Expected level of development
Australian Curriculum Mathematics V9: AC9M3N01
Numeracy Progression: Number and place value: P6
At this level, students learn to recognise, represent and order whole numbers up to 10,000 and beyond. This involves using number names, writing conventions and renaming numbers using place-value parts.
Use proportional models (such as bundling sticks or base 10 blocks) to model 1,754 as 1 thousand, 7 hundreds, 5 tens and 4 ones, and then demonstrate renaming by modelling it as 17 hundreds, 5 tens and 4 ones.
Other tools (such as place-value charts and number expanders) can be used to investigate the repeating patterns of place value. Students can explore and predict changes to numbers like 99, 199, 199, 1,009, 1,099, 1,999, 10,009… 99,999, when one, one ten or one hundred is added to each.
Include a focus on how number naming and writing conventions are used across different cultures.
Teaching and learning summary:
- Explore number sequences and ordering through discussions, play-based experiences, games and challenging tasks.
- Invite reasoning when representing and ordering numbers.
- Apply reading, writing, naming and ordering numbers in meaningful contexts.
- read, write and name numbers to at least 10,000
- represent and rename three-digit and four-digit numbers, for example, describe and model 1,034 as ‘1 thousand, 3 tens and 4 ones’ and also as ‘10 hundreds, 3 tens and 4 ones’ as well as ‘103 tens and 4 ones’
- count by ones, tens, and hundreds across hundreds barriers (e.g. 199, 200, 201…; 199, 209, 219…; 199, 299, 399…) and across thousands barriers (e.g. 999, 1,000, 1,001...; 999, 1,009, 1,019…; 999, 1,099, 1,199…)
- order sets of numbers which range from 0 to at least 10,000.
Some students may:
- not yet be able to identify place-value parts. They can count orally to 100 and beyond, but still think about two- or three-digit collections additively in terms of ones (e.g. understand 468 as the sum of 400 ones, 60 ones and 8 ones). To address this, consolidate place value understanding with two-digit numbers by comparing and ordering two-digit numbers, counting forward and backward by tens and ones, and by renaming (e.g. 32 is 3 tens and 2 ones, but it’s also 32 ones, as well as 2 tens and 12 ones).
- have difficulty naming, writing or modelling three- or four-digit numbers that involve teens (e.g. 213, 2,518) or zeros (e.g. 207, 2,057, 4,005). 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.
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 read, write and order numbers up to 10,000.
Why are we learning about this?
- We read, write and use numbers in everyday life.
What to do
Play games that involve large numbers. For example:
- ‘Hit it!’ is a fun game that involves three-digit numbers that can be accessed online.
- ‘Number Heads’ is a variation of ‘Celebrity Heads’. Instead of a celebrity name, each player wears any number up to 1,000 or up to 10,000 on their head and asks yes/no questions to help work out their number:
- ‘Is my number larger than 5,000?’
- ‘Is it less than 2,000?’
- ‘Is it an odd number?’
- Count, skip-count and use numbers every day.
- Go on a number hunt. Look for, recognise and read the numbers around you, for example, recognise and say numbers on signs, calendars, speed signs and houses.
- Take turns saying the next number when counting forward and backward by ones, tens and hundreds from a given starting number, for example: 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1,000, 1,001 etc.
- Use numbers in measurement contexts, such as making a recipe that involves using millilitres/litres, and grams/kilograms.
- Use a pedometer to read and think about large numbers when tracking your daily step count.
- read, write and say numbers up to 10,000
- count forwards and backward by ones, tens and hundreds
- know which of two three-digit or four-digit numbers is largest and explain why.
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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.
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
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
Culturally responsive pedagogy
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.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
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.
Revisit and introduce counting and place-value tools as students explore and represent numbers in different ways.Resource details
Number: place value (1)
Use these activities to consolidate students’ key understandings of numbers 100 and numbers to 1,000.Resource details
Hundreds and thousands
Use these activities to order and compare three-digit numbers. It includes use of a number line.Resource details
Programming using ones, tens and hundreds
Use this as a context to interact with written and spoken numbers and investigate how adding and subtracting 1, 10 or 100 affects a value.Resource details
Introduce and use number expanders to engage with renaming.Resource details
Use this authentic context to read, write, represent and compare three- and four-digit numbers to 2,000.Resource details
Number: place value (2)
Consolidate place-value understanding of numbers within 1,000 and then work with numbers to 10,000.Resource details
Order! order! 2
Use this game as a meaningful context to make, name and order four-digit numbers.Resource details
Use these activities to explore four-digit numbers. They include partitioning into place-value parts.Resource details
By the end of Year 3, students represent and order numbers up to and beyond 10,000.
Assessment: Countable units tool
Learn to address foundational challenges students may have with this topic.Resource details
Up to and through the hundreds
Use this task to gauge student understanding of number.Resource details
Use this task to gauge student understanding of number.Resource details
Mathematics Year 3: ACARA
Use this one-on-one interview to assess an ability to read, represent, count and continue number patterns with numbers to 10,000.Resource details
Use this task to gauge students’ understanding of three-digit or four-digit numbers.Resource details