product in Round 1.

• If Team 1 can place all five pairs on the five factors for Round 1, the team places a token on the words Round 1 and advances to Round 2.

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• Team 1 pairs the same 10 dice to see if it can place dice pairs on all of the factors in Round 2. If successful, the team places a token on the box that says Round 2 and advances to Round 3. * • When Team 1 can no longer place all 10 dice on a round, it is Team 2’s turn.

• Team winning 2 out of 3 games wins.

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• First team to complete Round 5 wins that game.

* If the first team to play completes all five rounds on its first toss, the team does not automatically win that game. If Team 2 is also able to complete five rounds on its first toss, the game is a tie. If Team 2 cannot complete all five rounds, Team 1 wins.

Variations

• Teams place a token on every factor on their chart for each dice pair. The first team to fill its chart wins.

• If a team can place pairs on all five factors in a round, toss again to proceed to the next round.

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Team 2

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Total

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Factor takeaway

SCORE

ROUND

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Team 2

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ROUND

Total

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SCORE

two-dice sum Green dice

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Factor takeaway

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Team 2

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Round 1

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Factor Factor Factor Factor Factor 9 3 15 5 8

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Factor Factor Factor Factor Factor 10 8 9 4 15

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Factor Factor Factor Factor Factor 6 4 12 3 10

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Factor rounds – ten-dice toss

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Remainder activities Contents

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Directions for remainder activities ............................................................. 82–84

Remainder table completion – multiple of 5 ÷ two-dice sum 86 Remainder table completion – prime number ÷ dice ...................... 87

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Remainder table completion – multiple of 5 ÷ dice ........................... 85

Remainder table completion – prime number ÷ two-dice sum .................................................................................. 88 Remainder table completion – write a division equation ............ 89 Remainder table completion – write a division equation (two-dice sum) ....................................................... 90

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Publ i cat i ons92 Remainder chart multiplication/division Student directions for remainder two-dice switch activities 93 •f or r evi ew pur posesonl y• Remainder chart – addition/division .................................................................... 91 ..................................................... .....

Remainder chart – two-dice switch ÷ dice .................................................... 94 Remainder chart – two-dice switch ÷ two-dice sum ....................... 95

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Remainder tic-tac-toe – addition/division ...................................................... 96 Remainder four-grid tic-tac-toe – addition/division ............................ 97 Remainder tic-tac-toe – multiplication/division ....................................... 98

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Remainder four-grid tic-tac-toe – multiplication/division ............. 99

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Directions for remainder activities Objectives • Practises co computing remainders.

• Practises identifying what numbers will result in the highest and lowest remainders.

• Practises using divisibility rules for 2, 5 and 10.

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• Recognises remainder patterns.

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Remainder activities are abstract and challenging.

Attaching the term ‘has how many’ to the ÷ sign creates a vivid image of the division process; 14 ÷ 3 becomes ‘14 has how many (sets of) 3?’

One strategy is to skip count by threes to 12 and determine how many more to 14 for the remainder. Another strategy would be to take 14 tokens and divide them into sets of 3 tokens, resulting in 4 sets of 3 with 2 left over.

Getting started – questions to ask: • How can you tell which numbers will result in the highest possible remainder? A remainder of 1? A remainder of 0?

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Introduce the remainder table completion, remainder chart, remainder two-dice switch and remainder tic-tac-toe activities by demonstrating on an overhead projector or interactive whiteboard.

• When are prime numbers helpful, and when are they a disadvantage?

• What is a good strategy for working out remainders?

• How can a hundreds chart help in figuring out remainders?

• Which is easier to find, the highest or the lowest possible remainder?

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• f o r r e v i e w p u r posesonl y• The equation ‘3 ÷ 5 =’ can be confusing. Students

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In some of the activities, it is possible for the dice toss to result in a zero remainder. Discuss this possibility with the students before play begins.

Additional suggestions

Remainder table completion How to play

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might say that 3 divided by 5 is not possible.

However, using tokens and inserting the term ‘has how many’ into the equation will easily clarify the confusion: Display 3 tokens. Three has how many sets of 5? None. What’s left over? 3. So what is the solution? Zero, remainder 3.

• Each team tosses a dice. Higher number goes first.

• Taking turns, teams toss one or two dice.

