Learning Sequences - Length
Peter works us through learning length with informal units in the first year of school to comparing area and perimeter in year 6. In each video Peter emphasises guess and check, imagining, precision, language and the notion of solving a problem. Each task should be experiential so consolidation is essential. This focus is length but it works the same for mass and capacity and later area
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1. Direct comparisons of lengths.
The focus is comparing (of two) and ordering (of 3 or more) objects directly
Start with comparing and ordering lengths such as streamers, unifix towers that are not aligned. -
2. Indirect comparisons of lengths using “string”
The focus is on using length, such as a length of streamer, to compare two lengths that cannot be aligned. Such as the length and width of a table, this table in this room and that table, the height of a chair and the width of a table, a vertical and horizontal like, the circumference and height ...
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3. Measuring lengths using a non-standard unit repeatedly (levels 1 and 2)
The focus is that the non-standard unit must be the same for a given measure, with a special focus on precision. Using, for example, icy pole sticks, feet lengths, to compare length and width of a table, how many icy pole sticks is the same as two tables.
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4. Making lengths of objects to a given instruction (levels 1 and 2)
Even though at this stage many students are ready for rulers and cm this is still worth doing. Tasks such as make and draw some rectangles (triangles, trapeziums) using 12 icy pole sticks, draw a line 5 sticks long then check it.
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5. Using metres and centimetres (levels 2 and 3)
The focus is first on metres (metre rulers) and centimetres (30 cm rulers). Later can introduce mm. Draw a line 10 cm long without using a ruler then check (emphasis on precision) draw a line 1 m long on a page, estimate and measure the length of a table, draw a rectangle 20 cm around than check.
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6. Using measuring scales flexibly (levels 2 and 3)
Sometimes we use a scale that does not start at zero (weighing a dog). The idea is to compare, order and measure objects using a broken ruler or a measuring tape.
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7. Estimating lengths using formal units (levels 3 and 4)
The focus is on experiences that have students using realistic estimates of the lengths of objects such as the width of a room, how far they can jump, the width of a page, estimate then measure half of this line.
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8. Converting between formal length units (levels 3 and 4)
Students are given measures such as width of a room is 650 cm convert to m. Diagrams with a mix of units to work out perimeters (how far around). The idea of a best unit.
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9. Using perimeter and area (levels 5 and 6)
Give a perimeter, find the possible area and vice versa, on grid paper, keep perimeter the same and change area and vice versa.
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10. Solving measurement problems (levels 5 and 6)
Examples of problems using measurement especially if the problems use units from different domains. Like how much money would be a 2 metres long line of $2 coins, how many carpet times, 30 cm by 30 cm would be needed to carpet this room, how far can you run in 10 seconds, how far in km/hr.
