• using non-standard units for linear measures:
  • real-life objects: length of a paper clip, a toothpick, a pen
  • personal referents (benchmarks): width of a finger, height, length of a foot, hand span, arm span, length of a stride
  • math learning tools: length of a relational rod, distance between the tick marks on a number line
• measuring lengths of objects:
  • placing enough paper clips, pens, or shoes, with no gaps or overlaps, to be equivalent to the length of an object, and counting them
  • iterating a toothpick, the width of a finger, or a relational rod, with no gaps or overlaps, until the end of an object is reached, and tracking the number of iterations
• measuring length as the distance between two points:
  • counting the number of steps or number of strides to get from one location to another (e.g., across the room, from the front entrance of the school to the classroom door)
  • marking two points on a number line and determining the distance between them
• comparing lengths to describe relationships:
  • comparing the counts of unit lengths based on the same non-standard unit

• A length is the distance between two points, in any direction. Width, height, and depth are all measurements that compare length, or the distance between two points.
• Units quantify comparisons and are used to change from comparison questions (Which is longer?) to measurement questions (How long? How much longer?).
• An appropriate unit is one that matches the attribute well (e.g., a unit of length to measure length, a unit of time to measure time) and is easy to repeat.
• To directly measure an object:
  • select a unit that matches the attribute being measured (e.g., a paper clip to measure length);
  • repeat (iterate) the unit or copies of the unit without gaps or overlaps;
  • determine how many units it takes to match the object completely;
  • choose smaller units (or partial units) for greater accuracy.
• Measurements of continuous quantities are always approximate. The smaller the unit chosen, the greater the potential accuracy of the measurement. If different-sized units are used to match an object more completely, each unit is counted and tracked separately.
• The size of the unit affects the count – there is an inverse relationship between the size of the unit and the number of units it takes to cover, match, or fill an attribute. The smaller the unit, the greater the count; the larger the unit, the smaller the count. Regardless of whether a small or large unit is used to measure the length of an object, the object’s length is constant; only the count changes. This is known as the conservation property.

• benchmarks:
  • centimetre: width of a finger, width of a pencil
  • metre: stride length, length of a baseball bat

• Standard units make it possible to reliably communicate measurements. Centimetres and metres are standard metric units for measuring length. There are 100 centimetres in 1 metre.
• Measurements of continuous quantities, such as lengths, are always approximate. The smaller the unit selected, the greater the potential accuracy. Different-sized units can be used to match an object more completely, but the count of each unit must be tracked separately.
• To measure a length that is, for example, between 1 metre and 2 metres, a combination of metres and centimetres can be used, or centimetres only, or rounding the length to the nearest metre.

Note

• In Grade 2, students do not use decimals in their measurements.
• Having familiar reference points (benchmarks) for centimetres and metres makes it easier to estimate the length of objects.

• linear measuring tools:
  • rulers, measuring tapes
  • constructed rulers made with 1 centimetre interlocking cubes
• determining a linear measurement using a measuring tool:
  • if the object is shorter than the tool:
    • starting at zero: the measure is the marking on the tool at the end of the object
    • starting at a value greater than zero: the measure is the difference between the marking on the tool and the distance from zero to the starting point
  • if the object is longer than the tool:
    • move (iterate) the tool repeatedly along the length of the object with no gaps or overlaps
• contexts:
  • measuring the distance from the front door of the school to the classroom door on a map
  • determining whether shapes have equal side lengths
  • marking the start and end of a race in the schoolyard
  • comparing students’ heights at the beginning and end of the year
  • comparing the height of a book and the height of the space between shelves on a bookshelf

• Rulers, measuring tapes, tape measures – in fact, all measuring tools – replace the need to lay out and count actual physical units. The measuring tool repeats the unit so there are no gaps or overlaps and includes a scale to keep track of the unit count.
• A scale – such as the scale on a ruler – starts at the beginning of the first unit, which is labelled 0 because no units have been laid out. At the end of the first unit, the scale is labelled 1, because 1 complete unit has been laid out. The scale continues to count full units.
• When the edge of an object is matched with the 0 on the measuring tool, the scale accurately keeps track of the count. However, a length can be measured from any starting point, as long as the count is adjusted based on the starting point to accurately reflect the length of the object.
• The distance between two end points stays constant, no matter where on the scale the count begins. A measurement counts the number of units between the start of a length and the end of a length.

• duration of some events:
  • 15 minutes for recess
  • 2 hours for a party
  • 40 minutes for lunch
  • 8 claps for each verse in a song
  • 3 sleeps in a weekend

• Measuring time involves questions such as: “What time is it?” and “How much time has passed?”.  The focus in Grade 2 is on the second question.
• The passage of time is measured by counting units of time that repeat in a regular and predictable manner: the beats of a metronome; the dripping of a faucet; the natural cycles of a day; the swing of a pendulum; the seconds, minutes, and hours of a clock.
• Similar to measuring physical length, a length of time can be measured using different units of different sizes. The smaller the unit of time used, the more precise the measurement. Similar to all continuous attributes, the measurement of time is always approximate.
• Around the world, standard units of time – seconds, minutes, hours – are used to communicate the length of time of an event. Measuring tools, such as stopwatches, keep track of the unit count.