e. Maha _____________ f. Puto _____________ 2. What is the title of the graph? _____________________________________________________ 3. What is the favorite snacks of grade IV pupils? _____________________________________________________ 4. How many pupils like pansitlucban than maha? _____________________________________________________ 5. How Many pupils like Banana que than kamote que? _____________________________________________________ I understand that ________________________________________________. I realized that __________________________________________________. PEL Learning Resource Material Mathematics G4 51
LEARNING ACTIVITY SHEET MATHEMATICS 4 SOLVING ROUTINE AND NON-ROUTINE LESSON 2 PROBLEMS USING DATA PRESENTED IN A SINGLE OR DOUBLE-BAR GRAPH. (Q4W5L2) Name of Learner: ____________________________________ Grade Level: ____________________________________ Section: ____________________________________ Date: ____________________________________ Solving a problem using a bar graph is an easy task. A bar graph uses a bar to show data. We must identify the four parts of the bar graph (title, labels, scales, bar) to analyze and interpret well the data in the graph. Number of pupils TITLE 100 Score on Filipino Test 10 8 90 80 90 60 50 70 80 60 50 50 40 30 90 80 70 20 12 Score on Filipino… 10 0 BARS 100 LABELS PEL Learning Resource Material Mathematics G4 52
1. What is the title of the graph? Score on Filipino Test 2. How many pupils scored 80? 90 pupils 3. How many pupils got 60 on the test? 10 pupils 4. How many pupils took the test? 250 pupils 5. If passing grades is 70, how many pupils passed the test? 232 pupils Learning Competency Solves routine and non-routine problems using data presented in a single or double-bar graph. (M4SP-IVh-4.4) PEL Learning Resource Material Mathematics G4 53
\\ Direction: Analyze the graph and answer the questions below. Pupils' Favorite Activities After School Games on Line 43 Talk on Phone 25 Watch TV 80 Play Sports 20 40 60 80 102 120 0 100 1. What is the title of the graph? A. Pupils’ Favorite Activities in School B. Pupils’ Favorite Games in School C. Pupils’ Favorite Play in School D. Pupils’ Favorite Subjects in School 2. Which after-school activity do pupils like most? A. Games on Line B. Talk on Phone C. Watch TV D. Play Sports PEL Learning Resource Material Mathematics G4 54
3. How many pupils prefer to watch TV than talk on phone? A. 43 C. 80 B. 55 D. 102 4. How many pupils like to play online games? A. 43 B. 25 C. 80 D. 102 5. List the categories in the graph from least to greatest? A. Games on Line, watch TV, play sports, talk to phone B. Talk on Phone, games on line, watch tv, play sports C. Watch TV, games online, watch tv, talk to phone D. Play Sports, watch tv, games on line, talk to phone Childrens' Favorite Color 30 25 25 20 20 15 15 10 10 10 55 5 0 Orange Blue Pink Green Violet Yellow Red PEL Learning Resource Material Mathematics G4 55
1. Which color do the children like most? _______________________________ 2. How many children choose red and green? ______________________________________ 3. How many children choose pink and orange? ______________________________________ 4. How many pupils choose blue than violet? ______________________________________ 5. What two colors got 5 votes? ______________________________________ Direction: Study the table and answer the questions below. Preferred Snacks of Grade IV-Lavender Snacks Number of Pupils Cookies 6 Sandwich 10 Crackers 5 6 Chips 8 Chocolates 2 Fruits 1. Which snack was preferred most? ____________________________________________________ PEL Learning Resource Material Mathematics G4 56
2. Which snack was preferred by only 2 pupils? _____________________________________________________ 3. How many pupils preferred chocolates? _____________________________________________________ 4. How many pupils preferred sandwiches than crackers? _____________________________________________________ 5. According to the table, what number corresponds to the number of pupils who preferred cookies and chips equally?_____________________________________________ 6. _____ I understand that ________________________________________________. I realized that __________________________________________________. PEL Learning Resource Material Mathematics G4 57
