Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.
Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board?
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., – ( – 3) = 3; 0 is its own opposite).
Represent and/or solve realworld and mathematical problems using rates, ratios, and/or percents.
Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage.
Identify, write, and evaluate numerical and algebraic expressions.
Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Use variables to represent two quantities in a real-world problem that change in relationship to one another.
Display, analyze, and summarize numerical data sets in relation to their context.
Display numerical data in plots on a number line, including line plots, histograms, and box-andwhisker plots.
Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation).
Describe any overall pattern and any deviations from the overall pattern with reference to the context in which the data were gathered.
Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
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