Division Facts and Extensions

Transcription

1 Division Facts and Extensions Objectives To review multiplication and division facts and apply basic facts to division with 1-digit divisors. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Generate equivalent names for whole numbers. [Number and Numeration Goal 4] Apply multiplication facts, related division facts, or extended facts to identify friendly numbers. [Operations and Computation Goal 2] Playing Name That Number Student Reference Book, p. 325 per partnership: 1 complete deck of number cards (from the Everything Math Deck, if available) Students apply number properties, equivalent names, arithmetic operations, and basic facts. READINESS Using Equivalent Names for Numbers Math Masters, p. 421 per partnership: 4 each of number cards 1 9 (from the Everything Math Deck, if available) Students complete name-collection boxes focusing on number properties to make equivalent names for numbers. Use friendly numbers to divide 2-digit by 1-digit numbers. [Operations and Computation Goal 3] Key Activities Students practice division facts and extended facts. They use multiples of a given number to rename numbers. They use friendly numbers to solve problems with 1-digit divisors. Ongoing Assessment: Informing Instruction See page 233. Ongoing Assessment: Recognizing Student Achievement Use journal page 99. [Operations and Computation Goal 3] Quadrangle Relationships Math Masters, p. 440A Students practice classifying and comparing relationships among quadrangles. Math Boxes 4 1 Math Journal 1, p. 100 Geometry Template Students practice and maintain skills through Math Box problems. Study Link 4 1 Math Masters, p. 102 Students practice and maintain skills through Study Link activities. ENRICHMENT Exploring More Divisibility Rules Math Masters, p. 103 Students apply divisibility rules to 5-, 6-, and 7-digit numbers. EXTRA PRACTICE 5-Minute Math 5-Minute Math, pp. 25, 28, and 183 Students solve division problems. Key Vocabulary dividend divisor quotient multiples Materials Math Journal 1, p. 99 slates per partnership: 4 each of number cards 1 9 (from the Everything Math Deck, if available) Advance Preparation For Part 1, make classroom posters showing the names of multiplication and division problem parts and relating those names to the three numbers of a fact family. Teacher s Reference Manual, Grades 4 6 pp. 16, Unit 4 Division

2 Getting Started Mathematical Practices SMP1, SMP2, SMP5, SMP6, SMP7, SMP8 Content Standards 5.OA.1, 5.OA.2, 5.NBT.2, 5.NBT.6, 5.NF.5a, 5.G.3, 5.G.4 Mental Math and Reflexes Use your slate procedures. Remind students to think of missing factors. Example: How many 9s are in 72? Think: 9 times what number equals 72? How many 3s are in 21? 7 How many 30s are in 210? 7 How many 3s are in 210? 70 How many 7s are in 49? 7 How many 70s are in 490? 7 How many 7s are in 490? 70 Estimate: About how many 4s are in 21? About 5 About how many 40s are in 210? About 5 About how many 4s are in 210? About 50 Math Message For each problem below, write two related division facts. 6 7 = = x 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Interactive whiteboard-ready epresentations are available at to help you teach the lesson. Algebraic Thinking Ask volunteers which 3 numbers are in the fact family for 6 7 = 42. 6, 7, and 42 Ask: Is this an addition/ subtraction or multipli cation/division fact family? Multiplication/ division How do you know? Sample answers: The numbers come from a multiplication fact; it can t be addition/subtraction because is not equal to 42. Fact families have opposite operations; division is the opposite of multiplication. Pose questions such as the following: Use the related multiplication and division facts for 6, 7, and 42 to write a statement similar to the following: 42 is 7 times as great as 6. Sample answer: 42 is 6 times as great as 7. In a related division fact, which number is the dividend? 42 Ask volunteers to state the related division facts, naming the divisor and the quotient. In 42 / 7 = 6, 7 is the divisor and 6 is the quotient. In 42 / 6 = 7, 6 is the divisor and 7 is the quotient. Which 3 numbers are in the fact family for 9 6 = x? 9, 6, and x Expect that some students might respond 9, 6, and 54. In this case, ask students whether they think x can be used as a member of the fact family. Yes, because x is a variable and represents a number. Ask volunteers to give the related division facts. x / 6 = 9; x / 9 = 6 Use the related multiplication and division facts for 6, 9, and x to write a statement similar to the following: x is 9 times as great as 6. Sample answer: x is 6 times as great as 9. What number is in the multiplication/division fact family with 20 and 5? 4 How do you know? 5 4 = 20; 20 / 5 = 4; there are 4 [5s] in 20. Conclude the discussion by summarizing that knowing one multiplication fact leads to knowing 2 division facts. Ask students to compare the size of a product to one of its factors, based on the other factor. Tell them, for example: Using the numbers 4, 5, and 20, NOTE Everyday Mathematics reinforces students understanding of the link between multiplication and division. It is expected that students who have automatic recall of the multiplication facts will be able to state related division facts. Lesson