Depending on the activity, the value of the dice or the sum of the two dice is the divisor.

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• A hundreds chart (page ix) is a useful tool to aid students in finding the highest or lowest possible remainder. It is also a visual tool to aid students in generalising how whole numbers work.

• If students are struggling to recall division facts, suggest they refer to the Division chart (page x), if necessary.

• Team circles a multiple in the first column that, when divided by the toss, will result in the largest remainder.

• Team records the remainder in the third column.

• After ten tosses, the team tallies the remainders.

• The team with the greatest total wins.

Variation • Team with the smallest remainder tally wins.

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Directions for remainder activities (cont.)

Remainder table completion: write a division equation (extra challenge!)

How to play

With the Remainder chart activities, students choose to play one of three games: Four in a row, Cross over or Square off (see game directions on page 35).

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• Each team tosses a dice. Higher number goes first. Teams share a chart.

• Taking turns, teams toss one or two dice. The value of the dice or the sum of the two dice is the remainder.

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Remainder charts

How to play

• Each team tosses a dice. Higher number goes first.

Remainder chart – addition/division

• Taking turns, the teams toss 2 dice, place the dice in Boxes 1 and 2 at the top of the chart, and find the sum.

• The team records the equation in the Write an equation box.

• Teams then toss a third dice and place it in Box 3 to create a division equation.

• Teams may not repeat an equation that appears on either chart.

• The team divides the sum by the number on the third dice and places a token on the remainder on the chart.

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• The team circles the remainder in the Remainder dice toss column and generates a division equation for that remainder.

(Example: 35 ÷ 6 = 5 remainder 5)

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C.Publ i cat i ons • If the remainder is not available, the team loses a turn.

• The fi• rst team complete itsi table wins.p f otor r ev ew ur po s es onl y•

Variations

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Each team or student is given a sheet of paper.

With one person tossing one or two dice to determine the remainder, teams or individual students race to see who can write the most division equations with that remainder in one minute. Or see who can be the first to write 5 equations or 10 equations.

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• First team to complete its chart according to the rules of the game being played wins.

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• If the remainder is not available, the team loses a turn.

Remainder chart – multiplication/division • Taking turns, the teams toss 2 dice, place the dice in Boxes 1 and 2 at the top of the chart, and find the product.

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• Teams then toss a third dice and place it in Box 3 to create a division equation.

• The team divides the product by the number on the third dice and places a token on the remainder on the chart.

• If the remainder is not available, the team loses a turn.

• First team to complete its chart according to the rules of the game being played wins.

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Directions for remainder activities (cont.)

Remainder two-dice switch

Variations • Teams place a token on every box in which the remainder appears.

How to play See page 93.

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• Teams replace opponent’s token with their own.

Variations

• Team with the smaller remainder tally wins.

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Remainder tic-tac-toe How to play: tic-tac-toe • Each team tosses a dice. Higher number goes first.

• What was your strategy in trying to win? Did you work on one quadrant at a time? Or did you look at all four quadrants simultaneously?

• Which strategy works best: trying to get the most three tokens in a row or trying to block your opponent?

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• After totaling the Remainder column, each team tosses a dice and divides the total by the toss. The team with the largest remainder wins.

Discussion

• Discuss what would happen if both teams agreed to use the same strategy at the same time. Try this out!

3 at the top of the chart to create a dice equation, and divides the sum (or product) by the number on the third dice.

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• Team 1 places a token on the remainder produced by the division equation.

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• Taking turns, the two teams continue playing until one team forms a tic-tac-toe vertically, horizontally or diagonally to win that game.

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• Team winning 2 out of 3 games is the winner.

How to play: four-grid tic-tac-toe

• Taking turns, teams place a token on one remainder in any of the four tic-tac-toe grids.

• When no more plays are possible, the teams count their tic-tac-toe wins. Team with the most tic-tac-toes wins.

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Remainder table completion: multiple of 5 ÷ dice How to play • Toss a dice.Which number in the first column of your chart will result in the highest remainder, when divided by the number tossed? Circle it.

• Next, record the number tossed in the box next to it (÷ Toss column).

• Then, record the remainder in the Remainder column.

• After you have filled the chart, total the remainders.

• Team with the largest remainder total wins.

