Welcome to Harcourt Mega Math: The Number Games


 Gillian Moody
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1 Welcome to Harcourt Mega Math: The Number Games Harcourt Mega Math In The Number Games, students take on a math challenge in a lively insect stadium. Introduced by our host Penny and a number of sporting bugs, students extend their familiarity of money, multiplication and division, graphing, and a wide assortment of other math skills and concepts. The Number Games is the first Harcourt Mega Math CD in a series for Grade 3, Grade 4, Grade 5, and Grade 6 students. It can be used alone, alongside other Harcourt print and electronic products for these grade levels, or in conjunction with its companion programs: Harcourt Mega Math Ice Station Exploration and Harcourt Mega Math Fraction Action. Together, the three programs cover the major topics in the third, fourth, fifth, and sixth grade math curricula. Figure 60: The Number Games Welcome Screen Harcourt Page 104
2 In The Number Games, Penny invites students to visit four areas of the stadium complex, each representing one of four mathematical topics: money, math review, multiplication and division, and graphing. Each topic, or module, provides students with a gamelike environment in which they are motivated to discover, learn, and practice; and a variety of interactivities and manipulatives support and encourage success. Within each module, students answer questions linked to specific skill levels, and advance to more challenging levels as they succeed. By using Grow Slides, they can monitor the progress they make, identify the skill levels for the entire module, or navigate to different levels within the entire module. The activities in The Number Games are designed to challenge students within a game or sports scenario. For example, in the module Tiny s Think Tank, Tiny the Ant hosts a game show. Four columns of three panels appear on a game board, and each column is headed by a topic. By clicking a panel on the board, students generate a question under one of the topics, and by answering the question correctly they reveal one piece of a hidden reward. By answering eight or more questions correctly, students reveal the reward, thus winning a round of the game. The game element motivates students to continue playing and to choose more challenging mathematical skills. Harcourt Page 105
3 What s Inside Harcourt Mega Math: The Number Games 1. At the Main Menu, click. 2. Then choose from four modules by clicking a stadium feature. 3. From any activity, click to return to the Main Menu. Harcourt Page 106
4 Buggy Bargains Overview Buggy Bargains is a store with a difference. In this module, students help a variety of wacky, wonderful bugs purchase their own unique brand of sporting equipment from the store s sales manager, Rick the Stick Insect. In the process, students learn to identify and represent money amounts, add and subtract sums of money, make change, and calculate sales tax and discounts. Figure 62: Opening Buggy Bargains Learning Opportunities Bills and Coins Count the value of combinations of bills and coins Determine fewest bills and coins to show amounts Number Operations Estimate the cost of two or more items Add two or three money amounts Subtract money amounts Use the unit cost to multiply and add money amounts Find the unit cost by dividing and add money amounts Make change using counting on and subtraction Sales Tax & Discounts Calculate sales tax amounts and total cost of items Calculate amount of discount and total cost of items Harcourt Page 107
5 All transactions in Buggy Bargains mirror reallife transactions, starting with the simple task of counting bills and coins to progressing to paying for taxed or discounted items. Initially, students identify items they can purchase with a given amount of money and pay for the item by dragging replicas of the corresponding bills and coins onto a counter. Students make change in two ways: either by counting on from the cost of the item to the amount paid for the item, and then dragging the amount onto the counter; or by completing the subtraction algorithm to find the difference, and then dragging the fewest number of bills and coins into an answer area. Purchasing items in Buggy Bargains reflects the multiple steps involved in making reallife purchases. For example, students estimate the total cost of items to be purchased, complete appropriate arithmetic algorithms to find the exact amount, calculate the change due, and drag bills and coins onto the counter to represent this amount. The computer corrects each step in the solution of a problem and provides supportive and instructive feedback and hints. In multistep problems that involve a sales tax or a discount, students select the decimal that reflects the percentage given and completes the corresponding decimal multiplication to find the amount to be added or subtracted from a given price. They then complete the problem to determine the final cost of the item. All the problem sets in Buggy Bargains offer students engaging and supportive interactivities. Each step in the solution process is assessed, providing students with appropriate feedback and additional guidance where needed. Audio and animations in conjunction with the manipulative bills and coins provide students with a rich and interactive learning environment in which they can advance their understanding of monetary transactions. Harcourt Page 108
