Multiplication Facts Survey

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1 Multiplication Facts Survey Objective To guide children as they determine which multiplication facts they still need to learn. 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 Identify square products. [Operations and Computation Goal 3] Describe patterns in factors and products. [Patterns, Functions, and Algebra Goal 1] Describe and apply the turn-around rule (Commutative Property of Multiplication) to generate multiplication facts. [Patterns, Functions, and Algebra Goal 4] Key Activities Children use a Multiplication/Division Facts Table to identify the facts they know and the facts they still need to learn. They take a timed multiplication facts survey. Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Operations and Computation Goal 6] Materials Math Journal 2, p. 159 Math Journal 1, Activity Sheets 3 and 4 Math Masters, p. 438A; pp. 438B and 438C (optional) transparency of Math Masters, p. 206 (Home Link 7 1) half-sheets of paper colored pencil or crayon scissors envelopes Practicing Multiplication/Division Facts with Fact Triangles, Fact Triangles Children practice multiplication basic facts using the second set of Fact Triangles. Math Boxes Math Journal 2, p. 160 Children practice and maintain skills through Math Box problems. Home Link Math Masters, pp. 209 and Children practice and maintain skills through Home Link activities. READINESS Exploring Turn-Around Facts Math Masters, p. 210 scissors Children identify turn-around facts on the Multiplication/Division Facts Table. ENRICHMENT Finding Patterns in the 9s Facts 1 sheet of paper Children identify and describe patterns in the products for 9s facts. Advance Preparation For Part 1, make one copy of Math Masters, page 438A for every 2 children. Math Masters, pages are Fact Triangles. Make copies of the Fact Triangles to send home with Home Link. Teacher s Reference Manual, Grades 1 3 pp Unit 7 Multiplication and Division

2 Getting Started Mathematical Practices SMP2, SMP5, SMP6, SMP7, SMP8 Content Standards 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.9 Mental Math and Reflexes Have children practice quick recall of basic multiplication facts. Suggestions: Examples: Home Link 7 1 Follow-Up Ask children to demonstrate different paths for escaping the labyrinth on a transparency of Home Link 7-1. Discuss which of the paths is the shortest. Math Message Each of the following products is a square product. Complete the number sentences on a half-sheet of paper. 3 3 = 9 Sample answer: 5 5 = = = 81 Draw an array to show one of the square products. 1 Teaching the Lesson Math Message Follow-Up SOLVING WHOLE-CLASS DISCUSSION Briefly review the answers. Have children make observations about the factors and the products. Point out that all the factors and their products are odd numbers. Make a chart (see below) on the board to record examples of factors and their products. Ask: If both factors are odd numbers, is the product odd or even? odd What is the result if both factors are even numbers? even What is the result if one factor is even and the other odd? even Products for even and odd factors Ongoing Assessment: Recognizing Student Achievement Math Message Use the Math Message to assess children s progress toward using arrays to model multiplication. Children are making adequate progress if they are able to draw an array to show one of the square products. Some children may be able to draw an array for each of the square products and discuss their similarities. [Operation and Computation Goal 6] Lesson 583

3 Date Student Page Time Multiplication/Division Facts Table Identifying the Multiplication Facts to Be Learned (Math Journal 2, p. 159) WHOLE-CLASS Math Journal 2, p. 159 EM3MJ2_G3_U07_ indd 159 2/12/10 10:14 AM NOTE To extend this activity to include basic multiplication facts through 12 12, go to By now, most children know the 1s, 2s, and 10s multiplication facts. Most children should also know all of the facts on the first set of Fact Triangles from Lesson 4-6. The purpose of the activity on journal page 159 is to let children know that there are only a few facts left to learn. Ask children to use light-colored crayons or pencils to color all the products above the square-number diagonal. Remind them that the square-number diagonal divides the table into two parts: Each product above the diagonal has a turn-around product below the diagonal. Next, children color the products for all remaining 1-facts, 2-facts, and 10-facts. Finally, they shade the remaining products from the first set of Fact Triangles, including those on the square-number diagonal, even though they are pre-shaded. The pre-shading indicates square products. The children s shading indicates products they already know. Ask: How many products are left unshaded? 16 This shows that if they know all the 1-, 2-, and 10-facts, all the facts from the first set of Fact Triangles, and the turn-around rule, they need to learn only 16 more facts. Have children examine the 16 products left unshaded. Discuss patterns they notice with the unshaded products. Date Time, Fact Triangles Student Page Adjusting the Activity Show children the 9s Facts-on-Fingers shortcut. Hold both hands open, palms down. To multiply a number less than 10 by 9 (for example, 7 9), count fingers, starting with the little finger of the left hand. If the factor is greater than 5, continue counting on the right hand, starting with the thumb. Bend down the last finger in your count. (For 7 9, the down finger is the right-hand index finger.) The number of fingers to the left of the down finger represents the tens digit in the product; the number of fingers to the right represents the ones digit (6 to the left and 3 to the right). 6 tens 3 ones The last finger in the count bends to separate the 10s and the 1s in the answer. 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 3 EM3MJ1_G3_U06_ indd 7 12/23/10 2:33 PM 584 Unit 7 Multiplication and Division

