NK 1 - Place value
- Understand that digits written in different places within a number have different values.
- Realise that only the digits 0-9 can be used in any number place and when one more is added to 9, the place value on the left is used.
- Understand how zero acts as a place holder.
- Read and write digits from 0-1000.
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Teacher notes
- It is important for students to understand that each digit in a number stands for a specific value depending on the place of the digit.
- Introducing a range of materials (especially those where the ten can be broken apart / joined such as ice block sticks, bags of beans, Unifix cubes) and linking the manipulation of these materials with written recording will help students to make sense of how our number system works and how it is recorded.
- Using materials and place value charts helps students develop an understanding that when ten is reached in any place, it can be exchanged for one in the place to its left, since this has the same value.
- Be mindful that students may diligently write digits into place value charts and go through the motions of exchanging materials for some time without fully comprehending the meaning behind what they are doing.
- Most students will need plenty of practice at exchanging 10 for 1, and 1 for 10 before this concept of unitising is properly understood. This is the foundation of our decimal system, so you should allow time to embed these ideas. For example, students could act out how a person who has nine $1 coins and is given another can exchange the coins for a $10 note and vice versa.
- Arrow cards are very useful for expanding and contracting written forms of a number.
- It is important to try to ensure that students are forming digits correctly and writing them clearly.
- Students who are reluctant writers or who find spelling difficult could be encouraged to refer to examples in the Student Resource Book orWord bank (Teacher resource sheet 80) when expanding numbers and writing them as words.
NK 2 – Ones and tens in numbers
- Understand nested place value, such as tens being nested in hundreds and ones being nested in tens.
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Teacher notes
- Nested place value allows students to understand the importance of the position of digits in a number and how they can be represented in different ways, for example in 367 the 6 stands for 6 tens but also 60 ones.
- Using place value materials is very important in developing students’ understanding of nested place value.
- Students who have not really understood the concept of exchanging ten ones for one ten and vice versa will often struggle with nested place value. It may be necessary to revisit conventional place value using materials for them to make sense of nesting.
- It can be tempting to show students a trick for finding the number of tens in a number (hiding the ones digit). This should be avoided as it will not help students to understand this important concept. If students notice this pattern, ask them to show why this might be true using place value materials (to demonstrate that there are no tens in the ones place).
- Provide students with opportunities to verbalise place value ideas and understandings.
NK 3 – Family of facts
- Learn that four addition and subtraction facts that all have the same three numbers form a ‘family’.
- Learn that the order of numbers in addition does not change the total (the commutative property of addition).
- Learn that addition and subtraction facts are ‘opposite’ operations that, 'undo’ each other (the inverse property of addition and subtraction).
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Teacher notes
- Using materials, such as counters, Unifix cubes or Cuisenaire rods, helps students develop an understanding of the relationship between addition and subtraction.
- A common misunderstanding that might arise is that numbers may also be ‘swapped’ within a subtraction equation. Using materials demonstrates why this is true for addition but not for subtraction. Students could explore this in groups and come up with a theory as to why it does not work for subtraction.
- Ensure that students realise the equation made with the three numbers must be 'true', that is, the quantities on each side of the equals sign must have the same value or they must 'balance'.
- Being able to fluently and accurately recall basic facts is critical for students’ progress through Year 3 (2A) & Year 4 (2B). You should be aware that while some students enjoy speed challenges, for others an emphasis on speedy recall can cause anxiety and be counterproductive.
- You can however assist all students to improve their recall of basic facts by helping them discover the patterns that link them. Knowing the relationship between addition and subtraction enables students who have learned one fact to recall three others.
- Relating the facts to a story also helps students make sense of the facts and to understand that the commutative property doesn’t work for subtraction.
NK 4 – Addition and subtraction basic facts
- Develop fluent and accurate recall of addition facts to 20 and subtraction facts to ten.
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Teacher notes
- Developing the ability to fluently and accurately recall basic facts is very important at Year 3 (2A) & Year 4 (2B). The goal is “automaticity” in recalling the fact from long term memory without needing to calculate each step.
- Encourage students to record and celebrate the facts they can recall fluently and accurately without calculation. Students will then be able to identify and spend time practising the facts they still need to learn.
- Encourage students to focus on learning a few facts at a time. They are less likely to feel overwhelmed and their progress will be more evident, which in turn will encourage them to keep practising.
- If students don’t have recall of their facts to 10, work on these first.
A good sequence to follow is to learn these: Make sure students understand and have learned facts correctly before they begin to work on automaticity. Using computer programs that give feedback, activities that self-correct, having answers on the back of flash cards or marking sheets, using a calculator to check answers (keying in the digits is another form of practice) are all good ways to check that facts are being recalled accurately.
NK 5 – Addition to and subtraction from a tens number
- Learn to make tens numbers using addition or subtraction.
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Teacher notes
- Students' knowledge of addition facts to 10 and 20 can be used to scaffold adding to and subtracting from other tens numbers.
- Using place value materials such as tens frames is helpful, as are number lines, particularly for students who are not secure in their backward and forward sequence to 100.
- This knowledge is essential for many mental strategies that are introduced at Year 3 (2A) & Year 4 (2B) of the curriculum.
NK 6 – Tens facts that make hundreds
- Combine basic facts and place value knowledge to solve addition and subtraction problems involving decades and hundreds.
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Teacher notes
- Encourage students to make the connection between basic facts that they know to find the answers to tens and hundreds facts. For example, “I know that 6 + 3 = 9 so 6 tens + 3 tens = 9 tens so 60 + 30 = 90 and 6 hundreds + 3 hundreds = 9 hundreds so 600 + 300 = 900”.
- Use place value materials such as wooden blocks to reinforce student understanding of ‘unitising’ (the concept that 10 ones is the same as 1 ten etc) which forms the basis of this strategy.
NK 7 – What comes 1, 10 or 100 before or after me?
- Add to or subtract from 1s, 10s and 100s numbers.
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Teacher notes
- Students tend to have most difficulty going forward and backward over tens and hundreds. It is very important to use materials or animations that compose (make tens or hundreds) and decompose (break tens or hundreds) in these sequences so that students understand what is occurring rather than relying entirely on rote memorisation.
NK 8 – Ordering whole numbers
- Use place value to determine the magnitude of numbers to order whole numbers.
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Teacher notes
- Encourage students to work logically and systematically as suggested in the example on page 55 of the student book, and to ‘think aloud’ to reinforce their own and others’ understanding. You might like to use place value materials or place value charts to provide further support for some students.
