Student Learning Path

S6192 Teaching number: 0 to 9 (RTN2)

Published 27/05/2013
TLF-ID S6192

This is a video for teachers describing the use of the Rathmell triangle as a teaching model for teaching rational counting of the numbers 0 to 9. Featuring a discussion between two mathematics educators, the video explains that the three points of the triangle model are representation, language and symbol. It then illustrates simple activities that can be used for moving back and forth between each of these points of the triangle. The video emphasises that rational counting is about quantity and it also includes a discussion about teaching the concept of 'zero'.

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S6191 Teaching place value: 20 to 99 (RPV1)

Published 27/05/2013
TLF-ID S6191

This is a video for teachers describing activities for teaching place value for the numbers from 20 to 99. Featuring a discussion between two mathematics educators, the video illustrates useful resources including concrete and pictorial representations of numbers, place value charts, number expanders and number flip-cards. The video refers to the use of the Rathmell triangle as a teaching model and illustrates mix-and-match activities that move back and forth between the points of the triangle: representation, language and symbol. The video also recommends an effective learning sequence for understanding place value for numbers 20 to 99.

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S6184 Using a hands-on approach to develop mental strategies for subtraction (BH04)

Published 27/05/2013
TLF-ID S6184

This is a video for teachers in which a hands-on approach to developing mental strategies for subtraction is discussed by two mathematics educators. The video demonstrates how children can use their fingers in groups of 10s and 1s to represent numbers and solve a subtraction problem using various mental strategies including 'partitioning and rearranging parts' and 'rounding and compensating'. The video also shows how the 'think addition' strategy can be used to find the difference between two numbers.

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S6181 Using a hands-on approach to represent numbers to 10 (BH01)

Published 27/05/2013
TLF-ID S6181

This is a video for teachers describing a hands-on approach to teaching the numbers to 10 and subitising in the early years. Consisting of a discussion between two mathematics educators, the video critiques the classroom use of various concrete representations of numbers to 10 including Cuisenaire rods, linking cubes and the 10 frame. The video illustrates how teachers could use different representations of numbers to 10 in a classroom situation, including how children can use their fingers to show numbers to 10 to an audience.

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S6193 Teaching place value: teen numbers (RPV2)

Published 27/05/2013
TLF-ID S6193

This is a video for teachers describing mix-and-match activities based on the Rathmell triangle model for teaching place value for numbers from 11 to 19. Featuring a discussion between two mathematics educators, the video discusses the prerequisites for teaching place value for teen numbers and suggests an effective learning sequence. It points out that the main difficulty with teen numbers is caused by the number name in English and discusses problems students can have in moving between name and symbol. The video illustrates useful resources including concrete and pictorial representations, 10 frames and cards with number names.

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S6195 Using language stages to develop multiplication concepts (CLSM)

Published 27/05/2013
TLF-ID S6195

This is a video for teachers in which two mathematics educators discuss the development of the concept of multiplication and demonstrate the models used to teach this concept, particularly the set model and array model. The video refers to the four language stages - child's language, materials language, mathematical language and symbolic language - and looks at how a student's vocabulary of multiplication develops through activities based on the set and array models. The video illustrates how storybooks can be used as the basis for multiplication activities for early years.

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S6194 Powerful strategies to help struggling students: bridge to 10 (SSS2)

Published 27/05/2013
TLF-ID S6194

This is a video for teachers describing an approach to help struggling students learn and apply the 'building to 10' strategy for addition. Featuring a discussion between two mathematics educators, the video emphasises the need to develop an understanding of this strategy in early years. The video illustrates how a sequence of activities for teaching the strategy would start from the concrete and move to the pictorial - giving a visual representation of the associative property - and then be expressed symbolically as equivalent number sentences. The video explains that the visual model can be used through subsequent years and modified to teach addition of decimals in late primary years.

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S6189 Using structured patterns to develop number combinations (BSPN)

Published 27/05/2013
TLF-ID S6189

This is a video for teachers showing how structured patterns, such as dice and domino patterns and the 10 frame, can help develop students' ability to subitise and can also be used to introduce addition. In the video two mathematics educators illustrate ways of using these structured patterns in the classroom and discuss a number of mental strategies for addition. They list four questions that can be asked about numbers represented in a 10 frame and also introduce the double 10 frame and triple 10 frame.

