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NA2-7: Generalise that whole numbers can be partitioned in many ways.

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Elaboration on this Achievement Objective

Students at level two should understand that numbers are counts that can be split in ways that make the operations of addition, subtraction, multiplication and division easier. From Level One students understand that counting a set tells how many objects are in the set. Building on this thinking at Level Two is to realise that the count of a set can be partitioned and that the count of each subset tells how many objects are in that subset. Also required is understanding that partitions of a count can be recombined. For example, a count of ten can be partitioned into 1 and 9, 2 and 8, 3 and 7, etc. This objective also involves critical choice of partitioning. For example, 8 + 6 = box. can be solved by partitioning 6 into 1 and 5, 2 and 4, 3 and 3. Of these partitions 2 and 4 is the best strategic choice since it recombines into a “ten and...” fact, that is, 8 + 6 = 8 + 2 + 4 = 10 + 4. At Level Two students are expected to understand the strategic importance of using place value as a way to partition numbers. Students should apply their partitioning generalisation to many problem types including combining (27 + 9 = box. ), separating (105 - 19 = box. ), comparing (45 + box. , = 106), duplicating (8 x 5 = box. ) and sharing (20 ÷ 4 = box. ).

 

Teaching resources for this Achievement Objective
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Coin Control

Level Two
Number and Algebra
Figure It Out activities
This is a level 2 algebra strand activity from the Figure It Out series. It also has an achievement objective from the Level 2 Number strategies substrand. A PDF of the student activity is included.

link repeated addition to multiplication

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Dual patterns

Level Two
Number and Algebra
Units of Work
This unit develops pattern-based thinking through the exploration of a pattern that has more than one attribute and more than one unit of repeat.
  • Create, describe and continue single-attribute and two-attribute repeating patterns with varying numbers of elements.
  • Identify and replace missing elements in a repeating pattern.
  • Identify, describe, and create composite patterns.
  • Identify the unit of repeat in a repeating pattern and apply known300
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Fraction bits and parts

Level Two
Number and Algebra
Units of Work
This unit explores the beginnings of proportional thinking by introducing fractions and associated language. The purpose for this unit is to make, name, and recognise wholes, halves, third parts, fourth parts and fifth parts of a variety of objects.
  • count in fractions forwards and backwards to a named whole number.
  • recognise the whole of an object, part of an object, and equal parts and their names.
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Fractions as numbers

Level Two
Number and Algebra
This unit explores fractions as an extension of the whole number system. Students learn the meaning of the numerator (top number) and denominator (bottom number) in fractions symbols. They also learn to express equal shares as fractions and to order related fractions.
  • Partition circles and lengths into equal parts and name the parts using fractions.
  • Write fractions in words and symbols.
  • Give the meaning of the numerator and denominator in a fraction.
  • Order fractions that have the same numerator or the same denominator.
  • Create a number line to show a set300
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Mapping relationships

Level Two
Number and Algebra
Units of Work
The purpose of this unit of two lessons is to develop relational thinking through the exploration and expression of the relationship between two related number patterns.
  • Recognise relationships between two number sets.
  • Use a ‘mapping diagram’ to show a number relationship.
  • Understand the connection between the coordinate systems of maps and graphs.
  • Identify a situation in which there is a unique relationship between two data sets.
  • Transfer mapped values onto a graph (an300
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Odd and even numbers

Level Two
Number and Algebra
Units of Work
The purpose of this unit is to explore a pattern that is central to our number system: odd and even numbers.
  • Identify even and odd numbers.
  • Independently investigate, recognise and report on the patterns and characteristics of even numbers and of odd numbers.
  • State generalisations about the addition and subtraction of even numbers and of odd numbers.
  • Investigate and recognise the results of adding and300
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One Hundred Hungry Ants

Level Two
Number and Algebra
Picture book activities
This is an activity based on the picture book One Hundred Hungry Ants.
  • Students will be able to model a whole number as an array created from a set of equal groups.
  • Students will be able to express the arrays they create as additive statements or multiplication statements.
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Partitions

Level Two
Number and Algebra
Units of Work
This unit is about partitioning whole numbers. It focuses on partitioning numbers to “make a ten” or a decade when adding whole numbers, for example 8 + 6 can be solved as (8 + 2) + 4. The unit uses measurement as a context.
  • Partition numbers less than 10.
  • Know and use "teen" facts.
  • Solve addition problems by making a ten, or making a decade.
  • Solve addition problems involving measurements.
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Something Adds Up

Level Two
Number and Algebra
Figure It Out activities
This is a level 2 algebra strand link activity from the Figure It Out series. A PDF of the student activity is included.

generalise the addition pattern for numbers that add to 100

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Train Talk

Level Two
Number and Algebra
Figure It Out activities
This is a level 2 algebra activity from the Figure It Out series. It also has the achievement objective from the Level 2 Number strategies substrand. A PDF of the student activity is included.

link repeated additon to multiplication

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Trimming Trees

Level Two
Number and Algebra
Figure It Out activities
This is a level 2 number activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.

know the number of ones and tens in numbers

partition numbers into ones and tens

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What's going on?

Level Two
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using their number knowledge to understand and use an unfamiliar process.
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What's my number?

Level Two
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using their knowledge of number operations to find an unknown.