LEARNING ACTIVITY SHEET LESSON 1 MATHEMATICS 4 DRAWING INFERENCES BASED ON DATA PRESENTED IN A DOUBLE BAR GRAPH. (Q4W6L1) Name of Learner: ____________________________________ Grade Level: ____________________________________ Section: ____________________________________ Date: ____________________________________ A double bar graph is used to display two sets of data on the same graph. For example, if you wanted to show the number of hours that students worked in one month compared to another month, we would use a double bar graph. The information in a double bar graph is related, and it compares one set of data to another. Double Bar Graph Helps us to compare or present more than one kind of information, situations or events instead of using just one bar. Used when each data contains two different sets of frequency data. It is used to compare both between and within data groups. Each data group is represented by two bars. How to construct a double bar graph? PEL Learning Resource Material Mathematics G4 58
1. Decide what title you will give the graph. 2. Decide if you want horizontal or vertical bars. 3. Choose a scale. 4. Put label on the axes. 5. Draw the bars. Study This: Scores in Mathematics With and Withour Preparation 100 90 80 80 70 60 60 90 Scores 60 80 50 70 With Preparation 70 Without Preparation 60 60 50 40 30 20 10 Carmela Cassandra Shea Stephen 0 Analyn Name of Pupils The title of the graph in Scores in Mathematics With and Without Preparation The scores of the pupils are stated on the left part of the graph. The names of the pupils are stated at the bottom part of the graph. There are two bars because we are comparing two data for each pupil: Without preparation and with preparation. The lowest score without preparation is 50 and the highest is 90. PEL Learning Resource Material Mathematics G4 59
Based on the data of the double bar graph, we can say that preparation helped pupils to score higher. Learning Competency Draws inferences based on data presented in a double bar graph. (M4SP-IVh-5.4) Direction: Study the graph then answer the following questions. Number of Bottles 120 Recycling Program 80 60 100 100 80 80 Week 4 80 60 20 60 Week 2 Week 3 40 Absulio's Class Oblefias' Class 40 20 0 Week 1 PEL Learning Resource Material Mathematics G4 60
1. What week did Absulio’s Class brought the most number of bottles? _____________________________________________________ 2. How many bottles didOblefias’ class has in week 3 and week 4? _____________________________________________________ 3. What week did the two classes collect the least number of bottles? _____________________________________________________ 4. What week did the two classes collect the most number of bottles? _____________________________________________________ 5. How many number of bottles are collected in all? _____________________________________________________ Draw bars on the graph correctly using the data below. You may use colors. Be careful in using your materials in drawing the graph. Mrs. Andal - yellow Mrs. Recto - blue Mrs. Andal’s class and Mrs. Recto voted on their favorite vegetables. Mrs. Andla’s class each pupil voted only once. Petchay got 10 votes, upo got 12, mustasa got 8, ampalaya got 5 and sitaw got 8. PEL Learning Resource Material Mathematics G4 61
While Mrs. Recto’s class each voted only once. Petchay got 15 votes, upo got 10, mustasa got 12, ampalaya got 7 and sitaw got 12. Childrens’ Favorite Vegetables Petchay upo mustasa ampalaya sitaw Make a double bar graph using the following data. Weekdays Number of Cans Monday 10 15 Tuesday 25 15 Wednesday 15 20 Thursday 40 30 Friday 20 24 IV-LAVENDER IV-LAUREL PEL Learning Resource Material Mathematics G4 62
I understand that ________________________________________________. I realized that __________________________________________________. PEL Learning Resource Material Mathematics G4 63
