1.26

Composition and calculation: multiples of 1000 up to 1, 000, 000

1.27

Negative numbers: counting, comparing and calculating

1.28

Common structures and the part-part-whole relationship   

1.29

Teaching point 1: Understanding of numbers composed of hundred thousands, ten thousands and one thousands can be supported by making links to numbers composed of hundreds, tens and ones.
 

Teaching point 2: Multiples of 1,000 up to 1,000,000 can be placed in the linear number system by drawing on knowledge of the place of numbers up to 1,000 in the linear number system.
 

Teaching point 3: Numbers can be ordered and compared using knowledge of their composition and of their place in the linear number system.
 

Teaching point 4: Calculation approaches for numbers up to 1,000 can be applied to multiples of 1,000 up to 1,000,000.
 

Teaching point 5: Numbers can be rounded to simplify calculations or to indicate approximate sizes.
 

Teaching point 6: Known patterns can be used to divide 10,000 and 100,000 into two, four and five equal parts. These units are commonly used in graphing and measures.

Teaching point 1: Positive and negative numbers can be used to represent change.
 

Teaching point 2: Our number system includes numbers that are less than zero; these are negative numbers. Numbers greater than zero are positive numbers.
 

Teaching point 3: The negative/minus symbol (−) is placed before a numeral to indicate that the value is a negative number.
 

Teaching point 4: Negative numbers can be shown on horizontal scales; numbers to the left of zero are negative (less than zero) and numbers to the right of zero are positive (greater than zero). The larger the value of the numeral after the negative/minus symbol, the further the number is from zero.
 

Teaching point 5: Knowledge of the positions of positive and negative numbers in the number system can be used to calculate intervals across zero.
 

Teaching point 6: Negative numbers are used in coordinate and graphing contexts.

Teaching point 1: Mathematical relationships encountered at primary level are either additive or multiplicative; both of these can be observed within the structure of part–part–whole relationships.
 

Teaching point 2: Problems in many different contexts can be solved by adding together the parts to find the whole. Different strategies can be used to calculate the whole, but the structure of the problem remains the same.
 

Teaching point 3: If the value of the whole is known, along with the values of all but one of the parts, the value of the missing part can be calculated. Different strategies can be used to calculate the missing part, but the structure of the problem remains the same.
 

Teaching point 4: Problems in many different contexts have the ‘missing-part’ structure.

Teaching point 1: If one addend is increased and the other is decreased by the same amount, the sum stays the same. (same sum)
 

Teaching point 2: If one addend is increased (or decreased) and the other is kept the same, the sum increases (or decreases) by the same amount.
 

Teaching point 3: If the minuend and subtrahend are changed by the same amount, the difference stays the same. (same difference)
 

Teaching point 4: If the minuend is increased (or decreased) and the subtrahend is kept the same, the difference increases (or decreases) by the same amount.
 

Teaching point 5: If the minuend is kept the same and the subtrahend is increased (or decreased), the difference decreases (or increases) by the same amount.
 

Teaching point 6: The value of the expressions on each side of an equals symbol must be the same; addition and subtraction are inverse operations. We can use this knowledge to balance equations and solve problems.