3 math lm q2

• 1. MathematicsLearners MaterialUnit 2Department of EducationRepublic of the Philippinesi3This instructional material was collaborativelydeveloped and reviewed by educators from public andprivate schools, colleges, and/or universities. We encourageteachers and other education stakeholders to email theirfeedback, comments, and recommendations to theDepartment of Education at [email protected].

2. iiMathematics Grade 3Learners MaterialFirst Edition, 2014Republic Act 8293, section 176 states that: No copyright shall subsist in anywork of the Government of the Philippines. However, prior approval of thegovernment agency or office wherein the work is created shall be necessary forexploitation of such work for profit. Such agency or office may, among other things,impose as a condition the payment of royalties.Borrowed materials (i.e., songs, stories, poems, pictures, photos, brandnames, trademarks, etc.) included in this book are owned by their respectivecopyright holders. Every effort has been exerted to locate and seek permission touse these materials from their respective copyright owners. The publisher andauthors do not represent nor claim ownership over them.Published by the Department of EducationSecretary: Br. Armin A. Luistro FSCUndersecretary: Dina S. Ocampo, Ph.D.Department of Education-Instructional Materials Council Secretariat(DepEd-IMCS)Office Address: 5th Floor Mabini Building, DepEd ComplexMeralco Avenue, Pasig CityPhilippines 1600Telefax: (02) 634-1054 or 634-1072E-mail Address: [email protected] 3. Table of ContentsLesson 29 Visualizing Multiplication of theiiiNumbers 6 and 71Lesson 30 Visualizing Multiplication of theNumbers 8 and 96Lesson 31 Stating Multiplication Facts forNumbers 1 to 1011Lesson 32 Commutative Property ofMultiplication15Lesson 33 Distributive Property of Multiplicationover Addition20Lesson 34 Associative Property of Multiplication 23Lesson 35 Multiplying 2- to 3-Digit Numbers by 1-Digit Numbers without Regrouping26Lesson 36 Multiplying 2- to 3-Digit Numbers by 1-Digit Numbers with Regrouping29Lesson 37 Multiplying 2-Digit Numbers 33Lesson 38 Multiplying Numbers by Multiples of 10and 10038Lesson 39 Multiplying 1- to 2-Digit Numbers by100041Lesson 40 Estimating Products 44Lesson 41 Multiplying Mentally 2-Digit by 1-DigitNumbers with Products up to 10047Lesson 42 Solving Problems involvingMultiplication of Whole Numbers50Lesson 43 Solving Problems involvingMultiplication with Addition and/orSubtraction of Whole Numbers55Lesson 44 Creating Problems involvingMultiplication without or with Additionor Subtraction58Lesson 45 Multiples of 1- to 2-Digit Numbers 61Lesson 46 Dividing Numbers up to 100 by 6, 7, 8,and 964Lesson 47 Stating Division Facts of Numbers up to1066Lesson 48 Dividing 2- to 3-Digit Numbers by 1- 71 4. ivDigit NumbersLesson 49 Dividing 2- to 3-Digit Numbers by 2Digit Numbers without and withRemainder76Lesson 50 Dividing 2- to 3-Digit Numbers by 10and 10079Lesson 51 Estimating Quotients 83Lesson 52 Dividing Mentally 2-Digit Numbers by1-Digit Numbers without Remainder87Lesson 53 Solving Problems involving Divisionwithout or with any Other Operationsof Whole Numbers91Lesson 54 Creating Problems Involving Division orwith any of the Other Operations ofWhole Numbers94 5. Visualizing Multiplication of the Numbers 6and 71Lesson 29Read the story problem below.Carla has crayons: 2 red, 2 yellow, 2 blue, 2 green, 2violet, and 2 orange crayons. How many crayons doesCarla have?Count the crayons.red yellow blue green violet orangeHow many groups of crayons are there?_________________________How many crayons are there in each group?_________________________How many crayons are there altogether?_________________________Repeated addition sentence: ____________________________Multiplication sentence: __________________________________ 6. Complete the multiplication table of 6.6 x 1 = 6 x 6 =6 x 2 = 6 x 7 =6 x 3 = 6 x 8 =6 x 4 = 6 x 9 =6 x 5 = 6 x 10 =Complete the multiplication table of 7.7 x 1 = 7 x 6 =7 x 2 = 7 x 7 =7 x 3 = 7 x 8 =7 x 4 = 7 x 9 =7 x 5 = 7 x 10 =2Activity 1 7. Complete the following multiplication sentences.3Activity 26 x4579 = ____= ____= ____ = ____Start here:3= ____Start here:7 x107621= ____= ____= ____= ____= ____ 8. Activity 3Multiply. Write the product in your notebook.1) 6 2) 7 3) 6 4) 7 5) 7x 3 x 8 x 9 x 8 x 94Activity 4A. Find the product.1) 7 2) 6 3) 6 4) 7 5) 7x 3_ x 6 x 8 x 7_ x 6_B. Get the product of the following numbers.1) 6 x 7 = 6) 7 x 3 =2) 7 x 5 = 7) 6 x 10 =3) 6 x 9 = 8) 6 x 9 =4) 6 x 4 = 9) 7 x 6 =5) 7 x 4 = 10) 6 x 9 = 9. Write the multiplication sentence. Then, find the product.1) If you multiply 6 by 3, what is the product?2) Multiply 6 by 7.3) Find a number to be multiplied by 7 to get 56?4) What number should be multiplied by 7 to obtain 63 as aproduct?5) The product of 6 and 9 is ____.5Activity 5 10. Mary Anns mother bought 8 boxes of donuts forMaryanns birthday. If there were 6 donuts in a box, howmany doughnuts were there in all?How are you going to solve the problem?Complete the Multiplication Table of 8.8 x 1 = 8 x 6 =8 x 2 = 8 x 7 =8 x 3 = 8 x 8 =8 x 4 = 8 x 9 =8 x 5 = 8 x 10 =6Lesson 30Visualizing Multiplication of the Numbers 8and 9Activity 1 11. Complete the multiplication table of 9.9 x 1 = 9 x 6 =9 x 2 = 9 x 7 =9 x 3 = 9 x 8 =9 x 4 = 9 x 9 =9 x 5 = 9 x 10 =Multiply the number 8 by the number that is indicated by thearrow.38 477562Activity 2 12. Fill in the blanks. Write your answer in your notebook.8@@@@@@@@@@@@@@@@@@@@@@@@@@@Repeated addition: ________________________Multiplication sentence: _____________________###################################Repeated addition: _______________________Multiplication sentence: ____________________000000000000000000000000000000000000000000000000000000Repeated addition: _______________________Multiplication sentence: ____________________#####Activity 31)2)3) 13. 