Student Learning Targets:

Reasoning Targets

• I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in mathematical problems in two and three dimensions.
  

Skills Domain (Performance) Targets

• I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world problems in two and three dimensions.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

• www.bigideasmath.com
  • Chapter 6 
• www.mathisfun.com
• www.khanacademy.org
  
  • try searching Pythagorean Theorem examples
• ccssmath.org

Vocabulary

• Pythagorean Theorem
• Leg
• Hypotenuse
• Right Triangle

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-8.2.4 Apply the Pythagorean Theorem to problems involving right triangles

**MAT-9-10-2.6 Use distance, midpoint, and slope to determine relationships between points, lines, and plane figures in the Cartesian coordinate system; e.g., determine whether a triangle is scalene, isosceles, or equilateral given the coordinates of its vertices.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-7.4.8. Use formulas to determine the volume of right cylinders

***MAT-8.4.3 Use formulas to determine the surface area and volume of right cones and spheres

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

Standards in this Domain

• MAT-08.NS.01 - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

• MAT-08.NS.02 - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ∏²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.1.3 Find the equivalent forms among fractions, decimals, and whole number percents

*MAT-8.1.1 Identify subsets of the real number system; i.e., natural and whole numbers, integers, rational and irrational numbers

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

Comparison to ND 2005 Mathematics Standards/Benchmark

Not Addressed

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

Standards in this Domain

• MAT-08.SP.01 - Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

• MAT-08.SP.02 - Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

• MAT-08.SP.03 - Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

• MAT-08.SP.04 - Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-8.3.2 Collect, organize, and display data using scatter and stem-and-leaf plot

***MAT-9-10.3.2. Interpret a given visual representation (i.e., circle graphs, bar graphs, histograms, stem-and-leaf plots, box-and-whisker plots, and scatter plots) of a set of data

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-11-12.3.4 Given a set of data exhibiting a linear trend, approximate an equation for the line of best fit (with or without technology) and use that model to make predictions

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

Comparison to ND 2005 Mathematics Standards/Benchmark

Not Addressed

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards