Multiplication and Division

Transcription

1 Multiplication and Division Objectives To guide exploration of the relationship between multiplication and division; and to provide practice with division facts. 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 Solve multiplication facts. [Operations and Computation Goal ] Use multiplication facts to generate related division facts. [Operations and Computation Goal ] Apply multiplication and division facts and extended facts to solve problems. [Operations and Computation Goal ] Write multiplication and division number sentences. [Patterns, Functions, and Algebra Goal ] Key Activities Students explore the relationships between multiplication and division. They use the Multiplication/Division Facts Table to solve division facts, and they use Multiplication/ Division Fact Triangles to generate fact families and to practice division facts. Ongoing Assessment: Recognizing Student Achievement Use journal page 6. [Patterns, Functions, and Algebra Goal ] Key Vocabulary dividend divisor quotient remainder fact family Materials Math Journal, p. 6 Student Reference Book, pp. 8A and 8B Study Link transparencies of Math Masters, pp. 08 and 0 (optional) º, / Fact Triangles slate Playing Beat the Calculator Student Reference Book, p. Math Masters, p. 6 calculator each of number cards 0 (from the Everything Math Deck, if available) Students practice multiplication facts. Math Boxes Math Journal, p. 6 Students practice and maintain skills through Math Box problems. Study Link Math Masters, p. 8 Students practice and maintain skills through Study Link activities. READINESS Playing Division Arrays Student Reference Book, p. 0 Math Masters, p. 0 number cards 6 8 (from the Everything Math Deck, if available) six-sided die 8 counters grid paper (optional) Students explore the connections between multiplication and division using a concrete model. ENRICHMENT Exploring the Relationship between Division and Fractions Math Masters, p. 86 Students use division facts to solve a fraction problem. EXTRA PRACTICE Practicing with Fact Families Math Masters, p. 8 Students complete Fact Triangles and write the related fact families. ELL SUPPORT Creating a Poster colored pencils, markers, or crayons Students create a poster for the terms dividend, divisor, quotient, and remainder. 80 Unit Multiplication and Division; Number Sentences and Algebra

2 Getting Started Mathematical Practices SMP, SMP, SMP, SMP, SMP, SMP6, SMP Content Standards.OA.,.NBT.6,.MD. Mental Math and Reflexes Have students name the next three numbers in each pattern. Suggestions: 0,,, 6, 8, 0 8,, 6,,, 6, 6, 0,, 8,, 0, 6,, 8, 0,, 0,, 0,,,, 8,, 8,,,, 6, 0,,, 6, 8, 0, 8,, 6, 0,, 6, 8, 60,, 8 6, 6,,,, 8, 6, 6, 8, 0, Math Message How many bags of oranges, with oranges in each bag, can be made with oranges? How many can be made with oranges? Study Link Follow-Up Have students represent the multiplication equations in Problems 6 with multiplicative comparison statements. For example, 0 is times as many as and 0 is times as many as. Teaching the Lesson Math Message Follow-Up (Student Reference Book, pp. 8A and 8B) WHOLE-CLASS DISCUSSION As you and the students discuss the first problem, use alternative statements such as these: How many s in? This is an equal-groups interpretation of the problem. is times as many as what number? This is a comparison interpretation of the problem. What number multiplied by gives? This suggests an area interpretation and points out the inverse relationship between multiplication and division. These interpretations are described on Student Reference Book, pages 8A and 8B. Point out that in the division fact / =, the number is the dividend, is the divisor, and is the quotient. In the second problem, there will still be oranges left over after making 8 bags with oranges in each bag. Remind students that is called the remainder. Adjusting the Activity ELL To help students keep the terms dividend and divisor straight, point out that the suffix -or indicates someone or something doing the action doctor, senator, tailor, generator, and so on. So the divisor is the number that is doing the dividing. The dividend is the number that is being divided. 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 Lesson 8

3 Date LESSON Time Multiplication and Division. Choose Fact Triangles. Write the fact family for each. = = = = / = / = = / = / = =. Solve each division fact. a. / = Think: How many s in? b. = / Think: is times as many as what number? c. 6 6 = 6 Think: 6 times what number equals 6? d. / 8 = Think: is 8 times as many as what number? Try This Equivalents / < (< means is less than ) _ _ > (> means is greater than ). A cashier has rolls of quarters and 6 rolls of dimes in the cash register. Each roll of quarters is worth $0, and each roll of dimes is worth $. a. How much are the rolls of quarters and dimes worth in all? $ 80 b. How many quarters are in roll? 0 quarters c. How many quarters are in the rolls? 00 quarters d. How many dimes are in roll? 0 dimes e. How many dimes are in the 6 rolls? 00 dimes f. There is also $.0 worth of half-dollars in the cash register. How many half-dollars is that? half-dollars Math Journal, p. 6 Student Page Answers vary. = = Exploring the Relationship between Multiplication and Division (Math Journal, p. 6; Math Masters, p. 0) WHOLE-CLASS DISCUSSION On the board, draw the, / Fact Triangle shown below, or use a transparency of Math Masters, page 0. Remind students of the following symbols: or for multiplication, and or / for division. Then show them how to use the Fact Triangle to generate a multiplication/division fact family:, / 6 6 = 6 = / 6 = / = 6 Do several more examples with the class. Then have students choose three of their Fact Triangles and record the fact families for those triangles in Problem on journal page 6. Adjusting the Activity Use a piece of paper to track across and up. For example, to solve 6 /, line up the bottom of a piece of paper along the top of the s row. Scan across the s row to find 6. Line up the right edge of the paper with the left side of the column containing 6. Then scan up that column to find the answer, 8, at the top Ongoing Assessment: Recognizing Student Achievement Journal page 6 Problem Use journal page 6, Problem to assess students ability to use conventional notation to write multiplication and division number sentences. Students are making adequate progress if they are able to record the appropriate fact families. Some students may use factors greater than 0. [Patterns, Functions, and Algebra Goal ] Using the Multiplication/ Division Facts Table for Division (Math Journal, p. 6; Math Masters, p. 08) WHOLE-CLASS You may want to use an overhead transparency of the Multiplication/Division Facts Table (Math Masters, page 08) to remind students how to use it for division. For example, to find the answer to /, move across the s row to the cell containing. Then move up the column containing to find the answer, 8, at the top. Tell students that the arrow (see below) from the to the can represent the question How many s in? , AUDITORY KINESTHETIC TACTILE VISUAL Have students complete Problems and on journal page 6 on their own or with a partner. 8 Unit Multiplication and Division; Number Sentences and Algebra

4 Practicing Division Facts with Fact Triangles Demonstrate the following procedure: PARTNER. Student A takes the top triangle from his or her OK pile and asks Student B a division fact from the triangle, such as divided by 6 is equal to what number?. Partners help each other. If Student B is not sure of the answer, Student A gives a clue. For example, if the fact is divided by 6, Student A can help Student B by asking, What number times 6 is equal to? or How many 6s in? or is 6 times as many as what number? If Student B still is not sure, Student A reads the answer.. Partners take turns asking and answering until they have gone through the triangles in both their OK and Try Again piles, or as long as time permits. Date LESSON Math Boxes. Write,, or to make each number sentence true. a.,8,8 b. 0,6 0,6 c. 6 million 6,000,000 d. 8,000,0 8 million, thousand e. 00 0, Make a ballpark estimate. Write a number model to show your strategy. Sample answers: 8,000 a.,68 8,,000 b.,60,,600,00,00. Complete. a.,,,,, Rule: 6 b.,,,,, 8 Rule: c.,,, 8,, Rule: Student Page 6 6,000. Complete. a. in. ft in. b. ft yd ft 8 c. ft yd d. in. yd ft,880 e. miles ft Time. The number of glasses of milk drunk by 0 students in a week: 6,,, 0, 8, 0,,, 0, 8 What is the range? Circle the best answer. A 8 B 0 C D 6. Solve mentally or with a paper-and-pencil algorithm. a. $. b. $.00 $.6 $.6 $. $.6 Math Journal, p. 6 Ongoing Learning & Practice Playing Beat the Calculator (Student Reference Book, p. ; Math Masters, p. 6) SMALL-GROUP NOTE For practice with facts through º, have students use the Online Master available at in place of Study Link. Students play Beat the Calculator to maintain automaticity with multiplication facts. Adjusting the Activity Have students play the extended-facts version of the game described on Student Reference Book, page. 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 Math Boxes (Math Journal, p. 6) INDEPENDENT Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons - and -. The skill in Problem 6 previews Unit content. Study Link (Math Masters, p. 8) INDEPENDENT Home Connection Students fill in the missing numbers in multiplication and division facts. STUDY LINK Missing Numbers Complete each fact by filling in the missing numbers. Use the Multiplication/Division Facts Table to help you / 6. / / 0. / / 8. 8 /. / 0.. /. 0 º Try This Sample answers.. º º 0. º º 6 Practice,66 Study Link Master , º, / ,88, ,00 6 Math Masters, p. 8 Answers vary. Lesson 8

5 Games Division Arrays Materials number cards 6 8 ( of each) Players to Skill six-sided die 8 counters Division and equal shares Object of the game To have the highest total score. Directions Student Page. Shuffle the cards. Place the deck number-side down on the table.. Players take turns. When it is your turn, draw a card and take the number of counters shown on the card. You will use the counters to make an array. Roll the die. The number on the die is the number of equal rows you must have in your array. Make an array with the counters. Your score is the number of counters in row. If there are no leftover counters, your score is double the number of counters in row.. Keep track of your scores. The player with the highest total score at the end of rounds wins. Dave draws a -card and takes counters. He rolls a and makes an array with rows by putting counters in each row. Two counters are left over. Dave scores because there are counters in each row. Marsha draws a -card and takes counters. She rolls a and makes an array with rows by putting counters in each row. Her score is * = 0 because there are counters in each Student Reference Book, p. 0 Differentiation Options READINESS Playing Division Arrays (Student Reference Book, p. 0; Math Masters, p. 0) PARTNER 0 Min To explore the connections between multiplication and division using a concrete model, have students play Division Arrays and record their work on Math Masters, page 0. Some students may find it helpful to organize the counters on grid paper. ENRICHMENT Exploring the Relationship between Division and Fractions (Math Masters, p. 86) PARTNER Min To apply students understanding of division, have them use division facts to solve a fraction problem. Both fractions and division involve sharing something equally or forming equal groups. Fraction notation is one way to write a division problem. Some students may solve the pizza problem by dividing each pizza into equal pieces. Each person gets piece, or _, of each pizza. So one person s share of the pizzas is three one-fourths, or _ of one pizza. Game Master LESSON Fractions and Division Division Arrays Record Sheet Your score is the number of counters per row. If there are 0 leftover counters, your score is double the number of counters per row. 0 Four friends want to share pizzas evenly. Each person cannot have a whole pizza, so the pizzas need to be divided.. How many slices of pizza should each person get? slices. Use a drawing to explain your answer. 6 Round Rows Counters Counters Leftover Score per Row in All Counters. Marisa says these expressions all mean the same thing: Sample 0 0 Total Score of Do you agree or disagree? Explain your answer. Sample answer: Agree. They are all different names for the same thing. of pizzas is of a pizza, so of. The fraction bar,, and all mean division. Math Masters, page 86 Division Arrays Record Sheet 0 Your score is the number of counters per row. If there are 0 leftover counters, your score is double the number of counters per row. Round Rows Counters Counters Leftover Score per Row in All Counters Sample 0 0 Math Masters, p. 0 Total Score 8 Unit Multiplication and Division; Number Sentences and Algebra

6 EXTRA PRACTICE Practicing with Fact Families (Math Masters, p. 8) INDEPENDENT Min. Fact Families Teaching Aid Master Complete each Fact Triangle. Write the fact family for each Fact Triangle.,., To practice the connection between multiplication and division, have students complete Fact Triangles and related fact families. ELL SUPPORT Creating a Poster SMALL-GROUP Min.,., To provide language support for division, have students create a poster representing the terms dividend, divisor, quotient, and remainder. Ask them to write a division number sentence and label all of the parts. Students can color code the number sentence so that each part is drawn in the same color as the label. Math Masters, p. 8 Planning Ahead Lesson -6 provides a detailed introduction to the World Tour. Read through the lesson well in advance, along with the related pages in the World Tour section of the Student Reference Book. In addition to a globe and a large map of the world, try to collect as many reference materials as possible for a World Tour Corner. The authors recommend several copies of an almanac, such as the World Almanac, a full-sized atlas, and several student atlases similar to the National Geographic World Atlas for Young Explorers (National Geographic Society, 00). Ask students to bring country guide books to school. Begin a collection of travel information, including airline schedules and fares, travel articles, weather reports, and currency exchange rates from the local newspaper or the Internet. Lesson 8