Inequalities

Solve word problems leading to inequalities of the form 𝑝𝑝𝑝𝑝+𝑞𝑞>𝑟𝑟or 

𝑝𝑝𝑝𝑝+𝑞𝑞<𝑟𝑟where p, q, and r are specific rational numbers and 𝑝𝑝>0.  (7.EE.4b)

Use variables to represent quantities in a real-world or mathematical problem, and construct two-step equations and inequalities to solve problems by reasoning about the quantities. (7.EE.4)

Random Samples and Populations

Use statistics to gain information about a population by examining a sample of the population. (7.SP.1)

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to informally gauge the variation in estimates or predictions. (7.SP.2)

Experimental Probability

Express the probability of a chance event as a number between 0 and 1 that represents the likelihood of the event occurring. (7.SP.5)

Collect data from a chance process (probability experiment). Approximate the probability by observing its long-run relative frequency. Recognize that as the number of trials increase, the experimental probability approaches the theoretical probability. (7.SP.6)

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (7.SP.8)

Theoretical Probability and Simulations

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (7.SP.7a)

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (7.SP.8)

Collect data from a chance process (probability experiment). Approximate the probability by observing its long-run relative frequency. Recognize that as the number of trials increase, the experimental probability approaches the theoretical probability. (7.SP.6)

Design and use a simulation to generate frequencies for compound events. (7.SP.8c)

Modeling Geometric Figures

Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (7.G.1)

Identify three-dimensional objects generated by rotating a two-dimensional (rectangular or triangular) object around one edge. (7.G.2)

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right cylinder. (7.G.3)

Investigate the relationship between three-dimensional geometric shapes. (7.G.5)

Circumference, Area, and Volume

Use the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (7.G.4)

Solve real-world and mathematical problems involving area of two-dimensional objects and volume and surface area of three-dimensional objects including cylinders and right prisms. (7.G.6)

Analyzing and Comparing Data

Use measures of center (mean, median and/or mode) and measures of variability (range, interquartile range and/or mean absolute deviation) for numerical data from random samples to draw informal comparative inferences about two populations. (7.SP.4)

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. (7.SP.3)