Copyright © 2010 by John Wiley & Sons, Inc. Dot Paper for 1,000 and More Dot Paper Diagrams 117 Copyright © 2010 by John Wiley & Sons, Inc. 10,000 Dots 118 Computation Connections Chapter 32 File Folder Activities Grades K–6 Ⅺ Total group activity Ⅺ × Cooperative activity Ⅺ × Independent activity Ⅺ Concrete/manipulative activity Ⅺ Visual/pictorial activity Ⅺ × Abstract activity Why Do It: This activity gives students practice with basic facts, com- putation, and problem solving by matching. It encourages students to work as individuals or in small groups and to self-check their answers. It can also be used as an alternate way for the teacher to test the students. You Will Need: Students will need manila file folders (amount will vary depending on what you feel needs reviewing), glue, library pocket envelopes (pockets made out of construction paper or 4- by 6-inch index cards will also work), 3- by 5-inch index cards, and marking pens. HowToDoIt: 1. This activity involves the use of file folders, pockets, and cards to help students review basic mathematical concepts or to test their knowledge in basic mathemat- ical facts. Glue the library pockets inside the file folders. The number of pockets depends on what is needed for the review or test. For example, if students need to review their multiplication facts, then their folder could 119 look like the one pictured in Example 1. Use the marking pens to write problems on the pockets and their answers on individual index cards. Prior to starting, hide an answer key to all the pockets in the Answer Cards pocket. 2. To begin, each student (or pair of students) must take all the individual answer cards and place them in the matching problem pockets. If students need to make pencil-and-paper computations for a given problem, they should use a small piece of scratch paper and place it in the same pocket as the answer card. Solutions should be checked against the answer key or by another player (sometimes with a calculator). If you choose to use the file folder as a test of a student’s knowledge, then the activity could be timed, with you checking the solutions. Examples: 1. Using the file folder below, a student must match mul- tiplication facts with the corresponding answers. 2. This file folder requires stu- dents to practice telling time from a clock face. Students match digital times to those on ‘‘regular’’ clock faces. Multiply 6 × 5 7 × 3 8 × 6 9 × 5 4 × 9 36 30 40 7 × 7 8 × 7 56 7 × 6 5 × 5 8 × 4 9 × 95 × 8 6 × 9 8 × 8 6 × 5 Answer Cards Time Answer Cards 5:15 6:00 9:00 3:00 Extensions: 1. Devise file folders for any area in which practice is needed. The players, after seeing how the folders are constructed, should make a variety of folders for one another. These file folders can be made for matching numerals with pictured amounts; practicing basic facts; exploring fractions, decimals, measurement, and geometric identification; working with the concepts of time and money; and solving short story problems, among other things. 120 Computation Connections 2. Older students can construct and use these file folders to provide special help for younger learners. Especially useful are folders dealing with numerals, number sense, place value, and basic math facts. The folders could also be at a math station in the classroom, and as students finish their regular work, they could go to the station to practice certain skills. 3. To increase the difficulty level for this activity and promote careful thinking, include more than a single correct answer card for certain problems (for example, a pocket reading ‘‘Find two numbers whose product is 36’’ might be answered with 4 × 9and6×6) or include a few wrong answers that do not correspond to any of the folder problems. One or both of these tactics can be used to turn this activity into a math quiz. File Folder Activities 121 Chapter 33 Beat the Calculator Grades 1–6 Ⅺ × Total group activity Ⅺ × Cooperative activity Ⅺ Independent activity Ⅺ Concrete/manipulative activity Ⅺ × Visual/pictorial activity Ⅺ × Abstract procedure Why Do It: Students will practice basic facts and mental math. This activity will help students become more proficient in recalling basic mathematical facts, and with this ability they will have fewer problems with more complicated mathematics. You Will Need: At least one calculator is required. If Beat the Calculator is to be a large group or whole class activity, the teacher can use a calculator placed on an overhead projection device, or even a virtual calculator found online. For small groups of two to five participants, only one calculator is necessary. How To Do It: 1. In a small group, with one calculator and three people, the following procedure works well: Student 1 calls out a math problem, such as 6 ×7. Student 2 uses a calcu- lator to solve the problem and state the answer. At the same time, Student 3 solves it mentally and says the answer. The first to give the correct answer (Student 2 or Student 3) wins. The players’ roles should eventu- ally be rotated. To make the activity more competitive, have students tally the number of wins for each student. 