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Team:

Multiple of 5

Team: ÷ Toss Remainder

Multiple of 5

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• Each team tosses a dice.

• Higher number goes first.

÷ Toss Remainder

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Remainder table completion: multiple of 5 ÷ two-dice sum How to play • Toss two dice and find the sum.Which number in the first column of your chart, when divided by the sum, will result in the highest remainder? Circle it.

• Next, record the sum of the toss in the box next to it (÷ Toss column).

• Then, record the remainder in the Remainder column.

• After you have filled the chart, total the remainders.

• Team with the largest remainder total wins.

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÷ Toss Remainder

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• Each team tosses a dice.

• Higher number goes first.

Dice activities for division

Remainder total =

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Remainder table completion: prime number ÷ dice How to play • Toss a dice.Which number in the first column of your chart will result in the highest remainder, when divided by the number tossed? Circle it.

• Next, record the number tossed in the box next to it (÷ Toss column).

• Then, record the remainder in the Remainder column.

• After you have filled the chart, total the remainders.

• Team with the largest remainder total wins.

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Prime number

Team: ÷ Toss Remainder

Prime number

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• Each team tosses a dice.

• Higher number goes first.

÷ Toss Remainder

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Remainder table completion: prime number ÷ two-dice sum p How to play • Toss two dice and find the sum.Which number in the first column of your chart, when divided by the sum, will result in the highest remainder? Circle it.

• Next, record the sum of the toss in the box next to it (÷ Toss column).

• Then, record the remainder in the Remainder column.

• After you have filled the chart, total the remainders.

• Team with the largest remainder total wins.

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37 che e r o t r s supe r 41 31

43

43

47

47

Remainder total =

88

Prime number

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• Each team tosses a dice.

• Higher number goes first.

Dice activities for division

Remainder total =

R.I.C. Publications® – www.ricpublications.com.au

Remainder table completion: write a division equation How to play • Toss a dice.The dice toss = a remainder. Circle the remainder in the Remainder dice toss column.

• Write a division equation in which the remainder = the dice toss.

Record the equation in the Write an equation box.

• Teams may not repeat an equation that appears on either chart.

• If the remainder is not available, lose a turn.

• First to complete their table wins.

r o e t s Bo r e p ok u S

Team:

Team:

Write an equation =

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Remainder dice toss

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• Each team tosses a dice.

• Higher number goes first.

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R.I.C. Publications® – www.ricpublications.com.au

4

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=

Dice activities for division

3 5

89

Remainder table completion: write a division equation (two-dice sum) How to play • Toss two dice and find the sum.The sum = a remainder.

Circle the remainder in the Remainder dice toss column.

• Write a division equation in which the remainder = the dice sum.

Record the equation in the Write an equation box.

• Teams may not repeat an equation that appears on either chart.

• If the remainder is not available, lose a turn.

• First to complete their table wins.

r o e t s Bo r e p ok u S

Team:

Team:

Write an equation

Remainder dice toss

=

5

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• Each team tosses a dice.

• Higher number goes first.

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Dice activities for division

11

R.I.C. Publications® – www.ricpublications.com.au

Remainder chart – addition/division How to play • Toss 2 dice. Place one in Box 1 and the other in Box 2.

Toss a third dice and place it in Box 3.

• Find the sum of the first two dice. Divide the sum by the number on the third. Place a token on the remainder.

• If the remainder is not available, lose a turn.

• Continue playing according to the rules of the game you’re playing until one team wins.

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• Choose an activity: Cross over, Four square, or Four in a row.

• Each team tosses a dice.

• Higher number goes first.

• Teams share a chart.

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R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

91

Remainder chart – multiplication/division How to play • Toss 2 dice. Place one in Box 1 and the other in Box 2.

Toss a third and place it in Box 3.

• Find the product of the first two dice. Divide the product by the number on the third dice. Place a token on the remainder.

• If the remainder is not available, lose a turn.

• Continue playing according to the rules of the game you’re playing until one team wins.

r o e t s Bo r e p ok u S

(

x Box 1

)÷ Box 2

Box 3

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• Choose an activity: Cross over, Four square, or Four in a row.

• Each team tosses a dice.

• Higher number goes first.

• Teams share a chart.

