We are beginning a new unit of study that involves irrational numbers, particularly square roots, and the Pythagorean Theorem. We start by examining perfect square numbers and the definition of square root both in theory and in context of geometry. Students will estimate the value of irrational square roots to between two integers and then to different place values. Students will be expected to find missing values in equations involving squares and square roots. They will also examine what happens when squaring a square root and if equality is maintained when adding, subtracing, multiplying and dividing square roots. Once square rooting is more comfortable, we will move into using square roots to find missing side lengths in right triangles and finding diagonal lengths on polygons and on coordinate grids. Students will use the Pythagorean Theorem to find the missing lengths and to determine if triangles are right triangles. They will also examine a geoemtric proof of the Pythagorean Theorem.
Common Core Math, Grade 8 Content Standards
- Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
- Work with radicals and integer exponents.
- Understand the connections between proportional relationships, lines, and linear equations.
- Analyze and solve linear equations and pairs of simultaneous linear equations.
- Define, evaluate, and compare functions.
- Use functions to model relationships between quantities.
- Understand congruence and similarity using physical models, transparencies, or geometry software.
- Understand and apply the Pythagorean Theorem.
- Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability
- Investigate patterns of association in bivariate data.
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
For more information: http://www.corestandards.org/Math/Content/8/introduction/