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S6190 Introduction to teaching addition number facts (CIAF)

Published 27/05/2013
TLF-ID S6190

This is a video for teachers illustrating how the 100 facts shown on an addition number facts chart can be taught using three mental strategies: 'count on', 'use doubles' - including 'doubles plus 1' and 'doubles plus 2' - and 'building to 10' (referred to as 'bridge to 10'). The video features two mathematics educators discussing how an understanding of each of these strategies can be developed using a four-stage approach: introduce, reinforce, practice, extend. The video emphasises the importance of teaching students how to think rather than just recalling facts, and it provides suggestions for teaching one of the strategies - 'doubles plus 1' - using visual models, activities and games.

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S6182 Using a hands-on approach to represent 10s and 1s (BH02)

Published 27/05/2013
TLF-ID S6182

This is a video for teachers describing a hands-on approach to teaching the numbers beyond 10. Featuring a discussion between two mathematics educators, the video emphasises the need to develop an understanding in early years of the importance of grouping in 10s. It examines the classroom use of various concrete representations of the number 10 such as bundling straws, linking cubes and base-10 blocks. The video illustrates how children can use their fingers in groups of 10s and 1s to represent numbers beyond 10 and explains how using this method can help to develop an understanding of place value.

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S6183 Using a hands-on approach to develop mental strategies for addition (BH03)

Published 27/05/2013
TLF-ID S6183

This is a video for teachers in which a hands-on approach to developing mental strategies for addition of one- and two-digit numbers is discussed by two mathematics educators. The video demonstrates how children can use their fingers in groups of 10s and 1s to represent and add two numbers using strategies such as 'building to 10' and 'partitioning and rearranging parts'. The video also shows how linking cubes can be combined with fingers for more complex additions, and illustrates the 'rounding and compensating' strategy using this method.

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S6185 Using mental strategies to add (BAMS)

Published 27/05/2013
TLF-ID S6185

This is a video for teachers featuring a discussion between two mathematics educators describing classroom activities to develop mental strategies for adding two- and three-digit numbers and decimal fractions. The video details how number sentences can be used in conjunction with linking cubes to develop student competence in adding two-digit numbers by encouraging the use of mental strategies such as 'building to 10', 'adding 10', 'partitioning and rearranging parts' and 'rounding and compensating'. The video also illustrates how these mental strategies for adding two-digit numbers can be applied when adding three-digit numbers and decimal fractions.

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S6188 Analysing patterns (skip counting) on a hundred board (BPHB)

Published 27/05/2013
TLF-ID S6188

This is a video for teachers illustrating how a hundred board starting at 1, with counters placed on multiples, provides a visual model to help students to skip count and to identify visual and number patterns in multiples. In the video two mathematics educators discuss skip counting by 1s, 5s, 4s, 3s, 9s, 6s, 8s and 7s, the order they suggest for teaching. They explain how these activities using the hundred board can also be used to introduce the concept of multiplication as repeated addition. The video also illustrates a sharing activity using three containers and a number line for introducing skip counting by 3.

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S6186 Comparing and developing mental computation strategies (BMSA and BMSQ)

Published 27/05/2013
TLF-ID S6186

This is two teacher videos describing mental computation strategies. BMSA describes and compares a range of strategies for addition. Two mathematics educators discuss the importance of mental computation for addition and explain that there is no one correct strategy. They describe and evaluate strategies, including counting on (the least efficient), using doubles and near doubles, 'building to 10', 'adding 10', 'partitioning and rearranging parts' and 'rounding and compensating'. The related resource BMSQ describes a teaching method based on the use of questioning to assist students to develop, reflect on, communicate and apply mental strategies. The two mathematics educators provide a sequence of questions that help students to reflect on and communicate their own mathematical thinking processes. This includes explanation, justification, alternative thinking, comparative thinking, generalisation, reflection, verification and application

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