IXL - Utah eighth-grade math standards

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Standards document:

2010 Common Core State Standards 2010 Common Core State Standards
2007 Utah Core Curriculum 2007 Utah Core Curriculum

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7-8.1 Students will expand number sense to understand, perform operations, and solve problems with rational numbers.

7-8.2 Students will use proportion and similarity to solve problems.

7-8.2.1 Model and illustrate meanings of ratios, percents, and decimals.
7-8.2.1.a Compare ratios to determine if they are equivalent.
7-8.2.1.b Compare ratios using the unit rate.
7-8.2.1.c Represent percents as ratios based on 100 and decimals as ratios based on powers of ten.
7-8.2.1.d Graph proportional relationships and identify the unit rate as the slope of the related line.
7-8.2.2 Solve a wide variety of problems using ratios and proportional reasoning.
7-8.2.2.a Set up and solve problems involving proportional reasoning using variables.
7-8.2.2.b Solve percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.
7-8.2.2.c Solve ratio and rate problems using informal methods.
7-8.2.3 Recognize similar polygons and use properties of similar triangles to solve problems and define the slope of a line.
7-8.2.3.a Define similar polygons as polygons with corresponding angles congruent and corresponding sides that are proportional.
7-8.2.3.b Identify pairs of similar triangles using two pairs of congruent angles, or two pairs of proportional sides with congruent included angles.
7-8.2.3.c Find missing lengths of similar triangles, including inaccessible lengths, using proportions.
7-8.2.3.d Define the slope of a line as the ratio of the vertical change to the horizontal change between two points, and show that the slope is constant using similarity of right triangles.

7-8.3 Students will develop fluency with the language and operations of algebra to analyze and represent relationships.

7-8.4 Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

7-8.4.1 Apply the properties of proportionality of different units of measure.
7-8.4.1.a Convert units of measure within the same system.
7-8.4.1.b Create and interpret scale drawings and approximate distance on maps using scale factors.
- Ratios and proportions: Scale drawings and scale factors (Seventh grade - J.13)
- Ratios and proportions: Scale drawings and scale factors (Eighth grade - H.13)
7-8.4.1.c Solve problems using scale factors.
7-8.4.2 Derive formulas for surface areas and volume of three-dimensional figures.
7-8.4.2.a Derive formulas for and calculate surface area and volume of right prisms and cylinders using appropriate units.
7-8.4.2.b Explain that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related and the cube of the scale factor describes how corresponding volumes are related.
7-8.4.2.c Find lengths, areas, and volumes of similar figures, using the scale factor.
7-8.4.2.d Select appropriate two- and three-dimensional figures to model real-world objects, and solve a variety of problems involving surface areas and volumes of cylinders and prisms.

7-8.5 Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

7-8.5.1 Calculate probabilities of events and compare theoretical and experimental probability.
7-8.5.1.a Solve counting problems using the Fundamental Counting Principle.
7-8.5.1.b Calculate the probability of an event or sequence of events with and without replacement using models.
7-8.5.1.c Recognize that the sum of the probability of an event and the probability of its complement is equal to one.
- Probability: Probability of opposite, mutually exclusive, and overlapping events (Seventh grade - Z.2)
- Probability: Probability of opposite, mutually exclusive, and overlapping events (Eighth grade - BB.2)
7-8.5.1.d Make approximate predictions using theoretical probability and proportions.
7-8.5.1.e Collect and interpret data to show that as the number of trials increases, experimental probability approaches the theoretical probability.
7-8.5.2 Formulate questions and answer the questions by organizing and analyzing data.
7-8.5.2.a Formulate questions that can be answered through data collection and analysis.
7-8.5.2.b Determine the 25th and 75th percentiles (first and third quartiles) to obtain information about the spread of data.
- Statistics: Quartiles (Eighth grade - CC.5)
7-8.5.2.c Graphically summarize data of a single variable using histograms and box-and-whisker plots.
7-8.5.2.d Compute the mean and median of a numerical characteristic and relate these values to the histogram of the data.
7-8.5.2.e Use graphical representations and numerical summaries to answer questions and interpret data.