---
title: "Measuring and Time"
book: "Primary & Middle School Mathematics"
subject: math
language: en
chapter: 6
exercises: 9
source: https://one-course.com/books/math/1/en/chapter/6-measuring-and-time
---

# Chapter 6 — Measuring and Time

Which pencil is longer? What day is it? How much does a sweet cost? This chapter compares lengths and measures them in centimeters, puts the days of the week in order, reads whole hours on the clock, and counts small coins.

## 6.1 Longer and shorter

**Method 6.1 (Comparing lengths).**

To compare two lengths, line them up with *one end matched*:

1. put both objects side by side, starting from the same line;
2. the one that reaches further is *longer* , the other is *shorter* ;
3. if both reach the same place, they are the *same length* .

Matching the start is the whole secret — comparing from crooked starts fools the eye.

![Two sticks, matched at the left: the blue one reaches further, so it is longer.](https://one-course.com/images/onecourse/chapters/math-1/g1-measure/fig-e8c35132ee61.svg)

*Two sticks, matched at the left: the blue one reaches further, so it is longer.*

**Definition 6.2 (The centimeter).**

To say *how* long, we measure with a ruler in *centimeters* (cm). Put the $0$ of the ruler at the start of the object, and read the number at its end.

![Measuring: the 0 at the start, read the end. This pencil is 5 cm long. (Millimeters and meters come in .)](https://one-course.com/images/onecourse/chapters/math-1/g1-measure/fig-cd1e17513f18.svg)

*Measuring: the $0$ at the start, read the end. This pencil is $5$ cm long. (Millimeters and meters come in [Chapter 19](https://one-course.com/books/math/1/en/chapter/19-measuring#ch-g3-measure).)*

## 6.2 The days of the week

**Example 6.3 (The seven days).**

The week has $7$ days, always in the same order:

$$
\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday,
Sunday.}
$$

After Sunday, Monday starts again. *Yesterday* is the day before, *tomorrow* the day after: if today is Wednesday, yesterday was Tuesday and tomorrow is Thursday.

## 6.3 Whole hours on the clock

**Method 6.4 (Reading a whole hour).**

When the long hand points straight up to the $12$, it is a whole hour: read the number the *short* hand points to. Short hand on the $3$, long hand on the $12$: it is $3$ o’clock.

![Whole hours: the long red hand on the 12, the short blue hand giving the hour. (Half and quarter hours come in .)](https://one-course.com/images/onecourse/chapters/math-1/g1-measure/fig-6c757967c90d.svg)

*Whole hours: the long red hand on the $12$, the short blue hand giving the hour. (Half and quarter hours come in [Chapter 12](https://one-course.com/books/math/1/en/chapter/12-money-and-measures#ch-g2-measure).)*

## 6.4 Small coins

**Example 6.5 (Making an amount).**

With coins of $1$, $2$ and $5$, many amounts can be made in several ways. To make $7$:

$$
5 + 2, \qquad
5 + 1 + 1, \qquad
2 + 2 + 2 + 1 .
$$

The biggest coins first is usually the quickest way, using the fewest coins.

![A five-coin and a two-coin make seven.](https://one-course.com/images/onecourse/chapters/math-1/g1-measure/fig-ae248e35b41a.svg)

*A five-coin and a two-coin make seven.*

## 6.5 Exercises

**Exercise 6.1 ★.**

Line up three pencils matched at one end. Which is the longest? Which is the shortest?

**Solution of Exercise 6.1.**

Answers depend on the pencils; the longest reaches furthest when they are matched at one end, the shortest reaches least far.

**Exercise 6.2 ★.**

Measure with your ruler: the long side of this book; your little finger; a spoon. Answer in whole centimeters.

**Solution of Exercise 6.2.**

Answers vary; each is read by putting the ruler’s $0$ at the start of the object and reading the whole centimeter at its end.

**Exercise 6.3 ★.**

Name the day: after Monday; before Sunday; two days after Friday.

**Solution of Exercise 6.3.**

After Monday: Tuesday. Before Sunday: Saturday. Two days after Friday: Sunday.

**Exercise 6.4 ★.**

Today is Thursday. What day was yesterday? What day is tomorrow? What day is in three days?

**Solution of Exercise 6.4.**

Yesterday: Wednesday. Tomorrow: Friday. In three days: Sunday.

**Exercise 6.5 ★.**

Draw a clock showing $6$ o’clock. Where is the short hand? Where is the long hand?

**Solution of Exercise 6.5.**

At $6$ o’clock the short hand points to the $6$ and the long hand points up to the $12$.

**Exercise 6.6 ★.**

Read the whole hour: short hand on $5$, long hand on $12$; short hand on $11$, long hand on $12$.

**Solution of Exercise 6.6.**

Short hand on $5$: $5$ o’clock. Short hand on $11$: $11$ o’clock.

**Exercise 6.7 ★.**

Make $8$ with coins of $1$, $2$ and $5$, in two different ways.

**Solution of Exercise 6.7.**

For $8$, for instance $5 + 2 + 1$ or $2 + 2 + 2 + 2$ (other correct answers exist).

**Exercise 6.8 ★.**

Leo has a $5$ coin and three $2$ coins. How much money has he altogether?

**Solution of Exercise 6.8.**

$5 + 2 + 2 + 2 = 11$. Leo has $11$.

**Exercise 6.9 ★★.**

A sweet costs $3$. Zoe pays with a $5$ coin. How much change does she get back? (Count up from $3$ to $5$.)

**Solution of Exercise 6.9.**

From $3$ up to $5$ is $2$: Zoe gets $2$ back.