Teaching Point 1.3 - Composition of Numbers 0-5
Apply the partitioning structure to the numbers to five, and introduce children to new concepts such as subitising, ordinality and the bar model.
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Teaching Point 1.4 - Composition of Numbers 0-10
Extend the partitioning structure to the numbers six to ten, explore the five-and-a-bit structure of the numbers, and introduce children to the concept of odd and even numbers.
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Teaching Point 1.5 - Additive structures: introduction to aggregation and partitioning
Progress to the use of abstract notation (+, − and =) as a way of representing the part–part–whole structure.
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Teaching Point 1.6 - Additive structures: introduction to augmentation and reduction
Introduce children to addition as augmentation, and subtraction as reduction (take away), using a ‘first…, then…, now…’ story representation and abstract notation (+, − and =); explore the inverse nature of the two operations.
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Teaching point 1: Numbers can represent how many objects there are in a set; for small sets we can recognise the number of objects (subitise) instead of counting them.
Teaching point 2: Ordinal numbers indicate a single item or event, rather than a quantity.
Teaching point 3: Each of the numbers one to five can be partitioned in different ways.
Teaching point 4: Each of the numbers one to five can be partitioned in a systematic way.
Teaching point 5: Each of the numbers one to five can be partitioned into two parts; if we know one part, we can find the other part.
Teaching point 6: The number before a given number is one less; the number after a given number is one more.
Teaching point 7: Partitioning can be represented using the bar model.
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Teaching point 1: The numbers six to nine are composed of 'five and a bit'. Ten is composed of five and five.
Teaching point 2: Six, seven, eight and nine lie between five and ten on a number line.
Teaching point 3: Numbers that can be made out of groups of two are even numbers; numbers that can't be made out of groups of two are odd numbers. Even numbers can be partitioned into two odd parts or two even parts; odd numbers can be partitioned into one odd part and one even part.
Teaching point 4: Each of the numbers six to ten can be partitioned in different ways. The numbers six to ten can be partitioned in a systematic way.
Teaching point 5: Each of the numbers six to ten can be partitioned into two parts; if we know one part, we can find the other part.
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Teaching point 1: combining two or more parts to make a whole is called aggregation; the addition symbol, +, can be used to represent aggregation.
Teaching point 2: The equals symbol, =, can be used to show equivalence between the whole and the sum of the parts.
Teaching point 3: Each addend represents a part, and these are combined to form the whole/sum; we can find the value of the whole by adding the parts. We can represent problems with missing parts using an addition equation with a missing addend.
Teaching point 4: Breaking a whole down into two or more parts is called partitioning; the subtraction symbol, −, can be used to represent partitioning.
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Teaching point 1: An addition context described by a ‘first…, then…, now…’ story is an example of augmentation. We can link the story to a numerical representation – each number represents something in the story.
Teaching point 2: A subtraction context described by a ‘first…, then…, now…’ story is an example of reduction. We can link the story to a numerical representation – each number represents something in the story.
Teaching point 3: Given any two parts of the story we can work out the third part; given any two numbers in the equation we can find the third one.
Teaching point 4: Addition and subtraction are inverse operations.
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