Development of content understanding (key concepts and ideas)
Students will know and be able to use the following exponential rules:
- Bases must be the same before exponents can be added, subtracted or multiplied.
- Exponents are subtracted when like bases are being divided.
- A number raised to the zero power is equal to one.
- Negative exponents occur when there are more factors in the denominator. These exponents can be expressed as a positive if left in the denominator.
- Exponents are added when like bases are being multiplied.
- Exponents are multiplied when an exponent is raised to an exponent.
- Several properties may be used to simplify an expression (North Carolina Unpacked Standards).
Students will also be able to apply these exponent rules to simplify expressions that contain numbers written in scientific notation. They will know how to convert between scientific notation and regular notation and to compare two numbers written in scientific notation.
Enabling students to experience the power of their minds and their capacities as learners and doers (powerful learning)
Throughout this entire unit, student will repeatedly figure out the rules of exponents and scientific notation for themselves by identifying and explaining patterns. Students then become positioned as teachers and are asked to share their knowledge with their classmates, taking care to explain the rules in the simplest, most understandable way possible.
Development of intellectual and academic habits of mind, work, and discourse, including habits of independent or collaborative thinking and doing typical of readers, writers, speakers, creators, researchers and thinkers in the discipline (ways of knowing)
Students will focus on the all-important mathematical habit of pattern-seeking. In the first part of the unit, they are tasked with finding a pattern that will reveal an exponent rule and then figuring out how to effectively communicate that pattern/rule to their classmates. In the second part of the unit, students will need to figure out how to apply those exponent rules that they discovered to scientific notation; this ability to adapt concepts to new scenarios is a key part of mathematics. Students also will need to go through a mini-lesson planning process, which closely mirrors the habits of real math teachers.
Literacy development, including capabilities of proficient readers, writers, and speakers
There will be plenty of opportunities in this unit for students to practice developing their speaking abilities, for they must teach other students different rules and concepts. Their ability to present clear, evidence-based arguments becomes central to their success, as well as that of their classmates who need to learn from them.
Development of trust and the classroom as a learning community
The jigsaw will promote trust in the classroom, for students will depend on each other to learn the necessary material. Students are trusting that each teaching group will teach their topic so well that they will leave the jigsaw understanding all the exponent rules and how to use them to simplify expressions. Throughout the unit, students are positioned as active learners seeking to make sense of different concepts and hypothesizing patterns and connections. They will turn to each other for rejection or confirmation of their hypotheses about the exponent rules and their applications to scientific notation.