Welcome to Harcourt Mega Math: Numberopolis

Transcription

1 Welcome to Harcourt Mega Math: Numberopolis In Numberopolis, Tally is ready to show students around town. With some help from some quirky urban friends, students discover how to model whole number operations, identify and make money amounts, use a number line, and explore probability. Numberopolis is the third Harcourt Mega Math CD in a series for Kindergarten, Grade 1, and Grade 2 students. It can be used alone, in conjunction with other Harcourt Mega Math CDs, or alongside other Harcourt School Publishers print and electronic products for these grade levels. Figure 48: Numberopolis Welcome Screen Harcourt Page 86

2 In Numberopolis, Tally invites students to visit four places in town, each representing one of four themes: story problems, money, number line, and probability. Each theme, or module, gives students ample opportunity 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. A cast of off-beat urban animals, rich graphics, engaging interactivities and familiar environments combine to help students to see the connection between concrete settings and abstract mathematical symbols and operations. For example, in the module Cross Town Number Line, students use a number line to count on or count back. By counting on from one number to another, students not only see the order of numbers in counting, but also familiarize themselves with the concept of simple addition. Before long they can number themselves amongst a long line of students proficient in math. Harcourt Page 87

3 What s Inside Harcourt Mega Math: Numberopolis 1. At the Main Menu, click. 2. Then choose from four modules by clicking a town feature. 3. From any activity, click to return to the Main Menu. Harcourt Page 88

4 Carnival Stories Overview Goldfish in motorized bowls, paint balls, and hamsters on scooters and in Ferris wheel cars provide the wacky backdrop for Carnival Stories. With the help of some free wheeling fish and happy hamsters, students learn to model and solve story problems involving addition, subtraction, multiplication, and division. Figure 50: Opening Carnival Stories Learning Opportunities Addition Stories Represent addends and identify their sum Represent one addend and a sum to find the missing addend Complete addition sentences that represent each story Subtraction Stories Represent the minuend and use take away to find the difference Represent two unequal quantities and compare to find their difference Complete subtraction sentences that represent each story Multiplication and Division Stories Represent equal groups to find a product Find 1-digit quotients by sharing and separating Complete number sentences that represent each type of number story Harcourt Page 89

5 In Carnival Stories, students apply arithmetic skills to solve story problems. Addition is a dynamic process that involves either combining addends or working backwards from a sum to find a missing addend. In combining addends, students first model the addition by using fish to represent each addend. They then drag a number to complete the addition sentence and show the sum. In missing addend problems, students work from the sum and represent either the first addend (the start number) or the second addend (the change number) to determine the value of the missing addend. Subtraction is modeled either by taking away objects from a set of objects that represent the minuend or by aligning two sets of objects and comparing the difference between them. In both cases, students are actively engaged in dragging objects into place and analyzing the representations to solve the problems. Story problems involving multiplication and division take place on a Ferris wheel. The number of cars on the wheel can represent a factor, a divisor, or a quotient, and the number of passengers within each car the other factor, the dividend, or the quotient respectively. In all cases, students complete a corresponding number sentence that reflects the action implied in the story and links the representation to its mathematical symbols. Carnival Stories offers students the opportunity to translate words and sentences into the language of arithmetical operations: addition, subtraction, multiplication, and division. In so doing, students are supported and guided by immediate audio responses and instructive animations. Harcourt Page 90

6 Using the Paintball Dispensers For some questions, students choose an answer by clicking the paintball dispensers to launch paintballs on the board. 1. Listen to the directions given, such as Here are twenty orange paint balls on the board. Launch eight green paint balls on the board. 2. Click or to launch a group of ten paintballs. To remove a group of ten paintballs, click. 3. Click or to launch a single paintball. To remove single paintballs, click. 4. Then click. Harcourt Page 91

7 Using the Scrambler Ferris wheel Choose an answer by clicking the car dispenser at the center of the Ferris wheel. With each click an extra car is added to the Ferris wheel until the maximum of 6 cars is on the wheel. Once the maximum has been reached, each subsequent click removes a car until there are no cars left on the Ferris wheel. 1. Listen to the directions provided, for example, Here's the story. Now you make the picture. There are six cars on the Ferris wheel. Each car has four hamsters. 2. Click to add cars to the Ferris wheel. 3. Click and move hamsters from the dispenser to each car. 4. Then click. Figure 52: Using the Scrambler-Ferris Wheel Harcourt Page 92