9Activity 4Find the value of n.1) 8 x 9 = n2) 8 x 5 = n3) 9 x 4 = n4) 9 x 5 = n5) 9 x 7 = nChoose the letter of the correct answer.1) 8 x 3 = ___ a. 34 b. 24 c. 21 d. 142) 8 x 7 = ___ a. 26 b. 36 c. 46 d. 563) 9 x 5 = ___ a. 15 b. 35 c. 55 d. 454) 9 x 8 = ___ a. 72 b. 27 c. 62 d. 265) 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = ___a. 24 b. 28 c. 32 d. 36 14. Find the product. Copy and write your answer on the chart.101)2)x 8 Product246789x 9 Product135789Activity 5 15. Study the table below and write the missing numbers.Work with your group.x 1 2 3 4 5 6 7 8 9 101 1 3 5 8 9 102 2 8 10 16 183 3 9 15 24 304 8 16 20 285 5 20 25 35 506 12 18 36 42 487 14 28 42 49 708 8 48 56 56 729 9 27 36 54 81 9010 20 30 60 9011Lesson 31Stating Multiplication Facts for Numbers 1 to 10Activity 1 16. 12Activity 2Give the product.1) 1 x 5 = 6) 6 x 1 = 11) 3 x 6 =2) 2 x 9 = 7) 7 x 3 = 12) 8 x 4 =3) 3 x 7 = 8) 8 x 8 = 13) 6 x 9 =4) 4 x 4 = 9) 9 x 10 = 14) 10 x 8 =5) 5 x 6 = 10) 10 x 2 = 15) 4 x 7 =Activity 3A. Using the numbers 2, 5, 6, 7, and 9, choose two numbers andfind their product. Make 5 number sentences and arrangetheir products from least to greatest.1) ______________________________2) ______________________________3) ______________________________4) ______________________________5) ______________________________ 17. B. Using the numbers 3, 4, 5, 6, and 8, choose two numbers andfind their product. Make 5 number sentences and arrangetheir products from greatest to least.1) ______________________________2) ______________________________3) ______________________________4) ______________________________5) ______________________________Give the product of each of the following pairs of numbers.1) 6 x 2 = 11) 8 x 5 =2) 7 x 8 = 12) 9 x 9 =3) 10 x 6 = 13) 2 x 7 =4) 4 x 4 = 14) 8 x 3 =5) 7 x 9 = 15) 6 x 6 =6) 3 x 7 = 16) 1 x 3 =7) 6 x 5 = 17) 9 x 3 =8) 7 x 5 = 18) 3 x 8 =9) 9 x 4 = 19) 6 x 8 =10) 5 x 8 = 20) 6 x 2 =13Activity 4 18. Write the missing number in your notebook.1) 5 x _____ = 50 6) 8 x _____ = 642) 3 x 9 = _____ 7) 8 x 3 = _____3) 6 x _____ = 30 8) 3 x _____ = 64) 7 x 5 = _____ 9) 10 x 8 = _____5) 4 x _____ = 40 10) 5 x _____ = 3014Activity 5 19. Study the picture. Write the multiplication sentence for each set ofobjects.Multiplication sentence: ________________________Multiplication sentence: ________________________If you were to write a relation symbol (>, < or =) between the twonumber sentences, what symbol would it be? Why?15Lesson 32Commutative Property of Multiplication 20. Find a partner. Perform the given exercise.Express the commutative property of multiplication by matchingcolumn A with column B. Write the letters of the correct answer.A B____ 1) 3 x 4 a. 3 x 8____ 2) 5 x 6 b. 2 x 6____ 3) 6 x 2 c. 4 x 5____ 4) 8 x 3 d. 7 x 9____ 5) 9 x 7 e. 4 x 3f. 6 x 5Write the missing factor in your notebook.1) 7 x 4 = ___ x 72) 2 x ___ = 5 x 23) 6 x 3 = 3 x ___4) 8 x ___ = 4 x 85) ___ x 9 = 9 x 716Activity 1Activity 2 21. Activity 3Read and solve. Illustrate the problem then show yoursolution and number sentence.Lilibeth draws 6 circles with 3 stars inside each circle. Howmany stars are there?Illustration and solution:17Number sentence:Ana draws 3 circles with 6 stars inside each circle. How manystars are there?Illustration and solution:Number sentence: 22. Compare Lilibeths stars with Anas stars: Write the relationsymbol in the box._________________ ____________________Lilibeths stars Anas starsAre they equal? Why? _________________________Activity 4Find the product. Write letter of the correct answer on your paper.181) 2 x 4 = ____2) 5 x 9 = ____3) 6 x 7 = ____4) 8 x 6 = ____5) 9 x 8 = ____a. 7 x 6b. 6 x 8c. 8 x 9d. 4 x 2e. 9 x 5f. 7 x 3 23. Complete the multiplication sentences by applying thecommutative property of multiplication. Find the product.1) 5 x 8 = x = _____2) 6 x 7 = x 6 = _____3) 7 x 9 = 9 x = _____4) x 6 = 6 x 4 = _____5) 3 x = 9 x 3 = _____6) x = 7 x 2 = _____19Activity 5 24. Rewrite the two-digit numbers in expanded form. Find theproduct.201) 12x 46) 6x 542) 25x 27) 7x 933) 39x 58) 9x 824) 41x 89) 2x 795) 57x 310) 3x 68Lesson 33Distributive Property of Multiplicationover AdditionActivity 1 25. Rewrite the multiplicand in expanded form.Multiply the multiplier in the ones and tens part of themultiplicand. Add the partial products to get the final product.211) 14x 26) 33x 22) 25x 57) 43x 23) 52x 28) 36x 54) 19x 39) 43x 65) 27x 410) 54x 7Activity 2 26. Activity 3Match the product in column A with the number sentence incolumn B.22A1) 572) 723) 2704) 2925) 435Ba. (30 x 2) + (6 x 2) = nb. (4 x 70) + (4 x 3) = nc. (10 x 3) + (9 x 3) = nd. (20 x 6) + (8 x 6) = ne. (40 x 6) + (5 x 6) = nf. (5 x 80) + (5 x 7) = nActivity 4Rewrite the multiplicand in expanded form. Find the productusing the distributive property of multiplication over addition.1) 15x 94) 63x 32) 29x 25) 82x 43) 38x 7 27. Lesson 34Associative Property of MultiplicationActivity 1There are three factors in each multiplication sentence. Useparentheses to group any two factors. How many ways canyou do it? Write all the possible ways. Find the value of G.231) 3 x 4 x 2 = G2) 1 x 6 x 6 = G3) 4 x 5 x 6 = G4) 6 x 2 x 3 = G5) 9 x 8 x 5 = GActivity 2Group two factors that would make multiplication easy, thengive the product.1) 2 x 3 x 5 = _______________________________2) 4 x 7 x 2 = _______________________________3) 6 x 1 x 4 = _______________________________4) 8 x 5 x 3 = _______________________________5) 9 x 4 x 5 = _______________________________ 28. Complete the puzzle by writing the products in the boxes.Down Across1) 9 x 1 x 6 2) 3 x 7 x 23) 7 x 3 x 1 4) 7 x 1 x 74) 4 x 5 x 2 5) 6 x 5 x 46) 3 x 1 x 8 8) 5 x 4 x 87) 5 x 2 x 9 9) 3 x 4 x 6A. Draw a if the number sentence is correct and a if it iswrong.