Spatial Sense · SHS1 Additional Mathematics

Lesson notes

Learning Objectives

Indicator: 1.2.1.LI.7 - Determine the acute angles between two intersecting lines with the aid of technological tools, e.g. GeoGebra.

By the end of the lesson, learners can:

Use GeoGebra (or an equivalent technological tool) to plot two intersecting lines and measure the angles formed at their point of intersection.
Identify which of the four angles formed by two intersecting lines is the acute angle, and state its measure in degrees.
Verify, using a technological tool, that the acute angle and the obtuse angle at the intersection are supplementary (they add up to 180 degrees).
Explain, in their own words, the relationship between the angle shown by a measuring tool and the acute angle between the lines when the tool displays the obtuse angle.
Communicate their findings clearly to a partner and to the whole class, using appropriate mathematical vocabulary such as “intersection”, “acute angle”, “obtuse angle” and “supplementary”.

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Curriculum details

Strand: Geometric Reasoning and Measurement (Strand 2)
Sub-strand: Spatial Sense (2.1)
Content standard: 1.2.1.CS.1 - Demonstrate knowledge and understanding of spatial sense in relation to lines and angles between intersecting lines. 1.2.1.LO.1 Describe the properties of lines, including parallel, perpendicular and midpoints. 1.2.1.LO.2 Derive the equation of a line in various forms, find the shortest distance between a point and a line and the perpendicular distance from an external point to a line. 1.2.1.LO.3 Solve problems on acute angles between two intersecting lines. 1.2.1.LO.4 Perform algebraic manipulations of Vectors and resolve vectors using the triangle, parallelogram and polygon laws of addition.
Indicator: 1.2.1.LI.7 - Determine the acute angles between two intersecting lines with the aid of technological tools, e.g. GeoGebra.
Suggested placement: Semester 2, Week 3 (Week 23 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. 154

Exemplars (from the NaCCA curriculum)

Learning experience: In pairs, learners manipulate technological tools to ascertain the acute angles of two intersecting lines.
Activity 1: Think pair and explore technological tools.
- Learners in pairs manipulate and explore available ICT tools individually to ascertain the acute angles of two intersecting lines.
- Learners share their experiences and findings from using the ICT tools.
Teaching and Learning Resources:
- SHS Curriculum
- Mathematical set calculators.
Assessment (1.2.1.AS.7). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 4 Extended critical thinking and reasoning.