Multiplication and Division Fact Families


 Sheila Ball
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1 Multiplication and Division Fact Families Objectives To review fact families and the Multiplication/Division Facts Table; and to guide children as they practice multiplication and 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 Use Fact Triangles and the Facts Table to generate multiplication and division fact families. [Operations and Computation Goal ] Look for patterns on the Facts Table. [Patterns, Functions, and Algebra Goal 1] Explore the inverse relationship between multiplication and division fact families. [Patterns, Functions, and Algebra Goal ] Apply the turnaround rule (Commutative Property of Multiplication). [Patterns, Functions, and Algebra Goal ] Key Activities Children use the Multiplication/Division Facts Table and Fact Triangles to find fact families and to practice multiplication and division facts. Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Patterns, Functions, and Algebra Goal ] Key Vocabulary Materials Math Journal 1, inside front cover Math Journal 1, Activity Sheets 1 and ; Activity Sheets and (optional) Student Reference Book, pp. 5 and 5 Home Link 5 Math Masters, p. 98 (optional); p. 1 transparencies of Math Masters, pp. 98 and 1 (optional) scissors slate paper envelope halfsheet of paper Practicing with, Fact Triangles, Fact Triangles Children practice multiplication and division with Fact Triangles. Math Boxes 6 Math Journal 1, p. 90 Children practice and maintain skills through Math Box problems. Home Link 6 Math Masters, pp Children practice and maintain skills through Home Link activities. READINESS Practicing Multiplication Facts with a Calculator Math Masters, p. 10 calculator Children skip count with calculators. ENRICHMENT Examining a Pattern Math Masters, p. 98 or Math Journal 1, inside front cover per partnership: halfsheet of paper, highlighters (optional) Children examine a pattern in the. Advance Preparation When you send Home Link 6 home, copy and attach Math Masters, pages 101 and 10. Teacher s Reference Manual, Grades 1 pp. 16, 17 7 Unit Multiplication and Division
2 Getting Started Mental Math and Reflexes Have children count chorally. They may use number grids, number lines, or calculators as needed. Skip count forward and backward by s, 5s, and 10s. Skip count forward and backward by s and 6s. Skip count forward and backward by s and 8s. Math Message Write the +, fact family for the numbers,, and on a halfsheet of paper. Home Link 5 FollowUp Have partners discuss the multiplicationfact shortcuts they like the best. 1 Teaching the Lesson Math Message FollowUp Ask a volunteer to share the fact family for,, and. + =, and  =. The fact family,, and is a doubles fact family. Mention that just like addition and subtraction fact families, there are also multiplication and division fact families. 1, = 1 1 = = 1 1 = Fact family for the numbers,, and 1 Ongoing Assessment: Recognizing Student Achievement Math Message Use the Math Message to assess children s progress toward using the +, , and = symbols. Children are making adequate progress if they are able to write the fact family. Some children may notice that the same numbers (,, and ) can be used to write a multiplication fact and a division fact using the,, and = symbols. [Patterns, Functions, and Algebra Goal ] Teaching Aid Master Multiplication/Division Fact Triangle Introducing Multiplication/ Division Fact Families (Math Masters, p. 1) Use a transparency of a blank Fact Triangle (Math Masters, page 1) or draw one on the board. Write the three numbers from a multiplication fact for example,,, and 1 in the corners of the triangle. Be sure the product is at the top under the large dot. Ask volunteers to name the fact family (the two multiplication facts and two division facts) for those numbers. = 1, = 1, 1 =, and 1 = Math Masters, p. 1 Lesson 6 7