____ 1) (3 x 4) x 2 = 3 x (4 x 2)____ 2) 2 x (8 x 3) = (3 x 7) x 2)____ 3) 4 x (5 x 2) = 4 x (7 x 3)____ 4) 8 x (6 x 2) = (8 x 6) x 2____ 5) 10 x (2 x 3) = (10 x 2) x 424Activity 312 35 6478 9Activity 4 29. B. Find the missing numbers1) 2 x (3 x 9) = (2 x ___) x 9 = ____2) (5 x 4) x ___ = 5 x (4 x 8) = ____3) (7 x 8) x 3 = ___ x (8 x 3) = ____4) (6 x 2) x 9 = 6 x (___ x 9) = ____5) 8 x (3 x 1) = (___ x 3) x 1 = ____Find the missing factor then get the product. Write youranswer in your notebook.1) (2 x 8) x ____ = 2 x (8 x 3) = ____2) (7 x ____) x 6 = (7 x 4) x 6 = ____3) 5 x (9 x 2) = (____ x 9) x 2 = ____4) (4 x ____) x 7 = 4 x (8 x ____) = ____5) ____ x (6 x 3) = (6 x ____) x 3 = ____25Activity 5 30. Lesson 35Multiplying 2- to 3-Digit Numbers by 1-DigitNumbers without RegroupingFind the product. Use your flats, longs and ones to get the answer.1) 42 2) 33 3) 23 4) 122 5) 242x 2 x 3 x 3 x 4 x 2Find the product. Use the place value method/long method.26tens ones1 2x 4tens ones4 3x 2tens ones5 3x 3Activity 1Activity 21) 2) 3) 31. 4) 5)Find the missing numbers in the sectors of the outer circle bymultiplying the number in the middle circle by 3.27hundreds tens ones4 1 2x 4hundreds tens ones3 1 4x 2Activity 3313311 121x 3213 23112 2321)2) 3)4)5)7) 6)8) 32. Do as indicated. Show your solution in your notebook and encircleyour final answer.1) What is 32 times 4?2) Multiply 312 by 2.3) Find the product of 112 and 4.4) What is the product of 103 and 3?5) How many items are there in 2 groups of 42 items?Find the product. Write your answer in your notebook.1) 32 2) 43 3) 12 4) 211 5) 212x 3 x 2 x 4 x 3 x 428Activity 4Activity 5 33. Lesson 36Multiplying 2- to 3-Digit Numbers by 1-DigitNumbers with RegroupingWhat is the product of 28 and 4?29Read and solve.Which of the two numbers is the multiplicand? multiplier?How will you solve this problem?Activity 1Find the product. Use your flats, longs and squares to get theanswer.1) 63 2) 45 3) 38 4) 327 5) 163x 6 x 7 x 8 x 4 x 5 34. Find the product. Use the place value method/long method.30tens ones8 5x 7tens ones6 4x 5tens ones7 3x 8hundreds tens ones7 1 6x 4hundreds tens ones4 2 3x 6Activity 21) 2) 3)4) 5) 35. Find the missing numbers in the sectors of the outer circle bymultiplying the number in the middle circle by 8.3672153 23631Activity 31)2) 3)4)5)7) 6)8)x 843 19324 472 36. Do as indicated. Show your solution in your notebook and encircleyour final answer.1) How many objects are there in 7 groups of 53 objects?2) What is 83 times 6?3) Multiply 253 by 5.4) Find the product of 351 and 8.5) What is the product of 509 and 8?Find the product. Write your answer on your notebook.1) 64 2) 73 3) 48 4) 732 5) 212x 9 x 6 x 7 x 4 x 832Activity 4Activity 5 37. Multiplying 2-Digit NumbersThe school librarian has bundled the books to bedistributed to different grade levels and sections. There are 36books in a bundle. How many books are there in 17 bundles?33Lesson 37Read the problem.What is asked for in the problem?What are the given?How can you solve the problem?Multiply by ones Multiply by tens436 36 36x 17 x 7 x 10___ ___ ______Add the two partial products36x 17___ partial products+ ______ product 38. Activity 1Use the given digits only once to make 2-digit factors that whenmultiplied will give the largest product. Copy the boxes in yournotebook and write the factors that will give the largest product.1) 0, 2, 3, 5342) 2, 3, 6, 73) 0, 5, 8, 9xProduct: __________xProduct: __________xProduct: __________ 39. Pick a number from Box X. Multiply it by a number from Box Y tofind the given answers. Show your solution in your notebook.Number 1 is already done for you.Box X Box Y40 22 28 41 15 3219 76 63 24 25 921) 608 2) 1 000 3) 1 140X = __19___ X = _______ X = _______Y = __32___ Y = _______ Y = _______4) 902 5) 1 512 6) 2 576X = _______ X = _______ X = _______Y = _______ Y = _______ Y = _______35Activity 2 40. 36Find the missing digits.1)3_x 12_4_32__8_2)60x _530_1_0_150_3)_8x 3622 _1_ 4__1_6_4)_5x 1922_25__5_ _5)43x 3__7212__14_2Activity 3 41. Activity 4Obtain the indicated products and compare the two productsusing >, < or =.371) 19 x 22 ____ 23 x 152) 64 x 14 ____ 16 x 563) 37 x 16 ____ 28 x 244) 29 x 32 ____ 45 x 135) 72 x 86 ____ 82 x 76Activity 5Find the missing numbers using the indicated operations.1) 73 x ___ = 365; 365 - ___ = 305; 305 x 9 = ____2) ___ x 8 = 200; 200 + ___ = 449; 449 x 6 = ____3) 39 x ___ + 78; (78 + 294) x 7 = ____4) ___ x 4 = 256; (256 178) x 5 = ____The sum of the four final products is ________. 