In this lesson, students compare experimental results with mathematical expectations of probabilities and determine odds for and odds against a given situation.
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Each of the 20 students in Mr. Anderson's class flipped a coin ten times and recorded how many times it came out heads. How many heads do you think you...
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Students create their own spinners and examine the outcomes given a specified number of spins in this student interactive, from Illuminations. Students learn that experimental probabilities differ according to the characteristics of the model. Students can also discuss how does the experimental probability compare with the theoretical probability?
CK-12 Middle School Math Concepts for seventh grade provides a complete textbook. It presents topics including algebraic thinking, patterns, decimals, decimal operations, fractions, fraction operations, integers, integer operations, ratios, rates, proportions, percents, percent applications, equations, solving equations, inequalities, functions, graphing functions, geometry, plane geometry, solid geometry, area, perimeter, surface area, volume, statistics including mean, median, mode and range, graphing and types of graphs, and probability.
In this lesson, students estimate probabilities by collecting data on an outcome of a chance experiment. Students use given data to estimate probabilities.
Students randomly select jelly beans (or other candy) that represent genes for several human traits such as tongue-rolling ability and eye color. Then, working in pairs (preferably of mixed gender), students randomly choose new pairs of jelly beans from those corresponding to their own genotypes. The new pairs are placed on toothpicks to represent the chromosomes of the couple's offspring. Finally, students compare genotypes and phenotypes of parents and offspring for all the "couples" in the class. In particular, they look to see if there are cases where parents and offspring share the exact same genotype and/or phenotype, and consider how the results would differ if they repeated the simulation using more than four traits.
In this lesson, students compare mathematical expectations and experimental probability; then explain any difference in the two numbers. Students use colored candy pieces (such as M & M's) for their data collection, comparisons, and explanations.
Students redesign and justify the packaging used in consumer products. Design criteria include reducing the amount of packaging material by 25%.
In this lesson, students determine the possible outcomes for simple chance experiments. Given a description of a simple chance experiment, students determine the sample space for the experiment. Given a description of a chance experiment and an event, students determine for which outcomes in the sample space the event will occur. Students distinguish between chance experiments with equally likely outcomes and chance experiments for which the outcomes are not equally likely.
Sample Learning Goals
Predict the bin where a single ball might fall
Repeat trials of 100 balls and compare the outcomes
Count the number of balls in a bin and relate that to the probability of falling in that bin
Compare and interpret empirical and theoretical statistics
Apply the plinko simulation as a model to other scenarios where there are weighted statistics
In this unit students will be able to understand the idea of likelihood, manipulate the mathematical formulas for probability and relative frequency, calculate possible outcomes, and make predictions of the probability of an event.
This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 7th Grade Math.
This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 7th Grade Math.
This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 7th Grade Math.
his task is intended as a classroom activity. Student pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.
With this task, students solve problems related to statistics and probability.
Given theoretical probabilities based on a chance experiment, students describe what they expect to see when they observe many outcomes of the experiment. Students distinguish between theoretical probabilities and estimated probabilities. Students understand that probabilities can be estimated based on observing outcomes of a chance experiment.
The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data.