Relationship Games
Fifth Grade CurriculumRepresenting Rules/Patterns/EquationsTable of ContentsTopicPageRelationshipsLesson GoalsRelationship Games:Mental Math Riddles Telephone Line Telephone Line Message CardsSolving Silly Stories Solving Silly EquationsVocabulary FlashcardsRelationship LessonCreature Activity CardsCreate-A-Monster Extension CardsRelationships in TablesGuided PracticeSubstitution StrategyGuided Practice 1234 - 78 - 910-1112 - 1819 – 2122 – 262728 – 3031 – 3334 – 3738 – 39 Relationships TEKS: 5.4 Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to;(B) represent and solve multi-step problems involving four operations with numbers using equations with a letter standing for an unknown quantity; (R)(C) generate a numerical pattern when a given rule in the form of y =ax or y = x + a and graph (R)(D) recognize the difference between additive and multiplicative number patterns given in a table or a graph. (S)Lesson Goals: Review relationship vocabulary words (see vocabulary list)Review that a relationship can be written at least 2 ways (2 is half of 4 and 4 is two times two).Review relationships in tables.Introduce the terms multiplicative and additive.Introduce that a letter can represent a variable in tables and equations (P represents the number of packages and M represents the number of marbles) Introduce that 3 x P can be written as 3 P and 3PVocabulary: one-half, two times, three times, four times, twice, double, triple, more than, less than, equal, one-third, one-fourth, additive, multiplicative, expression, relationship, independent variable, dependent variable, increase, sum, product, quotient, difference, greater than, fewer, decrease, inverse operationRelationship GamesUse the following games as warm-up activities. Game 1: Mental Math Riddles (Individual, Partner or Groups)Provide students with clues to a number using the relationship vocabulary words. You may choose to show some of the vocabulary flashcards as you say the relationship words (pages 12 - 18). Start off with one clue and increase the number of clues as the students understand the game. Allow time between each clue for students to process the math. Have students share the number only at the end of all of the clues. Examples: Start with…Take the number 4, double it. What is the new number?Work up to…. Take the number 3, triple it, and now increase it by 2. That number is 2 less than the number I am thinking of. What number am I thinking of?Since this game can be done with little/no prep work, this is a great game to use throughout the year while waiting in line at lunch, for the restroom, or during class changes.Game 2: Telephone Line (Teams)Use this game after you have introduced letters to represent variables in expressionsCreate teams by placing students into different lines. Give each student a folded “telephone message” (found on pages 4 - 8). The teacher whispers a given number into the ears of the first student in each line. The student writes their number on the “received line”, applies their given clue, writes the new number on the “send line”, and whispers the new number in the next student’s ear. The student line continues until the last student “rings in” (a play cell phone would be novel). TIP: begin with a short line of students and work your way up. Teacher must pre-select numbers and cards to be sure that they will work together. Otherwise a student may be asked to do something like find half of an odd number. ExampleFirst StudentSecond StudentThird StudentFourth StudentTeacher whispers“5”Telephone MessageReceived (R): 5Message: 2 RSend: 10Whispers to second student“10”Telephone MessageReceived (R): 10Message: Increase by 4Send: 14Whispers to thirdstudent“14”Telephone MessageReceived: 14Message: Find the sum of it and 4Send: 18Whispers to fourth student“18”Telephone MessageReceived: 18Message: R ÷ 2Send: 9Ring in“9”*You will need to run multiple copies of the cards in order to have enough copies for each line.Telephone Line Message Cards RECEIVED: __________MESSAGE: Double it!SEND: ___________RECEIVED: __________MESSAGE: Add it twice!SEND: ___________RECEIVED (R): _________MESSAGE: 2RSEND: ___________RECEIVED (R): _________MESSAGE: 2 x RSEND: ___________RECEIVED (R): _________MESSAGE: 2 RSEND: ___________RECEIVED (R): _________MESSAGE: Product of R and 2SEND: ___________RECEIVED: __________MESSAGE: Increase it by ____!SEND: ___________RECEIVED (R): _________MESSAGE: R + SEND: ___________RECEIVED: __________MESSAGE: Find the sum of it and 4!SEND: ___________RECEIVED (R): _________MESSAGE: R + 10SEND: ___________RECEIVED: __________MESSAGE: __ greater than it!SEND: ___________RECEIVED (R): _________ MESSAGE: R + 2SEND: ___________RECEIVED: __________MESSAGE: Decrease it by ____!SEND: ___________RECEIVED: __________MESSAGE: ___ fewer than it!SEND: ___________RECEIVED (R): _________MESSAGE: R-2SEND: ___________RECEIVED (R): _________MESSAGE: R - 10SEND: ___________RECEIVED: __________MESSAGE: Find the difference of it and 1!SEND: ___________RECEIVED (R): _________MESSAGE: R - SEND: ___________RECEIVED: __________MESSAGE: Find the product of it and 3!SEND: ___________RECEIVED: __________MESSAGE: Three times it!SEND: ___________RECEIVED: __________MESSAGE: Four times it!SEND: ___________RECEIVED: __________MESSAGE: Triple it!SEND: ___________RECEIVED (R): _________MESSAGE: 5 RSEND: ___________RECEIVED (R): _________MESSAGE: 3RSEND: ___________Game 3: Solving Silly Stories (Partners/Groups)Use silly stories for partners or table groups to solve. These examples (on pp. 8 - 9) are to use with your groups or write your own using the vocabulary words with the attached flashcards (pp. 12 - 18).Example:Take the number of wheels on a tricycle. (3)Multiply by the number of eggs in a dozen. (3 x 12 = 36)Subtract the number of hours in a day. (36 - 24 = 12)Solving Silly Stories1.Take half the number of tires on a car.Add the number of donuts in a dozen.Multiply the sum by the number of babies in twins.2.Multiply the number of toe nails a person has by the number of nostrils.Add the number of legs on an octopus.Double the sum.3.Take the number of donuts in a half dozen.Add quadruple the number of sodas found in a six pack.4.Double the number of legs on an insect.Divide by the number of eyes it has.Add the number of letters in b r o t h e r.5.Take the number of points on a star.Add the number of quarters in a dollar.Multiply the sum by the number of arms on a person.Divide by the number of babies in a set of triplets.6.Take the number of legs on an octopus.Multiply it by the number of legs on a spider.Solving Silly Stories*Teaching Tip: Use math related facts after the students have had practice with some of the simple stories. They can use a reference sheet (math chart, shapes, etc) during these problems. Here are some examples:1.Find the sum of the number of edges on a hexagon and the number of vertices in a cube.Then double the number.2.Take the number of hours in a day.Cut it in half.Multiply it by the number of days in a year.Increase the product by 16.3.Take the number of inches in a foot.Triple it.Divide the product by the number of quarts in a gallon.4. Find the difference between the number of centimeters in a meter and half the meters in a kilometer.5.Multiply the vertices on a triangular prism by the edges on a cube.Add the number of sides on a pentagon.6.Divide the number of minutes in an hour by the minutes in one-fourth of an hour.Game 4: Solving Silly Equations(Partners/Groups)Have students use the key at the top of the page to solve the Silly Equations. Students can make their own key and write their own Silly Equations.You can have students cut off the last column and glue it into the left side of their IMN.Work the example with the students. The completed example is shown below.Solving Silly EquationsUse the key below to solve the expressions:D- Number of donuts in a dozenW- Number of Wheels on a carQ – The number of sides on a quadrilateralF – Number of Fingers on 2 handsT – The number of wheels on a tricycleS – The number of legs of a spiderExample:T x S= 24 24 ÷ W = 6 6 + D = 18Solving Silly EquationsUse the key below to solve the expressions:D- Number of donuts in a dozenW- Number of Wheels on a carQ – The number of sides on a quadrilateralF – Number of Fingers on 2 handsT – The number of wheels on a tricycleS – The number of legs of a spiderExample:T x S= ÷ W = + D = D – 3 = F = + 4 = F + 26 = ÷ Q = T =Make your own key: S x W = F = D = S ÷ W = + D = - F = Make your own: D ÷ W = + S = - F = 120 – D = T = 54=Make your own:Relationship Flashcardsmore thanless thanfewertripleone-fourthgreater thanincreasedecreasethree timesfour timesequalone-thirdtwo timestwicedoubleone-halfaddsubtractmultiplydividesumproductquotientdifferenceInverse OperationadditivemultiplicativeRelationship LessonTEKS: 5.4 Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to;(B) represent and solve multi-step problems involving four operations with numbers using equations with a letter standing for an unknown quantity; (R)(C) generate a numerical pattern when a given rule in the form of y =ax or y = x + a and graph (R)(D) recognize the difference between additive and multiplicative number patterns given in a table or a graph. (S) Materials: Fraction circles, Fraction squares, or Fraction strips, task card, Blockhead/Circle Creature sheets (pp. 22 - 26), bags of color tiles, envelopes of color tiles, guided practice (pp. 23-26)Background Knowledge: The teacher will illustrate various relationships with the fraction pieces, numbers, and other concrete items. Relationship Vocabulary: one-half, two times, three times, four times, twice, double, triple, more than, less than, equal, one-third, one-fourth.Begin by having a discussion about the vocabulary. The point to be made is that relationships can be written 2 ways. (2 is half of 4 and 4 is double 2). You will want to practice with smaller numbers at first. Record this on the board.10 is two times ______. Are we looking for a bigger or smaller number? Why? (Smaller, because 10 is twice as big as the number we are looking for).What are other words for two times? (twice, double) 10 is two times 5. How did we find our answer? (10 = 2 x or 10 ÷ 2 = 5)What is another way we can write the relationship between the numbers 10 and 5?5 is one-half of 10.Repeat this process of writing the relationship 2 ways using whole numbers with various relationship vocabulary.Concrete Relationship Vocabulary ActivityPass out a set of fraction circle pieces to each table. Write the word bank on the board. Word Banktwicethree timesone-fourthdoubletripleequaltwo timesone-thirdmore thanone-halfless thanAsk the students to compare the one yellow piece (? circle) to one pink piece (? circle). What is the relationship between the two pieces? What is a number sentence that can be used to describe this relationship? Guide students to use letters to represent the colors and then complete the relationship using the mathematical symbols. Here are some examples that describe the relationship between the yellow and pink pieces:Yellow is one-half of pinkY = P ÷2Pink is two times yellow Pink is twice as much as yellowPink is double yellowP = 2 YP = 2YYellow is less than pinkY < PPink is more than yellow.P > YRepeat this process using other fraction pieces with various relationships. Pass out bag 1, (B) ( 9 color tiles) and envelope 1 (E) (27 color tiles).Ask the students to compare bag 1 (B) to envelope 1 (E). What is the relationship between the two amounts? What are some number sentences that can be used to describe the relationships? Bag 1 is one-third of 27B = 27 ÷ 39 is 18 less than 279 = 27 – 18Bag 1 has fewer color tiles than the envelopeB < E27 is three times 927 = 3 927 is triple 927 = 3 927 is 18 greater than 927 is 18 more than 927 = 9 + 18The envelope has more than two times the amount of color tiles than bag 1.E > 2 BRepeat this process using other bags of concrete items with various paring Creature Parts Activity:1.Each table or partners will receive fraction pieces and a blockhead/creature mat (found on pp. 22, 24 & 25). The students will place the appropriate pieces on top of the outlined figure.2.Using the creature, students will fill in the missing blanks of the corresponding relationship sheet using words in the word bank (pp. 23, 26 & 30). Encourage students to lay the pieces on top of each other to find the relationships.3.Share and discuss.Extension Cards (pg. 27):1.The teacher has students create their own blockhead/circle creature and write relationships and number sentences between its parts.2.The teacher uses the Create-A-Monster clue cards or has the students create the “monster”. Although the monsters may vary from group to group, the relationships will be the same. For example, if one of the clues is – The monster’s head is twice the size of his feet. One group may have the ? circle for the body and a whole circle for its head. Another group may have the ? circle for the head and a ? circle for the body. Both monsters will show the correct relationship, but look differently. Discuss with the group.3.You may make your own additional clue cards.Circle Creature 594360115570Circle CreatureKEYL – LegH – HeadA – ArmB - Body1.One leg is ______ the head.The head is ______ one leg. Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________2.The arm is ______ the head.The head is ______ the arm.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________3.The arm is ______ one leg.The leg is _____ the arm.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________4.The two legs are _____ to the head.The head is ______ to the two legsWrite two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________Word Banktwicethree timesone-fourthdoubletripleequaltwo timesone-third more thanone-halfless thanFraction SquaresBlockheadFraction TilesBlockhead14033546355KEYL – LegH – HeadA – ArmB - BodyBlockhead1.The head is ______ the body.The body is ______ the head.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________2.The arm is _____ the head.The head is _____ the arm.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________3.The body is ______ the leg.The leg is _____ the body.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________4.Two legs _____ the body.The body is _____ to the two legs.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ __________5.The hand is _____ the arm.The arm is _____ the hand.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________6. The head is _____ the hand.The hand is _____ the head.Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __________ ___________Word Banktwicethree timesone-fourth ofdoubletripleequaltwo timesone third ofmore thanone-half ofless thanExtension Cards11Create-A-MonsterHead is double his legsHis arm is one-fourth of his headBody is one-third of his head2Create-A-MonsterKEYL – LegH – HeadA – ArmB - BodyA = B÷3H = 4L4Create-A-MonsterHis feet and body are equal in sizeHis head is double his bodyHis arms are one-fourth the size of his head3Create-A-MonsterKEYL – LegH – HeadA – ArmB - BodyA = HB = 2 AL= 4 HRelationships in TablesIn this section we are going to look at organizing the relationships in tables. In the previous section, students discovered the relationships between the body parts of the creature. Provide each student with Circle Creature mat and the fraction circles so that they can identify which pieces represent the head (H) and the arm (A). Now the students can put the mats away. Ask students to place enough arm pieces (four 1/8 pieces) to completely cover the piece that was used for the creature’s head (1/2 piece). Review this problem (TN pp 23) along with the fraction circles. 2. The arm is ___14__ the head. The head is __4 X___ the arm. Write two number sentences to show this relationship using the letters in the key to represent the creature’s body parts. __A = H ÷4__ H = 4 A_Restate this relationship in words with the students. One creature’s head is the same size as four creature arms. (H = 4 A)One creature’s arm is 14 the size of the creature’s head. (A = H ÷ 4)Note: It is important to remind students that this is about the relationship between the sizes of body parts, not the number of body parts on creatures. If not reminded, students may become confused by the fact that each creature has 1 head and 2 arms.