3 you could say that 20 (the product) is 4 (one of the factors) times as great as 5 (the other factor). Ask: What other comparisons can you make using the product and the factors? Sample answers: 20 is 5 times as great as 4. Using 5: 4 times is 20. Using 4: 5 times is 20. Pose questions to have students compare the size of a product to one of its factors: 20 is how many times as great as one of its factors, 4? 5 times as great x / 9 = 6 means that x is how many times as great as its quotient, 6? 9 times as great 2 (4 + 5) is how many times as great as one of its factors, (4 + 5)? 2 times as great Practicing Division Facts and Extended Division Facts WHOLE-CLASS Use your slate procedures to practice division facts and their extensions. Dictate problems like the following, varying your language. For example, ask: What is 63 divided by 7? How many 7s are in 63? If necessary, give a clue, such as, Think: 7 times what number equals 63? 63 / / / / ,000 / ,000 / / / / / / ,900 / What number is 7 times as great as 6? 42 What number is 90 times as great as 7? 630 What number is one-fourth the size of 48? 12 What number is 1,000 times as great as 5? 5,000 Renaming Numbers º Use the following activity to prepare students for the mental division strategy on journal page 99. On a transparency, or the board, draw a name-collection box. Shuffle the cards (4 each of number cards 1 through 9). Turn over 2 cards and make a 2-digit number. PROBLEM SOLVING Write the number in the collection box tag. Ask volunteers what they think you should do next. Most students will recognize the name-collection box format and will respond that you should write equivalent names for the number in the box. Explain that for this activity, students will look for equivalent names that contain multiples of another number. Turn over a third card. Survey the class for equivalent names that contain multiples of the number from the third card. 232 Unit 4 Division

