VIEWS: 11 PAGES: 36 POSTED ON: 5/27/2012 Public Domain
Austin Independent School District Department of Curriculum and Instruction Mathematics Numerical Fluency Grade 6 Mathematics 1st Six-Weeks 2009-2010 Numerical Fluency Problems #1-1 through 1-25 (1-26 through 1-28 OPTIONAL) Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 1 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency Specification Sheet 1st Six Weeks: 29 Days NF Matrix TEKS TAKS Answer Problem # # Obj # Discuss Numerical Fluency Problems by having students share their multiple strategies. This sharing will help students become flexible, efficient, and accurate with numerical reasoning while learning the TEKS deeply. Strategy #1: Changing the order of the factors does not change the product such as 4 5 20 and5 4 20 . Strategy #2: Double a column to obtain twice as much such as doubling 1-1 128 L the products of the 3’s column gives the products to the 6’s column. For example, 3 4 12 so 6 4 212 24 . Strategy #3: Use the 5’s as a benchmark and add groups of a number to the product of the 5’s. For example, to recall 8 8 , do 5 × 8 + 3 × 8 = 40 + 24 = 64 . 112 6.1E 1 There are many possible rectangular arrays for 36 students. 1 row with 36 students, 2 rows with 18 students each, 3 rows with 12 students 1-2 128 L each, 4 rows with 9 students each, 6 rows with 6 students each, 9 rows with 4 students each, 12 rows with 3 students each, 18 rows with 2 students each, 133 6.2C 1 and 36 rows with 1 student each Number of 112 6.1E 1 Number of Students in Each Rows, r Row, s 1 100 2 50 4 25 133 6.2C 1 5 20 1-3 10 10 20 5 25 4 50 2 100 1 225 L 1 Since 5 groups of 8 are 40, one more group of 8 added to 40 makes 48. 128 L 2 6 8 = (5 8) + (1 8) 1-4 3 Since 3 groups of 8 are 24, 6 groups of 8 would be twice as much or 48. 205 L 4 6 8 = (3 8) 2 5 6 8 = 48, 8 6 = 48, 48 8 = 6, 48 6 = 8 1 Since 5 groups of 8 are 40, two more groups of 8 added to 40 makes 56. 128 L 2 7 8 = (5 8) + (2 8) 3 Since 10 groups of 8 are 80, three groups of 8 or 24 less than 80 makes 1-5 56. 205 L 4 7 8 = (10 8) - (3 8) 5 7 8 = 56, 8 7 = 56, 56 8 = 7, 56 7 = 8 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 2 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems NF Matrix TEKS TAKS Answer Problem # # Obj # 1 Answers will vary. Here are some possible number sentences. 121 L 4 15 = (4 5) + (4 5) + (4 5) 4 15 = (2 15) + (2 15) 1-6 4 15 = (4 10) + (4 5) 610 6.12A 6 2 4 15 = 60, 15 4 = 60, 60 4 = 15, 60 15 = 4 1 Answers will vary. Here are some possible number sentences. 121 L 29 15 = (20 15) + (9 15) 1-7 29 15 = (10 15) + (10 15) + (9 15) 610 6.12A 6 29 15 = (30 15) – 15 2 29 15 = 435, 15 29 = 435, 435 15 = 29, 435 29 = 15 1 Answers will vary. Here are some possible factor pairs. 112 6.1E 1 10 25, 3 25, 20 13, 5 13, 30 25, 7 25 2 Answers will vary. Here are some possible number sentences. 1-8 13 25 = (10 25) + (3 25) 13 25 = (20 13) + (5 13) 610 6.12A 6 13 25 = (30 25) - (7 25) 3 13 25 = 325, 25 13 = 325, 325 13 = 25, 325 25 = 13 1 50 groups of 18 is closer to the product of 47 18 because it is 3 groups 135 6.2D 1 of 18 more than the product, whereas, 40 groups of 18 is 7 groups of 18 1-9 less than the product. 136 L 2 20(17) is closer to 22 17 because it is 34 less 22 17, whereas, 25 17 is 51 more than 22 17. 130 L 1 2 pieces of rope 2 3 buses 1 3 2 dollars or $2.50 133 6.2C 1 2 Help students think about remainders. Depending on the context of the 1-10 situation, remainders are dropped sometimes, sometimes they are rounded up, and sometimes a fractional remainder makes sense. Do NOT teach 605 6.11A 6 division with fractions or decimals at this time. Help students make sense of the remainder by thinking about what the whole amount. In this case the whole amount were the 40 band students. The remainder of $20 was to be split evenly among the 40 band students; each of the 40 band students gets 610 6.12A 6 $0.50 of that remainder of $20. 1 4 26 = (2 26) + (2 26) 2 4 26 = (4 20) + (4 6) 133 6.2C 1 3 26 1-11 135 6.2D 1 X 4 24 = (4 x 6) = 4 rows of 6 80 = (4 x 20) = 4 rows of 20 136 L 104 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 3 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems NF Matrix TEKS TAKS Answer Problem # # Obj # 1 The missing dimension on the left is 9. The missing dimension on the top is 20. 