Measurement · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.3.2.LI.1 - Solve problems that involve identifying and comparing referents for SI and imperial area measurements of regular, composite and irregular 2D shapes, including decimal and fractional measurements and verify the solutions.

By the end of the lesson, learners can:

Identify at least three common referents for SI area measurements (cm², m², km²) and three for imperial area measurements (in², ft², yd²) and state the approximate size each referent represents.
Compare and order SI and imperial area measurements by converting between the two systems using given conversion factors.
Estimate the area of regular, composite and irregular 2D shapes using appropriate referents, including shapes with decimal and fractional dimensions.
Solve word problems involving area measurements in both SI and imperial units, showing all working and verifying solutions by checking reasonableness against referents.
Justify the choice of a particular referent for estimating a given area measurement in a practical situation.

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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.1 - Solve problems that involve identifying and comparing referents for SI and imperial area measurements of regular, composite and irregular 2D shapes, including decimal and fractional measurements and verify the solutions.
Suggested placement: Semester 2, Week 7 (Week 27 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. 119

Exemplars (from the NaCCA curriculum)

Experiential Learning: In small groups, learners identify and compare referents for area measurements in SI and imperial units.
Example: Learners in groups investigate to validate t you tube he following referents in the tables.
Referents for Linear Measurement

Table row giving referents for an inch: thumb length and the thickness of a hockey puck. — A table with a green header reading "Imperial Measurement" and "Referent". The row shown reads "Inch - Thumb length; Thickness of a hockey puck;".

 Imperial Referent Measurement Inch Thumb length; Thickness of a hockey puck; Foot A standard floor tile in a classroom

Table row giving referents for a yard: an arm span from the nose, and the length of a guitar. — A table row reading "Yard - An arm span from the tip of the nose, a yardstick length of a guitar".

 Yard An arm span from the tip of the nose, a yardstick length of a guitar Mile Distance walked in 20 minutes, lights to the railway crossing.

Table row giving referents for millimetres: the thickness of a dime or a fingernail. — A table with a green header reading "SI Measurement" and "Referent". The row shown reads "millimetres - Thickness of a dime or fingernail".

 SI Measurement Referent millimetres Thickness of a dime or fingernail centimetres width of a fingernail, black keys on a piano, crayon, paper clip, or AA battery

Table row giving referents for a metre: doorknob height, volleyball net width, metre stick, waist height. — A table row reading "meter - distance from a doorknob to the floor, width of a volleyball net, meter stick, waist height".

 meter distance from a doorknob to the floor, width of a volleyball net, meter stick, waist height kilometre Distance walked in 15 minutes, lights to the bridge.
Referents for Area

Table row: the area of a floor tile is about 1 square foot. — A table with a green header reading "Referent" and "Measurement". The row shown reads "Area of a floor tile - approximately 1 square foot".

 Referent Measurement
Area of a floor tile ≈1 ft 2 Area of a postage stamp ≈1 in 2

Table row: the area of a fingernail is about 1 square centimetre. — A table row reading "Area of a fingernail - approximately 1 square centimetre".

 Area of a fingernail ≈1 cm 2 Area of an exterior house ≈ 2 m 2 door

Table row: an exercise notebook is about 93.5 square inches or 600 square centimetres. — A table row reading "Area of exercise notebook - approximately 93.5 square inches or 600 square centimetres".

 Area of exercise notebook ≈ 93.5 in 2 or 600 cm 2 Area of an ice rink surface ≈ 1500 m 2 or 17 000 ft 2

Table row: a sheet of plywood is about 32 square feet or 3 square metres. — A table row reading "Area of a sheet of plywood - approximately 32 square feet or 3 square metres".

 Area of a sheet of plywood ≈ 32 ft 2 or 3 m 2
Experiential Learning: In mixed-gender/ability groups, engage learners to use their experiences from their investigations on referents for linear and area measurements to estimate an area measurement using a referent.
Teaching and Learning Resources:
- Mathematical sets.
- Technology tools such as computers, mobile phones, etc.
- Computer software applications like GeoGebra.
Assessment (1.3.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.