Year level: 6

Strand: Number / Measurement

Lesson length: 45–60 mins

In this lesson, students learn about place value and how it extends beyond whole numbers. Students play a board game that draws on their knowledge of adding decimals to tenths, hundredths and thousandths with and without regrouping.

### Achievement standard

Students use all 4 operations with decimals and connect decimal representations of measurements to the metric system.

### Content descriptions

Students apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers. AC9M6N04

Students multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers. AC9M6N06

Students convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem. AC9M6M01

### General capabilities

Numeracy

The following formative assessment items are suggested for this lesson:

• Provide the sheet Exit Tickets. Ask students to choose a month, for example, Month 7 the Koala weighs 3.5 kg. Ask the student how many more kg to reach 10kg? Ask them how they worked that out to see what strategies they used. A follow-up question can include how long do you think it would take to reach 10kg and have them explain their answer. Look for their use of identifying patterns in the data, estimation and doubling strategies.
• Note the student responses to Exit Tickets and use this information to further support students in subsequent lessons.
• 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 rightmost 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.
• 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.
• When dividing or multiplying by a multiple of 10, students are often encouraged to ‘hop the dot’ or ‘add a magic zero’. This is unhelpful language for learning. The decimal point never moves and always remains between the ones and tenths. The language of adding a zero confuses students when fractional numbers are involved: for example, 10 x eighteen and a half is not 180.5 or 108.5 it is 185.
• When adding and subtracting decimals (and whole numbers) with their head, students often miss that a 1 (or 10) is made when counting on. For example, if finding out how much is needed to reach 100 from 32, they start with 70 because 30 + 70 is 100, not remembering that 2 + 8 will make a 10 so only 60 is needed to start with. The same is with decimals, 0.32 only needs 0.68 to make 1. Starting with adding the next friendly (decade) number will help avoid this by thinking 32 and 8 more make 40; 40 and 60 more make 100 or 0.32 and 8 hundredths makes 0.4, 0.4 and 0.6 make 1.
• Students incorrectly read decimals, again applying their whole number thinking, for example, 0.36 is read as zero point thirty-six, instead of stating that we write zero point three six and read it as thirty-six hundredths.

## What you need:

• Lesson plan (Word)

• Printed cards and recording sheet (Word)

• Die net with decimals (Word)

• Exit Ticket: Target weight! (Word)