3 Write a few more triplets of numbers in the triangle. Children write the fact families on their slates. A volunteer reads the results as the others check their slates. In the previous lesson, children used arrays to demonstrate a turnaround rule for multiplication. Ask: Is there a turnaround rule for the division facts in each fact family? No Have children give examples to show that there is no turnaround rule for division; for example, 6 divided by gives a different answer than divided by 6. Some children may recognize that division problems, such as 6, can be thought of as fractions: 6 is equivalent to _ 6 or 1_. Finding Patterns in the Facts Table (Math Journal 1, inside front cover; Math Masters, p. 98) DISCUSSION Teaching Master Algebraic Thinking Ask children to study the Multiplication/ Division Facts Table on the inside front cover of the journal. You may also display a transparency of the table (Math Masters, page 98). Give children a few minutes to examine the table. Have them describe patterns they find. Examples: Going across the second row and down the second column, the numbers increase by 1. In the third row and third column, the numbers increase by, and so on. In the 10column and the 10row, all of the numbers end in 0. In the 5column and the 5row, all of the numbers end in 0 or 5. In the column and the row, all of the numbers end in an even number. In the diagonal, moving from upper left to lower right, the numbers increase by, 5, 7, 9, and so on Page Multiplication/Division Title Facts Table Using the Facts Table and Fact Families (Student Reference Book, pp. 5 and 5) Math Masters, p. 98 Model how to use the table to find products. Example: 5 7 =? and 7 5 =? Find the 5row. Go across the 5row to the 7column. That number is 5. This shows that 5 7 = 5. Find the 7row. Go across the 7row to the 5column. That number is 5. This shows that 7 5 = 5. Have children practice other multiplication examples, including 8 1 =? and 1 =?. Use the Multiplication/Division Facts Table to highlight the special property of 1 in multiplication. If a number is multiplied by 1, the number is not changed. 8 1 = 8; 1 =. 7 Unit Multiplication and Division
4 1 Next, demonstrate how to use the Multiplication/Division Facts Table to find quotients. Example: 8 =? Find the row. Go across the row until you find 8. Go up that column to the heading, which is 7. This also shows that 8 = 7. Find the column. Go down the column until you find 8. Go across the row to the heading, which is 7. This also shows that 8 = 7. Have children practice other division examples including 6 1 =? and 7 7 =?. Use the to highlight the special property of 1 in division. If a number is divided by 1, the number is not changed. If a number is divided by itself, the result is 1. For example, 6 1 = 6 and 7 7 = 1. Call out multiplication facts. Ask children to highlight the facts with a sheet of paper as shown in the margin. Then children state the corresponding division facts. Alternately, children highlight division facts on the table as you call them out. They then state the corresponding multiplication facts., , Practicing with Fact Triangles (Math Journal 1, Activity Sheets 1 and ) PARTNER Have children cut out the Multiplication/Division Fact Triangles from Activity Sheets 1 and at the back of their journals. Review the procedure for practicing the facts with Fact Triangles. While one child covers a number on a Fact Triangle, the partner tells the multiplication or division fact for the exposed numbers The guide may be positioned either way to show 7 = 8, 7 = 8; or 8 = 7 and 8 7 =. NOTE Have children store their Fact Triangles in their tool kits in envelopes. Some teachers have children write the fact families on the backs of the Fact Triangles. This should be an ongoing project, done a few at a time. Date 6 Student Page Time Multiplication/Division Fact Triangles 1 Links to the Future 6 8 These Fact Triangles present the easier facts. In Unit 7, children will use the harder Fact Triangles (Activity Sheets and ). Do not expect all children to master all of the easier facts at this time. Children will have more opportunities to practice the facts in later units. Adjusting the Activity Have children practice with the Fact Triangles on Activity Sheets and as appropriate. 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 Journal 1, Activity Sheet 1 Activity Sheet 1 Lesson 6 75