LEARNING ACTIVITY SHEET MATHEMATICS 4 RECORDING FAVORABLE OUTCOMES LESSON 2 IN A SIMPLE EXPERIMENT (E.G. TOSSINGA COIN, SPINNING A WHEEL, ETC.) (Q4W6L2) Name of Learner: ____________________________________ Grade Level: ____________________________________ Section: ____________________________________ Date: ____________________________________ PROBABILITY is the measure of the likeness than an event will occur of how like something is to happen. The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event its \"favorable outcomes\". The number of favorable outcomes is the number of choices (such as rolling a two on a die) and the probability is found by comparing this to the total number of outcomes (six in the case of a dice). Tossing a coin, throwing a dice and spinners are other examples of experiment. PEL Learning Resource Material Mathematics G4 64
Mother and Farah went to Ongville’s store. After they have paid all that they have bought, the cashier gave them a free ticket. They will spin for a free item. We always see the spinners in television game shows, product promotions, amusement parks and even in the classrooms. It brings joy and excitement for the player to win. Learning Competency Records favorable outcomes in a simple experiment (e.g. Tossing a coin, spinning a wheel, etc.). (M4SP-IVi-9) Direction: Toss a coin 5 times then record the outcomes. The one who gets first 3 heads is the winner. Try not to hit anyone in tossing the coin. PEL Learning Resource Material Mathematics G4 65
Toss Outcome (Head or Tail) First Second Third Fourth Fifth Carmela and Cassandra are playing snakes and ladders. They throw a die carefully to decide the number of steps they are going to make. 1. How many possible outcomes when one of them throw a die? _______ 2. How many possible outcome/s that 1 will show up? ________ 3. How many possible outcome/s that 5 will show up? ________ 4. How many possible outcome/s that 7 will show up? ________ 5. How many possible outcome/s that even numbers will show up? ________ PEL Learning Resource Material Mathematics G4 66
Direction: Do the following as indicated. Do this with a partner. Throw the die carefully. You’ll need: Snakes and ladders board, a die Procedure: 1. Throw a die alternately 10 times. 2. Record score each you throw the die. 3. The player with highest score wins. Throw of Dice SCORE PLAYER # 1 PLAYER #2 1st 2nd 3rd 4th 5th PEL Learning Resource Material Mathematics G4 67
6th 7th 8th 9th 10th TOTAL I understand that ________________________________________________. I realized that __________________________________________________. PEL Learning Resource Material Mathematics G4 68
LEARNING ACTIVITY SHEET MATHEMATICS 4 EXPRESSING THE OUTCOME IN A LESSON 1 SIMPLE EXPERIMENT IN WORDS, SYMBOLS, TABLES, OR GRAPHS. (Q4W7L1) Name of Learner: ____________________________________ Grade Level: ____________________________________ Section: ____________________________________ Date: ____________________________________ In probability theory, an outcome is a possible result ofNumber of Heads Appear an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). Let’s study the graphical represention of the result of tossing coin in 5 attempts 5 4 3 2 1 0 Jay Ben Lito Carlo PEL Learning Resource Material Mathematics G4 69
Based on the graph, we can easily tell that: Jay got 2 Heads and 3 Tails Ben got 3 Heads and 2 Tails Lito got 1 Head and 4 Tails Carlo got 4 Heads and 1 Tail We may put the results in table. Carlo B. A. Players Heads Tails / Jay Ben Lito X / / X/ / Jay 2 3 / Ben 3 2 X/ X Lito 1 4 Carlo 4 1 //X XXX X/ X You may express outcomes of your simple experiments by using graphs, tables, words or symbols. Learning Competency Express the outcomes in a simple experiment in words and symbols, tables or graphs. (M4SP-IVi-10) PEL Learning Resource Material Mathematics G4 70
Number of Heads AppearDirection: Choose players you want to play with tossing coins. Toss a coin carefully 5 times alternately. Don’t hit anyone while tossing the coin. Record the number of heads you got by coloring the graph. 5 4 3 2 1 0 Players Direction: Choose players you want to play with a die. Throw a die alternately 10 times. Record your result and add. The player got the highest score wins. Player Score Board PEL Learning Resource Material Mathematics G4 71
