Counting Whole Numbers to Millions in Groups for Primary 4

Counting Whole Numbers to Millions in Groups for Primary 4

Performance Objectives

By the end of the lesson, students should be able to:

1. count in thousands up to one million;
2. count in 5’s, 7’s, 12’s and 60’s;
3. Convert seconds into minutes and hours.

Understanding Whole Numbers and Place Value to Millions

Whole numbers are the numbers used for counting and measuring. They include 0, 1, 2, 3, 4, and so on, without any fractions or decimals.

Every digit in a whole number has a place value. This place value tells how much the digit is worth. As numbers get larger, more place values are used.

A million is a very large number. It is written as 1,000,000. It has seven digits. Understanding place value helps in reading, writing, and counting these large numbers.

The place values up to millions are:

1. Ones
2. Tens
3. Hundreds
4. Thousands
5. Ten Thousands
6. Hundred Thousands
7. Millions

Observe the place value chart below to see how digits are arranged in a number up to millions.

When reading large numbers, the digits are grouped in threes from the right. Each group is separated by a comma. For example, 1,000,000 is read as “one million”. The number 5,243,167 is read as “five million, two hundred and forty-three thousand, one hundred and sixty-seven”.

Counting in Thousands up to One Million

Counting in thousands means adding 1,000 each time. This helps in counting large numbers more easily. When counting in thousands, only the thousands, ten thousands, hundred thousands, and millions places change.

How to Count in Thousands

To count in thousands, start with a number and keep adding 1,000 to it. For example, if counting from 1,000:

1. $1,000 + 1,000 = 2,000$
2. $2,000 + 1,000 = 3,000$
3. $3,000 + 1,000 = 4,000$
4. $4,000 + 1,000 = 5,000$

This pattern continues up to one million. Here are some examples of counting in thousands:

1. Starting from $10,000$: $10,000, 11,000, 12,000, 13,000, 14,000, 15,000$
2. Starting from $100,000$: $100,000, 101,000, 102,000, 103,000, 104,000$
3. Starting from $500,000$: $500,000, 501,000, 502,000, 503,000, 504,000$
4. Counting towards one million: $995,000, 996,000, 997,000, 998,000, 999,000, 1,000,000$

Counting in Groups (Skip Counting)

Counting in groups, also known as skip counting, means counting by a certain number each time. Instead of counting one by one, a fixed number is added repeatedly. This skill is useful for quick counting and understanding multiplication.

Counting in 5s

When counting in 5s, 5 is added to the previous number each time. This is like counting the fingers on a hand or the toes on a foot.

Examples of counting in 5s include:

1. $5, 10, 15, 20, 25, 30, 35, 40, 45, 50$
2. $100, 105, 110, 115, 120, 125$
3. $230, 235, 240, 245, 250, 255$

Learners can use objects like bottle covers or sticks to practise counting in 5s by making bundles of five.

Counting in 7s

Counting in 7s means adding 7 to the previous number each time. This is useful for understanding the number of days in a week.

Examples of counting in 7s include:

1. $7, 14, 21, 28, 35, 42, 49, 56, 63, 70$
2. $70, 77, 84, 91, 98, 105$
3. $140, 147, 154, 161, 168$

There are 7 days in one week. Counting in 7s helps to find out how many days are in several weeks. For example, 2 weeks have $2 \times 7 = 14$ days. 3 weeks have $3 \times 7 = 21$ days.

Counting in 12s

Counting in 12s means adding 12 to the previous number each time. This is useful for understanding units like dozens or months in a year.

Examples of counting in 12s include:

1. $12, 24, 36, 48, 60, 72, 84, 96, 108, 120$
2. $120, 132, 144, 156, 168$
3. $240, 252, 264, 276, 288$

There are 12 months in one year. Counting in 12s can help find the number of months in several years. For example, 2 years have $2 \times 12 = 24$ months. 5 years have $5 \times 12 = 60$ months.

Counting in 60s

Counting in 60s means adding 60 to the previous number each time. This is very important for understanding time, as there are 60 seconds in a minute and 60 minutes in an hour.

Examples of counting in 60s include:

1. $60, 120, 180, 240, 300, 360, 420, 480, 540, 600$
2. $600, 660, 720, 780, 840$
3. $1,200, 1,260, 1,320, 1,380, 1,440$

Converting Time Units: Seconds, Minutes, and Hours

Time is measured in different units. The most common small units are seconds, minutes, and hours. These units are related to each other by the number 60.