42. Lesson 38Multiplying Numbers by Multiples of 10 and 100You know repeated addition by tens. How do you do this in38multiplication?Activity 1Find the product. Write your answer in your notebook.1) 45 x 10 = _________ 6) 46 x 50 = _________2) 37 x 20 = _________ 7) 361 x 20 = _________3) 68 x 80 = _________ 8) 44 x 40 = _________4) 219 x 10 = _________ 9) 7 x 700 = _________5) 350 x 10 = _________ 10) 27 x 300 = _________Activity 2Find the product. Write your answers in your notebook.1) 2 x 5 = ______; 20 x 5 = _____; 200 x 5 = ______2) 3 x 6 = ______; 30 x 6 = _____; 300 x 6 = ______3) 4 x 7 = ______ ; 40 x 7 = _____; 400 x 7 = ______4) 5 x 8 = ______; 50 x 8 = _____; 500 x 8 = ______5) 6 x 9 = ______; 60 x 9 = _____; 600 x 9 = ______ 43. Write the missing numbers in your notebook.1) 30 x ______ = 3002) 150 x 5 = _______3) ______ x 6 = 604) 76 x 100 = _______5) 90 x ______ = 9 000Read each problem carefully then find the product.1) Rita has 23 sets of pechay seedlings. Each set has 50 pechayseedlings. How many pechay seedlings are there in all?2) A craftsman finishes 200 table lamps in a month. How manytable lamps can he finish in 3 months?39Activity 3Activity 4 44. Complete the table below. Multiply the numbers on the firstcolumn by the numbers on the top row. An example is given foryou to follow.x 100 10 20 50 50024 2 4005367Find the product. Write your solutions in your notebook.1) 415 x 20 = ___________2) 98 x 60 = ___________3) 65 x 70 = ___________4) 77 x 100 = ___________5) 215 x 30 = ___________40Activity 5Activity 6 45. Find the product. Write the answer in your notebook.1) 4 x 1 000 = ______ 6) 6 x 1 000 = ______2) 3 x 1 000 = ______ 7) 8 x 1 000 = ______3) 5 x 1 000 = ______ 8) 12 x 1 000 = ______4) 7 x 1 000 = ______ 9) 39 x 1 000 = ______5) 2 x 1 000 = ______ 10) 46 x 1 000 = ______Read, analyze and solve the given problems. Write your solutionon your paper.1) Mr. Bryan collected about 1 000 eggs from his poultry farmlast month. If this continued for 5 months, how many eggswould Mr. Bryan get?2) The price of an item was PhP1 000. It was twice theprice of another item that was on sale. How much was theprice of the item that was on sale?41Lesson 39Multiplying 1- to 2-Digit Numbers by 1000Activity 1Activity 2 46. Activity 3Find the product.1) Mang Badong, the baker, bakes 1 000 pandesals in 1 hour.How many pandesasl can he bake in 5 hours?2) A basket of calamansi contains 1 000 calamansi. How manycalamansi are there in 8 baskets?Find the product. Write the correct answer on your paper.1) 3 x 1 000 300 3 000 30 000 300 0002) 6 x 1 000 600 6 000 60 000 600 0003) 7 x 1 000 700 7 000 70 000 700 0004) 5 x 1 000 50 500 5 000 50 0005) 9 x 1 000 900 000 90 000 9 000 9006) 10 x 1 000 100 000 10 000 1 000 1007) 46 x 1 000 4 600 46 000 460 460 0008) 30 x 1 000 30 000 300 000 3 000 3 000 0009) 28 x 1 000 2 800 280 280 000 28 00010)78 x 1 000 780 7 800 78 000 780 00042Activity 4 47. Activity 5Where did the Genie come from? To find out, solve the followingand write the matching letter below each answer. Do this on yourpaper.1) 1 000 2) 1 000 3) 1 000 4) 1 000 5) 1 000x 8 x 17 x 5 x 43 x 556) 1 000 7)1 000 8)1 000 9) 1 000x 7 x 17 x 8 x 121) 2) 3) 4) 5) 6) 7) 8) 9)43AnswerLetterHe came out of the M __ ___ ___ ___ ___ A ___ ___!A 17 000 C 55 000 G 5 000I 43 000 L 7 000 M 8 000P 12 000 48. 1) 73 2) 87 3) 74 4) 473 5) 664x 5 x 6 x 4 x 6 x 86) 38 7) 76 8) 52 9) 89 10) 179x 23 x 44 x 48 x 23 x 2944Estimate each product.Round off the multiplicand and multiplier then estimate theproduct.1) 331 ____ 2) 241 ____ 3) 284 ____X 29 ____ x 46 ____ x 21 ________ ____ ____4) 145 ____ 5) 782 ____X 35 ____ x 12 ________ ____Lesson 40Estimating ProductsActivity 1Activity 2 49. Activity 3Estimate and solve each problem.1) There are 12 ball pens in each box. About how many ball pensare there in 38 boxes?2) Jeffs marbles are about three times as many as Johns. Johnsmarbles are as many as Nathaniels marbles. Nathaniel has 126marbles. About how many marbles does Jeff have?45Activity 4Find the estimated product.1) About 125 passenger jeepneys pass by a particular house inone hour. About how many passenger jeepneys would havepassed by in 12 hours?2) In an aviary, there are about 33 birdhouses, each having about17 birds. About how many birds are there in all? 50. Activity 51) 83 2) 67 3) 165x 9 x 41 x 374) 122 5) 76x 56 x 5246Estimate the product.Activity 6Find the factors that when multiplied will give each estimatedproduct on the left.1) 60 6 x 14 5 x 18 5 x 132) 150 4 x 34 4 x 36 5 x 283) 270 9 x 24 9 x 26 8 x 314) 360 6 x 53 7 x 47 6 x 585) 4 500 8 x 542 7 x 684 9 x 487 51. Treasure HuntingTrace the path by finding the product of the multiplication factswritten on the trees starting from START. Follow the arrows until youreach the finish line.47Lesson 41Multiplying Mentally 2-Digit by 1-Digit Numberswith Products up to 100Activity 1 52. What did the boy say when he met his teacher? Look at thehidden message by determining the indicated products. Find thecorresponding letter in the code that matches each answer.Write your answer in your notebook.12 13 23 11 12 13 13 26 20 22 23x 5 x 2 x 2 x 4 x 3 x 2 x 3 x 1 x 3 x 2 x 348A 36B 28C 59D 54E 69F 66G 53H 39I 60J 77K 61L 30M 44N 48O 34P 38Q 41R 42S 46T 26U 72V 94W 76X 89Y 57Z 16 53. Activity 3Read each problem carefully. Write only the product on yourpaper.1) Elvie planted 3 rows of sampaguita. Each row had 12sampaguita plants. How many sampaguita plants did sheplant in all?2) Francis planted 11 plots with eggplant seedlings. Each plothas 8 eggplant seedlings. How many eggplant seedlings didhe plant?3) The fare of each passenger is PhP20. How much will thejeepney driver receive if there are 5 passengers?4) A farmer prepares 4 plots for vegetables. How manyseedlings will be needed if each plot is planted with 12seedlings?5) You need 2 oranges to make a glass of orange juice. Howmany oranges do you need to make 13 glasses of orangejuice?49Activity 4Solve mentally.1) 11 2) 12 3) 23 4) 24 5) 13x 7 x 2 x 3 x 2 x 3 54. Solving Problems involving Multiplicationof Whole Numbers50Lesson 42Week: 4Read the problem.The family of Mr. Ruiz enjoys harvesting star apples intheir backyard. They placed them in 9 baskets. Each basketcontains 15 star apples. How many star apples did theyharvest in all? 55. Solve each problem on your paper. You can also show youranswer by illustration.1) Mang Hayden gathered 25 baskets of atis. If each basketcontained 45 atis, how many atis were there in all?2) If each basket of atis costs PhP120, how much will MangHayden receive for 25 baskets of atis?3) Mr. Santos sells school supplies. He has 15 boxes of pencils. Ifthere are 12 pencils in each box, how many pencils does hehave?4) Ofel saves PhP25 a day in her piggy bank. Howmuch money will she save in twelve days?5) Ador could read 25 pages of his favorite book in a day. If heread the book for 11 days, how many pages does the bookhave?51Activity 1 56. Study the illustrations below then answer the questions that follow.1) How many mangoes are there in all?