4 Use follow-up questions to guide students to see that the largest multiple can be broken into smaller parts to make other equivalent names. Allow partners time to try at least three different name-collection boxes, drawing them on scrap paper or using slates. Circulate and assist. Using a Mental Division Strategy (Math Journal 1, p. 99) WHOLE-CLASS Explain that using equivalent names for numbers, knowing multiplication and division facts, and recognizing fact extensions in order to break numbers into friendly parts will simplify calculations. Refer students to journal page 99. As a class, discuss the presented division strategy. Have students complete Problems 1 6. Remind them to use multiplication to check their results. Circulate and assist. Date LESSON 4 1 Time Mental Division Strategy Fact knowledge can help you find how many times a 1-digit number will divide any large number. Example: Divide 56 by 7 mentally. Think: How many 7s in 56? Or think: 7 times what number equals 56? Continue: Since , there must also be 8 [7s] in 56. So 56 divided by 7 equals 8. Knowing basic facts helps you break the larger number into two or more friendly numbers numbers that are easy to divide by the 1-digit number. Example: Divide 96 by 3 mentally. Break 96 into friendly numbers. Here are two ways. 90 and 6. Ask yourself: How many 3s 60 and 36. Ask yourself: How many 3s in 90? (30) How many 3s in 6? (2) in 60? (20) How many 3s in 36? (12) Total: Total: So 96 divided by 3 equals 32. Check the result: Complete the following statements. List the friendly parts that you used and 12; 36 and 6 13 R5 60 and 23; 72 and divided by 3 equals divided by 4 equals. (friendly parts for 42) (friendly parts for 68) divided by 6 equals divided by 7 equals. (friendly parts for 83) (friendly parts for 99) 5. Fifteen-year-old oak trees are often 6. The job of interviewing 500 students about 25 feet tall. Rose, a 15-year-old in a school is to be divided equally among girl, is about 5 feet tall. How many times 10 interviewers. How many students taller are the trees than Rose? About 5 times taller Math Journal 1, p. 99 Student Page and 28; 20 and R1 77 and 22; 70 and 29 should each interviewer talk to? 50 students Ongoing Assessment: Informing Instruction Watch for students who use paper-and-pencil exclusively, rather than mental arithmetic. Encourage these students to try to visualize what they might write before they actually write anything. Survey the class for methods of breaking numbers into friendly parts. Use follow-up questions to help students recognize how to use a multiple of the divisor. Adjusting the Activity Have students break the dividend into two friendly numbers so that one number is the divisor times 10 and the other is the remaining part. For 42 divided by 3, use 3 10, or 30, as the first friendly number, and 12 as the second. For larger dividends, it might be necessary to use the divisor times a multiple of 10. For 132 divided by 3, use 3 40, or 120, as the first friendly number and 12 as the second. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Date LESSON Write the value of each of the following digits in the numeral 34,089,750. a. 4 b. 8 c. 5 d. 9 e. 3 Math Boxes millions ten-thousands tens thousands ten-millions Student Page Time 2. Write the following numbers in standard notation. a. 6 2 = b = c = d. 8 3 = , e. 3 4 = Ongoing Assessment: Recognizing Student Achievement Journal Page 99 Problems 1 4 Use journal page 99, Problems 1 4 to assess students facility using multiplication and division facts for division with 1-digit divisors. Students are making adequate progress if they successfully identify friendly numbers and use these to solve the problems. [Operations and Computation Goal 3] 3. Roger had saved $10.05 from his allowance. Then he bought a paint-bynumbers kit for $7.39. How much money does he have left? $ Use your full-circle protractor to measure angle CAT. C Circle the best answer. A. about 318 B. about 50 T A 4. Javier has $5.00 to buy school supplies. He wants one pack of pencils for $1.38, a notebook for $2.74, and some writing paper for $1.29. If he has enough money, how much change will he get back? Not enough money If not, how much more money does he need? $ Complete the table. Fraction Decimal Percent 65_ 100 1_ 3 13_ 0.3 or or 2_ 5 4_ 100, 4_ 10 1_ % or 33 1_ 3 % 65% 40% 5% C. about 42 D. about Math Journal 1, p. 100 Lesson

5 Name Date Time Venn Diagram Teaching Aid Master 2 Ongoing Learning & Practice Properties of Kites Properties of Parallelograms no pairs of parallel sides 2 pairs of sides are the same length exactly 2 pairs of parallel sides Math Masters, p. 440A sides of equal length next to each other quadrangle sides of equal length opposite each other Playing Name That Number (Student Reference Book, p. 325) Students practice applying number properties, equivalent names, arithmetic operations, and basic facts by playing Name That Number. Quadrangle (Quadrilateral) Relationships (Math Masters, p. 440A) Students practice and extend their thinking about classifying and comparing relationships among quadrangles. Draw a Venn diagram on the board with the headings Properties of Parallelograms and Properties of Kites. (See margin.) Briefly review how to use a Venn diagram. The properties unique to parallelograms are listed below the label Properties of Parallelograms, and properties unique to kites are listed below Properties of Kites. The properties the two shapes have in common are listed in the intersection of the two ovals. Students complete Math Masters, page 440A with a partner. Assign additional pairings for additional practice. Possible pairings include square and rectangle, trapezoid and parallelogram, kite and rhombus, square and rhombus, and parallelogram and rhombus. Study Link Master Name Date Time Math Boxes 4 1 (Math Journal 1, p. 100) INDEPENDENT STUDY LINK 4 1 Uses of Division Use multiplication and division facts to solve the following problems mentally Remember: Break the number into two or more friendly parts. Example: How many 4s in 71? Break 71 into smaller, friendly numbers. Here are two ways. 40 and 31. Ask yourself: How many 4s in 40? (10) How many 4s in 31? (7 and 3 left over) Think: What multiplication fact for 4 has a product near 31? (4 7 28) Total 17 and 3 left over. 20, 20, 20, and 11. Ask yourself: How many 4s in 20? (5) How many 4s in three 20s? (15) How many 4s in 11? (2 and 3 left over) Total 17 and 3 left over. So 71 divided by 4 equals 17 with 3 left over. 19 Sample answer: 30 and divided by 3 equals divided by 8 equals. (friendly parts for 57) (friendly parts for 96) 3. The diameter of Earth, about 8,000 miles, 4. The weight of an object on Earth is is about 4 times the diameter of the 6 times heavier than its weight on the moon. What is the approximate moon. An object that weighs 30 lb diameter of the moon? on Earth weighs how many pounds on the moon? 8,000 mi About 2,000 mi Practice Solve. Then write the other problems in the fact families. 5. 1, , , ,803 unit Math Masters, p Sample answer: 80 and 16 5 lb unit Mixed Review Math Boxes in this lesson are paired with Math Boxes in Lesson 4-3. The skill in Problem 6 previews Unit 5 content. Writing/Reasoning Have students write a response to the following: Explain your answer to Problem 4. Sample answer: I added to find the total cost for the supplies Javier wanted. It was more than $5.00, so I subtracted $5.00 from the total cost to see how much more money he needed. Study Link 4 1 (Math Masters, p. 102) INDEPENDENT Home Connection Students use friendly numbers, division facts, and related multiplication facts to solve division problems and number stories. 234 Unit 4 Division