The relationships between these units are:

1. $60 \text{ seconds} = 1 \text{ minute}$
2. $60 \text{ minutes} = 1 \text{ hour}$

Understanding these relationships allows for conversion from one unit to another.

Converting Seconds to Minutes

To convert seconds into minutes, divide the number of seconds by 60, because there are 60 seconds in 1 minute.

Worked Example 1: Convert 180 seconds into minutes.

We know that $60 \text{ seconds} = 1 \text{ minute}$.

So, to convert 180 seconds to minutes, divide by 60:

$$
180 \text{ seconds} \div 60 = 3 \text{ minutes}
$$

Therefore, 180 seconds is equal to 3 minutes.

Worked Example 2: Convert 450 seconds into minutes and remaining seconds.

Divide 450 by 60:

$$
450 \div 60
$$

We can think: $60 \times 7 = 420$.

So, $450 \div 60 = 7$ with a remainder of $450 – 420 = 30$.

Therefore, 450 seconds is equal to 7 minutes and 30 seconds.

Converting Minutes to Hours

To convert minutes into hours, divide the number of minutes by 60, because there are 60 minutes in 1 hour.

Worked Example 3: Convert 120 minutes into hours.

We know that $60 \text{ minutes} = 1 \text{ hour}$.

So, to convert 120 minutes to hours, divide by 60:

$$
120 \text{ minutes} \div 60 = 2 \text{ hours}
$$

Therefore, 120 minutes is equal to 2 hours.

Worked Example 4: Convert 200 minutes into hours and remaining minutes.

Divide 200 by 60:

$$
200 \div 60
$$

We can think: $60 \times 3 = 180$.

So, $200 \div 60 = 3$ with a remainder of $200 – 180 = 20$.

Therefore, 200 minutes is equal to 3 hours and 20 minutes.

Converting Seconds to Hours

To convert seconds directly to hours, divide by 60 twice (once for minutes, then once for hours), which means dividing by $60 \times 60 = 3,600$.

Worked Example 5: Convert 7,200 seconds into hours.

First, convert seconds to minutes:

$$
7,200 \text{ seconds} \div 60 = 120 \text{ minutes}
$$

Next, convert minutes to hours:

$$
120 \text{ minutes} \div 60 = 2 \text{ hours}
$$

Alternatively, divide by 3,600 directly:

$$
7,200 \text{ seconds} \div 3,600 = 2 \text{ hours}
$$

Therefore, 7,200 seconds is equal to 2 hours.

Converting Minutes to Seconds

To convert minutes into seconds, multiply the number of minutes by 60, because there are 60 seconds in 1 minute.

Worked Example 6: Convert 5 minutes into seconds.

Multiply 5 by 60:

$$
5 \text{ minutes} \times 60 = 300 \text{ seconds}
$$

Therefore, 5 minutes is equal to 300 seconds.

Converting Hours to Minutes

To convert hours into minutes, multiply the number of hours by 60, because there are 60 minutes in 1 hour.

Worked Example 7: Convert 3 hours into minutes.

Multiply 3 by 60:

$$
3 \text{ hours} \times 60 = 180 \text{ minutes}
$$

Therefore, 3 hours is equal to 180 minutes.

Converting Hours to Seconds

To convert hours directly to seconds, multiply by 60 twice (once for minutes, then once for seconds), which means multiplying by $60 \times 60 = 3,600$.

Worked Example 8: Convert 1 hour into seconds.

First, convert hours to minutes:

$$
1 \text{ hour} \times 60 = 60 \text{ minutes}
$$

Next, convert minutes to seconds:

$$
60 \text{ minutes} \times 60 = 3,600 \text{ seconds}
$$

Therefore, 1 hour is equal to 3,600 seconds.

Other Time Units as Groups

Just like seconds, minutes, and hours, other time units also involve counting in groups. These are often seen on a calendar.

The common time units are:

1. $7 \text{ days} = 1 \text{ week}$
2. Approximately $4 \text{ weeks} = 1 \text{ month}$ (some months have more, some less)
3. $12 \text{ months} = 1 \text{ year}$

Understanding these groups helps to organise time and plan activities. For example, knowing there are 7 days in a week helps in counting how many days pass in a certain number of weeks.