Exercices for students from math logic(5-8)en
Download as DOCX, PDF1 like154 views
The document contains sample exercises for students in grades 5-8 that involve logic puzzles, word problems, and math equations. The exercises cover topics like determining owners of objects based on clues, finding numbers of books on shelves given constraints, identifying dance partners of students, and identifying who is telling the truth among children being questioned. The assistant provides step-by-step solutions and reasoning for each exercise.
Exercices for students from math logic(5-8)en
- 1. 1 Teaching Method and Flexible Tools -MATERIALS FOR STUDENTS- (EXECICES FOR STUDENTS 5-8) This project has been funded with support from the European Commission. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.
- 2. 2 8th grade 1) Aurel, Felix and Claudiu have balls of different colours. One is blue, one is green and one is red. Felix is a friend of the owner of the green ball and a classmate of the owner of the blue ball. Claudiu and the owner of the blue ball would like to attend an athletic competition. Determine the owner and the colour of each ball. Answers: Aurel is the owner of the ……………… ball. Felix is the owner of the ………………ball. Claudiu is the owner of the ……………… ball. Correct answers: Aurel is the owner of the blue ball. Felix is the owner of the red ball. Claudiu is the owner of the green ball. 2) On four shelves of a library there are books numbered according to the following string of numbers: 20, 27, 12, 17. Determine the number of the books on each shelf, given that the following sentences are true: a) There are not 20 books on the first shelf. b) There are 12 books on the second shelf. c) There are not 17 books on the third shelf. d) The fourth book has the highest number of books. Answers: On the first shelf there are………… books. On the second shelf there are ………… books. On the third shelf there are………… books. On the fourth shelf there are………… books. Răspuns: On the first shelf there are…17……… books. On the second shelf there are …12……… books. On the third shelf there are…20……… books. On the fourth shelf there are…23……… books. 3) 4 couples of students in our school are attending a dancing competition. The girls' names are: Mia, Ioana, Lora and Ana. The boys' names are: Ene, Nae, Teo and Van. Determine the members of each pair, given the fact that: a) Van is Mia's brother. b) Lora has two brothers, but her partner is his parents' only child.
- 3. 3 c) Nae is Ana's partner. d) Mia and Teo used to be partners, but they separated when Teo met his current partner. Answers: Mia is ……………….' s partner. Ioana is ……………….'s partner. Lora is ……………….'s partner. Ana is ……………….'s partner. Răspuns: Mia is Ene' s partner. Ioana is Van's partner. Lora is Teo's partner. Ana is Nae's partner. 4) WHO ATE THE JAME? Identify the “thief” knowing that only one of the children is telling the truth. 1) Andrei: “One of the girls ate the jam.” 2) Bianca: “Dorina ate the jam.” 3) Claudiu: “It wasn't me.” 4) Dorina: “It was one of the boys.” If only one of the children is telling the truth, then ............................. ate the jam. Answer: The truth value of the sentences: The “thief” 1) 2) 3) 4) Number of true sentences and number of false sentences Andrei F F T T 2 T and 2 F Bianca T F T F 2 T and 2 F Claudiu F F F T 1 T and 3 F Dorina T T T F 3 T and 1 F If only one of the children is telling the truth, then ... Claudiu ... was the one who ate the jam. WHO BROKE THE VASE? 5) One of the four brothers (Alina, Bogdan, Corina and Daniel) broke a vase. When their mother asks them who did it, they answer: 1) Alina: “Bogdan broke the vase.” 2) Bogdan: “Daniel broke it.” 3) Corina: “I didn't do it.” 4) Daniel: “Bogdan is lying.” Identify the child who broke the vase, knowing that: a) only one child is lying;
- 4. 4 b) only one child is telling the truth. a) If only one child is lying, it is ……………………… and ……………………… broke the vase. b) If only one child is telling the truth, it is ………………….. and ……………………… broke the vase. Answer: The truth value of the sentences: The child who broke the vase 1) 2) 3) 4) Number of true sentences and number of false sentences Alina F F T T 2 T and 2 F Bogdan T F T T 3 T and 1 F Corina F F F T 1 T and 3 F Daniel F T T F 2 T and 2 F a) If only one child is lying, it is … Bogdan ... and … Bogdan … broke the vase. b) If only one child is telling the truth, it is … Daniel ... and … Corina … broke the vase.