122 (Note: Students will soon discover that if they have practiced their basic facts, they will be able to ‘‘beat the calculator’’ nearly every time.) 2. Beat the Calculator may also be played as a whole class activity. In this case, you or a leader operates the calculator, while students simultaneously do the mental math and call out answers; a chosen judge calls out the problems and determines the winner of each round. The object of the activity is therefore to determine which method is faster and more efficient for obtaining the solutions to basic fact problems: using a calculator or just memorizing the fact. Example: In the small group situation above, Sean had called out 5 × 9. Susan has been attempting to solve the problem with a calculator before Randy could do so mentally. However, because Randy had mastered his 5s multiplication facts, he was able to beat the calculator. Extensions: 1. Young students might try counting with a calculator by entering a number (try 1), an operation (try +), and pressing the equal button multiple times (====) to make the calculator count by 1s. They can also start with any number, like 20, and enter 20 + 1 = ===. They might further try counting forward (addition) or backward (subtraction) by any multiple; for example, they can Beat the Calculator 123 enter 3 +3 ====and see what happens. (Note: Learners should use a calculator that has an automatic constant feature built in; most basic calculators do. To test this, simply try the calculator; if it ‘‘counts’’ as noted above, it has the needed constant.) 2. Students might use a calculator that has an automatic constant to individually practice basic multiplication facts. For example, to practice the 4s facts, they can enter 4 ×=, which the calculator holds in its memory. Then any number entered will be multiplied by 4 when the = key is pressed. Thus the student might enter 8, mentally think what the answer should be, press =, and see that the answer displayed is 32. 3. Advanced students can work in pairs, taking turns trying to beat the calculator with such tasks as 2 ×12 ÷8 +3 −5 = or 7 + 32 ÷ 4 − 5 × 2 = .(Note: In these cases, be certain that the players use the proper order of operations. The mnemonic ‘‘Please Excuse My Dear Aunt Sally’’ sometimes helps students remember the order: parentheses, exponents, multiply or divide from left to right, and add or subtract from left to right. Students are frequently unclear about this concept, so even if the calculator has a built-in order of operations feature, the students should be taught to put parentheses as shown here: 7 +(32 ÷4) −(5 ×2). The answers to the two problems in this Extension are 1 and 5, respectively. 124 Computation Connections Chapter 34 Floor Number Line Actions Grades K–6 Ⅺ Total group activity Ⅺ × Cooperative activity Ⅺ Independent activity Ⅺ × Concrete/manipulative activity Ⅺ × Visual/pictorial activity Ⅺ × Abstract procedure Why Do It: Students will physically act out computation and mathemati- cal problem-solving situations. You Will Need: This activity requires a walk-on number line, which can be constructed using soft chalk, tape, and number cards, or a large roll of paper with a marking pen. HowToDoIt: 1. To construct the number line, write large numerals about 1 foot apart either on the playground or floor using soft chalk, or on a large roll of paper using a mark- ing pen. If the number line will be used more than once, itcanbemadebytapingnumbercardstotheflooror using some more permanent method on the playground surface. Problems at the beginning will likely make use of the numerals 0 through 10, but as the work becomes more difficult, the number line can be expanded to 100 125 or more. If signed numbers are to be used, it should also be extended from 0 to −1, −2, −3, and so on. 2. Students will solve math problems using this walk-on number line. The examples below show how to begin. Once students understand the procedure, have them try some of the problems in the Extensions section or other problems created by you or the students. Students should be ready both to explain how they ‘‘walked out’’ each problem and to use pencils and paper to show the same solution. Examples: 1. For 4 + 3, students begin at 0 and take 4 steps to the number 4. Then they take 3 more forward steps and check the number on which they are now standing; it should be 7. (See the solid arrow in the illus- tration below.) Finally, students should keep a record by writing 4 +3 = 7 in their notebooks. 2. For such a problem as 9 ÷4, stu- dents begin at the 9 and move toward the 0, taking 4 steps at a time and holding up a finger for each time. Beginning at the 9, they step to 8, 7, 6, and 5 and hold up 1 finger; then they step to 4, 3, 2, and 1 and hold up 2 fin- gers. They have therefore taken 4 steps 2 times, but still need to get to 0; this will require 1 more step. Thus 9 ÷4requires2setsof 4 steps with 1 step remaining, so 9 ÷ 4 = 2, with a remainder of 1. 