4 Administering a Facts Survey (Math Masters, pp. 438A 438C) INDEPENDENT Explain to children that they will find out for themselves how many of the 16 facts they already know and how many they have yet to learn. Distribute the survey on Math Masters, page 438A. At your signal, children have 90 seconds (approximately 5 seconds per problem) to complete as many problems as possible. Adjust the amount of time as you see fit, but remember that children should not be given enough time to figure out the answers. The point is to know the answers from memory. Decide how you would like to have the surveys corrected. Children may correct their own or you may correct them yourself. Note that the reason for administering the survey is to help children to identify the facts they still need to learn; it is not to give a grade. Once the surveys are corrected, consider having children write the facts they still need to learn on the Notes page at the back of Math Journal 2. They will be able to access these facts quickly for continued practice. Plan to assess children s progress on the Facts Survey once every couple of months. Math Masters, pages 438B and 438C are alternate versions of the same 16 facts. Multiplication Facts Survey = = = = = = = = = = = = = = = = _438A_445_449_EMCS_B_MM_G3_U07Proj_ indd 438A Teaching Aid Master Multiplication Facts Survey = = = = = = = = = = = = = = = = 72 Math Masters, p. 438A 3/16/11 12:34 PM NOTE Have children write their initials on the back of each Fact Triangle in case they misplace them. Cutting Out Fact Triangles (Math Journal 1, Activity Sheets 3 and 4) INDEPENDENT After children have cut out the Fact Triangles on the Activity Sheet card stock pages, review how to use Fact Triangles to generate fact families and to practice the multiplication and division facts. Remind children that they need to learn the multiplication and division facts so they can solve multiplication and division problems with larger numbers. Provide children frequent opportunities to practice their facts with the Fact Triangles. The year-end goal for third grade is to demonstrate automaticity with facts through NOTE For additional Fact Triangles for facts through 12 12, go to Teaching Aid Master Multiplication Facts Survey = = = = = = = = = = = = = = = = 72 Multiplication Facts Survey = = = = = = = = = = = = = = = = 72 Math Masters, p. 438B _438A_445_449_EMCS_B_MM_G3_U07Proj_ indd 438B 3/16/11 12:34 PM Lesson 585

5 py g g p Teaching Aid Master Multiplication Facts Survey = = = = = = = = = = = = = = = = 45 Multiplication Facts Survey 3 2 Ongoing Learning & Practice Practicing Multiplication/Division Facts with Fact Triangles PARTNER Partners practice basic facts using their Fact Triangles. Children keep track of the facts they miss and direct their partners to focus on those facts during a second round. Encourage children to store their Fact Triangles in an envelope when they are not using them. py g g p 4 8 = = = = = = = = = = = = = = = = 45 Math Masters, p. 438C Math Boxes (Math Journal 2, p. 160) INDEPENDENT Mixed Practice The Math Boxes in this lesson are paired with the Math Boxes from Lesson 7-4. The skill in Problem 6 previews Unit 8 content. Home Link (Math Masters, pp. 209 and ) INDEPENDENT _438A_445_449_EMCS_B_MM_G3_U07Proj_ indd 438C 3/16/11 12:34 PM Home Connection Children share with someone at home their progress with the multiplication facts. Send home Math Masters, pages (which are the same Fact Triangles as Activity Sheets 3 and 4) so children can practice multiplication facts. Date Math Boxes Student Page Time 3 Differentiation Options 1. Draw the lines of symmetry. There are 2 lines of symmetry. 3. Solve = 150 1,300 = , = ,000 6,000 = 9, = 1, Complete the number-grid puzzles Unit Draw a trapezoid. Then draw a line segment that intersects the two parallel sides. Sample answer: I have 3 vertices. All my sides are different lengths. I have one right angle. What am I? Fill in the circle for the best answer. A. trapezoid B. kite C. hexagon D. right triangle 6. Shade 1_ 3 of the rectangle. Sample answer: READINESS Exploring Turn-Around Facts (Math Masters, p. 210) SMALL-GROUP 5 15 Min To provide experience with turn-around facts, have children compare two halves of the Multiplication/Division Facts Table. They cut out the Multiplication/Division Facts Table on Math Masters, page 210 along the dotted lines and fold it diagonally from right to left along the blank squares. Notice that equal factors and products fold onto themselves. Ask children why this happens. The same factors are used in order along the top row as are used down the first column. The products of the turn-around facts are the same Math Journal 2, p. 160 EM3MJ2_G3_U07_ indd 160 1/18/11 3:34 PM 586 Unit 7 Multiplication and Division