Make a spinner like this Add Subtract Get a partner and play the game. 10 20 1. You and your partner start at 100 points each Divide Multiply 2. Spin the wherever the spinner landed, do the suggested Math operations. by 2 by 5 3. After 5 spins, the player with the highest points win. I understand that ________________________________________________. LEARNING ACTIVITY SHEET LEARNING ACTIVITY SHEET I realized that ___________M__A__T_H_E__M__A_T_I_C__S__4______________________. PEL Learning Resource Material Mathematics G4 72
LEARNING ACTIVITY SHEET LESSON 2 MATHEMATICS 4 EXPLAINING THE OUTCOMES IN AN EXPERIMENT (Q4W7L2) Name of Learner: ____________________________________ Grade Level: ____________________________________ Section: ____________________________________ Date: ____________________________________ An outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique and different outcomes are mutually exclusive (only one outcome will occur on each trial of experiment). All of the possible outcomes of an experiment from the element of a sample space. Let’s study the given situation. Stephen is spinning the spinner like the one shown in the figure while he is playing a game. What is the chance that he spins 5 on his next turn. PEL Learning Resource Material Mathematics G4 73
Read and Understand the Question. The question is looking for the probability of getting 5 when you spin the spinner. Make a Plan. There are 6 equal sections and 1 of the section is labeled 5. Carry out the Plan. Since 1 out of 6 sections is labeled 5, the chance is equal to Study the spinner below. Let us answer the question by just looking at the spinner. 1. On which color is the spinner equally likely to land? There are two sections having equal parts. It is equally likely the spinner to land on green and blue. 2. On which color is the spinner least likely to land? There is only 1 section with yellow, so the spinner is least likely to land on color yellow. 3. On which color is the spinner most likely to land? There are more red than any other color. The spinner is most likely to land on red. 74 PEL Learning Resource Material Mathematics G4
4. On which color the spinner more likely to land, yellow or green? There are three green sections while there is only one yellow section so the spinner is more likely to land on green. Learning Competency Explains the outcome in an experiment. (M4SP-IVj-11) Direction: Answer the following questions by shading the circle 1. On which color is the spinner less likely to land? Green Yellow Neither green or yellow 2. On which color is the spinner more likely to land? Blue Red Neither blue or red 3. If you select a marble without looking, how likely is that you will pick a white one? certain probable impossible PEL Learning Resource Material Mathematics G4 75
4. If you select a marble without looking, how likely is that you will pick a white one? certain probable impossible Direction: Shade the circle of your answer. There are 30 marbles in the pouch 20 plain marble and 10 black marble. 1. If you’ll get a marble in the pouch, how likely is it that you’ll pick a plain marble? certain probable impossible 2. If you select a marble in a pouch, how likely is that you will pick a black marble? certain probable impossible 3. If you select a marble in a pouch, how likely is that you will pick a red marble? certain probable impossible PEL Learning Resource Material Mathematics G4 76
Direction: Explain the situation. If you’ll toss 3 1-peso coins once, how likely is it that you’ll get 2 Heads. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ I understand that ________________________________________________. I realized that __________________________________________________. PEL Learning Resource Material Mathematics G4 77