8 Lulu s Lunch Counter Overview In Lulu s Lunch Counter there is no such thing as a free lunch! But the food is wholesome, so in Lulu s diner students assist some famished felines in purchasing some mouth-watering food. The lunch counter provides students with an opportunity to identify coins and bills, and to represent different amounts. They use combinations of coins and bills to purchase various dishes, add and subtract sums of money, and make change. Figure 53: Opening Lulu s Lunch Counter Learning Opportunities Coins Identify coins and count collections of coins Add money with and without regrouping Subtract money with and without regrouping Make the same amount using the fewest coins Compare amounts to prices Make change Bills and Coins Identify decimal notation for an amount of money Add dollars and cents without regrouping Subtract dollars and cents without regrouping Make equivalent sets of bills and coins Compare money amounts Harcourt Page 93

9 All transactions in Lulu s Lunch Counter mirror real-life transactions. In this module, students assist customers in buying food by identifying and using coins and bills. In the process, they count out coins, make change, add and subtract amounts of money, compare amounts or prices, and form equivalent sets of coins or bills. To buy the mouthwatering dishes or to make change, students drag replicas of coins and bills from simulated wallets and cash registers. Coins are displayed as heads or tails, and students are expected to be able to identify a coin by seeing either of its sides. Problems in this module are carefully sequenced to allow for gradual familiarity and practice. Students begin by solving problems that involve amounts up to 10, and progress to solving problems involving amounts up to 25, 60, 99, and eventually $5.00. Students drag coins and bills to represent specified amounts, to represent the sum of or difference between two amounts, and to make change. Conversely, they input the values of amounts represented by one or more sets of coins, and determine whether they have enough money to pay for the items. Payment with coins and bills is supported by displays of their corresponding values, and students are often asked to complete corresponding number sentences, including addition and subtraction algorithms, as they appear. In Lulu s Lunch Counter, students are given ample time and space to become familiar with coins and bills, and their value. Audio and animations enrich the interactive nature of the problems posed, and the immediate evaluation of answers provide students with encouraging feedback and additional guidance where needed. Harcourt Page 94

10 Using the Coin and Bill Dispenser For many questions, students choose an answer by clicking and dragging coins and/or bills from dispensers to the counter to show an amount of money. 1. Follow the directions given. For example, Put four cents on the counter. 2. Click and drag coins and/or bills from the dispenser to the counter to show the amount of money. 3. To remove a coin, click and drag it back to the dispenser. 4. Then click. Figure 54: Using the Coin Dispenser Harcourt Page 95

11 Using the Regroup Arrow When a subtraction problem requires regrouping, use the Regroup Arrow to regroup from the tens place to the ones place. 1. Follow the directions given. For example, How much more does the milk cost than the juice? Subtract. Click the arrow if you need to regroup. 2. Click the regroup arrow to regroup 1 ten as 10 ones. 3. Answer the question by using the number input pad. 4. Then click. Figure 55: Using the Regroup Arrow to Subtract Harcourt Page 96

12 Cross Town Number Line Overview High above the nighttime rooftops of Numberopolis, a carrier pigeon counts his way on the Cross Town Number Line. In his cable car or on a pogo stick, the pigeon helps students understand the value of a number line for skip counting, ordering, and comparing numbers, and also for addition and subtraction fact strategies. Figure 56: Opening the Cross Town Number Line Learning Opportunities Order numbers up to 1,000 Count on to add Count back to subtract Skip count by 2s, 5s, 10s, 25s, 50s, and 100s Investigate patterns of odd and even numbers Compare numbers to 1,000 using symbols Round numbers to the nearest 10 Harcourt Page 97

13 Counting underlies all other number concepts in arithmetic and forms the basis of the early elementary math curriculum. As they count, students learn the names, symbols, and sequence of the whole numbers, and they use these skills to anticipate the operations of addition and subtraction. One of the most powerful visual models for developing counting proficiencies is the number line. On a number line a student can see the order of numbers and the even distances between them. Throughout Cross Town Number Line, students interact with a number line in a variety of ways to compare, order, and use the count on and count back strategies. By dragging numbers to the number line or the cable car along it, young students begin to understand that numbers go on in a predictable sequence and that this sequence can be used to solve many different kinds of problems about numbers. Students also interact with a pogo-riding pigeon to understand skip counting and to explore other sequences and patterns, such as odd and even numbers. An interactive number line also helps students understand more profoundly the concept of rounding, as well as the operations of addition and subtraction. All the problem sets in Cross Town Number Line offer students engaging and supportive interactivities. Answers are immediately evaluated, providing students with appropriate feedback and additional instruction where needed. Audio and animations, in addition to a dynamic number line model, enrich the interactive nature of the problems posed, and provides students with an excellent foundation for learning the operations that come next in the curriculum. Harcourt Page 98

14 Using the Number Line Car Many questions require students to choose an answer by clicking and dragging the car to a number on the number line. 1. Listen to the directions given. For example, Let's add. Count on one. 2. Click and drag the car to the right to count on one. 3. Then click. Figure 57: Moving the Number Line Car Harcourt Page 99

