advertisement

Section 3 Problem Solving Exemplars Reason Logically Level A Teacher’s Notes Strategy: Level A Reason Logically Ordering Resources: A worksheet for each child Previous Knowledge Children understand what “heavier” means Compare two objects and see if children can tell which is heavier. Compare three objects with clear differences of weight and see if children can put them in order. Compare unseen objects e.g. an elephant and a mouse and see if children understand the concept of “heavier”. Children can write the number of the objects for both parts if they have not yet mastered writing letters. Extension: Questions If a fork weighs 3 cubes, how many cubes do you think a cup weighs? If a jotter weighs 8 beads, how many beads do you think a book weighs? Ordering Name: ………………………………………… Look at these pictures. 1 2 3 4 5 6 1. Write the number or name in order – heaviest first. 2. Write the number or name in order – lightest first. Teacher’s Notes Strategy: Level A Reason Logically What can I buy? Resources: Problem can be put on display board or children can use the worksheet. Previous Knowledge: Addition to 50 (involving carrying figure) Subtraction within 50 (decomposition) If a child has difficulty point out: a) Price of chocolate and what would be left out of 50p. b) The fact that there is no change. Solution: Tablet costs 30p Extension: Last sentence of problem could read: “How much is the tablet if when he buys it he has 2p change left?” The amount of change can vary. What can I buy? Name: ……………………………………………. Scott has 50p to spend. 50p A lollipop costs 20p and chocolate costs 25p. If Scott buys chocolate, he cannot buy tablet, but if he buys a lollipop he can buy tablet. How much is the tablet if he buys it, he has no change? tablet lollipop 20p chocolate 25p tablet? Reason Logically Level B Teacher’s Notes Strategy: Level B Reason Logically Sort it Out Resources: Worksheet Previous Knowledge: Nil Discuss the meaning of consecutive with the children. Solution: 4 1 2 There are other solutions. 3 5 Sort it Out Name: ………………………………………………… Read carefully: 2 is consecutive to 1 and 3 3 is consecutive to 2 and 4 On the houses below, arrange the number 1 to 5 so that no two consecutive numbers are joined by a line. Teacher’s Notes Strategy: Level B Reason Logically Weigh It Up Resources: Worksheet, pencil Previous Knowledge: Experience of 2 pan balance Solution: Weigh It Up Name: ………………………………………………………… Put these pictures in order. One picture is still to be finished. Draw the rest of the unfinished picture to show the balance when three weights are used. Write down how you found your answer Key: parcel is this shape weight is this shape Reason Logically Level C Teacher’s Notes Strategy: Level C Reason Logically Arrange the Counters Resources: Worksheet, coloured counters in 4 colours Previous Knowledge: Quarters Solution: Arrange the Counters Name: ……………………………………….. Here are 8 counters ¼ are red ¼ are blue ¼ are yellow ¼ are white Use coloured counters to show these fractions. There must not be 2 counters of the same colour next to each other on the lines. Teacher’s Notes Strategy: Level C Reason Logically Search for a Number Resources: Worksheet Previous Knowledge: Multiplication and division by 2 - 9 Solution: 1. 73 4. 51 2. 70 5. 18 3. 32 6. 15 Search for a Number Name: …………………………………. These children want you to find their numbers. Ben: My number is inside the circle and inside the triangle. It is not inside the square. It is greater than 20. Jill: My number is inside all three shapes. It can be divided by 5 without a remainder. It is greater than fifty. Tony: My number is not in the circle and not in the square but it is in the triangle. It is an even number and can be divided exactly by 8. Sula: My number is in the circle but not in the triangle and not in the square. It is an odd number. Erin: My number is even. It is inside the square. It can be divided exactly by 9, 3, and 2. It is less than 40. Ali: My number is not in any of the shapes. It is less than 20, but more than 10. It can be divided exactly by 5. Teacher’s Notes Strategy: Level C Reason Logically MacDonald Family Resources: Worksheet Previous Knowledge: Nil Solution: The least number is four. 2 boys and 2 girls MacDonald Family Name: ……………………………………………………. What is the smallest possible number of children in the MacDonald family, if each child has, at least, one brother and at least one sister. Teacher’s Notes Strategy: Level C Reason Logically Code Cracker Resources: Worksheet Previous Knowledge: Addition to 15 Solution: Code Cracker Name: ……………………………………. Task 1 Below are the names of 5 drinks all written in code. The same symbol always stands for the same letter. Hint: One of the drinks is coffee and one is tea. Crack the code and find the drinks. Task 2 Below are the names of 5 sports all written in code. The symbols in this case stand for different letters than those in Task 1. Hint: David Beckham is famous for one of these sports. Crack the code and find the sports. Contd. Code Cracker (contd.) Name: ………………………………………………….. Task 3 Use the CODEX system to decode these messages: a) J WJOA b) TWRA JK c) JYGAKUJDCUJFYK HFJYD PL PCUIAPCUJSK NCGFRVJUA CVA SFWFRV AXSJUJYD Use the CODEX system to code these messages. You supply the missing answers: d) My name is? e) My hobby is? f) My favourite pop group is? TASK 4 PCOA LFRV FEY SFHAX CYH KFPA SFHAH PAKKCDAK Code Cracker Name: ………………………………………………….. You are now going to read and write secret messages. In CODEX the code letter C stands for the real letter A, The code letter T stands for B, the code letter S stands for C and so on. Codex you will notice that the all code letters are on the outer ring and the real letters are on the inner ring. 2 letters are missing from the CODEX code letters – they are J and Z. Let J stand for I and Z stand for Z itself. For example Code letters Real Letters PCUIK JK NRY MATHS IS FUN Code Cracker Name: …………………………………………. This means 5 + 4 = What are these sums? Use the code to make up some of your own. 9 Reason Logically Level D Teacher’s Notes Strategy: Level D Reason Logically Eliminate! Resources: Worksheet Previous Knowledge: Nil This lesson teaches the child to use information contained in a problem to eliminate all but the correct answer from a given set of possibles. Pass out the worksheet and instruct the children to complete it. Once the children have completed the worksheet, the results Should be discussed with the class. Allow the children to analyse each clue in the detective problem and explain how it can be used to eliminate a suspect. By itself, the first clue will not eliminate a suspect since being ‘registered at a hotel’ does not necessarily indicate that he spent the night. Ask the children which clue they used first to solve the second problem. There may be some discussion of the exact order, however there will probably be agreement on the use of clues b, c, and e, before a and d. The choice of the first clue is important. Children should learn to read all the statements first and then determine which one is easiest to use and/or which one will eliminate the most choices. Solutions: Q1. Harry Carry Q2. 8706 Eliminate! Name: ……………………………………… Ace Detective Thistle Bines of the Glasgow Murder Squad is investigating a murder at the Old Granada Hotel. Five men are being held as suspects. “Giant” Gerry Green. He is 250cm tall, weighs 140kg, and loves his dear mother so much that he has never spent a night away from home. Harry Carry. He is a 200kg Sumo wrestler. “Hi” Peter Grey. He is a small man only 130cm tall; he hates high places because of a fear of falling. “Curly” Boots. His nickname is a result of his totally bald head. Henry “The Claw” Brown. He lost both of his hands in an accident. 1. Use the following clues to help Detective Bines solve this crime: a) The killer was registered at the hotel. b) Before he died, the victim said the killer had served time in prison with him. c) Brown hair from the killer was found in the victim’s hand. d) The killer escaped by diving from the third floor balcony into the river running by the hotel, and then swimming away. e) Smudges were found on the glass table top indicating that the killer wore gloves. Contd. Eliminate! (contd.) Name: …………………………………………………… 2. Find the number described by the clues below. Circle the correct number. a) It is divisible by 4 b) It is larger than 8641 c) It is an even number d) The sum of the digits is 21 e) It is less than 9756 9078 6552 8948 9884 9341 9714 3242 8643 10341 1874 Which clue(s) should you use first …………………….. 5483 9096 9462 What does this eliminate? …………………… 8832 2359 8706 8814 Teacher’s Notes Strategy: Level D Reason Logically Best Clues Resources: Worksheet Previous Knowledge: Children should have done Worksheet ELIMINATE During discussion with the class, re-emphasise the choice of the first clue to be used. A statement is chosen first because it; 1) 2) is the easiest one to use, or will eliminate the most possibilities. Solution: 1) Since the blue marble was picked, can the other marble be red? No. Explain: A red marble would be mean Box 2 has the correct line which contradicts clue (d). What is the correct lid for Box 2? Black. 