The Game First to 21 - Essay Example

Task number: Task Type: Task Weighting: Due: Context: Data Representation and Analysis (Stage 5 This task provides with the opportunity to demonstrate their standard achievement of the following outcome(s): Students Learn about Students Learn to constructing a cumulative frequency table for ungrouped data constructing a frequency table for grouped data constructing a histogram for grouped data finding the mean using the class centre finding the modal class Specifically: The mean (average) is calculated by summing the data elements, then dividing by the number of elements. Data are a collection of representative information about a population of objects or individuals; they can be numeric or categorical. Data, to be most useful, need to be ordered. Numeric data are ordered from least to most or most to least. Other types of data can have other ordering schemes, such as alphabetic or geographic. On a bar chart the horizontal axis shows the groupings, while their height on the vertical axis shows their magnitude. Both axes are labeled with units. A line plot has a horizontal axis that groups the categories of data. The height of the points along the vertical axis indicates the magnitude, or number of data elements, in each category. Students should know graphing conventions, including how to draw, label, and set a scale on each axis, and how to read it. They should be able to plot data points and draw bars indicating the number of each element. construct frequency tables and graphs from data obtained from different sources read and interpret information from a cumulative frequency table or graph (Communicating) compare the effects of different ways of grouping the same data (Reasoning) Specifically: Collect data, order them, and prepare them for plotting. Represent a data set on either a bar chart or a line plot. Calculate the range, maximum, and minimum of a numerical data set. Calculate the mean, median, and mode of a numerical data set. Differentiate among mean, median, and mode. Follow the conventions of graphing for both line plots and bar charts—including accurate scaling and labeling of axes for both. Recognize a number line in an axis. Demonstrate understanding of how landmarks vary with the size of a data set, or with changes in the individual elements of that data set. Check the calculations for landmarks to see if the values accord with other general measures of the data (in other words, be able to answer, "Does this value make sense?"). Description of Activity: Step 1: For the first activity, they begin an exploration by guessing the number of raisins in a box. They revise their guesses to make informed estimates. Finally, they compute the measures of center, and tally and graph the data. Step 2: The next activity is an application of learning from the first activity. As the students work in pairs, they measure the length of their cubit (forearm from elbow to fingertip), and then measure others students’ cubits too. The data they will derive shall be organized and analyzed for measures of center, which will be represented on a bar chart of line plot. Presentation mode:  Raisin Activity: 1. Teacher unlocks understanding of vocabulary words such as minimum, maximum, range, mode, median, mean, to set the base of understanding for all children. Mean—the sum of the data points, divided by the number of data points; also known as the average Median—the data point with the same number of data points above and below it. (If there is an even number of data points, the median is taken as the number halfway between the two middle points.) Mode—the most frequently occurring value Maximum—the largest data value Minimum—the smallest data value Range—the spread or difference between the smallest and largest data points 2. After going through the vocabulary words, teacher zeroes in on the concept of organizing and analyzing data. 3. Raisin boxes and worksheets are distributed and students working in pairs guess how many raisins are in the box. Later on, they open the box and estimate how many raisins there are. 4. They put in the data about the raisins on the worksheets to compare the guesses and estimates, and go around the pairs to collect data garnered by the whole class in order to get for the minimum, maximum and median and mode. 5. They plot the grouped data into a graph. Cubits Activity 1. Students measure their own cubit (forearm from elbow to tip of middle finger) and then measure other students’ cubits of their choice. 2. They then organize the data they have collected in their data sheets. They likewise find landmark values (maximum, minimum, median and mode) so this may be analysed later. 