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Negative Numbers (Operations (Adding to zero: Recognise pairs of equal…
Negative Numbers
Operations
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Subtracting positive numbers: Subtract one positive integer from another. Recognise that subtracting a larger from smaller integer results in a negative number.
Combining Integers: Combine positive and negative integers using addition and subtraction.
Add and subtract positive and negative integers. Use continuous number line model. Use charges model?
Doesn't include subtracting negatives.
Subtracting negative numbers: Seeing the minus sign as 'opposite of' and subtraction in a calculation. 5 - (-2) where taking away negative 2 is equivalent to adding 2. Subtraction as difference - number line.
Reasoning multiplicatively with negatives: Be aware of a number of ways of explaining negative multiplication and division. Includes distributive law arguments, patterns in multiplication and inverses, enlargements, repeated addition / subtraction ...
Making equivalent calculations: Recognise that numbers can be represented by any number of equivalent combinations of additions and subtractions.
Conceptual Understanding
Knowing zero: Recognise and work with zero as a benchmark value that has multiple meanings in mathematics, including:
- the empty set
- the whole number preceding 1
- less than any positive rational number
- a position on a number line
- a starting position for measurement
Comparing quantities: Relate subtraction to comparison situations in which the difference between two collections of objects (or images) needs to be found.
Knowing the minus sign: Work flexibly with numerical expressions that contain the minus sign.
Recognise that the minus sign may be interpreted to mean: subtraction; a negative number; and taking the opposite, and that its meaning may change during the calculation and equation solving process.
Linking order and cardinality: Understand that the number succeeding a given number denotes a cardinality one larger than the given number, and similarly for one less.
Extend this reasoning to numbers two more or two less than a given number and so on.
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Properties
Using the successor principle: Begin to recognise that every (whole) number has a succeeding number.
Changing quantities: Recognise addition and subtraction in 'change' situations where addition is related to an increase, and subtraction to a decrease in quantity.
Modeling
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Extending patterns in multiplication: Extend patterns in multiplication backwards to include negative numbers.
Real World Applications
Beginning to notice negative numbers: Become increasingly aware of negative numbers that arise in contexts such as temperature and debt.
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Strategies/Methods
Counting flexibly: Use a variety of strategies to count and compare the numerosity of collections of items up to and beyond 100, using conventional number names and symbols.
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