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Math Mammoth Statistics & Probability is a worktext covering graphing, statistics, and probability topics for 4th- 7th grades. Being a worktext means that it contains both the instruction and exercises.
The book starts with the easiest topics: reading and making bar graphs, histograms, various kinds of line graphs, and circle graphs. Most of these lessons are best suited for 4th and 5th grades. However, to create circle graphs, the student needs to calculate percentages, which is normally studied in 6th grade, so this lesson may be left for 6th or 7th grade.
The next section deals mostly with the concept of average, including how average and mode relate to bar graphs. This is also meant for 4th-5th graders.
The rest of the statistics lessons are for about 6th grade level, starting with the lesson, Understanding Distributions. The concept of distribution is a fundamental theme in the study of statistics. A distribution is basically how the data is distributed. The distribution can be described by its center, spread, and overall shape. The shape is read from a graph, such as a dot plot or bar graph.
Two major concepts when summarizing and analyzing distributions are its center and its variability. We study the center in the next lessons about mean, median, and mode. Students not only learn to calculate these values, but also relate the choice of measures of center to the shape of the data distribution and the type of data. In the lesson Measures of Variation we study range, interquartile range, and mean absolute deviation. The last one takes many calculations, and the lesson gives instructions on how to calculate it using a spreadsheet program, such as Excel.
Then in the next lessons, students learn to make several different kinds of graphs: histograms, boxplots, and stem- and-leaf plots. In those lessons, students continue summarizing distributions by giving their shape, a measure of center, and a measure of variability.
The book also includes an optional statistics project, in which the student can develop investigative skills.
Probability is a topic that in the past was only taught in high school—for example, I personally encountered it the first time in 12th grade. However, in recent years it has "crept" down the grade levels. The most recent standards, The Common Core Standards, require the study of probability in 7th grade.
We start with the concept of simple (classic) probability, and then expand into probability involving two events. The exercises involve tree diagrams, dice, flipping coins, picking marbles, using spinners, and probability involving statistics, which are the usual types of situations in the study of probability.
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