- 5. 5 7th grade 1) In the grid below there are 10 mathematical terms. Find them and write them in the space on the right. The words can be spelled downwards, upwards, from left to right, from right to left or diagonally. E T E N I S R P F H I L Î N O T A A O S A H E D I A M E T R U N G M L M O P B A C E D N E A V P M O N I B F U N V O O E I E I R A S T T R E T E O R E M A Answers: DIAMETRU, ROMB, SFERA, ELEMENT, SUMA, CUB, BINOM, TEOREMA, ARIE, UNGHI (DIAMETER, RHOMBUS, SPHERE, ELEMENT, SUM, CUBE, BINOMIAL, THEOREM, AREA, ANGLE) 2) Which number should replace the question mark? Answer: 9
- 6. 6 3) Which number should replace the question mark? Answer: 2 4) How can you write the following numbers: 23, only by using the figure 2? 34 only by using the figure 3? 56 only by using the figure 5? 100 only by using the figure 9? Note: You can use mathematical symbols to solve this problem. Answers: 22+2/2=23 33+3/3=34 55+5/5=56 99+9/9=100 5) Use multiplication, division and addition of the natural numbers to write the figure 5, only by using the figure 2 four times. Answers: (2 x 2) + (2 : 2 ) = 5 ( 2 : 2) + (2 x 2) = 5 (2 : 2 ) + 2 + 2 = 5
- 7. 7 6th grade 1) How many combinations are there for Valeria, Martin and Tina to sit on a 3-person bench? Each on them could be the first one on the bench and any of the other two could sit right next to the first person. 1 (the first), 2 (the second), 3 (the third) I.a) Valeria, Martin, Tina b) Valeria, Tina, Martin II.a) Martin, Valeria, Tina b) Martin, Tina, Valeria III.a) Tina, Valeria, Martin b) Tina, Martin, Valeria There is a total number of 6 combinations for the three children to sit on the bench. 2) Consider the following picture: ara is sitting next to Ana, but not at the end of the table. rina is sitting at one end, but not next to Ana. ▪ Ana is on Mara's left, but not at the end. ▪ Ileana is at one end, but not next to Mara. Read the description and write the name on the corresponding tag. Solution: The first piece of information reveals the fact that Mara is seated at one of the two middle seats; according to the second statement Irina must sit on one of the two seats at the end of the table. The third information is more clarifying: Ana is seated in the middle (because she is not at the end of the table), and the first part of the sentence is clear- «Ana is on Mara's left». The last sentence shows that Ileana is seated at the end, but not next to Ana (according to the negation). Therefore, the correct order of the names on the tags is: Irina, Mara, Ana, Ileana.
- 8. 8 3) A RAGGED PROBLEM RAG's wearing a rag Sitting on a rag next to a rag. How many rags are there? Solution: Rag is the name of a dog made famous in a poem written by Tudor Arghezi, therefore it is not a torn piece of cloth, as in the other uses of the word. Therefore there are: one rag covering the dog, another rag on which the dog is sitting and another rog next to it, which means 1+1+1=3 rags in total. 4) TROUBLESOME DOTS Oana has a red dress with 11 white dots, and the three mushrooms she picked have 7, 5 and 6 white dots. How many white dots are there left, knowing the fact that her mother used cleaning powder to wash them? Solution: There are the 7+5+6=18 white dots on the mushrooms, because Oana's mother only washed the dress, not the mushrooms. 5) When he reaches his football practice, Robert and three of his colleagues shake hands. How many times does Robert shake hands? How many hand shakes have there been? Solution: 3 times 6) TIME You played For 98 minutes. You sang for 8 minutes You ran for 14 minutes. There may be many minutes, But how many hours are there? Solution: 2 hours
- 9. 9 5th grade 1) A father is 38 years old and his children are 8,6,4 and 2 years old. After how many years will the father's age equal the sum of his children's ages (at that time)? Solution: ▪ At present, the children's ages amount to 20 years, which is 18 years less than the father's age. Each year the father's age increases by one each year, and the sum of the children's ages increases by four each year, therefore the difference of age decreases by 3 each year. ▪ 3+3+3+3+3+3=18 years. ▪ Therefore 6 years would be necessary to get the required eqaulity. 2) A book has 100 pages. How many figures were necessary to number the pages of the respective book? Solution: ▪ There are 9 figures between 1 and 9. ▪ 99-9=90 ▪ Between 10 and 99 there are 90 numbers made of 2 figures each, 90+90=180 figures. ▪ The number 100 is made of 3 figures. ▪ Therefore the total number of figures is 9+180+3= 192. 3) Two fathers and two sons ate 3 apples. Each of them ate 1 apple. How is that possible? Solution: They were a son, a father and a grandfather. 4) Snow-White bought some things from a merchant. If a belt costs as much as 3 combs, and a comb costs as much as 3 apples, how many apples does a belt cost? Solution: 1 belt = 3 combs 1 comb = 3 apples => 1 belt = 3 + 3 + 3 = 9 (apples)
- 10. 10 5) Find the largest natural number which consists of four distinctive even numbers, so that the hundred figure is the double of the ones. Solution: ▪ For the largest number, the thousand figure must be 8. ▪ The hundred figure cannot be 6 or 2 because the halves thereof (the one) is 3 or 1, neither of which is an even number. Therefore the hundred figure is 4 and there are 2 possibilities: 8402 or 8462. The correct answer is 8462.