6 Using the Coin and Bill Dispensers For many questions, students choose an answer by clicking and dragging bills and coins from dispensers to the counter to show an amount. 1. Use the correct amount to pay for this item. 2. Click and drag bills and coins from the dispensers to the counter to show the correct amount to be paid for the item. To remove a bill or coin, click and drag it back to the dispenser. 3. Then click. Harcourt Page 109
7 Using the Regroup Arrow When a subtraction problem requires regrouping, use the regroup arrow to regroup a dollar as ten dimes and a dime as ten pennies. You might need to click the arrow more than once to complete the regrouping. 1. What change is the customer owed? 2. Click the regroup arrow to regroup as needed. 3. Answer the question by using the number input pad. 4. Then click. Figure 64: The Regroup Arrow Harcourt Page 110
8 Tiny s Think Tank Overview Test your mathematical skills in a fabulous game show Tiny s Think Tank! In each round, students must solve a variety of problems and clear the game board to reveal a graphic prize. Questions allow students to show off their skills in addition, subtraction, multiplication, division; conversion of both metric and customary units of length, weight, and capacity; time, temperature, patterns, decimals, and mixed numbers. Tiny the ant wants you to come on down! Figure 65: Opening Tiny s Think Tank Learning Opportunities Number Sense Identify the place value of a digit (to the hundred thousands place) Identify the digit in a given place of a number (to the hundred thousands place) Identify whole numbers based on their properties Whole Number Operations Add 3 and 4digit whole numbers Subtract 3 and 4digit whole numbers Multiply by 2 and 3digit whole numbers Harcourt Page 111
9 Decimal and Fraction Operations Add and subtract decimals to thousandths Multiply and divide decimals Add and subtract mixed numbers Shapes & Patterns Identify plane figures based on their properties Complete geometric patterns Complete number sequences Measurement Find elapsed time and start and end times Convert customary units Convert metric units Find change in temperature ( F and C) In Tiny s Think Tank, a quiz show format motivates students to solve a variety of questions. Each round of the game presents a unique pool of 12 questions chosen at random from the categories listed above. Some of the questions are designed to address featured skill levels; others are cumulative review questions. If students answer 8 or more of the questions correctly, they will win a graphic prize and will move on to a new round of the game. If students repeat a round at the same skill level, a new set of featured questions and review questions will be chosen at random. Within each round of the game, many questions present nonroutine kinds of problems that require students to apply higher order thinking skills to solve. Students might be asked, for example, to identify one or more mystery numbers based on a set of clues. Some problems are relatively straightforward and have a unique answer, such as, I am the sum of 35 and 47. Others might be seen as more challenging and have more than one answer, such as, I am an odd number greater than 10 but less than 50. Students also solve computation problems in nonroutine ways. Rather than finding the 4 or 5digit product of two whole numbers, students see the algorithm and must enter digits to complete both the partial products and the final product. To provide additional challenges, the three multiplication problems in one column of the game board differ in difficulty level. In question 1, the easy level question, students identify only 2 missing digits. In questions 2 and 3, the medium and hard level questions, students identify 3 or 4 missing digits respectively. Tiny s Think Tank offers students the chance to practice basic arithmetic skills and to solve various patterning problems in an engaging and supportive environment. Answers are immediately evaluated, providing students with appropriate feedback and additional instruction where needed. Harcourt Page 112
10 Playing the Game There are 12 questions for each skill level. The 12 questions in each round are generated from a pool of questions specific to the skill level chosen on the grow slide, and from a pool of cumulative review questions. Each topic on the grow slide will always have at least two columns supporting that topic. A question lies behind each panel on the game board. A heading at the top of one or more columns of panels indicates the topic for the questions in those columns. Figure 66: Tiny s Think Tank Harcourt Page 113
