Year level: 4

Strand: Number

Lesson length: 60 mins

In this lesson, students learn about place value and how it extends beyond whole numbers. They use decimal notation to name and represent decimals and use materials to model decimals. These models help students to order and compare decimals that include tenths, hundredths and thousandths.

After completing the lesson, a relevant follow-up activity is Decimats (understanding fractions).

### Achievement standard

By the end of Year 4, students use their understanding of place value to recognise, represent and compare tenths, hundredths and thousandths in decimal form.

### Content descriptions

Students recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals. AC9M4N01

### General capabilities

Numeracy

• Provide the exit ticket, which enables students to choose and compare two decimal numbers from a table.
• Assess students’ proficiency in naming numbers and accurately comparing the numbers identifying the larger number.
• Observe if they can accurately record the number using a place value chart.

Some students may:

• apply their whole number thinking when reading and interpreting decimal numbers and will assume that decimal numbers with more digits have a higher value, for example, 0.36 is larger than 0.5, just as 36 is larger than 5; this is known as the ‘longer is larger’ misconception. Using materials, such as decimats, can help students to model and compare decimals and overcome this common misconception.
• incorrectly interpret a decimal fraction, for example, 2.75 should be read as ‘two and seventy-five hundredths’. Reading it as ‘two point seven five’ can lead to confusion and a misunderstanding of the decimal's value. Using place value helps reinforce the understanding of the relative sizes of the digits and their positions in the decimal number. Understanding place value is crucial when working with decimal fractions.

Prior to this lesson, it is assumed that students have knowledge of:

• Place value: the value of a digit as determined by its position in a number relative to the ones place. For integers, the ones place is occupied by the right-most digit in the number before the decimal point.
• Base 10: a number system which uses the digits 0–9, and the value of the digit is determined by its face value and its place value, for example, 283 = 2 × 100 + 8 × 10 + 3 × 1 and 283 = 200 + 80 + 3.
• Decimal: used to describe aspects of the base 10 number system. The decimal point separates the whole number part of a number from its decimal part.