_________2) How many pencils are there in all?_________3) How many flowers are there in all?_________52 57. Activity 3Read, analyze and solve the following problems. Write thenumber sentence for each problem.1) If the product is 45, what are the possible factors?2) One of my factors is 23 and my product is 345. What is53the other factor?3) Ryans mother saves PhP650 every month. How muchwill be her savings in 8 months?4) A one-way promo plane ticket from Manila to Cebucosts PhP1 540. If there were 10 passengers with one-waypromo tickets, how much did all their tickets cost?5) If one week is equivalent to 7 days and there are 52weeks in a year, how many days would there be in oneyear? 58. Read and solve.1) A bus can accommodate 60 passengers. How manypassengers can be accommodated in 15 buses?2) Three vendors sold small flags at PhP5 at the Luneta Parkduring the Independence Day celebration. These vendorswere able to sell 320 flags. How much was the total sale ofthe three vendors?3) The Grade III class of 47 pupils used bottle caps for theirproject. Each child used 25 pieces of bottle caps. How manybottle caps did the children use?4) Roger spends PhP645 for his transportation per month. Howmuch is his total transportation expenses for 9 months?5) Joana can type 32 words per minute. How many words canshe type in 40 minutes?54Activity 4 59. Read and solve each problem carefully. Write your answer onyour paper.1) The class of Miss Santos went to the audio visual room towatch an educational film. In the room are 8 long tables with6 chairs at each table. She has 55 students. Would all herstudents be able to sit? If not, how many chairs do they stillneed?2) A film is 45 minutes long. It was shown to grade three to sixpupils. Because the viewing room is not big enough, only onegrade level was allowed to watch at a time. There is a 10-minute interval between the viewing for each grade level.How many minutes was the viewing room used?3) Ofelia had a PhP1 000 bill. She bought 2 kilograms of meat atPhP160 a kilo, vegetables for PhP85 and 4 kilos of fish whichcost PhP130 a kilo. How much money did she have after allher purchases?55Lesson 43Solving Problems involving Multiplicationwith Addition and/or Subtraction of WholeNumbersActivity 1 60. Solve the problems carefully. Write your answer in your notebook.1) Ordin bought 4 pineapples at PhP20 each. How muchchange will he get if he gave PhP100 to the seller?2) The choir members made pastillas for their fund raisingproject. They made 8 packs of pastillas with 25 pieces ineach pack. Miss Hilario ordered 4 more packs. How manypieces of pastillas did the choir members prepare?3) Mrs. Mendoza and her class went to Tagaytay for aneducational trip. Before going home, she bought 45pasalubong items for her co-teachers. If each item costsPhP25 and she gave the seller PhP1 500, how much was herchange?Read, analyze and solve the following problem. Write your answerin your activity sheet.1) Analiza bought 4 kilos of lanzones at PhP60 a kilo. How muchchange did she get from a PhP500 bill?2) Edmond has four PhP200 bills, four PhP100 bills, ten PhP50 billsand twelve PhP20 bills. How much money does Edmondhave?3) Mang Lester gathered 128 mangoes from one tree andtwice as many mangoes from a bigger tree. How manymangoes did he gather in all?56Activity 2Activity 3 61. 4) Dolly has 12 stamps. Mila has twice as many stamps. If Dollysfriend gives her 12 more, how many stamps will Dolly andMila have?5) For their fund raising activity, the Math Club sold 50 kilos ofused pieces of paper and 205 bottles. If one kilo of papercould be sold at PhP7 and each bottle costs PhP1, howmuch will the club raise?Read, analyze, and solve the following problems. Write youranswers in your notebook.1) Mel has five PhP1 coins, two PhP5 coins and seven PhP10coins. How much money does she have in all?2) Cliff has 25 one-peso coins. Nicolette has 3 times more one-pesocoins than Cliff. How many one-peso coins do theyhave in all?3) Chrisse has 12 sheets of art paper. Cherry has twice as manyas Chrisse. Ena has 14 pieces more than Cherry. Armina hasas many pieces of art paper as Chrisse and Cherry. Howmany pieces of art paper do the four girls have?57Activity 4 62. Make a word problem given these situations.581)2)Lesson 44Creating Problems involving Multiplicationwithout or with Addition or SubtractionActivity 1How will I make aproblem with thesedata?2 boxes of donuts with12 donuts in eachbox, Hmm!16 cupsPhP5.00 price of eachcup4 cups not bought 63. Create a word problem given these situations.591)2)Activity 2Problem again! Ok, noproblem!3 trays of eggs12 eggs per tray5 eggs not placed in anyof the trays9 balloons3 sistersPhP15 per balloon 64. A. Make problems involving money and show your solutions inyour notebook.1) Using multiplication and addition2) Using multiplication and subtractionB. Complete the problems below then solve.1) John has ____ pencil cases. There are 12 pencils of differentcolor in each case. How many pencils does he have?2) There are ____ dozens of eggs in a box. One dozen wassold. How many eggs are left in the box? (Hint: one dozen= 12)3) In a mathematics class, fourteen pupils are seated in a rowand ___ of the pupils were absent. If there are 4 rows in theclassroom, how many pupils are present in the Math class?60Activity 3 65. Lesson 45Multiples of 1- to 2-Digit NumbersFind the next six multiples of each of the numbers given below. Writeyour answers in your answer sheet.611) 32) 53) 74) 85) 96) 117) 138) 159) 2410)33Activity 1 66. 