NK - 1 – Place value | Pg 17
- Understand that digits, written in different places within a number, have different values.
- Understand how zero acts as a place holder.
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Teacher notes
- It is important for students to understand that each digit in a number represents a value which is determined by its place in the digit.
- Place value charts help students develop an understanding that when ten is reached in any place, it can be exchanged for one of the place to its left, and vice versa, since these have the same value.
- Most students will need lots 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 teachers should take time to embed these ideas.
- Different materials are appropriate for conveying different aspects of place value.
- Early understanding is best developed with two-digit numbers, so that the ten can be broken apart / joined, for example, ice block sticks, bags of beans, unifix cubes etc. Wooden place value blocks, money, abacus and arrays are introduced later and are more easily managed for numbers with three or more digits.
Arrow cards are very useful for expanding and contracting written forms of a number.
- Linking the manipulation of these materials with written recording, is important for helping students to make sense of how our decimal number system works.
- Counting systems in Māori and many other languages use a consistent place value system for counting (avoiding the confusion around –teen numbers). Place value is an excellent opportunity to explicitly recognise the value of any languages spoken by children in your classroom.
NK - 2 – Hundreds in hundreds and thousands | Pg 25
- Understand nested place value i.e. nested in thousands are hundreds and tens and ones, nested in hundreds are tens and ones, and nested in tens are ones.
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Teacher notes
- Nested place value allows students think flexibly about numbers, and to decompose and compose numbers in more than one way. It is an important concept that is built on later when students begin to use written forms.
- Using place value materials is very important as it helps students develop an understanding of nested place value.
- Students who have not really understood the concept of exchanging ten 1s for one 10, ten 10s for 100, ten 100s for 1000 and vice versa, will often struggle with nested place value. It may be necessary to revisit conventional place value with materials so that they have further opportunities to make sense of nesting.
- It can be tempting to show students a trick for finding the number of tens or hundreds in a number (hiding the last 1 or 2 digits). This should be avoided, as it will not help students to understand this important concept. If students notice this way of getting the right answer, ask them to show why this might be true using place value materials (i.e. there are no hundreds in the tens or ones place).
NK - 3 – Addition and subtraction basic facts | Pg 28
- Achieve fluent and accurate recall of addition facts to 20 and subtraction facts to ten.
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Teacher notes
- Being able to fluently and accurately recall basic facts is critical for students’ progress through Level 2. Be aware that students process at different speeds. The goal is “automaticity”, knowing the answer without needing to calculate. By this stage many students will have learned most of these basic facts and be working to achieve fluency in their recall.
- It is a good idea to identify any facts that the student still needs to work out, so these can be the focus of practise.
- Encourage students to use a fact they know (for example to add ten and subtract one for a +9 fact), rather than counting strategies to work out the answers to any facts they can’t recall. Subtraction knowledge is often slower to develop, so being able to use knowledge about a family of facts can be particularly helpful.
NK - 4 – Adding to and subtracting from tens, hundreds and thousands | Pg 35
- Use addition and subtraction facts and place value knowledge to roll over tens and hundreds.
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NK - 5 – Doubles and halves | Pg 39
- Recall of doubles to twenty and halves of even numbers to twenty.
- Use doubles and halves to twenty to calculate doubles and halves of numbers to 100.
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NK - 6 – What comes 1, 10 or 100 before or after me? | Pg 43
- Know sequencing 1, 10s and 100s before and after numbers to 1000.
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NK - 7 – Rounding to the nearest ten or hundred | Pg 47
- Know how to round up or down to the nearest ten or hundred.
- Know that a number half way between two tens numbers or two hundreds numbers is rounded up.
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Teacher notes
Discuss with students where rounding might be helpful in everyday life and how rounding to tens or hundreds affects the precision of a calculation. For example, rounding up the cost of groceries means you can be sure you will have enough to pay for them when you get to the check out. Rounding to the nearest $1 is helpful in this situation but rounding to the nearest $10 or $100 is not. Rounding can also be helpful for checking whether an answer is reasonable.
NK - 8 – Ordering whole numbers | Pg 49
- Order whole numbers in the range 0-1000.
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Teacher notes
- Encourage students to start from the digit closest to the right of the number and work towards the left when ordering numbers.
- Don’t always give students numbers with the same number of digits to order so that they need to be aware of the value of the place as well as of the digit.
