Expected level of development
Australian Curriculum Mathematics V9: AC9M2N02
Numeracy Progression: Number and place value: P5
At this level, students consolidate part-part-whole knowledge when partitioning and describing two-digit numbers and extend this to three-digit numbers. They partition, rearrange, regroup and rename numbers to 999, and establish clarity about the role of zero.
Use physical and virtual materials (e.g. abacus, bundling sticks, beads) and tools (e.g number lines, hundred charts and place value charts) to explore and model two- and three-digit numbers in different ways. Involve students in collecting initiatives to create authentic contexts for grouping, counting, and representing two- and three-digit numbers. For example, they might collect bread tags, ring pulls, and bottle lids for reusing or recycling. Additionally, they might collect natural materials like pebbles, gumnuts, leaves and twigs.
Make explicit the importance of grouping in tens and hundreds. Consolidate the idea that 10 ones is 1 ten and 1 ten is 10 ones. Support students to understand that 10 tens is 1 hundred and that three-digit numbers comprise hundreds, tens and ones/units. Ensure opportunities to recognise, represent and rename numbers in different ways. Experiences must include numbers containing one or more zeros.
Teaching and learning summary:
- Use play-based experiences, stories and classroom talks, in conjunction with explicit teaching, to support student understanding of place value.
- Encourage reasoning when using partitioning to explore and describe two- and three-digit numbers.
- Apply to everyday contexts, including money using dollar values.
- understand the importance of grouping in tens and hundreds and use this to describe their thinking
- flexibly rename numbers using the place value parts of hundreds, tens and ones, for example, can rename 245 as 24 tens and 5 ones, as well as 2 hundreds and 45 ones
- flexibly rename numbers that have internal zeros, for example, read 807 as ‘eight hundred and seven’ and can rename it as 80 tens and 7 ones
- order and rename three-digit numbers without materials (e.g. 247 is 2 hundreds, 4 tens and 7 ones, or 2 hundreds and 47 ones, or 24 tens and 7 ones)
- explain the role of zero.
Some students may:
- be able to count a collection (e.g. 36) and record the total but they may not understand the significance of the digits, that is, that the 3 represents 3 tens and the 6 represents 6 ones.
- be able to identify place-value parts (e.g. they can say that there are 4 hundreds, 6 tens and 8 ones in 468) but still think about two- or three-digit collections additively in terms of ones (understand 468 as the sum of 400 ones, 60 ones and 8 ones).
To address these, focus on grouping tens and build the foundational understanding required – that 10 ones is 1 ten, and 1 ten is 10 ones. Provide repeated opportunities to apply and develop this understanding with two-digit numbers up to 99 before working with three-digit numbers.
Some students may:
- have trouble naming, writing or modelling three-digit numbers that involve teens (e.g. 213, 319) or zeros (e.g. 207, 405). To address this, provide repeated opportunities to make, name, rename and write these kinds of numbers using concrete materials and tools such as place value charts.
Address misunderstandings students may have with this topic.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
- We are learning to understand and use numbers up to 999.
Why are we learning about this?
- We use numbers and counting in everyday life.
What to do
Use two- and three-digit numbers every day. Here are some ideas:
- Use numbers when measuring, such as making a recipe that involves using millilitres or litres, and grams or kilograms.
- Play ‘General number knowledge’.
- Choose a two-digit number and take turns at sharing what you know about it.
- Person 1: chooses 35 and says ‘I know that 35 is how many years old Dad is’.
- Person 2: ‘I know that 35 is too many days for a month’.
- Person 1: ‘I know that 35 is 3 tens and 5 ones’.
- Person 2: ‘I know 35 is 5 less than 40’.
- Once you run out of ideas, it’s Person 2’s turn to choose a number.
- When tidying up at home, notice ‘how many’ are in a collection. Organise objects so they’re easier to count.
- Play board games such as Snakes and Ladders that involve two- or three-digit numbers.
- Play 'Guess my number' or similar games. How to play:
- Player 1 writes a secret three-digit number on a piece of paper.
- Player 2 asks yes/no questions about it until they guess it. For example, you could ask questions like:
- Is it larger than 500?
- Does it have an odd number in the hundreds place?
- Player 1 then provides an answer.
- Use the answers to work out which numbers it could not be and those numbers that it could be.
- Try and use questions that will reduce the number of possible numbers each time.
- explain how two-digit numbers (10–99) are made up of tens and ones
- explain how three-digit numbers (100–999) are made up of hundreds, tens and ones
- describe two- and three-digit numbers in different ways.
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A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.Go to resource
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.Go to resource
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.Go to resource
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.Go to resource
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.Go to resource
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
Number: place value – two-digit numbers
Use these activities over time to consolidate understanding when representing, ordering and comparing two-digit numbers.Go to resource
Classroom talks: Year 2 – place value
Run whole-class talks regularly for 5 to 15 minutes to consolidate and build upon foundations in understanding of place value.Go to resource
Use picture storybooks to connect key concepts to real life and to spark curiosity around two- and three-digit numbers.Go to resource
reSolve: Counting large collections
Use the context of counting collections to deepen place value understandings through justifying the count.Go to resource
Representation stations: Year 2 – Place value
Revisit and introduce counting and place value tools, and facilitate students as they represent numbers to 200.Go to resource
reSolve: Place Value Cards
Use this sequence to explore the multiplicative place-value properties of numbers. Students learn to represent numbers up to 1000 as multiples of 100s, 10s and 1s.Go to resource
reSolve: Authentic Problems: What’s For Lunch?
Use this guided inquiry unit to apply and further develop key place value understandings in a meaningful context.Go to resource
Building with tens and hundreds
Use this unit to deepen place value understanding to three-digit numbers.Go to resource
Place value: tools and games
Use the number expanders as a tool to represent three-digit numbers, and the games to apply and develop knowledge.Go to resource
Number: Place value
Use these lessons to represent and partition numbers to 100 and then to 1000.Go to resource
Wishball challenge: hundreds
Use this game that uses place value knowledge, addition and/or subtraction as part of game play.Go to resource
Classroom Talk Prompts - Year 2 Place value
Use this slidedeck for a class number talk on place value.Go to resource
By the end of Year 2, students order and represent numbers to at least 1,000. They apply an understanding of place value to partition, rearrange and rename two- and three-digit numbers, and regroup partitioned numbers to assist in calculations.