Measurement · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.3.2.LI.2 - Estimate the perimeter and area of a given regular, composite or irregular 2D shape [kites, parallelogram, rhombus and trapezoids].

By the end of the lesson, learners can:

Estimate the perimeter of regular, composite and irregular 2D shapes by comparing side lengths and using referents (e.g., a stride, a hand span, or a known length such as a exercise book edge).
Estimate the area of a parallelogram, rhombus, kite, and trapezoid using the formula for each shape, and verify the estimate using a grid or graph paper.
Decompose a composite or irregular shape into simpler familiar shapes (rectangles, triangles, parallelograms) to estimate its total area.
Use the half-square rule to estimate the area of irregular shapes on a grid where parts of squares are occupied.
Justify their estimation strategy in writing or orally, comparing estimates from different methods and explaining which is more accurate and why.

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Curriculum details

Strand: Geometry Around Us (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: 1.3.2.CS.3 - Demonstrate conceptual understanding of the measurement of perimeter and area of circles and quadrilaterals. 1.3.2.LO.3 Identify and compare referents for SI and imperial area measurements, estimate the perimeter and area of 2D shapes [kites, parallelogram, rhombus and trapezoids], and volume of prisms, and solve problems that involve a given regular, composite or irregular 2D shapes.
Indicator: 1.3.2.LI.2 - Estimate the perimeter and area of a given regular, composite or irregular 2D shape [kites, parallelogram, rhombus and trapezoids].
Suggested placement: Semester 2, Week 8 (Week 28 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. 121

Exemplars (from the NaCCA curriculum)

Experiential Learning: In small groups, engage learners to investigate the area of 2-D shapes (both regular and irregular) and estimate the perimeter using geodot.
Example 1: Find the area of the shape on the grid:

A tilted blue square on a grid, its area counted as four whole cells numbered 1 to 4 and eight half cells. — A square grid with a blue square drawn on it at 45 degrees, so its corners meet the grid lines. Its cells are counted for area: the four whole cells are numbered 1, 2, 3 and 4 and the eight triangular part-cells around the edge are each marked one half.

Solution: For this problem, some part of the shape does not occupy complete squares. Because of that, we need to approximate its perimeter. If it occupies about 1/2 of the unit square, we can combine two such halves to form an area of 1 square unit.
Example 2: Find the area of the shape:

A blue arrow-shaped polygon drawn on a square grid. — A blue arrow-shaped polygon drawn on a square grid, pointing to the right, with a notch cut into its tail.

Solution: Think! We will first have to decompose it and rearrange the pieces into a shape that will make it easy to

Three grids showing a blue triangle cut and rearranged into a rectangle to find its area. — Three square grids in a row joined by arrows, showing a blue triangle being cut and rearranged: first the triangle alone, then with a cut line and the cut piece shaded, then the pieces reassembled inside a rectangle. The words "determine the area." sit to the right.

 determine the area.
Example 3: Investigate the perimeter and area of the following shapes.

Three grid shapes: a step polygon marked 2, 5, 4; a square frame 6 with a 2 hole; a pentagon marked 3, 2, 2, 6. — Three shapes on square grids, labelled A, B and C. A is a step-shaped polygon with edges marked 2, 5 and 4; B is a square frame with outer edges marked 6 and a square hole marked 2; C is a house-shaped pentagon with edges marked 3, 2, 2 and 6.

A rhombus with diagonals d1 and d2 and a parallelogram with base b and height h, each with its area formula. — Two yellow quadrilaterals with their area formulas. A rhombus with its diagonals d1 and d2 drawn carries "Area of a rhombus = one half times d1 times d2 square units"; a parallelogram with base b and height h carries "Area of a parallelogram = base times height = b times h square units".

Teaching and Learning Resources:
- Mathematical sets.
- Technology tools such as computers, mobile phones, etc.
- Computer software applications like GeoGebra.
Assessment (1.3.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.