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Long and Short - Measuring Length using Non-Standard Units

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Length is a measure of how long an object is from one end to the other. For example, when comparing two pencils, the one that extends further is called 'longer' and the other 'shorter'.

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Non-standard units are objects or body parts used to measure length before using a ruler. Examples include using your hand, arm, or even small items like paper clips or crayons.

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A Handspan is the distance from the tip of the thumb to the tip of the little finger when the hand is fully stretched out. Imagine placing your palm flat on a desk and stretching your fingers as wide as possible to measure its width.

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A Cubit is the length from the tip of your middle finger to your elbow. This is often used to measure longer items like the edge of a bed or a classroom table. Visualise laying your forearm along the edge of an object to see how many 'arm-lengths' it is.

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A Footspan or Pace is the distance measured by the length of a foot or a full step. This is useful for measuring the length of a room or a playground. Picture walking heel-to-toe along a straight line to count your steps.

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Finger width is a small non-standard unit used for very short objects. You can measure the thickness of a book or the length of an eraser by seeing how many fingers wide it is.

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The main limitation of non-standard units is that they vary from person to person. For example, if a child measures a table, it might be 1010 handspans long, but for a tall adult, the same table might only be 66 handspans long because the adult has a larger hand.

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To measure accurately using non-standard units, you must place the units end-to-end without leaving any gaps or overlapping them. If you are using matchsticks to measure a pencil, they must form a perfectly straight line.

📐Formulae

Length=Number of non−standard unitsLength = Number\ of\ non-standard\ units

Total Distance=Total Number of PacesTotal\ Distance = Total\ Number\ of\ Paces

If count of Unit A>count of Unit B (for the same object), then size of Unit A<size of Unit BIf\ count\ of\ Unit\ A > count\ of\ Unit\ B\ (for\ the\ same\ object),\ then\ size\ of\ Unit\ A < size\ of\ Unit\ B

💡Examples

Problem 1:

Rohan measures the length of his study table using his handspan. He finds that the table is exactly 88 handspans long. If one of his handspans is roughly 1212 centimeters, what is the total length of the table in centimeters?

Solution:

Total Length=Number of handspans×Length of one handspanTotal\ Length = Number\ of\ handspans \times Length\ of\ one\ handspan Total Length=8×12Total\ Length = 8 \times 12 Total Length=96 cmTotal\ Length = 96\ cm

Explanation:

We multiply the number of non-standard units (handspans) by the length of a single unit to find the total length.

Problem 2:

Meena and her father both measure the length of a garden path using their footsteps. Meena counts 2020 footsteps, while her father counts 1212 footsteps. Why is there a difference in their measurements?

Solution:

Meena′s count=20Meena's\ count = 20 Father′s count=12Father's\ count = 12 Difference=20−12=8 footstepsDifference = 20 - 12 = 8\ footsteps

Explanation:

The measurements are different because non-standard units like footsteps are not fixed. Since the father's foot is larger, he covers more distance in one step, resulting in a smaller count (1212). Meena's foot is smaller, so she needs more steps (2020) to cover the same distance.