6 3 Differentiation Options Teaching Aid Master Name Date Time Equivalent Names for Numbers READINESS Using Equivalent Names for Numbers (Math Masters, p. 421) 5 15 Min To provide experience with finding equivalent names for numbers, have students use name-collection boxes, focusing on number properties and relationships. For example, they might use multiples of ten, add 0, or multiply by 1 to make equivalent names. Partners take turns dealing two cards from a deck comprised of 4 each of the numbers 1 9. Each partner uses the numbers on the cards to form a 2-digit number. Their numbers can be the same or different. Partners write their numbers in one of the name-collection box tags on Math Masters, page 421 and find as many different equivalent names for the number as they can. Math Masters, p. 421 NOTE In Part 1, students rename numbers using multiples of given numbers. However, do not restrict the forms of the equivalent names students collect for this activity. ENRICHMENT Exploring More Divisibility Rules (Math Masters, p. 103) Min To apply students understanding of divisibility, have them solve problems using divisibility rules for prime numbers. Partners complete Math Masters, page 103. After partners finish, have them create and exchange 6-digit numbers to test for divisibility by 7, 11, or 13. They might also find numbers that are divisible by more than one of these primes. Products of multiples of primes are easy to find. Example: (65 7) (89 13) = 526,435 EXTRA PRACTICE SMALL-GROUP 5-Minute Math 5 15 Min To offer students more experience with whole-number division, see 5-Minute Math, pages 25, 28, and 183. Name Date Time LESSON 4 1 Testing for Divisibility by 7, 11, and 13 Use these divisibility rules to test large numbers. To test if a number is divisible by 7: Take the rightmost digit. 25,809 Double it Subtract the result from the 2, ,562 remaining digits. Repeat, each time doubling the 2, rightmost digit and subtracting, until the result is small enough to know that it is, or is not, 21 is divisible by 7, so 25,809 is divisible by 7. divisible by Is 33,992 divisible by 7? To test if a number is divisible by 11: 2. Is 9,723 divisible by 11? To test if a number is divisible by 13: Teaching Master Yes, because 14 is divisible by 7 Find the sum of every other digit. 10, Find the sum of the digits that are left Subtract is divisible by 11, so 10,648 is divisible by 11. No, because 1 is not divisible by 11 Multiply the rightmost digit by 4. 1,166, Add the result to the remaining 116, ,701 digits. Repeat, each time multiplying 116, the rightmost digit and adding, 11, , until the result is small enough to 1, , know that it is, or is not, divisible by , so 1,166,923 is divisible by Is 89,362 divisible by 13? Yes, because 91 is divisible by 13 Math Masters, p. 103 Lesson

7 Name Date Time Venn Diagram Copyright Wright Group/McGraw-Hill 440A