LEARNING ACTIVITY SHEET MATHEMATICS 4 LESSON 1 SOLVING ROUTINE AND NON-ROUTINE PROBLEMS INVOLVING A SIMPLE EXPERIMENT.(Q4W8L1) Name of Learner: ____________________________________ Grade Level: ____________________________________ Section: ____________________________________ Date: ____________________________________ In solving a problem involving a simple experiment, divide the number of ways of an event by the total numbers of possible outcomes. Let’s study and analyze the given problem A spinner has 4 equal sections colored red yellow, blue and green. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red? The problem asked us to find some possibilities involving a spinner. The possible outcomes are landing on red, yellow, blue and green. One event of this experiment is landing on blue. Solution: The chances of landing on blue are 1 in 4 and that is (one fourth) The chances of landing red are 1 in 4, and that is (one fourth) The probability of landing on blue is one fourth. PEL Learning Resource Material Mathematics G4 78
To measure the probability follow this formula: Probability = The number of ways Event can occur The total number of Possible Outcomes An experiment is a situation involving a chance that leads to results called outcomes. An outcome is the result of a single trial of an experiment. An event is one or more outcomes of an experiment. Probability is the measure of how likely an event occur Example 2: Study the table, it shows the results of a card experiment. Each time a card was picked, it was returned to the bag. CARD EXPERIMENT OUTCOME NUMBER Blue 12 Yellow 10 Red 8 Total 30 1. How many trials of picking a card were made? 2. How many times was yellow card picked? 3. What is the experimental probability of picking a red card? Answers: 1. We will get the sum of the number blue, yellow and red cards 12 + 10 + 8 = 30 2. The yellow card was picked 10 times as shown on the table. PEL Learning Resource Material Mathematics G4 79
3. A red card was picked 8 times out of 50 trials. Hence, The number of ways Event can occur Probability = The total number of Possible Outcomes = Number of times a red card was picked The total number of Possible Outcomes =8 The experimental probability of 50 picking a red card 4 = 25 Learning Competency Solves routine and non-routine problems involving a simple experiment. (M4SP-IVj-12) Read each question and circle the letter of your answer. 1. Which of the following is an experiment? a. spinning a spinner c. rolling a die b. tossing a coin d. all of the above 2. Which of the following is an outcome? a. rolling a die c. landing on yellow b. spinning a spinner d. tossing a coin PEL Learning Resource Material Mathematics G4 80
3. Which of the following is an event? a. Number of dice b. Number of coins c. Number of chances to land in one color of the spinner d. Number of cards 4. Mrs. Santos let her pupils played during their English subject. She let them pick all the vowels, what is the probability of choosing a vowel from the alphabet? a. 10/26 b. 21/26 c. 5/26 d. 8/26 5. Kian made cut-outs of the moon and sun. Without looking, what is the probability of picking sun? i. 2/6 B. 4/6 C. 2/8 D. 4/8 Solve the following problems. 1. Miguel bought 9 smiley balls and 3 sad face balls. He put it together in a bag. What is the probability of picking sad face balls?_________________ PEL Learning Resource Material Mathematics G4 81
2. Jane made cut-outs of paper dolls, 5 girls and 5 boys. She put it all in a box. What is the probability of picking girls paper doll?________________________ 3. Stephen made a spinner having 2 red,3 blue and 5 green. If she spins, what is the probability of the arrow to land on red?________________________ 4. Melanie combined 8 apples and 10 oranges in a basket. What is the probability of picking oranges?________________________ 5. Ben-ben and his playmates put their 20 dragon ball cards and 30 NBA cards in a box. What is the probability of picking dragon ball cards?________________________ Answer the question below. 1. If you were to roll the dice one time what is the probability it will land on 3? 2. If you were to roll the dice one time what is the probability it will NOT land on a 2? 3. If you were to roll the dice one time, what is the probability of it landing on an even number? 4. If you were to roll the dice one time what is the probability it will land on 3 and 4? PEL Learning Resource Material Mathematics G4 82
