Real Number System · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.1.1.LI.1 - Develop the real number system using the closure property.

By the end of the lesson, learners can:

Define the subsets of the real number system (natural numbers, whole numbers, integers, rational numbers, irrational numbers) and state examples of each.
Explain the closure property of an operation on a set in their own words.
Determine whether given subsets of real numbers are closed under addition, subtraction, multiplication, and division by testing examples and counterexamples.
Identify which subsets of the real number system are closed under which operations and present findings to the class.
Apply the closure property to decide whether the sum, difference, product, or quotient of two numbers in a given set remains in that set.

Sign in with your phone number to read the full note and download the GES plan - free.

Sign in with phone number

Curriculum details

Strand: Numbers for Everyday Life (Strand 1)
Sub-strand: Real Number System (1.1)
Content standard: 1.1.1.CS.1 - Demonstrate knowledge and understanding of real number systems and the operations of the various subsets. 1.1.1.LO.1 Apply the relationships and differences between the set of rational and irrational numbers and use them to solve problems.
Indicator: 1.1.1.LI.1 - Develop the real number system using the closure property.
Suggested placement: Semester 1, Week 1 (Week 1 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 29

Exemplars (from the NaCCA curriculum)

Problem-based Learning, Talk for Learning, Experiential Learning, and Group Work/Collaborative Learning. Review learners' knowledge of basic concepts of numbers, deal with their misconceptions or preconceptions about such concepts, audit their difficulties and transition to develop the set of real numbers, using closure properties and applying such to solve real life problems. While doing so, encourage learners to be truthful and honest in their responses within their collaborative groups.
Examples: i. Establish, through a variety of differentiated strategies, the set of real numbers (rational and irrational) using models such as number lines, number tracks, algebraic tiles, multibase arithmetic blocks, etc., in a socio-emotional learning environment that ensures the development of values such as diversity, equity and respect for others.
ii. Extend the closure property to determine if the subsets of real numbers are closed with respect to addition (+), multiplication (*), division (÷) and subtraction (-). Include steps for establishing other properties of real numbers (i.e., additive and multiplicative inverses, distributive, etc.). Be mindful of values such as self-confidence, diversity and leadership in achieving strategic critical thinking.
Teaching and Learning Resources:
- Fractional boards
- square or grid paper
- multi-base blocks
- algebraic tiles
- video clips
- cardboards
- models
- SHS Mathematics curriculum
- Technology tools: computer, mobile phone, calculator, YouTube videos, etc.
- Number line
- Number track
- Wheel of Theodorus.
- Twine
- cylinders
- Tape measure or rule.
Assessment (1.1.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.