1) Fill in each train couch with the appropriate number by adding thecommon difference to get the next multiple of a number in the trainbox.18 24 30 ___ ___ ___2) Fill in each train couch with the appropriate number by multiplying thefirst number by 2, then 3, then 4, and so forth, to get the next multiple ofa number in the train box.19 ___ 57 76 ____ ____Match the series of numbers in column A with the correct multiplesin column B.A B62a. multiples of 2b. multiples of 3c. multiples of 6d. multiples of 7e. multiples of 10Activity 2Activity 31)2)3)4)300, 303, 306, 309 31290, 80, 70, 60, 50, 40147, 140, 133, 126, 119150, 144, 138, 132, 126 67. Activity 4Write the next 3 numbers which are multiples of the same number as the twonumbers given in the box.15, 18, ___, ___, ___27, 36, ___, ___, ___96, 104, ___, ___, ___105, 120, ___, ___, ___51, 68, ___, ___, ___631)2)3)4)5)Activity 5Multiply the numbers along the first column by 12, 23, and 37.x 12 23 371) 192) 263) 374) 435) 68. Read and solve.1) Mr. Door arranged his 72 books on shelves. He placed 9books on each shelf. How many shelves did he use?2) Coach Eric bought 64 basketball balls to be used by theplayers in the inter-year level competitions. There are 8 teamsin all. How many balls will be given to each team?Solve the problems and show your solutions.1) If there are 56 trees to be planted in a 7-row farm, how manytrees will be on each row?2) If there are 48 pomelos that will be placed in 6 boxes, howmany pomelos will be contained in each box?64Lesson 46Dividing Numbers up to 100 by 6, 7, 8, and 9Activity 1Activity 2 69. Activity 3Read, analyze and solve the following problems.1) Boknoy bought pens in 3 different colors: 2 red, 2 blue, and 2black. If he paid PhP96 to the cashier, how much is the priceof each pen?2) There are 72 dalandan in a box to be distributed to 8 pupils.How many dalandan will be given to each pupil?Analyze and solve the problems below.1) There are 30 pupils in a class. If the teacher will divide themequally into 3 groups, how many pupils will be in eachgroup?2) 18 star apples will be distributed to 6 children. How many starapples will be given to each child?65Activity 4 70. Lesson 47Stating Division Facts of Numbers up to 10Activity 1From the given multiplication () or division () fact, build a thefirst answer and then write 3 related whole family of facts. Findnumber sentences.Example: 6 x 2 = 12; 2 x 6 = 12; 12 2 = 6; 12 6 = 2668 x 7 = ____72 9 = ____48 6 = ____10 x 7 = ____35 5 = ____Activity 2Find the product then write the division facts for eachmultiplication sentence.1) 5 x 7 = ____, ____ ____ = ____ or ____ ____ = ____2) 3 x 9 = ____, ____ ____ = ____ or ____ ____ = ____3) 8 x 6 = ____, ____ ____ = ____ or ____ ____ = ____ 71. 4) 10 x 2 = ____, ____ ____ = ____ or ____ ____ = ____5) 4 x 8 = ____, ____ ____ = ____ or ____ ____ = ____67Activity 3Write the missing division fact.1) 10 ___ = 5 6)___5 15___10 602) 7) 81 9 = ___3) 42 7 = ___ 8)39 ___12___ 244) 9) ___ 7 = 95) 48 ___ = 8 10) 64 ___ = 16 72. Copy the puzzle and complete it by writing the appropriatenumber.36 ___ = 6___ x 3 = 278 x 7 = ___2 ___=___ 2 = ___68Activity 4 73. Answer the following on your paper.1)Write the division facts for the given illustration below.______________________________2) Give one division fact/sentence for 6 x 3 = 18.____________________________3) Given 5, 4 and 20, write one multiplication and onedivision sentence. ___________________________4) Write the missing number in this division sentence.36 ___ = 125) Write a division sentence for this problem.There are 40 balloons and 8 tables in a room. Fiveballoons are in each table.___________________________69Activity 5 74. Activity 6Complete the multiplication sentences then write the divisionsentences.70MultiplicationSentenceDivisionSentenceDivisionSentence1) 2 x 9 = ____2) 3 x ___ = 213) 9 x 7 = ___4) ___ x 6 = 365) 8 x ___ = 726) 12 x 4 = ___Activity 7Solve for the quotient in two ways:a. using visualizationb. by division process1) Lolo Ben has 48 hectares of land. If he is to divide itequally among his 11 children, how many hectares will begiven to each? How many hectares will be left?2) A bookstore has 80 copies of a bestseller book. The booksare arranged in stacks of 10, how many stacks will therebe? 75. Dividing 2- to 3-Digit Numbers by 1-DigitNumbers71Lesson 48Activity 1Answer the following.1) What is 72 3?2) What is the remainder if you divide 651 by 8?3) The teachers prepared 63 garlands for visitors. If the garlandswere to be divided equally in 5 trays, how many will be ineach tray? How many will be left?4) Bitoy harvested 136 mangoes. If he is going to divide themangoes into 4 big baskets, how many mangoes were therein each basket?Activity 2Tell whether there is a remainder or not. If there is, then write whatit is. Show all your solutions in your notebook.1) 54 8 = ______________2) 76 4 = ______________3) 331 7 = ______________ 76. 