This integrated unit combines measurement of area with multiplication, and algebraic thinking.
Area is an attribute, a characteristic of an object. The attribute of area is the space taken up by part of a flat or curved surface. Usually, we begin by helping students think of area as an attribute before formally measuring it. Use contexts in which students compare flat spaces by size such as comparing pancakes or footprints. Note that “biggest” may be perceived in different ways. The most common confusion is between area (the space covered) and perimeter (the distance around the outside).
Different contexts can be used to explore the attribute of area. In these lessons, the main context used is around measuring land. Suppose some students think that a playing field is bigger than another because they spend longer walking across one field. “How many steps would it take to cross each field?” is an example of an enabling prompt. Partitioning and combining shapes are also useful ways to promote understanding of conservation of area and can lay groundwork for ideas about the areas of triangles, rectangles, trapezia, parallelograms and other polygons in later years.
Formal measuring of area with units will only make sense to students if they relate their methods to the process of measuring other attributes such as length and mass. Students need to see the need for units and identify the qualities of units that are appropriate. They also need to realise that a number alone does not convey a measure unless the unit is stated as well.
Units require the following properties:
The standard units of area in real life are the square centimetre (cm2), square metre (m2), hectare (ha.) and square kilometre (km2). While the proportional difference between metres and centimetres is manageable with length, the proportional difference between square centimetres and square metres makes size comparison difficult.
Consider the relationship between square centimetres and square metres. There are 100 x 100 (i.e. 10 000) square centimetres in one square metre. That is the same relationship as between square metres and hectares. A hectare is 10 000 m2. Hectares are used to measure areas of land. Think of a hectare as an area that is 100m by 100m. That means that 10 x 10 = 100 hectares are in one square kilometre. Square kilometres are used to measure large areas of land. For example, Rakiura/Stewart Island has an area of 1 746 km2 or 174 600 hectares.
Sessions One and Two
A suitable unit for measuring area must have these qualities:
Session Three
The area of a flat shape is conserved (stays constant) as parts of it are moved to different places on the shape. Any shape can be ‘morphed’ into a shape with the same area by ‘giving and taking’.
Session Four
Area is the amount of flat space enclosed by a shape. Perimeter is the distance around the outside of a shape. Shapes with the same area can have different perimeters, and shapes with the same perimeter can have different areas.
Session Five
A growing pattern can be structured by looking at how the figures are organised. Noticing structure helps with counting the area of a figure, and with predicting further figures in the pattern. Identifying sameness and difference in figures can help in creating a rule (generalisation) for all figures in the pattern.
Observations of students during this unit can be used to inform judgments in relation to the Learning Progression Frameworks. Click for tables of guidelines.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
Task can be varied in many ways including:
The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. Look for everyday examples when your students encounter area. Examples might involve spaces that are meaningful to them, such as their own bedroom, lounge, or section at home. Portions of food, such as pancakes or pies, can be compared by area. Students interested in environmental issues might be motivated by contexts such as the areas covered by drift nets or oil spills. Students might find comparing the size of land areas interesting, e.g. How many times does Rarotonga fit into the North Island? Which is larger Upolo (Samoa) or Espiritos Santos (Vanuatu)? Students may wish to share iwi and hapū connections and compare the size of areas that they whakapapa back to. For example, children living in the South Island may whakapapa back to Taranaki iwi. High achieving students might be interested in population density.
Students are expected to have some experience with measurement of other attributes, such as length, using informal units. They should also have some knowledge of multiplication facts and understanding of how to apply multiplication to finding the number of items in arrays. Consider what multiplication strategies your students are confident using. Your students might benefit from revisiting multiplication strategies at the beginning of these sessions, or might benefit from visual reminders of the strategies.
In this lesson students apply their understanding of area to a growing pattern. The task can be used to assess several aspects of mathematics, including multiplicative thinking, measurement, algebraic thinking and equations and expressions.
Dear parents and whānau
This week we are investigating problems about area, the amount of flat space. We will look at suitable units to measure area so that no gaps or overlaps occur. We will learn to use multiplication to count the number of units in an area efficiently and how to record measurements of area using numbers and units, like 24m2 (twenty-four square metres).
We will also investigate a growing pattern with area and predict further members in the pattern.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/fill-it-flat-space at 8:44pm on the 26th February 2024