Area Units Model

• Overall dimensions: 14.7 x 14.7 cm
• Material: durable safe material
• Design: square base divided into equal square units, with a set of removable elements
• What it shows: the structure of square units and the relations between units of area
• Method of demonstration: laying out and rearranging the elements within the plane of the base
• Application: proving and illustrating statements about the areas of geometric figures, including equality of areas of figures composed of the same parts, additivity of area and equal-area figures

Product passport: ULABS-M004 (PDF)

Operation

• Unpack the product and check its completeness against the list of elements. Inspect the edges: burrs, flash and chips that prevent the elements from fitting tightly against one another are removed with fine-grained abrasive paper.
• Check that all elements go freely into the base and come out of it without sticking in the recesses. Elements laid edge to edge must leave no visible gaps: the whole demonstration rests on this tight fit.
• Before the lesson, measure with a ruler the side of a cell of the base and the side of a unit square on the product itself. The overall size of 14.7 x 14.7 cm does not set the pitch of the grid, so without this check a cell cannot be treated as a square centimetre: the model shows the relations in its own unit squares.
• Place the base on the demonstration desk so that its plane is well visible to the whole class, and sort the elements by shape and size beside it.
• Unit square: show a single square element and agree to treat its area as the unit. Place it against the grid of the base and confirm that it covers exactly one cell.
• Area of a figure: lay out an arbitrary figure on the base with several unit squares, edge to edge, without gaps or overlaps. The number of squares used is the area of the figure.
• Larger unit of area: compose a larger square from unit squares, its side containing several unit segments, and count how many unit squares it took. The larger square contains as many unit squares as the product of the number of unit segments of its side by itself.
• Comparing figures: lay out two figures of different shape on the base and place the elements of one onto the other. If all elements fit with nothing left over, the figures are equal in area; if cells remain free, the areas differ by the number of uncovered unit squares.
• Proof by rearrangement: break a figure down into its elements and compose another figure from the same elements. The set of parts has not changed, so the areas of both figures are equal; this is the basis of the proofs of the area formulas for a rectangle, a triangle and a parallelogram.
• After the demonstration, return the elements to their initial position and check the count against the number of elements in the base.

Safety

• Use the product only for the purpose described in the passport; students work with it under the supervision of a teacher.
• Recommended for learners aged 10 years and older (grade 5 and above) in general secondary education institutions.
• Protect the product from impacts, falling, excessive mechanical loads, moisture, direct sunlight and heaters.
• Keep small components in the supplied packaging and check completeness after every lesson: without one element the figure cannot be laid out and the proof cannot be completed.
• Do not use the elements as a ruler, a prop or a cutting mat: a chipped edge no longer gives a tight fit.

Maintenance

• Wipe the base and the elements with a soft dry or slightly damp cloth. Do not use abrasive powders or solvent cleaners: a scratched surface loses contrast, and a worn grid makes counting the unit squares impossible.
• Do not leave the product under load or near heaters: pressure and heat warp the base and the elements stop fitting tightly into it.

Storage and Transport

• Storage temperature: +5 °C to +40 °C, relative humidity 60 percent, non-condensing, in a dry, clean, ventilated room protected from direct sunlight, moisture, dust and heat sources.
• Operating conditions: air temperature +5 °C to +40 °C, relative humidity 40 to 60 percent, atmospheric pressure 84 to 107 kPa.
• Put the elements into the base and the model into its packaging; keep the storage place dry.
• The product is supplied packed in the manufacturer's packaging; during transport, protect the packing from precipitation and impacts.

Compliance and Disposal

• The product complies with the general product safety requirements established by European Union legislation.
• The product is not electrical or electronic equipment, therefore the WEEE marking does not apply to it.
• The product contains no hazardous substances and is disposed of as municipal solid waste after separation by material.

Warranty

• Repair of defects and replacement of defective parts or covered equipment for three (3) years.
• Availability of spare parts and consumables for five (5) years.