133 6.2C 1 2 9 28 = (9 20) + (9 8) 3 28 X 9 72 = (9 x 8) = 9 rows of 8 1-12 135 6.2D 1 180 = (9 x 20) = 9 rows of 20 252 4 9 28 = 252; 28 9 = 252; 252 28 = 9; 252 9 = 28 136 L 1 432 pencils 2 The table below shows all the possible arrangements of cement squares 112 6.1E 1 for the patio. Number of Cement Number of Rows, r Squares in Each Row, s 1 48 2 24 1-13 128 L 3 16 4 12 6 8 8 6 12 4 16 3 133 6.2C 1 24 2 48 1 1 2 26 10 x 20 = 200 x 34 10 x 20 = 200 24 = 4x6 133 6.2C 1 10 x 20 = 200 80 = 4 x 20 4 x 20 = 80 180 = 30 x 6 10 x 6 = 60 600 = 30 x 20 1-14 10 x 6 = 60 884 34 x 26 10 x 6 = 60 6 x 4 = 24 136 L 34 x 26 = 884 3 34 26 = 884; 26 34 = 884; 884 26 = 34; 884 34 = 26 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 4 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems NF Matrix TEKS TAKS Answer Problem # # Obj # 1 10 x 10 = 100 2 10 x 10 = 100 42 133 6.2C 1 10 x 10 = 100 X 10 x 10 = 100 17 2 x 10 = 20 14 =7x2 7 x 10 = 70 280 = 7 x 40 7 x 10 = 70 20 = 10 x 2 7 x 10 = 70 400 = 10 x 40 1-15 7 x 10 = 70 714 = 42 x 17 7x2 = 14 42 x 17 = 714 136 L 3 42 17 = 714; 42 17 = 714; 714 42 = 17; 714 17 = 42 1 Answers will vary. Here is one possibility. 45 39 = 40 39 + 5 39 = 1560 + 195 = 1755 133 6.2C 1 2 Answers will vary Here is one possibility. 45 1-16 X 39 45 =9x5 360 = 9 x 40 150 = 30 x 5 136 L 1200 = 30x 40 1755 = 45 x 39 Strategies will vary. Efficient methods should be both accurate and quick. 1 72 14 = 10 72 + 4 72 = 720 + 288 = 1008 133 6.2C 1 2 27 X 56 42 =6x7 1-17 120 = 6 x 20 350 = 50 x 7 1000 = 50x 20 136 L 1512 = 56 x 27 3 32(95) = 100 32 – 5 32 = 3200 – 160 = 3040 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 5 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems NF Matrix TEKS TAKS Answer Problem # # Obj # 1 441 2 10 420 3 10 112 6.1E 1 399 4 10 378 5 Answers will vary. Here are a 357 few possibilities. 336 315 a b 294 3 63 273 5 105 252 10 210 231 13 273 210 15 315 1-18 189 168 147 133 6.2C 1 126 105 84 64 42 21 1 420 112 6.1E 1 2 20 3 20 4 210 133 6.2C 1 5 420 1-19 6 630 7 840 8 1050 136 L 9 1680 10 2100 1 21 crayons 1-20 133 6.2C 1 2 Students should be using division strategies that make sense to them, but are also efficient strategies. 1 Both Marta and James arrange their division problems vertically and write 133 6.2C 1 their groups of 21 to the right side of the problem. Both Marta and James subtract groups of 21 until no groups of 21 remain of the original 504. 1-21 James method is different than Marta’s method because he subtracts 20 136 L groups of 21 as a first step, whereas Marta only subtracts 10 groups of 21 as the first step. 2 n = 24 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 6 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems NF Matrix TEKS TAKS Answer Problem # # Obj # 1 2 38 18 = 20 18 + 10 18 + 8 18 = 360 + 180 + 144 = 684 378 360 342 3 Miguel’s method 135 6.2D 1 324 306 n 288 270 18 576 252 - 180 10 groups of 18 234 396 left over 216 - 360 20 groups of 18 198 36 left over 180 - 36 2 groups of 18 162 0 32 groups of 18 144 1-22 126 4 Gloria’s method 108 90 72 n 54 18 576 36 -540 136 L 18 30 groups of 18 36 left over - 36 2 groups of 18 0 32 groups of 18 1 10 x 18 = 180; 20 X 18 = 360; 30 x 18 = 540; 40 x 18 = 720; 50 x 18 = 900; 100 x 18 = 1800 133 6.2C 1 n 1-23 2 18 954 900 = 50 group of 18 136 L 54 54 = 3 groups of 18 0 133 6.2C 1 1 54 1-24 136 L 2 86 Strategy #1: Changing the order of the factors does not change the product such as 4 5 20 and5 4 20 . Strategy #2: Double a column to obtain twice as much such as doubling the products of the 3’s column gives the products to the 6’s column. For 1-25 128 L 1 example, 3 4 12 so 6 4 212 24 . Strategy #3: Use the 5’s as a benchmark and add groups of a number to the product of the 5’s. For example, to recall 8 8 , do 5 × 8 + 3 × 8 = 40 + 24 = 64 . 1-26 108 L 1 1 $47.16 2 $12.89 3 0.124 4 $70.01 optional 127 6.2B Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 7 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems NF Matrix TEKS TAKS Answer Problem # # Obj # 1-27 108 L 1 9.5 – 2.75 = 6.75 inches optional 127 6.2B 108 L 1-28 1 C 227 6.2B 1 optional 2 $50.05 223 6.5A 2 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 8 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-1 Complete the following multiplication table. X 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 8 9 10 11 2 2 6 8 10 12 16 18 20 22 3 3 6 12 18 24 30 4 4 8 12 20 24 40 5 5 10 15 20 30 35 45 50 60 6 6 12 18 24 30 54 60 7 35 8 8 16 24 9 9 18 45 54 63 90 10 10 20 30 40 60 70 90 11 11 22 12 60 List 3 strategies you used to recall facts you did not know. 1. 2. 3. Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 9 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-2 The Super Bowl is going to be held in Austin this year. The Super Bowl Committee has decided that the 36 students in Ms. Grant’s class at Fulmore Middle School will march in the pre-game parade. They will march in a variety of rectangular arrays such as the one shown below. Write down as many of the possible marching arrangements for the 36 students that you can. Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 10 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-3 The Super Bowl Committee changed their minds. They decided all 100 sixth graders at Fulmore Middle School may march in the pre-game parade. The 100 students will march in a variety of rectangular arrays. One of the Fulmore sixth graders wrote the following equation to help find all the possible arrangements. r s 100 A variable, often a letter of the alphabet, represents a quantity that changes. In the equation above, the variable r represents the number of rows. The variable s represents the number of students in each row. Create a table of data for the two variables. In the table write as many possible marching arrangements for the 100 students that you can. Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 11 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-4 1 Describe in words how to use 5 8 to find the product of 6 8 . 2 Write a horizontal number sentence using 5 8 that shows how to find the product of 6 8 . 6 8 = _______________________ 3 Describe in words how to use 3 8 to find the product of 6 8 . 4 Write a horizontal number sentence using 3 8 that shows how to find the product of 6 8 . 6 8 = _______________________ 5 What is the multiplication and division fact family for 6 8 ? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 12 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-5 1 Describe in words how to use 5 8 to find the product of 7 8 . 2 Write a horizontal number sentence using 5 8 that shows how to find the product of 7 8 . 7 8 = _______________________ 3 Describe in words how to use 10 8 to find the product of 7 8 . 4 Write a horizontal number sentence using 10 8 that shows how to find the product of 7 8 . 7 8 = _______________________ 5 What is the multiplication and division fact family for 7 8 ? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 13 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-6 Multiplication Cluster 45 2 15 4 10 4 15 1 Using one or more factor pairs from the Multiplication Cluster, write a horizontal number sentence that shows how to find the product of 4 15. 4 15 = ________________________________ 2 What is the multiplication and division family for 4 15? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 14 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-7 Multiplication Cluster 10 15 20 15 30 15 9 15 29 15 1 Using one or more factor pairs from the Multiplication Cluster, write a horizontal number sentence that shows how to find the product of 29 15. 29 15 = ________________________________ 2 What is the multiplication and division family for 29 15? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 15 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-8 There are 13 classes of 6th grade mathematics at Porter Middle School. Each class has 25 students. 1 Create a cluster of factors pairs that could be used to find the total number of students in the 13 classes. Multiplication Cluster ______________ ______________ ______________ ______________ 13 25 2 Using one or more factor pairs from the Multiplication Cluster, write a horizontal number sentence that shows how to find the product of 13 25. 13 25 = ____________________________ 3 What is the multiplication and division family for 13 25? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 16 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-9 Without doing any calculations, decide which expression is a closer estimate to the multiplication problem in each rectangle. Explain your reasoning. 1 40 groups of 18 47 18 50 groups of 18 2 20(17) 22 17 25 17 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 17 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-10 1 A rope is 100 feet long. How many pieces of rope, each 40 feet long, can be cut from the rope? 2 100 people from Lamar Middle School are going on a field trip. Each bus holds 40 people. How many buses are needed for the field trip? 3 A $100 prize was given to 40 band students who entering a marching contest. If the money is shared equally, how much will each student receive? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 18 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-11 The array below models the multiplication problem 4 26. 