Understanding the Phrase 'Half Past' - First Grade Mathematics

Have you ever heard someone say: "It is half past four," and wondered what that means? The word "past" means beyond or after. The phrase "half past" is a lovely, traditional way to say that half of an hour has passed since the hour began! Since one full hour is represented by a complete circle on the clock, "half past" means the minute hand has traveled through half of the circular clock face. In this chapter, you will connect the concept of fractions (halves) to the clock, explore the phrase "half past," and become bilingual in reading clock language.

Cutting the Clock in Half

Picture an analog clock as a delicious round pie or pizza.

The Half-Clock Pizza:
                 12
             .---+---.
            /    |    \
           /     |     \
       9  |      |      |  3
           \     |     /
            \    |    /
             '---+---'
                 6
        Left Side | Right Side

The Halfway Split

If you draw a vertical line from the 12 straight down through the center to the 6, you split the entire clock circle into two equal halves! When the minute hand begins at 12 and travels down to 6, it has covered the entire right half of the clock. That is why we call it HALF PAST!

Translating "Half Past" to Digital Numbers

Every time you hear "half past," your brain can instantly translate it into :30.

Translating Clock Language:
Phrase: "Half past two"      ->  Digital: 2:30  (30 minutes past 2)
Phrase: "Half past seven"    ->  Digital: 7:30  (30 minutes past 7)
Phrase: "Half past ten"      ->  Digital: 10:30 (30 minutes past 10)
Phrase: "Half past twelve"   ->  Digital: 12:30 (30 minutes past 12)

The Two Names for the Same Time

Just like a puppy can be called "a puppy" or "a young dog," the time 5:30 has two names: Name 1: "Five-thirty" (reading the digits). Name 2: "Half past five" (describing the fraction of the hour). Both names describe the exact same second in the universe!

Seeing "Half Past" on the Hands

Let us look at how the clock hands behave at half past nine (9:30).

Hands at Half Past Nine:
                 12
            11        1
        10                2
       9\         +         3
        8\                4
             7   |    5
                (6)

The Hand Clues:

  1. The minute hand is pointing directly down at 6 (halfway around).
  2. The hour hand has moved halfway past the 9, pointing right between 9 and 10! Together, they tell the story: "It is half past nine!"

Practice Exercises

Exercise 1: Explain why the time 4:30 is called "half past four." Connect your answer to the shape of the clock.

Exercise 2: Translate these phrases into digital time notation: Half past one = : Half past six = : Half past eleven = :

Exercise 3: Translate these digital times into "half past" word phrases: 3:30 = Half past _ 8:30 = Half past _ 12:30 = Half past ____

Exercise 4: At half past three, which two numbers is the hour hand sitting between?

Solutions and Explanations

Solution to Exercise 1: The time 4:30 is called "half past four" because exactly half of an hour (30 minutes out of 60) has passed since 4 o'clock. On an analog clock, the minute hand has traveled halfway around the circular clock face from 12 down to 6.

Solution to Exercise 2: Half past one = 1:30 Half past six = 6:30 Half past eleven = 11:30

Solution to Exercise 3: 3:30 = Half past three 8:30 = Half past eight 12:30 = Half past twelve

Solution to Exercise 4: At half past three (3:30), the hour hand is sitting halfway between the 3 and the 4.