-13525564770Head169Arm4122848The head is equal to 4 armsIt is also important to state the inverse relationship:1 arm is equal to ? of the head Complete the table with your students. Guide them through the process as needed. Now let’s take a look at another type of table.The carnival is offering bonus tickets with every purchase of carnival tickets. The table below shows the different numbers of tickets purchased and the number of bonus tickets that are given. Purchased Tickets (P)Bonus Tickets (B)39815252228334581 Guide the students to write an equation that shows the relationship between the 2 sets of data. The number of tickets purchased + 6 = The number of bonus tickets (P + 6 = B)The inverse relationship can also be written as:The number of bonus tickets – 6 = The number of tickets purchased (B - 6 = P)Have the students look at the two tables (p. 30). Discuss the similarities and differences between the two tables. By the end of the conversation, the Circle Creature table should be labeled as having a multiplicative relationship and the Ticket table as additive relationship. Select the appropriate problems from the guided practice to model with your class and for partner/group work.Relationships in Tables-259080220980Circle CreatureHead (H)169Arm (A)4122848Write 2 number sentences that show the relationship in the table. ____________________ _____________________What type of relationship is this? _______________Carnival Tickets The carnival is offering bonus tickets with every purchase of carnival tickets. The table below shows the different numbers of tickets purchased and the number of bonus tickets that are givenPurchasedTickets (P)BonusTickets (B)39815252228334581Write 2 number sentences that show the relationship in the table. ____________________ _____________________What type of relationship is this? _______________Relationships Guided PracticeWord Banktwo timesthree timesfour timesone-thirdone-halfone-fourth1.Write a statement and number sentence that describes the relationship between the fish and the pieces of fish food._________________________________ ________________Write a statement and number sentence that describes the inverse relationship between the fish and the pieces of fish food._________________________________ ________________Is this an example of an additive or a multiplicative relationship? How do you know? ____________________________________________________________________Word Bankmore thanless thantwiceone-half2.Write a statement and number sentence that describes the relationship between the flowers and the containers___________________________ ________________Write a statement and number sentence that describes the inverse relationship between the flowers and the containers._________________________________ ________________Is this an example of an additive or a multiplicative relationship? How do you know? ___________________________________________________________________Word Bankdoubletriplethree timestwo timesone-halfone-third3. Set A (A)Set B(B)931241552483010Write a statement and number sentence that describes the relationship between the numbers in Set A and the numbers in Set B._________________________________ ________________Now write a statement and number sentence that describes the inverse relationship between the numbers in Set A and the numbers in Set B. __________________________________ _______________Is this an example of an additive or a multiplicative relationship? How do you know? ____________________________________________________________________Number of Gumballs1015202530Price$20$30$40$50$604.Write a statement and number sentence that describes the relationship between the number of gumballs and the prices._________________________________ ________________Now write a statement and number sentence that describes the inverse relationship between the number of gumballs and the prices. __________________________________ _______________Is this an example of an additive or a multiplicative relationship? How do you know? ___________________________________________________________________Word Banktimesone-halfmore thanFamily Size Yogurt BoxesNumber of Boxes18202224Total Number of Yogurts364044485. Write a statement and number sentence that describes the relationship between the number of boxes and the number of yogurts._________________________________ ________________Now write a statement and number sentence that describes the inverse relationship between the number of boxes and the number of yogurts. __________________________________ _______________Is this an example of an additive or a multiplicative relationship? How do you know? ____________________________________________________________________ TicketsTheaterMovie 61892111231527Word Banktwo timesthree timesfour timeslessmore6. Write a statement and number sentence that describes the relationship between the number of theater tickets sold and the movie tickets sold._________________________________ ________________Write a statement and number sentence that describes the inverse relationship between the number of theater tickets sold and the movie tickets sold._________________________________ ________________Is this an example of an additive or a multiplicative relationship? How do you know? ____________________________________________________________________ Substitution StrategyYou may refer to this strategy as the “cross off”, “plug it in”, or “substitution” strategy. The student will select a set of related numbers off of a chart, table or number machine and substitute the word(s) with a number that represents them. Students will then read the sentences using the numbers to determine which statement(s) is true. The students will then substitute another set of numbers off of the chart to confirm that their answer choice is correct.Example 1:Step 1The students will begin the four step process. 