5. If you were to roll the dice one time, what is the probability of it landing on an odd number? I understand that ________________________________________________. I realized that __________________________________________________. PEL Learning Resource Material Mathematics G4 83
Mathematics 4 Mathematics 4 Teacher’s Guide Exploring the World of Mathematics 4 Understanding Mathematics 4 TG Mathematics 4 21 Century Mathletes 6 Mathematics 4 Learner’s Material PEL Learning Resource Material Mathematics G4 84
PEL Learning Resource Material Mathematics G4 85 Key to Correction: (Q4W5L2 Key to Correction: (Q4W3L3) Key to Correction: Activity 1 Answer may vary. Activity 1 Activity 2 Answer may vary. 1. Amount of rice the box contain (Q4W3L2) Activity 3 Answer may vary. 2. l = 45 cm, W = 50 cm, h = 40 cm 3. Multiplication / V = l x w x h Activity 1. Key to Correction: (Q4W4L1) 4. V = l x w x h 1. B Activity 1 Activity 2 Activity 3 = 45cm x 50 cm x 40 cm 2. B = 90 000 cm3 3. D 1. C 1 5 1. Laurel 4. A 5. 90 000 cm3 of rice the box contain 5. C 2. B 2. Pansit Lucban 2. SPED-GT Activity 2 Activity 2. 3. A 3. 15 3. 87 1. Volume/ Amount of water filled in the swimming 1. 36 cubic m. 4. C 4. Bihon 4. 13 pool 2. 125 cubic cm. 2. l = 25 m, W = 15 m, h = 6 m 3. 40 cubic m. 5. D 5. 51 5. 251 3. Multiplication / V = l x w x h 4. 126 cubic cm. 4. V = l x w x h 5. 105 cubic m. = 25m x 15m x 6m Activity 3 = 2 250 m3 5. 2 250 m3 is the volume of the swimming pool 1. 100 cubic m. 2. 378 cubic cm. Activity 3 3. 400 cubic cm. 1. 162 cm3 4. 216 cubic m. 2. 2 700 cm3 5. 392 cubic m. 3. 240 000 cm3 4. 84 000 cm3 5. 24 m3 Key to Correction: (Q4W3L1) Key to Correction Key to Correction Key to Correction (Q4W2L1) (Q4W1L1) (Q4W1L1) (Q4W3L2 Activity 1 Activity 1 Activity 1 Activity 1. 1. d 1. 36 m2 6. 27 m2 1. True 2. d 2. 112 cm2 7. 82 m2 2. False 3. c 3. 40 cm2 8. 95 m2 3. True 4. a 4. 80 m2 9. 44 m2 4. False 5. c 5. 120 m2 10. 55 m2 5. False Activity 2 Activity 2 Activity 2 Activity 2. 1. 96 m2 1. 18 m2 6. 42 cm2 1. 10 cubic cm or 10 cm³ 2. 3750 cm2 2. 90 cm2 7. 74 m2 2. 50 cubic cm or 50 cm³ 3. 10,1250 cm2 3. 48 m2 8. 245 m2 3. 23 cubic cm or 23 cm³ 4. 25,600 cm2 4. 35 cm2 9. 80 cm2 4. 29 cubic cm or 29 cm³ 5. 720 m2 5. 300 m2 10. 150 m2 5. 486 cubic cm or 486 cm³ Activity 3 Activity 3 Activity 3 Activity 3 A. 27 m2 1. A = 28 cm2 6. 144 cm2 1. 40 cubes B. 160 m2 2. B = 30 cm2 7. 63 m2 2. 200 cubic cm or 200 cm³ C. 100 m2 3. C = 15 cm2 8. 240 m2 3. 525 cubic cm 0r 525 cm³ D. 22,200 cm2 4. D = 75 cm2 9. 260 cm2 4. 490 cubic cm or 490 cm³ E. 120 cm2 5. E = 40 cm2 10. 252 m2 5. 847 cubic cm or 847 cm³
PEL Learning Resource Material Mathematics G4 86 Key to Correction: Key to Correction: Key to Correction: (Q4W8L1) (Q4WL2) (Q4W7L1) Activity 1 Activity 1 Activity 1 1. D 1. Yellow Answer may vary. 2. C 2. Red 3. C 3. Certain Activity 2 4. C 4. Probable Answer may vary. 5. C Activity 2 Activity 3 Activity 2 1. Certain Answer may vary. 1. 9/12 or 3/4 2. Probable 2. 5/10 or 1/2 3. Impossible` 3. 2/10 or 1/5 4. 10/18 or 5/9 Activity 3 5. 20/50 or 2/5 Answer may vary. Activity 3 1. 1/6 2. 5/6 3. 3/6 or ½ 4. 2/6 or 1/3 5. 3/6 or 1/2 Key to Correction: Key to Correction: Key to Correction: Key to Correction: (Q4W6L1) (Q4W5L2) (Q4W5L1) Activity 1 Activity 1 Activity 1 Activity 1 KELA 2 1. a LAYNE 2 1. Week 3 1. A 2. c 2. 80 bottles 2. D 3. b 3. Mrs. Absulio-week 1 3. B 4. d 4. A 5. a Mrs. Oblefias- week2 5. B 4. Mrs. Absulio-week 3 Activity 2 Activity 2 1.Favorite Fruits Mrs. Oblefias- week3&4 2.Papaya, Bayabas, 5. 520 1. Yellow mansanas, ponkan, 2. 20 saging at manga Activity 2 3. 25 3. Saging 4. 10 4.Bayabas at Ponkan Teacher may vary 5. Orange and violet 5.250. Activity 3 Activity 3 Activity 3 1. a. 75 Teacher may vary 1.Sandwich 2. fruits b. 45 Activity 2 3. 8 pupils c. 40 4. 5 pupils d. 60 Carmela 6 5. 6 pupils e. 20 Cassandra 6 f. 15 2. Favorite Snacks of Activity 3 Grade IV pupils 3. PansitLucban Answer may vary. 4. 55 5. 20
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