Multiplication
Number
Embedded Files
Definition
Definition
Multiplication is the development of efficient multiplicative strategies for counting large collections of objects. An initial strategy is the process of repeated addition (adding the same number again and again). As students become more proficient in multiplicative strategies, they recognise that to determine how many shoes in 100 pairs of shoes, it is more efficient to add 2 lots of 100, instead of 100 lots of 2. (National Numeracy Learning Progression)
Other strategies involve developing some flexible number properties to be able to multiply large whole numbers.
This unit of work is to provide resources on how to multiply with whole numbers only using multiplicative strategies. For multiplication involving decimals, percentages and fractions please refer to the relevant units of work on decimals, fractions and percentages.
Teaching and learning activities
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials.
Select the download all icon to download all available activities or select each activity separately.
Knowing how to multiplyTeacher guided - Strategies on how to multiply by whole numbers only using repeated addition and flexible number properties.
Multiplicative problemsSolving a range of familiar and routine problems involving multiplication with whole numbers only.
Download all (ZIP)Download the resource pack containing all activities.
PLAN2 Areas of focus
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.
Relevance to the numeracy test marking
Relevance to the numeracy test marking
According to the ACSF, the feedback for a Level 3 performance in the HSC minimum standard online numeracy test for multiplication with whole numbers states that:
Individuals performing at this level are able to “select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts. They are also able to interpret and comprehend mathematical information in written material, diagrams, charts and tables”. They can use large whole numbers in words and figures and demonstrate their ability to calculate with whole numbers.
At Level 3, students must demonstrate their ability to calculate with whole numbers and perform a range of familiar and predictable calculations with multiplication related to small whole number values.
Connections with ACSF Level 3 descriptors
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how multiplication with whole numbers are assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Focus area: Explicitness and Complexity of mathematical information
Level 3 performance features:
Interprets and comprehends a range of everyday mathematical information that is embedded in familiar and routine texts · Interprets and comprehends whole numbers
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts.
Focus area: Mathematical knowledge skills: number and algebra
Level 3 performance features:
Calculates with whole numbers
Connections with Numeracy Learning Progression
Connections with Numeracy Learning Progression
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to multiplication with whole numbers are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Number Sense and Algebra
Sub-element: Multiplicative Strategies (MuS)
MuS2 — Perceptual multiples
MuS2 — Perceptual multiples
represents authentic situations involving equal sharing and equal grouping with drawings and objects (e.g. draws a picture to represent 4 tables that seat 6 people to determine how many chairs they will need; uses eight counters to represent sharing $8 between four friends)
MuS3 — Figurative (imagined units)
MuS3 — Figurative (imagined units)
uses perceptual markers to represent concealed quantities of equal amounts to determine the total number of items (e.g. to count how many whiteboard markers in four packs, knowing they come in packs of 5, the student counts the number of markers as 5, 10, 15, 20)
MuS4 — Repeated abstract composite units
MuS4 — Repeated abstract composite units
uses composite units in repeated addition using the unit a specified number of times (e.g. interprets ‘four lots of three’ additively and calculates 3 + 3 + 3 + 3 answering ‘12’)
MuS5 — Coordinating composite units
MuS5 — Coordinating composite units
identifies and represents multiplication in various ways and solves simple multiplicative problems using these representations (e.g. modelling as equal groups, arrays or regions)
identifies and represents multiplication and division abstractly using the symbols × and ÷ (e.g. represents 3 groups of 4 as 3 × 4; uses 9 ÷ 3 to represent 9 pieces of fruit being equally shared by 3 people)
MuS6 — Flexible strategies for single digit multiplication and division
MuS6 — Flexible strategies for single digit multiplication and division
draws on the structure of multiplication to use known multiples in calculating related multiples (e.g. uses multiples of 4 to calculate multiples of 8)
interprets a range of multiplicative situations using the context of the problem to form a number sentence (e.g. to calculate the total number of buttons in 2 containers, each with 5 buttons, uses the number sentence 2 × 5 = ?; if a packet of 20 pens is to be shared equally between 4, writes 20 ÷ 4 = ?)
demonstrates flexibility in the use of single-digit multiplication facts (e.g. 7 boxes of 6 donuts is 42 donuts altogether because 7 × 6 = 42; multiplying any factor by one will always give a product of that factor i.e.: 1 × 6 = 6; if you multiply any number by zero the result will always be zero)
uses the commutative and distributive properties of multiplication to aid computation when solving problems (e.g. 5 × 6 is the same as 6 × 5; calculates 7 × 4 by adding 5 × 4 and 2 × 4)
MuS7 — Flexible strategies for multiplication and division
MuS7 — Flexible strategies for multiplication and division
uses known mental and written strategies such as using the distributive property, decomposition into place value or factors to solve multiplicative problems involving numbers with up to three digits and can justify their use (e.g. 7 × 83 equals 7 × 80 plus 7 × 3; to multiply a number by 72, first multiply by 12 and then multiply the result by 6; 327 × 14 is equal to 4 × 327 plus 10 × 327)
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