1. The table shows the number of Skittles bags and the total number of Skittles in the bags. Which relationship between the number of bags of Skittles and the total number of Skittles is true? Skittles in BagsNumber of bags 4 6 9Total Number of Skittles 32 48 72The number of bags is 8 times the total number of Skittles. The number of bags is 28 more than the total number of Skittles. The total number of Skittles is 8 times the number of bags. D. The total number of Skittles is 28 more than the number of bags. Step 2 Guide students to write a number sentence to show the relationship in the table. You can use B for bags and S for number of Skittles.B x 8 = SS ÷ 8 = BStep 3At the strategy step, they will select a set of related numbers off of the table.The students will substitute the numbers in for the words in the answer choices.1. The table shows the number of Skittles bags and the total number of Skittles in the bags. Which relationship between the number of bags of Skittles and the total number of Skittles is true? Skittles in BagsNumber of bags 4 6 9Total Number of Skittles 32 48 72 4 = 8 x 32A. The number of bags is 8 times the total number of Skittles. NT 4 = 28 + 32B. The number of bags is 28 more than the total number of Skittles. NT 32 = 8 x 4C. The total number of Skittles is 8 times the number of bags. T 32 = 28 + 4D. The total number of Skittles is 28 more than the number of bags. TThe student will now need to substitute another set of related numbers to see which relationship is true.1. The table shows the number of Skittles bags and the total number of Skittles in the bags. Which relationship between the number of bags of Skittles and the total number of Skittles is true? Skittles in BagsNumber of bags 4 6 9Total Number of Skittles 32 48 72 4 = 8 x 32A. The number of bags is 8 times the total number of Skittles. NT 4 = 28 + 32B. The number of bags is 28 more than the total number of Skittles. NTTry #2 32 = 8 x 4The total number of Skittles is 8 times the number of bags. T 48 = 8 x 6 TTry #2 32 = 28 + 4D. The total number of Skittles is 28 more than the number of bags. T 48 = 28 + 6 FExample 21. The table shows the number of Skittles bags and the total number of Skittles in the bags. Which relationship between the number of bags of Skittles and the total number of Skittles is true? Skittles in BagsNumber of bags (B) 4 6 9Total Number of Skittles (S) 32 48 72B = 8 x S B = S + 28 C. S = 8 x B S = B + 28 Since students will write the relationship between the 2 sets of numbers two ways, they should be able to select the correct answer. Students can also use the same substitution strategy to show the correct answer.= 8 x 4 B = 8 x S F 6 = 48 + 28 B = S + 28 F 48 = 8 x 6S = 8 x B T 48 = 6 + 28 S = B + 28 F Please note that as the year progresses the numbers will become larger making them more difficult. In the beginning of the year, we will be using relationships that only use facts up to 12.Guided Practice ProblemsSteven and his friends were at a carnival. They had to buy tickets to get on the rides. The table below shows the relationship between the price of the tickets and the total number of tickets. Which statements about the relationship between the price and the total number of tickets are true?Price$5$15$20$30$35Total Number of Tickets1030406070 Us the substitution strategy to determine if each statement is true or not true about the table. The price is half the total number of tickets. The price is twice the total number of tickets. The total number of tickets is twice the price. The total number of tickets is three times the price. The price is 2 times the total number of tickets. Write two equations to describe the relationship in the table where P is the price and T is the total number of tickets.____________________________ ___________________________Clarissa and her friends were making necklaces using stones and beads. The table below shows the relationship between the number of stones and beads used in the necklaces. Which of the statements below are true?Total Number of Stones23578Total Number of Beads1218304248 The number of stones is half the number of beads. The number of stones is double the number of beads. The number of beads is 6 times the number of stones. The number of beads is 3 times the number of stones. The number of stones is the number of beads divided by 6. Write two equations to describe the relationship in the table where S is the number of stones and B is the number of beads.____________________________ ___________________________ ................
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