Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-5.2.7 Describe properties of congruent (BPS: and similar figures with proportionality) figures and use them to solve problems

*MAT-7.2.4 Identify relationships between congruent figures and similar figures

*MAT-2.2.5. Identify congruent figures from a selection of similar figures

*MAT-4.2.4 Use motion geometry to show that shapes are congruent or similar

*MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

• *** 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-9-10.4.2 Describe the effects of scalar change on the area and volume of a figure; eg., the effects of doubling one or more edges of a solid on its surface area and volume.

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

• *** 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-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

*MAT-7.2.4 Identify relationships between congruent figures and similar figures

• *** 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-8.2.3 Identify the angles formed and the relationships between the angles when parallel lines are intersected by a transversal

• *** 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

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