724) 502 5 = ______________5) 912 3 = ______________6) 935 9 = ______________Activity 3Fill each box with the correct number to complete thenumber puzzle.56 ___ = 7 x 4 = ___12 x 8 = ___ 2 = ___350 ___ = 5 x ___ = 2451)2)3)4)200 4 = ___ x 18 = ___ 77. Activity 4Fill in the blanks. Write the answer on your paper.1) When 83 is divided by 5, the quotient is ________ and theremainder is ________.2) When 133 is divided by 4, the quotient is ______ and theremainder is ________.3) When 670 is divided by 9, the quotient is _______ and theremainder is ________ .73Activity 5Answer the following:1) Divide: 4 922) Is there any remainder if 96 is divided by 7? What is theremainder?3) 258 6 = 43, is the number sentence correct? Why?Justify your answer.4) Find the quotient: 708 8.5) Eight hundred sixty-three divided by nine is equal to______. 78. Activity 6Use any of the digits: 0, 3, 6, or 7 to come up with two 2-digitnumbers and two 3-digit numbers. Divide the number usingthe given divisor.742- or 3-digitNumberDivisor Quotient1) 42) 63)74) 9 79. Solve the division expressions. Follow the direction in every stationin order to reach the finish line. Write your answer in yournotebook.StartAdd 91 to the sumof the three remainders.What is the final answer? _______________75Activity 7423 4Add the remainder in Start tothe dividend in Station 1 beforeanswering Station 1.Finish line(319 + ____) 5Use the quotient in Station 1as dividend in Station 2._____ 3Add the threeremainders. 80. Lesson 49Dividing 2- to 3-Digit Numbers by 2-DigitNumbers without and with RemainderFind the quotient. Solve on your own paper.1) 2) 3) 4)76Activity 1131 12 =________484 24 =________84 14 =________541 18 =________216 18 =________77 11 =________5) 6) 7)448 12 =________ 81. 771) 96 122) 45 153) 68 164) 188 225) 475 25Activity 2Find the quotient. Write thesolutions on your paper.Activity 3Fill in the blanks. Choose your answers from the numbers in thebox. Write your answers on your paper.1 11 236 20 71. The divisor is 12. The dividend is 84. What is the quotient?2. The remainder in 295 14 is ________3. If the quotient is 30 and the dividend is 600, what is thedivisor?4. 322 14 is _______5. The divisor is 80. The dividend is 880. What is the quotient? 82. Determine the quotient and the remainder (if there is any) tocomplete the table below. Write your answer in your notebook.Dividend Divisor Quotient Remainder1)54 212) 108 273) 380 764) 633 575) 648 3278Activity 4 83. A. Give the missing number and write your answers on yourpaper.1) 650 10 = _____ 4) 486 102) 780 _____ = 78 5) 903 1003) 180 _____ = 18B. Analyze and solve. Write your answers on your paper.1) How many 100s are there in 600?2) Two-thousand and five hundred has how manyhundreds?3) 5 000 is how many hundreds?4) 400 is equal to how many tens?5) 780 has how many tens?79Lesson 50Dividing 2- to 3-Digit Numbers by 10 and 100Activity 1 84. Look at the cards below. Write the letter of the correct answer inyour answer sheet.1) Im 6. My number sentence is:a. 600 100 = nb. 600 10 = nc. 60 5 = nd. 116 10 = n2) Im 80. My number sentence is:a. 8 000 10b. 8 000 100c. 800 100d. 800 1003) Im 53. My number sentence is:a. 53 1b. 530 100c. 530 1 000d. 5 300 104) Im 27. My number sentence is:a. 2 700 100b. 2 700 10c. 270 100d. 270 15) Im a quotient 22 with a remainder of 4. My numbersentence is:a. 2 240 10b. 2 204 10c. 2 240 100d. 2 204 10080Activity 2 85. Activity 3Find the quotient. Write your answers on your answer sheets.1) 560 10 5) 620 102) 800 100 6) 810 103) 430 10 7) 900 104) 750 10 8) 1 000 100Copy the number box in your notebook. Find the quotient thenencircle the answer in the box. To find the answer, you may movedown, across or diagonally.9 6 1 5 40 3 2 6 35 4 0 2 78 6 6 1 77 1 3 0 581Activity 410) 90 109) 120 108) 100 104)750 105)620 106)810 107)400 101) 560 102) 800 1003) 430 10 86. Activity 5Complete the table. Write a number sentence on the appropriatecolumn. Write your answers on your answer sheets.82QuotientNumber sentenceDivisor: 10 Divisor: 100Example: 4 40 10 400 1001) 92) 73) 364) 605) 78Activity 6Find the quotient using any method. Write your answers on youranswer sheets.1) 480 10 6) 400 100 11) 49 102) 560 10 7) 500 100 12) 75 103) 610 10 8) 600 100 13) 125 1004) 820 10 9) 800 100 14) 366 1005) 950 10 10) 900 100 15) 950 10 87. Lesson 51Estimating QuotientsActivity 1Estimate the quotients. Write the answers on your paper.83Given Round offthe divisorThink ofcompatiblenumbersEstimate1) 184 112) 338 483) 508 214) 677 565) 889 78Activity 2A. Write the closest number to 38 that can be evenly dividedby the following:1) 4 ________2) 6 ________3) 8 ________4) 5 ________5) 9 ________ 88. 84B. Estimate each quotient.1) 19 62) 29 43) 35 44) 68 85) 93 5C. Estimate the quotient.1) 119 232) 321 803) 431 614) 753 905) 821 89Activity 3Solve the problems in two minutes. After 2 minutes, solve on theboard.1) There are 65 pupils visiting a museum. If they are divided intoeight groups, about how many pupils are in each group?2) Your class is studying the properties of matter. The 47 pupils inyour class will be divided into groups. Each group willresearch one of the 3 properties of matter. About how manypupils will be in each group?3) There are 736 Grade I pupils in Gregorio Elementary School. Ifpupils will be distributed into 12 sections, about how manypupils will be in each section? 89. Activity 4Every day at the baseball field, a different number of baseballplayers show up. Estimate how many teams can be formed eachday. (Hint: There are 9 players in a baseball team.)Read and complete the table.Day Number ofPlayers85Number ofTeams1) Monday 732) Tuesday 373) Wednesday 824) Thursday 555) Friday 46Activity 5A. Estimate each quotient and explain your answer whether it isgreater than or less than the exact quotient. Write youranswer in your answer sheet.Estimate > or < ExactQuotient1) 64 72) 83 93) 130 8 90. 864) 396 45) 850 96) 244 377) 300 598) 397 49) 230 7310) 545 50B. In which of these situations would an estimate beacceptable alternative to an exact. Write estimate ifestimate is acceptable and exact if it is necessary to obtainthe actual quotient.______ 1) Finding your average grade for each learning area.______ 2) Finding the number of pupils in your class.______ 3) Finding the number of hours you watch TV in a week.Activity 6A. Estimate the quotient. Write the answer on your paper.1) 253 50 = _____ 4) 270 32 = _____2) 360 7 = _____ 5) 432 18 = _____3) 554 6 = _____B. Write a real life problem in your notebook in which youestimate the quotient of two numbers. 91. Find the quotient mentally. Write the method used in finding thequotient.Number Sentence Method Used1) 45 3 = _____2) 57 3 = _____3) 76 2 = _____4) 85 5 = _____5) 96 6 = _____87Lesson 52Dividing Mentally 2-Digit Numbers by 1-DigitNumbers without RemainderActivity 1 92. Complete each table by finding the quotient mentally.Divide by 5.Given Answer1) 352) 453) 504) 605) 75Divide by 6.Given Answer1) 182) 243) 364) 485) 54Divide by 9.Given Answer1) 272) 453) 634) 725) 8188Activity 2 93. Activity 3Give a division sentence that can be answered mentally using thegiven number as dividend.1) 18 6) 722) 26 7) 803) 40 8) 864) 55 9) 905) 63 10) 96Activity 4Read and give your answer mentally. Explain the method used.Suppose you are given PhP75.00 and you are asked to spend theentire amount, what items will you buy from the list below? Why?Item Available Numberof Items89Price per ItemA. pencil 12 pieces PhP6.00 eachB. pad paper 5 pads PhP15.00 per padC. crayons 4 boxes PhP25.00 per boxD. notebook 5 pieces PhP17.00 each 94. Construct a division sentence with each of the following asdividend.1) 18 6) 632) 24 7) 763) 39 8) 814) 45 9) 905) 48 10) 9890Activity 5 95. Read and answer. Use different strategies in finding the answer.Explain your answer. Write your answer in your answer sheet.1) Mother packs 60 sandwiches for the party. If there are 7tables in the party with 7 guests, do you think mother hasenough sandwiches for them?2) Ana has PhP850 to spend for food. If she spends PhP120 aday for food, how long will the money last?3) Mr. Santos harvested 2 161 mangoes. How many baskets willhave 200 mangoes each? How many remaining mangoeswill be put in one basket?91Lesson 53Solving Problems involving Division withoutor with any Other Operations of WholeNumbersActivity 1 96. Read and solve the problems below.Use any methods in solving the problems such as throughillustrations, groupings, and the like.1) If 32 pieces of cupcakes will be given to 8 pupils, howmany pieces of cupcakes will each receive?2) If Mrs. Ramos has PhP750, is it possible for her to allotPhP90 each to her 5 children and 2 nieces as their schoolallowance for 3 days? Why?3) If you have 15 packs of noodles, 20 kilos of rice and 5bars of laundry soap, how will you distribute this to 5households? Make your own list.4) Is it possible to have 35 pieces of PhP50 in PhP6 000?92Why?5) Look at the list of objects that you can buy with yourPhP500.00.Item Unit Selling PricePhP235PhP125PhP200PhP20PhP5Activity 2 97. 93PhP25PhP3Activity 3Illustrate or show different ways of grouping and solving the givenproblems. Write your answer on your answer sheet.1) Group 76 into 12.2) How many twenty-pesos are there in PhP920?3) How many 50s are there in PhP750?4) How many groups of 5s are there in125?5) Group 600 by 100s.Activity 4If you are given PhP200, how will you spend it? Make your owntable about what items you are going to buy and how mucheach costs. Write your answer in your notebook.Amount Given: PhP200Item/s to be bought Price/Cost 98. Creating Problems involving Division or withany of the Other Operations of Whole NumbersSix children were playing in the backyard.Two more children came to join. Then they picked24 guavas.94Lesson 54Read the story.Using the story above, make questions that can be answeredusing division or with other operations. 99. Make a problem with corresponding reasonable answerbased on the given situation. Write your answer on youranswer sheet.1) A class of 45 pupils received a donation of 100 packs ofpowdered milk.2) Teresa told her brother that she was able to count 100 feetof chicken and goat in their farm.95Activity 1Problem:Answer:Problem:Answer: 100. Activity 2Develop number riddles such as:Mr. Santos has 4 daughters. Each of his daughtershas a brother. How many children does Mr.Santos have?Exchange your riddle with a classmate and solve each others96riddles.Activity 3Do the following exercises with your group members. Make a wordproblem using the given data. Write your answer on your answersheet.1) a shirt costs PhP75; PhP2002) 1 000 eggs; 24 trays3) PhP500 in coins4) 3 canned goods per pupil; 384 canned goods5) 835 kilograms of rice; 5 kilograms each employee 101. Activity 4Answer the following on your paper.1) Make a division problem whose quotient will have noremainder.2) Write a division word problem in which the remainder isa. 3 b. 5 c. 4 d. 0 e. 1Activity 51) Draw a picture and write a word problem about 3 friendswho planted a total of 84 pechay and each of theirgarden plots have the same number of pechay.2) Write a number sentence and illustrate to solve thisWilly says, If I want to learn 15 words in 6days, I can learn 2 words each day. Doyou agree or disagree? Explain.Leila has 13 glasses of pineapple juice tosell to 6 people.97problem.3) Talk about this:Will each person get more or less than 2 glasses? How doyou know?