11 1. Click any panel to generate a question. A question will appear, covering the entire game board (Figure 67). Figure 67: Question Screen 2. When the answer to the question is given, the game board will reappear. If the question is answered correctly, the panel that you clicked will disappear, revealing a portion of a graphic prize (Figure 68). If the question is not answered correctly, the panel will remain in place but will no longer be available as a choice. Figure 68: Revealed Graphic Indicates Correct Answer Harcourt Page 114
12 3. When all 12 questions have been attempted, the number of panels that have disappeared will indicate how many of the 12 questions were answered correctly (Figure 69). Figure 69: Uncovered Panels Indicate Correct Answers 4. When 8 or more questions are answered correctly, the game board will clear, and the student will win a graphic prize! If fewer than 8 questions are answered correctly, the student can repeat the round to try and clear the game board to win the graphic prize. Figure 70: Graphic Prize Harcourt Page 115
13 Up, Up, and Array Overview Join a dizzying array of adventurous bugs as they engage in a variety of sporting activities such as sky diving and golf. Set in a sports viewing tower, Up, Up, and Array uses the model of a rectangular array to help students master the fundamental skills of whole number multiplication and division. The array helps students understand the concepts of multiplication and division, and recognize their inverse relationship. It also enhances students ability to memorize multiplication and division facts and to multiply and divide with greater numbers. Figure 71: Opening Up, Up, and Array Learning Opportunities Multiplication and Division Facts Model multiplication facts from 5 to 12 Model division facts from 5 to 12 Multiplication Multiply by multiples of 10 Multiply by 1digit numbers Multiply by 2digit numbers Division Divide with remainders Divide 2 and 3digit numbers by 1digit divisors Divide 2 and 3digit numbers by 2digit divisors Harcourt Page 116
14 The problems in Up, Up, and Array are designed to help students understand the principles behind multiplication and division algorithms. In the first set of multiplication problems, for example, students see a rectangular array in which the number of rows and columns equal the first and second factors in a multiplication sentence. In multiplication problems involving 2 and 3digit multipliers, as students enter each partial product, the corresponding numbers of elements in the array are highlighted and grouped. When students add the partial products in the algorithm, the groups representing the partial products combine in the array to show the total number of objects in the complete array, and thus the product of the multiplication. Throughout these steps, students learn not just how to use the algorithm, but more significantly why the algorithm works. A manipulative that illustrates the principles behind an algorithm is also used to introduce the concept of long division. Students are presented with the divisor and dividend, a set of objects arranged in rectangular arrays that represent the dividend, and the number of groups into which the objects are to be distributed. In problems that involve 2digit quotients, students click a tens distributor to distribute equal numbers of tens into each group. When the maximum number of tens has been distributed, students move on to clicking a ones distributor to distribute the maximum number of ones equally into each group. As students work with the manipulative, the numbers in the algorithm change to reflect their work. Finally, the computer validates that the students have either distributed all the objects in the array or have left a valid remainder. In this way, students learn why the algorithm works. Students then practice long division using algorithms. As they work through the order of division, their answers are evaluated and the objects on screen are distributed to reflect their work. The quotient and remainder, if any, in the algorithm correspond to the distribution of objects in the model. All of the problem sets in Up, Up, and Array offer students engaging and supportive interactivities. Answers are immediately evaluated, providing students with appropriate feedback and additional instruction where needed. Audio and animations along with virtual manipulatives enrich the interactive nature of the problems posed, and provide students with a concrete model to help them understand the concepts of multiplication and division. Harcourt Page 117
15 Using the Ones and Tens Distributor Choose an answer by clicking or to divide the golf balls equally among the holes. 1. Follow the directions given. For example, Divide the golf balls equally among the holes. First divide the tens. 2. If and are both available, all possible groups of 10 must be distributed before becomes active. 3. Once the maximum number of tens has been distributed, the will no longer be active. Harcourt Page 118
16 4. Click to divide single golf balls among the holes. 5. Then click. Figure 73: Using the 1s Distributor Harcourt Page 119