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Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

Directions for remainder two-dice switch How to play • Each team tosses a dice. Higher number goes first.

Round 1

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1. Team 1 tosses two dice and places one in each of the boxes at the top of the chart to create a two-digit number. Both teams record the two-digit number in the Two-digit # column on their chart.

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Teac he r

2. Taking turns, both teams toss a dice, record the number in the middle column, divide the twodigit number by the tossed number, and record the remainder in the first row of the Remainder column.

3. Team 1 switches the dice in the boxes so that the one in the Tens place is now in the Ones place and the one in the Ones place is now in the Tens place, creating a new two-digit number (example: 32 becomes 23). Both teams record the two-digit number in the second row of their chart.

4. Teams each toss a dice, record the number in the middle column, divide the two-digit number by the tossed number, and record the remainder in the Remainder column.

5. This ends Round 1.

© R. I .

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Rounds 2–5

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6. Taking turns tossing and switching the two dice, the two teams play 4 more rounds and tally their Remainder columns.

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R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

93

Remainder two-dice switch ÷ dice

Ones r o e t s Bo r e p ok u S

Team:

Twodigit #

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Tens

Team:

÷ Toss Remainder

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Dice activities for division

Remainder total =

R.I.C. Publications® – www.ricpublications.com.au

Tens Ones r o e t s Bo r e p ok u S

Team:

Twodigit #

Team: ÷ Sum Remainder

Twodigit #

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÷ Sum Remainder

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R.I.C. Publications® – www.ricpublications.com.au

Remainder total =

Dice activities for division

95

Remainder tic-tac-toe Addition/division How to play • Toss 2 dice. Place one in Box 1 and the other in Box 2.Toss a third and place it in Box 3.

• Find the sum of the first two dice. Divide the sum by the number on the third. Calculate the remainder.

• Find the remainder on the tic-tac-toe grid and place a token on it. If the remainder is not available, lose a turn.

• First team to get three in a row wins that game.

• Team winning 2 out of 3 games wins.

r o e t s Bo r e p ok u S

(

+ Box 1

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Box 3

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Teac he r

• Each team chooses a coloured token.

• Each team tosses a dice.

• Highest number goes first.

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Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

Remainder four-grid tic-tac-toe Addition/division How to play • Toss 2 dice. Place one in Box 1 and the other in Box 2.Toss a third and place it in Box 3.

• Find the sum of the first two dice. Divide the sum by the number on the third. Calculate the remainder.

• Find the remainder on any of the four tic-tac-toe grids. Place a token on only one square in one of the four grids.

• If the remainder is not available on any grid, team loses a turn.

• Team with the most ‘threes in a row’ wins.

r o e t s Bo r e p ok u S

(

+ Box 1

ew i ev Pr

Teac he r

• Each team chooses a coloured token.

• Each team tosses a dice.

• Highest number goes first.

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Box 3

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R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

97

Remainder tic-tac-toe Multiplication/division How to play • Toss 2 dice. Place one in Box 1 and the other in Box 2.Toss a third and place it in Box 3.

• Find the product of the first two dice. Divide the product by the number on the third. Calculate the remainder.

• Find the remainder on the tic-tac-toe grid and place a token on it. If the remainder is not available, lose a turn.

• First team to get three in a row wins that game.

• Team winning 2 out of 3 games wins.

r o e t s Bo r e p ok u S

(

x Box 1

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Box 3

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• Each team chooses a coloured token.

• Each team tosses a dice.

• Highest number goes first.

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Dice activities for division

R.I.C. Publications® – www.ricpublications.com.au

Remainder four-grid tic-tac-toe Multiplication/division How to play • Toss 2 dice. Place one in Box 1 and the other in Box 2.Toss a third and place it in Box 3.

• Find the product of the first two dice. Divide the product by the number on the third. Calculate the remainder.

• Find the remainder on any of the four tic-tac-toe grids. Place a token on only one square in one of the four grids.

• If the remainder is not available on any grid, team loses a turn.

• Team with the most ‘threes in a row’ wins.

r o e t s Bo r e p ok u S

(

x Box 1

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Teac he r

• Each team chooses a coloured token.

• Each team tosses a dice.

• Highest number goes first.

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Box 3

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R.I.C. Publications® – www.ricpublications.com.au

Dice activities for division

99