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International Baccalaureate · PYP 1

Measuring Length, Mass and Capacity

⌚ ~122 min ▢ 13 blocks ✓ 58 exercises ➣ Prerequisites : Numbers to 100, Comparing and Ordering Numbers, Subtraction Within 20, Adding and Subtracting to 100, Comparing Lengths, Comparing Masses, Comparing Capacities; Hotter or Colder
I Longer, Shorter or Taller?
Definition — Longer and Shorter
When two objects start at the same place, if one goes further, it is longer; the other one is shorter. If they end at the same place too, they have the same length.
Figure
The red ribbon is longer than the blue one. The blue and green ribbons have the same length.
Method — Line Up to Compare Lengths
To compare two objects, we can check which is longer or shorter.
Lay them side by side and carefully line up one end on the same line. The object that goes further is longer. The other is shorter.
If we stand them up, the one that is higher is taller. The other is shorter.
Example
Figure
The girl is taller than the boy.
The boy is shorter than the girl.
Skills to practice
  • Comparing Children's Heights
  • Comparing Block Heights
II What Is Mass?
Definition — Mass
Mass tells us how heavy something is. When we compare two objects, the heavier one has more mass and the lighter one has less mass. For example, a big book is heavier than a feather.
Method — The Balance
A pan balance has two pans: when it is empty, they rest at the same height.
  1. We put one object on each pan.
  2. The pan that goes down holds the heavier object.
  3. If the two pans stay level, the objects have the same mass.
Figure
The marble side goes down: the marble is heavier than the sweet. With two sweets, the pans stay level: same mass.
Figure
Skills to practice
  • Comparing the Masses of Objects
III Things We Can Compare
We can compare two objects in different ways.
We can look at their length — which one is longer.
We can look at their mass — which one is heavier.
Length and mass are things we can measure.
Report an error
Example
Figure
The book is heavier than the key. (mass)
Skills to practice
  • Comparing Masses
IV Capacity

Léa has two containers of different shapes: a wide salad bowl and a tall narrow bottle. She fills each of them to the brim and wants to know which one holds more water.
Figure
Say how to find out which container holds more, without guessing.

The eye is not enough: the salad bowl looks bigger because it is wide. To decide, Léa pours with the same glass and counts.
Figure
The bottle holds more, although it looks smaller.
Counting glasses only works between people who use the same glass. To be understood by everyone, capacity is measured with shared units.


Definition — Holds More and Holds Less
When two containers are full, the one with more water in it holds more. The other one holds less. If they have just as much water, they hold the same.
Definition — Capacity
The capacity of a container is the quantity of liquid it can hold. It says what can be poured into it, not how big the container looks.
Skills to practice
  • Counting Glasses
V Measuring with a Unit
Comparing tells us which object is longer or heavier, but not how much.
To put a number on a measure, we choose a unit and count.
Report an error
Definition — Measuring
To measure an object, we choose a unit and count how many of them fit.
The result, called the measure, has two parts: a number and a unit.
Method — Measure with a unit
Use the same unit for the whole measurement. Line the units up right next to the object, with no gaps and no overlaps. Then count how many you used.
Example
Figure
The cucumber is 4 erasers long.
The number is \(4\); the unit is the eraser.
Method — Measuring Mass with a Unit
We measure a mass with a balance:
  1. Put the object on one pan.
  2. On the other pan, put identical units (all the same), one by one, until the two pans are level.
  3. Count how many units you used: the mass of the object is that number of units, for example 3 weights.
Example
Figure
The book balances 3 equal weights.
Its mass is \(3\) weights: the number is \(3\), the unit is the weight.
Skills to practice
  • Measuring Length with a Unit
  • Measuring Lengths with Blocks
  • Measuring Mass with a Unit
VI A Measure Is a Number and a Unit
The same object can be measured with different units. The number then changes, but the length stays the same.
So a measure must always give both the number and the unit. The number alone does not say how long an object is.
Report an error
Example
Figure
The same cucumber is 4 erasers long (a) or 2 carrots long (b).
Different unit, different number — same length.
Skills to practice
  • Measuring One Object with Two Units
VII Going further
Skills to practice
  • Writing Comparisons with Signs
  • Writing Measures with Numbers
  • Solving Length Problems
  • Solving Mass and Capacity Problems
  • Quiz