17 ArachnaGraph Overview The competition is heating up in the sports stadium. In ArachnaGraph, students join a cast of swift and sprightly bugs as they test their athletic ability in track and field events. As they work with pictographs, bar graphs, and line plots, students learn to analyze and represent data, as well as determine the median, mode, and range. Towards the end of the module, students are introduced to the coordinate plane and learn to plot points, read and create line graphs, and work with algebraic equations in terms of x and y. Figure 74: Opening Arachnagraph Learning Opportunities Graph and Analyze Data Interpret pictographs Read and make bar graphs and doublebar graphs Read and interpret data in a line plot Identify the median, mode, and range of data in a line plot Read and interpret line graphs and doubleline graphs Graph on the Coordinate Plane Locate points on a coordinate plane Plot points using their coordinates Use function tables to identify equations and plot points Harcourt Page 120
18 ArachnaGraph is all about graphing. Students start by analyzing pictographs that require them to interpret a key that represents the graphed data. The problems that follow focus on bar graphs, with students first analyzing the graphed data, and then using an animated control interactivity to create bar graphs and doublebar graphs that represent given data. Students progress next to solving problems involving line plots. They analyze these onedimensional graphs to draw conclusions about the data represented and to identify the median, mode, and range of the data. Other graphs include line graphs and doubleline graphs that show change over time. Students analyze trends and make predictions based on the data shown in these more complex graphs. Other skill levels in this module focus on graphing in the coordinate plane. The emphasis here is on using coordinates to locate points in a plane, plotting points given their coordinates, and examining function tables that contain values of x and y, where x and y are integers. Students graph the ordered pairs (x, y) in the corresponding quadrants in the plane, and identify an algebraic equation that expresses the relationship between the variables, for example, y = x + 2. All the problem sets in ArachnaGraph offer students engaging and supportive interactivities. Each step in the solution process is assessed, providing students with appropriate feedback, and additional guidance where needed. Audio and animations provide students with a rich and interactive learning environment in which they can advance their understanding of both analyzing and making graphs. Harcourt Page 121
19 Using the Bar Graph Some questions require students to choose an answer by clicking and dragging arrows to make the bars on a bar graph. 1. Follow the directions given, such as Now make bars to show the number of each type of animal at the games. Drag the arrows to make each bar. 2. Click and drag each arrow to make the bars on the graph. 3. Then click. Figure 75: Making a Bar Graph Harcourt Page 122
20 Grow Slide Levels for The Number Games Each of the four learning activities in The Number Games has a Grow Slide with progressive difficulty levels. Buggy Bargains A. Count Bills and Coins to $10 B. Count Bills and Coins to $99 C. Use Fewest Coins and Bills D. Make Change E. Add Two Money Amounts F. Add Three Money Amounts G. Add Money Amounts to $ H. Calculate to Make Change I. Add and Subtract Money Amounts J. Multiply Money Amounts K. Multiply and Make Change L. Multiply and Add Money Amounts M. Divide Money Amounts N. Divide and Make Change O. Divide and Add Money Amounts P. Multistep Problems Q. Sales Tax R. Compute Total Cost with Sales Tax S. Discount T. Compute Total Cost with Discount Tiny s Think Tank A. Place Value of Whole Numbers B. Add 3 and 4Digit Numbers C. Subtract 3 and 4Digit Numbers D. Elapsed Time E. Time on a Calendar F. Multiply by 2Digit Numbers G. Multiply by 3Digit Numbers H. Identify Shapes I. Identify Numbers J. Geometric Patterns K. Number Patterns L. Add and Subtract Decimals M. Convert Customary Linear Units N. Convert Customary Units of Capacity O. Convert Customary Units of Weight P. Temperature Q. Convert Metric Units R. Multiply Decimals S. Divide Decimals T. Identify Numbers  Advanced U. Geometric Patterns  Advanced V. Number Patterns  Advanced W. Add and Subtract Mixed Numbers X. Review Up, Up, and Array A. Multiplication Facts to 5s B. Multiplication Facts 6, 7, and 8 C. Multiplication Facts 9 and 10 D. Multiplication Facts 11 and 12 E. Division Facts to 5s F. Division Facts 6, 7, and 8 G. Division Facts 9 and 10 H. Division Facts 11 and 12 I. Multiply Multiples of 10 J. Multiply by 1Digit Numbers K. Multiply by 2Digit Numbers L. Division with Remainders M. Divide 2 Digits by 1Digit Numbers N. Divide 3 Digits by 1Digit Numbers O. Long Division with 1Digit Divisors P. Zeros in Division Q. Divide 2 Digits by 2Digit Numbers R. Divide 3 Digits by 2Digit Numbers S. Long Division with 2Digit Divisors T. Review ArachnaGraph A. Interpret Data in a Pictograph B. Read Bar Graphs C. Make Bar Graphs D. Make DoubleBar Graphs E. Read a Line Plot F. Interpret Data in a Line Plot G. Locate Points on a Grid H. Graph on a Coordinate Plane I. Read Line Graphs J. Interpret Data in a Line Graph K. DoubleLine Graphs L. Graph Relationships Harcourt Page 123
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