15 Wash n Spin Overview Explore probability with a cast of improbable canines! Wash n Spin is set in a beauty salon for dogs, and as they are groomed, students are introduced to probability. They use fun and familiar items to understand events and outcomes, and they use a spinner to conduct simple experiments. Figure 58: Opening the Wash n Spin Learning Opportunities Events and Outcomes Determine the likelihood, certainty, or impossibility of an event Decide which of two or more outcomes of an event is more or most likely Decide which of two or more outcomes of an event is less or least likely Decide when outcomes in a given event are equally likely Experiments Determine the outcomes and their number in a probability experiment Use a probability model to conduct probability experiments Use data in a tally table to predict future outcomes Harcourt Page 100

16 The technology and engaging setting of Wash n Spin gives young students a unique opportunity to explore simple ideas in probability. To begin, students examine color spinners or jars and trays of colored objects and predict which outcomes in each case are likely or unlikely to turn up, or which are certain or impossible. In events that have two or more outcomes, students consider probabilities that are more or less likely, most or least likely, or equally likely. Familiar items - such as hair clips, dog biscuits, combs, and shampoo - set against an off-beat and colorful background provide friendly, supportive practice in highly engaging and interactive ways. In this module, students are also asked to conduct their own experiments using a spinner. For example, students are asked to spin a pointer ten times and then to examine the results displayed in a tally table. Using these data, students answer questions that require them to analyze the data. Conversely, students are given data in a tally table that displays the results of having spun a pointer ten times, and are asked to use these data to predict and record the outcomes in another ten spins of the pointer. Wash n Spin allows students to conduct their own experiments and check the resulting outcomes with their predictions. All the problem sets in Wash n Spin offer students engaging and supportive interactivities. Answers are immediately evaluated, providing students with appropriate feedback and additional instruction where needed. Audio and animations enrich the interactive nature of the problems posed, and provide students with a foundation for understanding the nature of probability. Harcourt Page 101

17 Using the Probability Spinner Some questions require students to conduct a probability experiment by clicking a button to spin a pointer. 1. Follow the directions given. For example, Spin the pointer to see the outcomes of ten spins. 2. Click. Figure 59: Using the Probability Spinner Harcourt Page 102

18 Grow Slide Levels for Numberopolis Each of the four learning activities in Numberopolis has a Grow Slide with progressive difficulty levels. Carnival Stories Addition Stories to 10 Subtraction Stories to 10 Comparison Stories to 10 Choose Addition or Subtraction to 10 Missing Addends to 10 Addition Stories to 12 Subtraction Stories to 12 Missing Addends to 12 Comparison Stories to 12 Choose Addition or Subtraction to 12 Addition Stories to 20 Subtraction Stories to 20 Addition and Subtraction Stories to 20 Missing Addends to 20 Comparison Stories to 20 2-Digit Addition Stories 2-Digit Subtraction Stories 2-Digit Comparison Stories Multiplication Stories Division Stories - Sharing Division Stories - Separating Cross Town Number Line Order Numbers 0-5 Order Numbers 6-10 Order Numbers to 10: Count On 1 or 2 0 to 10: Count Back 1, 2, or : Count On to Add 0-12: Count Back to Subtract 0-20: Count On to Add 0-20: Count Back to Subtract 0 to 20: Find Missing Addends 0-30: Skip Count by 2s, 5s, and 10s Even/Odd Numbers to : Count Up/Back 1 or 2 Order Numbers to : Count Forward/Backward Count 10 More, 10 Less to : Skip Count by 2s, 5s, and 10s 0-100: Skip Count by 3s and 4s Even/Odd Number Patterns to 100 Compare/Order Numbers to 100 Round Numbers to the Nearest 10 Compare/Order Numbers to 1,000 Skip Count by 25, 50, and 100 to 1,000 Lulu s Lunch Counter Count Pennies to 10 Identify Penny, Nickel, Dime and Equivalents Add Pennies to 10 Subtract Pennies from 10 Count Groups of Nickels and Pennies Count Groups of Dimes and Pennies Count Collections of Dimes, Nickels, and Pennies Half Dollar and Dollar Make the Same Amount Count Coins to 99 Add Money as Cents Add Money as Cents with Regrouping Same Amounts Using Fewest Coins Compare Amounts Compare Amounts to Prices Subtract Money as Cents Make Change Subtract Money as Cents with Regrouping Money as Dollars and Cents Add and Subtract Money with Dollars and Cents Make Equivalent Sets Compare Money Amounts Wash n Spin Likelihood of a Given Situation Certain or Impossible Events Likely and Unlikely More Likely and Less Likely Most Likely and Least Likely Possible Outcomes Equally Likely Predict Outcomes Harcourt Page 103