1 The following array shows a way to divide the array above into groups. 26 2 2 Using the dimensions from the array above, write a horizontal number sentence that shows how to find the product of 4 26. 4 26 = ____________________________________ 2 The following array shows another way to divide the array into groups. 20 6 4 Using the dimensions from the array above, write a horizontal number sentence that shows how to find the product of 4 26. 4 26 = ____________________________________ 3 Complete the following vertical number sentence for 4 26. 26 X 4 (4 x 6) 4 rows of 6 (4 x 20) 4 rows of 20 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 19 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-12 The array below models the multiplication problem 9 28. 1 The following array shows a how to divide the array above into groups to find the product of 9 28. Find each missing dimension. 8 2 Using the dimensions from the array above, write a horizontal number sentence that shows how to find the product of 9 28. 9 28 = ____________________________________ 3 Complete the following vertical number sentence for 9 28. 28 X 9 (9 x 8) 9 rows of 8 (9 x 20) 9 rows of 20 4 What is the multiplication and division family for 9 28? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 20 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-13 1 At the Austin ISD Warehouse, there are 72 pencils in each box. The Mathematics Department at Murchison Middle School ordered 6 boxes of pencils. How many pencils were ordered? Record your answer and fill in the bubbles below your answer. Be sure to use the correct place value. 2 Eric bought 48 cement squares to make a rectangular patio. He created an equation, r s = 48, to find the different rectangular arrangements for the patio. If r represents the number of rows and s represents the number of squares in each row, what are all the possible arrangements for the rectangular patio? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 21 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-14 1 To multiply 34 26, Janie used the following array model. Complete the multiplication equations and find the total product. 20 6 10 x 20 = ______ 10 10 x 20 = ______ 10 x 20 = ______ 4 x 20 = ______ 10 10 x 6 = ______ 10 x 6 = ______ 10 x 6 = ______ 10 6 x 4 = ______ 4 34 x 26 = ______ 2 To multiply 34 26, Greg used the following array model. Complete the vertical multiplication strategy to find the total product. 20 6 26 x 34 4x 6 4 x 20 30 x 6 30 30 x 20 34 x 26 4 3 What is the multiplication and division family for 26 x 34? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 22 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-15 1 To multiply 17 42, Roy used the following array model. Complete the multiplication equations and find the total product. 10 7 10 x 10 = ______ 10 x 10 = ______ 10 10 x 10 = ______ 10 x 10 = ______ 10 2 x 10 = ______ 7 x 10 = ______ 10 7 x 10 = ______ 7 x 10 = ______ 7 x 10 = ______ 10 7 x 2 = ______ 2 42 x 17 = ______ 2 To multiply 17 42, Sandra used the following array model. Complete the vertical multiplication strategy to find the total product. 10 7 42 x 17 7x 2 40 7 x 40 10 x 2 10 x 40 42 x 17 3 What is the multiplication and division 2 family for 42 x 17? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 23 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-16 In recent Numerical Fluency problems you have used the following multiplication strategies. Clusters Horizontal number sentences Arrays Vertical number sentences 1 Compute 45 39 using one of the above strategies. 2 Compute 45 39 using another one of the above strategies. Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 24 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-17 Use an efficient method to compute each of the following problems. Be prepared to explain why your method makes sense and why it is efficient. 1 72 14 2 27 56 3 32(95) Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 25 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-18 1 Complete the Multiple Tower below for 21. 2 How many multiples of 21 does it take to get to 210? 3 What value of x makes the following equation true? x 21 210 4 What value of y makes the following equation true? 210 21 y 5 Use the Multiple Tower for 21 to find at least 3 pairs of numbers that make the following equation true. a 21 b _____ 63 42 21 Save your Multiple Tower for use during the next few days. Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 26 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-19 Use the Multiple Tower you built for 21 to answer the following problems. 1 After 210, what is the next multiple of 21 that has a 0 in the ones place value? 2 What value of a makes this equation true. a 21 = 420 3 What value of r makes this equation true? 420 21 = r Compute the following factor pairs to get some Landmark Numbers for 21. 3 10 21 = ______ 4 20 21 = ______ 5 30 21 = ______ _____ 6 40 21 = ______ 63 42 7 50 21 = ______ 21 8 80 21 = ______ 9 100 21 = ______ Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 27 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-20 There are 129 crayons. Six children will share the crayons equally. How many crayons will each child receive? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 28 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-21 Marta and James looked at the Multiple Tower for 21 and then used different methods for the same division problem. 1 Be prepared to explain the similarities and differences of their methods. 2 Find the value for n that makes the division problem true. 441 Marta’s method 420 n 399 21 504 378 - 210 10 groups of 21 357 294 left over 336 - 210 10 groups of 21 315 84 left over 294 - 84 4 groups of 21 273 0 n groups of 21 252 231 210 James’ method n 189 21 504 168 - 420 20 groups of 21 147 84 left over 126 - 84 4 groups of 21 105 0 n groups of 21 84 63 42 21 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 29 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-22 1 Complete the Multiple Tower for 18. (Keep it for tomorrow’s Numerical Fluency.) 2 Solve 38 18 by using a horizontal number sentence. 3 Complete Miguel’s division problem below and find the value of n that makes the problem true. Miguel’s method n 18 576 - 180 10 groups of 18 396 left over - 20 groups of 18 left over - ? groups of 18 1 n groups of 18 4 Complete Gloria’s division problem below and find the value of n that makes the problem true. Gloria’s method n 18 576 - 30 groups of 18 left over 18 - ? groups of 18 0 n groups of 18 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 30 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-23 1 Compute the following factor pairs to get some Landmark Numbers for 18. Landmark Numbers 10 18 = _____ 20 18 = _____ 30 18 = _____ 40 18 = _____ 50 18 = _____ 100 18 = _____ 2 Use your Multiple Tower for 18 and the Landmark Numbers for 18 to find the value of n that makes the following division problem true. n 18 954 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 31 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-24 Record your answer and fill in the bubbles below your answer. Be sure to use the correct place value. 1 There are 972 seats in the Austin High School Theater. There are 18 seats in each row. How many rows of seats are in this theater? 2 There are 1806 peach trees in the orchard. There are 21 rows of peach trees. How many trees are in each row of the peach orchard? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 32 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-25 Complete the following multiplication table. X 1 2 4 5 6 7 8 3 9 10 11 12 1 2 4 5 6 3 2 2 8 10 12 6 3 3 6 12 18 2 4 4 8 12 20 24 5 5 10 15 20 30 35 6 6 12 18 24 30 7 35 8 24 9 10 11 12 List 3 strategies you used to recall facts you did not know. 1. 2. 3. Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 33 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-26 Use an algorithm to find the value of the variable that makes each equation true. 1 $ 35.17 + $ 11.99 = w 2 15.7 – 2.81 = n 3 z + 37.6 = 37.724 4 $100 - x = $ 29.99 Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 34 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-27 Harold made a drawing of his rectangular kitchen. The length of the drawing was 9.5 inches, and the width of the drawing was 2.75 inches less than the length. Find the width of the drawing. Kitchen 9.5 inches Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 35 of 36 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems Numerical Fluency 1-28 David bought 2 shirts at Foleys. One shirt cost $23.50. The other shirt was on sale for $5.95 off of the original price of $32.50. 1 Which equation can be used to find n, the total amount David paid for the 2 shirts? A n = 23.50 + (5.95 + 32.50) B n = (32.50 – 5.95) – 23.50 C n = (32.50 – 5.95) + 23.50 D n = (32.50 – 23.50) – 5.95 2 How much did David pay for the two shirts? Austin ISD Secondary Mathematics Department 1st Six Weeks 2009-2010 Page 36 of 36