General Information
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Test Item Specifications
s Square roots and cube roots may be used to represent solutions to equations. Radicands may not include variables.
Neutral
Allowable
Sample Test Items (3)
| Test Item # | Question | Difficulty | Type |
| Sample Item 1 | What is the value of p in the equation shown?
|
N/A | EE: Equation Editor |
| Sample Item 2 | A cube with an edge of length s has a volume of 64 units. What is the length of s? |
N/A | EE: Equation Editor |
| Sample Item 3 | A square is cut in half on the diagonal, creating two equal triangles. Each triangle has an area of 0.32 square units. What is the side length, in units, of the original square? |
N/A | EE: Equation Editor |
Related Courses
| Course Number1111 | Course Title222 |
| 1205050: | M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 1205070: | M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 1204000: | M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 7812030: | Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current)) |
| 7912115: | Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated)) |
Related Resources
Formative Assessments
| Name | Description |
| Roots and Radicals | Students are asked to solve simple quadratic and cubic equations and represent solutions using square root and cube root symbols. |
| The Root of the Problem | Students are asked to evaluate perfect square roots and perfect cube roots. |
| Dimensions Needed | Students are asked to solve problems involving square roots and cube roots. |
Lesson Plans
| Name | Description |
| Generalizing Patterns: The Difference of Two Squares | This lesson is designed to help teachers assess how well students can work with square numbers. Upon completion of the lesson, students should be able to describe and explain their findings and why results are possible or impossible. This lesson is a bridge towards proofs. The materials required for this lesson are worksheets, plain paper, large sheets of paper for making posters, and felt-tip pens. The entire lesson requires 110 minutes, broken down into a 20-minute pre-lesson, an 80-minute lesson (or two 40-minute lessons), and a 10-minute follow-up lesson. |
| Discovering Kepler's Law for the Periods of Planets | Students listen to a video that describes Kepler's determination that planetary orbits are elliptical and then will use data for the solar distance and periods of several of the planets in the solar system, then investigate several hypotheses to determine which is supported by the data. |
Original Student Tutorials
| Name | Description |
| Square Root Part 3: Simplifying Radicals | Learn how to simplify radicals in this interactive tutorial. |
| Square Root Part 2: Non-Perfect Squares | Learn what non-perfect squares are and find the decimal approximation of their square roots in this interactive tutorial. |
| Square Root Part 1: Perfect Squares | Learn what perfect squares are and find their square roots in this interactive tutorial. |
Tutorials
| Name | Description |
| Finding the square root of a decimal | Students will learn how to find the square root of a decimal number. |
| Finding cube roots | Learn how to find the cube root of -512 using prime factorization. |
| Introduction to cube roots | Students will learn the meaning of cube roots and how to find them. Students will also learn how to find the cube root of a negative number. |
| Introduction to square roots | Students will earn about the square root symbol (the principal root) and what it means to find a square root. Students will also learn how to solve simple square root equations. |
Student Resources
Original Student Tutorials
| Name | Description |
| Square Root Part 3: Simplifying Radicals: | Learn how to simplify radicals in this interactive tutorial. |
| Square Root Part 2: Non-Perfect Squares: | Learn what non-perfect squares are and find the decimal approximation of their square roots in this interactive tutorial. |
| Square Root Part 1: Perfect Squares: | Learn what perfect squares are and find their square roots in this interactive tutorial. |
Tutorials
| Name | Description |
| Finding the square root of a decimal: | Students will learn how to find the square root of a decimal number. |
| Finding cube roots: | Learn how to find the cube root of -512 using prime factorization. |
| Introduction to cube roots: | Students will learn the meaning of cube roots and how to find them. Students will also learn how to find the cube root of a negative number. |
| Introduction to square roots: | Students will earn about the square root symbol (the principal root) and what it means to find a square root. Students will also learn how to solve simple square root equations. |