2) Can Box Y contain the red and black marbles? No. Explain: If so, then Box X would have red marbles. This contradicts clue (d). What are the correct lids for Boxes, A,B,C? Box Correct Lid X Y Z Red-Black Red Black Best Clues Name: …………………………………………….. Study the clues that are given below and explain how they can tell exactly which marbles are in each box. X Y Red Lid a) b) c) d) e) Black Lid Z Red-Black Lid One box contains 2 red marbles. One box contains 2 black marbles. One box contains 1 red and 1 black marble. None of the lids is on its correct box. Jason reached into the box with the red-black lid and pulled out a black marble. 1. Since a black marble was picked, can the other marble be red?………………………………….Explain…………………………………………………………… ……………………………………………………………………………………………….. What is the correct lid for box 2 …………………………………………… 2. Can box Y contain red and black marbles? …………………………….. Explain……………………………………………………………………………………………… What are the correct lids for boxes X,Y and Z? Box X Y Z Correct Lid Teacher’s Notes Strategy: Level D Reason Logically More Best Clues Resources: Worksheet Previous Knowledge: Children should have completed Worksheet BEST CLUES During discussion with the class, re-emphasise the choice of the first clue to be used. A statement is chosen because it; 1) is the easiest one to use, or 2) will eliminate the most possibilities Solutions: Q1 Winner is circled. Game 1 2 3 4 5 6 Home Team Dons Gers Jags Dons Jags Gers Visitors Gers Dons Dons Jags Gers Jags Team Won Lost Q2 Dons 1 3 9371 Jags 3 1 Gers 2 2 More Best Clues Name: ………………………………………… 1. Three teams in the Motherwell Football League played each other at home and away. Find the win – loss record for the six games shown in the schedule below, if: a) The Dons never defeated the Jags. b) The Gers never lost a home game. c) The Gers lost 2 games. Game 1 2 3 4 5 6 Home Team Dons Gers Jags Dons Jags Gers Visitors Gers Dons Dons Jags Gers Jags Jags Gers Team Dons Won Lost Contd. More Best Clues (contd.) Name: ……………………………………………………….. 2. Study the clues. Eliminate all but the correct number. 9135 5731 5241 2537 8361 3715 1693 1935 7591 5263 5313 9731 3175 3174 9371 7621 1469 a) The sum of the first and last digit is equal to the sum of the two middle digits. b) The four digits in the number are all different. c) The hundreds digit is small than the thousands digit and the ten digit. d) All of the digits are odd. e) The units digit is the smallest natural number. Reason Logically Level E Teacher’s Notes Strategy: Level E Reason Logically Brain Teasers Resources: Worksheets 1 and 2 Previous Knowledge: Square numbers 1. Issue Worksheet 1 instructing the children to complete it, paying close attention to any hints given. 2. After the children have completed the problems discuss the strategies used, allowing the children time to explain their reasons for choosing a particular clue with which to begin the elimination process. 3. In problem 1, children may use the clue divisibility by five to develop a list of solutions since the multiples of five are familiar and easy to write. You may point out that the multiples of nine would be a better choice as the list would be shorter. When using the third clue, elimination can be used to narrow the list of numbers to be squared. 4. As the list of possible solutions contains only numbers with 5 in the units, the whole numbers chosen to be squared must also contain 5 in the units. 5. In problems 2 and 4 a table is given in order that the children fill in the blanks as they read the clues. Constructing tables as organisers should be discussed. Follow-up work, Worksheet 2. Contd. Teacher’s Notes – Level E Brain Teasers – Worksheet 1 (contd.) Solutions: 1. (i) (ii) b, d, e. List the multiples of 5 between 200 and 400 which are odd. Check if divisible by 9 and not a square number. Note that if the sum of the digits equals nine then the number is divisible by nine. (iii) 315 is the number. 2. Colour Picture Country 3. Red Tower France White Fountain Germany Blue Flower Denmark Green Castle England Make a list of multiples of 5 that are odd. Check division by 3 and 4 for a remainder of 1. 4. (a) Name Debbie Lisa Erin (b) Hat Erin Debbie Lisa Gloves Lisa Erin Debbie No, if so she would have to wear Erin’s hat. Brain Teasers Worksheet 1 Name……………………………………………………………… 1. Who am I? Clues: a) I am not even. b) I am greater than 200 c) I am not a square number d) I am divisible by 5. e) I am less than 400 f) I am divisible by 9 2. Linda received four stamps from England, Denmark, France and Germany for her collection. The stamps are not marked so she does not know which stamp came from each country. A fellow stamp collector gave her the following clues:- The French stamp is red The English stamp has a picture of a castle. The white stamp has a picture of a fountain. The flower is on the blue stamp The Danish stamp is not white. The tower is not on the green stamp. Use the clues and complete the table below. Colour Picture Country Contd. Brain Teasers Worksheet 1 (contd.) Name……………………………………………………………… 3. Farmer Murray was on his way to market when a case of eggs fell off the back of his lorry. Looking at the mess on the road a passer-by asked how many eggs were in the case. “When I counted in twos there was one left over, when I counted in threes or fours there was one left over, but when I counted in fives there were no eggs left over”, said farmer Murray. If farmer Murray had less than 100 eggs in the case what are the possible numbers of eggs he could have had? 4. Lisa, Erin, and Debbie left school together. In their rush to leave, they mixed up their hats and gloves. Each one wore someone else’s hat and the gloves that belonged to yet another. If Debbie wore Erin’s hat, work out whose hat and gloves each girl wore. a) Name Debbie Lisa Erin Hat Erin b) Can Lisa be wearing Debbie’s gloves? Gloves Teacher’s Notes Level E Brain Teasers - Worksheet 2 Solutions: 1. 2. Zam Zut Zill Zap Zot Make a list of multiples of 7 that are odd. Check division by 3 and 4 for a remainder of 1. 7 3. Family Dog 4. Place Colour Dog 21 Brown German Shepherd 1 Yellow Terrier 35 49 Mitchell 2 Purple Setter Simpson Poodle 3 Green Collie 4 Red Poodle Brain Teasers Worksheet 2 Name ……………………………………………. 1. An archaeologist digging on a site found a set of pots used by an ancient tribe. There were five different sized pots with the names, Zill, Zap, Zam, Zot and Zut. After studying some scrolls which were also found, he realised the names were not on the correct jars. Zap Zam Zut Zot Zut Zill Zot Use the clues and place the correct name on each jar shown below. Clues: a) A Zut is bigger than a Zot b) A Zill is never the smallest. c) A Zut is not the biggest. d) Only one thing is small than a Zap. e) A Zam is bigger than a Zill. f) More than one thing is bigger than a Zill. Contd. Brain Teasers Worksheet 2 (contd.) Name: …………………………………………….. 2. Joe has a collection of compact discs. When he puts them in piles of two, he has one left over. He also has one left over when he puts them in piles of 3 or piles of 4. He has none left over when he puts them in piles of 7. What is the least number of compact discs he can have? 3. a) b) c) d) e) f) The Brown family, the Mitchell family and the Simpson family lives in 3 houses on the same side of Well Street. The Browns live next to the Mitchells. There are no children in the middle house. The family on the right does not have a German Shepherd dog. Kathy thinks her poodle is the best dog a person can have. Lynn Brown and Kathy Simpson are best friends and go to the same primary school. The German Shepherd and the poodle are not neighbours. From the clues determine which family lives in which house and who has which dog. Contd. Brain Teasers Worksheet 2 (contd.) Name: …………………………………………….. 4. There was a dog show in which four places were awarded. A poodle, collie, setter, and terrier all entered. All had collars of different colours. There were no ties. Find which dog won each place and the colour of his collar. a) b) The poodle wore the red collar, not the green collar. The collie received the place next to the dog with the purple collar. The dog with the yellow collar received first place. The dog with the purple collar was second. The colours of the poodle’s collar and the terrier’s collar mix to form orange. c) d) e) Reason Logically Level F Santa’s Reindeer Name ……………………………………………. Santa sends his reindeer to Scotland to deliver the Christmas parcels. A certain number of reindeer leave Lapland. A third of them get lost due to bad weather, 45 give up due to exhaustion and 315 arrive safely in Stirling. How many reindeer left Lapland? Who will pull Santa’s sleigh? Name: ……………………………………………….. It is Christmas Eve, and Santa has to choose the reindeer that will pull his sleigh around the world. This year, Santa has a special way of selecting his reindeer. There are 100 reindeer altogether, and each is looked after in its own stable by its own elf. Santa asks each elf to visit the stables. If a door is open the elf has to close it and vice versa. To start with all the doors are closed. The first elf goes to all the stables and opens all the doors. The second elf goes only to every second stable so he closes doors, 2,4,6,8, etc. The third elf visits the third stable and every third stable after that, closing and opening doors. The fourth elf visits every fourth stable, the fifth elf every fifth stable and so on, until the 100th elf visits only the last stable. The reindeer that Santa decides to take with him are those whose doors are open after all the elves have visited. Find out Which reindeer go? Does Rudolph who lives in stable 100 go? Other questions If you are given a particular stable number, how can you decide if the reindeer in that stable will go?