Wayne RESA

Unit PlannerBig Ideas Math 8

Wayne Resa - Math / Grade 8 / Mathematics / Big Ideas Math 8 / Week 21 - Week 23
2 Curriculum Developers
Unit Abstract

Eighth Grade

  • Understand that every rational number has a decimal expansion that terminates or repeats.

  • Understand that numbers that are not rational are irrational.

  • Compare irrational numbers using rational approximations.

  • Evaluate square roots and cube roots, including those resulting from solving equations.

  • Explain a proof of the Pythagorean Theorem and its converse.

  • Use the Pythagorean Theorem to find missing measures of right triangles and distances between points in the coordinate plane.

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Expectations/Standards
MI: Mathematics
MI: Grade 8
The Number System
8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1. Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
Expressions & Equations
8.EE.A. Work with radicals and integer exponents.
8.EE.A.2. Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational.
Geometry
8.G.B. Understand and apply the Pythagorean Theorem.
8.G.B.6. Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.B.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
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Practice Standards

Students will have opportunities to:

  • SMP1 - Make sense of problems and persevere in solving them

  • SMP2 - Reason abstractly and quantitatively

  • SMP3 - Construct viable arguments and critique the reasoning of others

  • SMP4 - Model with Mathematics

  • SMP5 - Use appropriate tools strategically

  • SMP6 - Attend to precision

  • SMP7 - Look for and make use of structure

  • SMP8 - Look for and express regularity in reasoning

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Concepts from Previous Units

Sixth Grade

  • Fluently divide whole numbers.

  • Evaluate expressions with whole-number exponents.

  • Divide fractions.

  • Fluently add, subtract, multiply, and divide decimals.

  • Find distances between points with the same x- or y-coordinate.

Seventh Grade

  • Convert rational numbers to decimals using long division.

  • Add, subtract, multiply, and divide rational numbers.

  • Understand that every quotient of integers (non-zero divisor) is a rational number.

Connections to Upcoming Units

Geometry

  • Use the Pythagorean Theorem and the Converse of the Pythagorean Theorem.

  • Find side lengths and solve real-life problems involving special right triangles.

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Key Terms / Vocabulary

Teacher Edition Vocabulary: inverse operations, equal sides, square root, perfect square, radical sign, radicand, V=lwh, V=s2, cube root, perfect cube, theorem, legs, hypotenuse, Pythagorean Theorem, irrational number, real numbers, distance formula, converse, conjecture, expression, substitute, x-coordinate, y-coordinate


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Lesson Plan Sequence

The following lesson plan sequence is obtained from Big Ideas Learning (2015). Each lesson is aligned with a learning objective to inform the teachers on what students should be able to do at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day.

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Language Support

The use of sentence stems as a language support are beneficial to all students, including English Language Learners. The use of sentence stems encourages the learning of mathematics in a language rich environment which has an impact on other learning as well. The sentence stems are a beginning place for supporting students' use of academic language and encourage discussion and writing as students learn content.

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