5 Date 6 1. Write,, or Complete. yd Rule Math Boxes ftt yd 5. Lengths (in.) of 1 cats, including the tails: 0, 9, 8,, 9, 5, 16, 7, 9, 6, 8, 1, What is the maximum length? Fill in the oval for the best answer. 6 inches 16 inches 9 inches 0 inches ft Answers vary. Time. Write the fact family Math Journal 1, p. 90 Student Page. Use the dots to show a 7by6 array. What is the number model? Fill in the empty frames. 1,107 6,107 7,107,107 5, Rule 1,000,107, Ongoing Learning & Practice Practicing with, Fact Triangles PARTNER Have partners use their Fact Triangles to practice basic multiplication and division facts. At first, children should limit themselves to finding products. That is, one partner covers the number below the large dot, and the other gives the product of the uncovered factors. When children are well on their way to learning products, they can cover one of the other two numbers to practice finding missing factors. Math Boxes 6 (Math Journal 1, p. 90) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9. The skill in Problem 6 previews Unit 5 content. Writing/Reasoning Have children answer the following question: When a number is multiplied by 1, the number does not change. What can you say about dividing a number by 1? Sample answer: When a number is divided by 1, the number does not change. Home Link 6 (Math Masters, pp ) INDEPENDENT 0 06 Page, Fact Title Page Triangles Title continued HOME LINK Tell someone at home about multiplication/division fact families. 1. The numbers, 5, and 10 form the following facts: Knowing 6 and 6 helps me know 1 6 and The numbers, 7, and 1 form this multiplication/division fact family: Write the fact family for each, Fact Triangle Home Link Master Home Connection Children review multiplication and division fact families. Send home copies of Math Masters, pages 101 and 10, which contain Fact Triangles. Differentiation Options READINESS Practicing Multiplication Facts with a Calculator (Math Masters, p. 10) INDEPENDENT 15 0 Min To provide experience skip counting on a calculator, have children use their calculators to complete the tables on Math Masters, page 10. Review the steps for counting by 1s on the calculator. Children can program the calculator using the following steps: Math Masters, p Unit Multiplication and Division
6 TI 1. Press ON/C. This clears your calculator.. Press 0. This is the starting number.. Press +. This tells the calculator to count up.. Press 1. This tells the calculator to count by 1s. Casio 1. Press. This clears your calculator.. Press 1. This tells the calculator to count by 1.. Press. This tells the calculator to count up.. Press 0. This is the starting number. Now the calculator is ready to count by 1s. Without clearing their calculators, have children press the key. Press the key repeatedly as the class counts together by 1s. Once they recall this routine, have them work on Math Masters, page 10. When children have completed the page, discuss how calculator counting might help them learn their facts. Have children read aloud the counts they have recorded on the master. = = 6 Teaching Master Multiplication Facts & Calculator Counts 1. Use your calculator to count by s. Complete the table below. One Two s Three s Four s Five s Six s Seven s Eight s Nine s Ten s Use your calculator to count by s. Complete the table below. One Two s Three s Four s Five s Six s Seven s Eight s Nine s Ten s Use your calculator to count by 6s. Complete the table below. One 6 Two 6s Three 6s Four 6s Five 6s Six 6s Seven 6s Eight 6s Nine 6s Ten 6s How can counting on your calculator help you learn your multiplication facts? Sample answer: If I can count by s, I know the products to the facts. If I can count by any number, then I know which numbers are the products to that number s multiplication facts. Math Masters, p. 10 ENRICHMENT Examining a Pattern (Math Masters, p. 98; or Math Journal 1, inside front cover) PARTNER 15 0 Min To further explore the Multiplication/Division Facts Table, have children examine a pattern in the table. Together, they circle a number on the table. Then, they circle the number in the square above, to the right, below, and to the left of the chosen number. Next, they add the starting number plus the four circled numbers. Children record their starting number and the sum of the five circled numbers on a halfsheet of paper as shown. They repeat this several times and look for a pattern in the recorded numbers. The product of the starting number and 5 is always equal to the sum of the five numbers. Ask: How does this pattern work? Sample answer for the example: I made the 6s into s and added the leftovers to the s to make them into s. So I had five s Starting Sum of Number 5 Numbers = 0 Sample recording sheet Lesson 6 77
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