126 Computation Connections [...]... Charts 10 10 10 20 30 40 50 60 70 80 90 100 9 9 18 27 36 45 54 63 72 81 90 8 8 8 16 24 32 40 48 56 64 72 80 7 7 7 14 21 28 35 42 49 56 63 70 6 6 6 12 18 24 30 36 42 48 54 60 5 5 5 10 15 20 25 30 35 40 45 50 4 4 4 8 12 16 20 24 28 32 36 40 3 3 3 6 9 12 15 18 21 24 27 30 2 2 2 4 6 8 10 12 14 16 18 20 1 1 1 2 3 4 5 6 7 8 9 10 × 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 × 1 2 3 4 5 6 7 8 9 10 10 10... 100 × 1 2 3 4 5 6 7 8 9 10 10 10 10 9 9 9 18 27 36 45 54 63 72 81 90 8 8 8 16 24 32 40 48 56 64 72 80 7 7 7 14 21 28 35 42 49 56 63 70 6 6 6 12 18 24 30 36 42 48 54 60 5 5 5 10 15 20 25 30 35 40 45 50 4 4 4 8 12 16 20 24 28 32 36 40 3 3 3 6 9 12 15 18 21 24 27 30 2 2 2 4 6 8 10 12 14 16 18 20 1 1 1 2 3 4 5 6 7 8 9 10 × 1 2 3 4 5 6 7 8 9 10 × 1 138 2 3 4 5 6 7 8 9 10 Computation Connections Copyright... chart depicts 5 × 3 (as 5 groups of 3) = 15 10 10 20 30 40 50 60 70 80 90 100 9 9 18 27 36 45 54 63 72 81 90 8 8 16 24 32 40 48 56 64 72 80 7 7 14 21 28 35 42 49 56 63 70 6 6 12 18 24 30 36 42 48 54 60 5 5 10 15 20 25 30 35 40 45 50 4 4 8 12 16 20 24 28 32 36 40 3 3 6 9 12 15 18 21 24 27 30 2 2 4 6 8 10 12 14 16 18 20 1 1 2 3 4 5 6 7 8 9 10 × 1 2 3 4 5 6 7 8 9 10 Extensions: Have students complete the... selected corner numbers 23, 16, 8, and 12 for this Subtraction Square 23 7 16 23 7 16 4 11 8 1 11 8 7 12 4 8 12 4 Step 1 23 3 8 Step 2 7 4 4 16 23 1 7 4 16 3 1 0 0 11 3 7 12 3 3 4 Step 3 148 8 11 4 12 0 3 7 8 0 3 3 4 8 4 8 Step 4 Computation Connections 2 The corner numbers were 16, 2, −11, and 0 for this Subtraction Square 16 14 2 1 2 3 2 0 0 0 0 2 0 5 1 2 0 16 2 1 13 0 2 3 11 2 2 –11 Extensions: 1 When appropriate,... column of the game are shown below Player 1 S K U N K 8 6 (Stop) Player 2 Numbers Rolled and Scores S K U N K 8 3+5=8 6 4+ 2=6 11 6 + 5 = 11 5 +4= 9 9 SKUNK 1+3 =4 14 144 0 Computation Connections Extensions: 1 Paste blank stickers on the dice and write two- or three-digit numbers on them; let numbers with repeating digits (such as 77 or 333) be the SKUNK numbers Play the game using addition 2... Your problem is: × = 5 Figure out some more cross-line problems and share them with the class 6 Try cross-line multiplication for two-digit multiplication 2 3 x 6 138 23 x 63 144 9 9 12 12 18 Add 1 from the 18 to the 2 in 12 24 All middle line crossings Add 2 from the 24 to the 2 in the 12 Cross-Line Multiplication 135 Chapter 37 Highlighting Multiplication Grades 2–6 × Ⅺ × Ⅺ × Ⅺ Ⅺ × Ⅺ × Ⅺ Total group... Connections 2 The object of this multiplication game was to achieve the least product Five spins gave the numbers 9, 4, 3, 1, and 7 in that order Three players’ problems are shown below Because the answers 14, 993, 34, 049 , and 13,871 come up, Player 3 is the winner 3 1 9 4 3 1 1 4 3 × 4 7 × 7 9 × 9 7 (Player 1) (Player 2) (Player 3) Extensions: Challenge students with a variety of question types 1 Young... which is 4/ 12; and shade 1 /4 of another rectangle, which is 3/12 Next, they draw the 4/ 12 and the 3/12 onto the third rectangle grid for a total of 7/12 (Note: When students draw the 4/ 12 and 3/12 onto one grid, they should not overlap the shading.) 4 then 3 + = 1 4 = 3 12 12 units 1 3 = 4 12 4 3 7 + = 12 12 12 or 1 7 1 + = 4 12 3 2 For a slightly harder problem, guide students through the steps for First... problems and have their classmates use the number line to figure out the solutions 1 8 + 3 4 20 ÷ 5 2 7 − 4 *5 −2 + 4 3 4 × 6 *6 −3 + 4 *(Hint: Face in the direction of the first signed number, and then change direction every time the sign of the number changes.) Floor Number Line Actions 127 Chapter 35 Egg Carton Math Grades K–6 × Ⅺ × Ⅺ × Ⅺ × Ⅺ Total group activity Cooperative activity Independent activity... successful when using printed Subtraction Squares (see reproducible handout) and single-digit numbers 3 Players might attempt a variety of arrangements For instance, try a single-digit number in one corner, a two-digit number in another, a three-digit number in the third corner, and a four-digit choice in the last 4 Able players might be able to complete Subtraction Squares that incorporate fractions . multiplication for two-digit multiplication. 2 3 x 3 6 3 12 12 18 24 9 x6 2 183 Add 1 from the 18 to the 2 in 12. All middle line crossings Add 2 from the 24 to the 2 in the 12. 944 1 Cross-Line Multiplication. illus- tration below.) Finally, students should keep a record by writing 4 +3 = 7 in their notebooks. 2. For such a problem as 9 4, stu- dents begin at the 9 and move toward the 0, taking 4 steps. they step to 4, 3, 2, and 1 and hold up 2 fin- gers. They have therefore taken 4 steps 2 times, but still need to get to 0; this will require 1 more step. Thus 9 ÷4requires2setsof 4 steps with