3. This ungrouped data will be plotted on a bar graph or a line plot or both. Resources required: Worksheets for recording data boxes of raisins paper ruler and pens for creating graphs Criteria for assessing learning outcomes (rubric): The following outcomes are assessed to see if tasks have been effective: Student knows how to collect data from various sources and record it into a data sheet. Student understands the meanings of mean, mode, maximum, minimum and range. Student can identify them, and compute for it (ex. Mean) if necessary. Student knows how to plot the data on the charts. Students are generally familiar with bar charts. Certain conventions apply to bar charts and line plots: Axes must be labeled and scaled. The horizontal axis can be ordered arbitrarily or in a natural order (a number sequence, or high to low). If the graph plots values against their frequency in the data, then the values are displayed along the horizontal axis, while the height of each column indicates the number of data elements that have that value. Values with zero frequency are not represented. Line plots have similarities both to bar charts and to coordinate plots. Line plots follow these conventions: Axes must be labeled and scaled. The horizontal axis is generally ordered naturally with a number line. If the graph plots values against their frequency in the data, the height of a column indicates the number of data elements that have that value. Feedback: The first task shows students how to go about guessing, estimating, and all the preliminary information necessary to gather, organize, and analyze the data and values derived. It also introduce students to representations of data namely the bar graph and the line plot. From the knowledge and skills they derive from this activity, they get to apply it to the second task. Whereas the first task offered grouped data since everyone used the same data sources, the second task offered ungrouped data where students can collect from various sources of their choice. The first task may be considered teacher-directed while the second task gives the students more leeway to conduct their own investigations.    Task number: Task Type: Task Weighting: Date Due: Context: Probability: The Language of Chance This task provides students with the opportunity to demonstrate their standard achievement of the following outcome(s): Students Learn about Students Learn to A student: develops a positive attitude to mathematics and appreciates its capacity to provide enjoyment and recreation develops rules to represent patterns arising from numerical and other sources performs simple calculations in relation to the likelihood of familiar events justifies his/her response to a given problem using appropriate mathematical terminology. ordering everyday events from the very unlikely to the almost certain using a list or table to identify the sample space (set of all possible outcomes) of a simple experiment or game performing experiments and determining whether or not the outcomes are equally likely Description of Activity: First to Twenty One: The game First to 21 gives students opportunities to explore the differences between mathematical and social fairness. With the deck of cards, each player takes one and adds up the value of the cards they pick until they reach the value of 21 or over. The last player who picks that card reaching 21 or over wins. Presentation mode: 1. Students will be working in pairs. For each pair, they should have a tally sheet where they record who wins per game and how many games were played. 2. On a deck of cards, set aside all the cards for 4,5,6,7 and 8 cards and keep the rest of the cards except for the 20 cards. Shuffle these remaining cards and place the deck face down. 3. Player 1 goes first and chooses the top card and says its value. Player 2 does the same and adds the value of his card to that of Player 1’s. The two players take turns taking a card and announcing its value, adding it to the combined value (sum of first two values). This keeps on until one player takes a value to be added to the combined value to reach 21 or over, then that player wins. 4. Students are encouraged to play the game at least 50 times. In repeated games, the students will realize a pattern that player 2 almost always wins the game. Because there is a high statistical probability of winning the game for the person who draws the fourth card. 5. First to 21 is not fair game because players do not have an equal chance of winning. That is because player 1 draws cards 1, 3 and if needed, 5 while player 2 draws cards 2 and 4. There is not as many winning three draw combinations as there is with four draw combinations. 6. Teacher processes the pattern of the player 2 winning most of the games by looking into the percentages each player wins and investigates with the concept of chances and probability using this example. Resources required: Tally sheet Deck of cards Pen Criteria for assessing learning outcomes (rubric): The following outcomes are assessed to see if tasks have been effective: Student has developed a positive attitude towards games of chances Student recognizes patterns arising from numerical and turn combinations. Student performs simple calculations in relation to the likelihood of familiar events Student realizes the logic of probability enough not to take things personally. Student justifies his/her response to a given problem using appropriate mathematical terminology. Feedback: The game First to 21 involves students experientially in understanding the concepts of probability rather than simply talking to them about it. Player 1 seems to be on the losing end all the time giving students an experience of mathematical unfairness. This concept may conflict with their understanding of social fairness, however, processed effectively, students will get to delineate the two and understand that there are things that they have no control over just because it is chance and probability. Applied to real life, they just have to play their cards right, so to speak. Read More