6 Have children find a few turn-around facts on the table. Next, have children fill in the blank boxes along the diagonal fold line and share their strategies. Ask children why these numbers are not mirrored like the others. Both factors are the same number; they are square products; the turn-around fact is exactly the same. ENRICHMENT Finding Patterns in the 9s Facts SMALL-GROUP Min To apply children s understanding of patterns, have them identify and describe patterns they see in the products for 9s facts. First, children write the 9s facts on paper in a column and look for patterns among the factors and products. Then, they write a description of the patterns they find. Encourage children to test their patterns by continuing to multiply 2-digit numbers by 9. Consider making a class book of the children s work. Possible 9s facts patterns: The digits in the tens place (first column) of the products column are in order starting at 0, 1, 2,... 9 and repeat as the factors get larger. The digits in the ones place (second column) of the products column are in backwards order starting at 9, 8, 7,... 0 and repeat as the factors get larger. The sum of the digits of the products equals 9. (3 9 = 27, = 9; 11 9 = 99, = 18, = 9) For 1 9 through 9 9, the product of the first factor multiplied by 10, minus that factor is the product of the first factor multiplied by 9. For example, (4 10) - 4 = 36 and 4 9 = 36. For 1 9 through 9 9, digits in the product are predictable. The first factor minus 1 is the first digit in the product. The second digit of the product is 9 minus the first digit in the product. For example, 5 9: first digit of product is 4; 5-1 = 4. The second digit of product is 5; 9-4 = 5. Thus, 5 9 = 45. Have children describe the patterns they see using words like factor, product, more, less, multiplied by, larger, smaller, and so on. y g g HOME LINK, Factors and Products Family Listen to your child explain what factors and products are before he or she writes the answers Note in the table. Then listen as your child tells you what he or she knows about multiplying by 1, multiplying by 0, and multiplying numbers that result in square products. Fact Triangles for the remaining multiplication/division facts are included with this Home Link. Please return this Home Link to school tomorrow. 1. Explain to someone at home what factors and products are. Find the missing products and factors in the table. 2. Write what you know about the products when you multiply by Write what you know about the products when you multiply by The product is always Write what you know about facts with square products The factors are always the same number. Practice Write these problems on the back of this page. Make a ballpark estimate for each. Solve. Show your work. 5. 7, ,623 Unit +6, ,189 3, _EMCS_B_MM_G3_U07_ indd 209 ballpark estimate ballpark estimate 14,000 3,100 Turn-Around Page Title Facts Home Link Master The product is the same as the other factor. Math Masters, p. 209 Teaching Master Factor Factor Product /17/11 1:18 PM Math Masters, p. 210 EM3MM_G3_U07_ indd 210 2/12/10 9:51 AM Lesson 587

7 Multiplication Facts Survey = 9 3 = Copyright Wright Group/McGraw-Hill Copyright Wright Group/McGraw-Hill 8 5 = 7 6 = 8 8 = 9 7 = 6 8 = 9 9 = 4 8 = 8 3 = 9 5 = 7 7 = 7 8 = 9 6 = 4 9 = 9 8 = Multiplication Facts Survey = 9 3 = 8 5 = 7 6 = 8 8 = 9 7 = 6 8 = 9 9 = 4 8 = 8 3 = 9 5 = 7 7 = 7 8 = 9 6 = 4 9 = 9 8 = 438A

8 Multiplication Facts Survey = 8 5 = 9 7 = 6 8 = 9 9 = 4 8 = 8 3 = 6 6 = 9 5 = 7 7 = 7 8 = 9 3 = Copyright Wright Group/McGraw-Hill 7 6 = 9 6 = 4 9 = 9 8 = Multiplication Facts Survey = 8 5 = 9 7 = 6 8 = 9 9 = 4 8 = 8 3 = 6 6 = 9 5 = 7 7 = 7 8 = 9 3 = Copyright Wright Group/McGraw-Hill 7 6 = 9 6 = 4 9 = 9 8 = 438B

9 Multiplication Facts Survey = 8 3 = Copyright Wright Group/McGraw-Hill 9 7 = 6 6 = 6 8 = 8 8 = 8 5 = 9 3 = 9 9 = 7 7 = 9 6 = 9 8 = 7 8 = 7 6 = 4 9 = 9 5 = Multiplication Facts Survey 3 Copyright Wright Group/McGraw-Hill 4 8 = 8 3 = 9 7 = 6 6 = 6 8 = 8 8 = 8 5 = 9 3 = 9 9 = 7 7 = 9 6 = 9 8 = 7 8 = 7 6 = 4 9 = 9 5 = 438C

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