Foundation Skills & Pathways · TAFE Foundation Ski lls & Pathways v2 Page . 8. of . 50. Cooperative grouping . When students work in supervised, cooperative groups, they are able

Foundation Skills & Pathways

Booklet 7

Support the development of numeracy skills

CHCEDS006

Student notes

2017

CHCEDS006 Numeracy Skills

TAFE Foundation Skills & Pathways v2 Page 2 of 50

Numeracy Skills

Unit Name: Support the development of numeracy skills

Unit Codes: CHCEDS006

Unit Purpose:

This unit describes the skills and knowledge required to implement numeracy programs as identified by the teacher to assist students requiring additional numeracy support.

Application

This unit applies to education support work in a variety of contexts and the work is to be undertaken with appropriate guidance, support and supervision by a nominated teacher or other education professional.

Elements of Competence:

1. Apply developmental and learning approaches to basic numeracy skills under supervision of teacher

2. Implement a numeracy support program 3. Support student numeracy programs.



ELEMENTS OF COMPETENCE Elements define the essential outcomes.

Performance criteria specify the level of performance needed to demonstrate achievement of the element.

1. Apply developmental and learning approaches to basic numeracy skills under supervision of teacher

1.1 Identify the skills and knowledge required by students to make meaning of numbers and basic computations 1.2 Identify numeracy processes that are relevant and appropriate to the student’s ability and year level according to specified guidelines and practices of the school 1.3 Identify links between mathematical/numeracy processes and maths support strategies 1.4 Apply learning models and language to meet student needs

2. Implement a numeracy support program

2.1 Provide a numeracy support program as directed by the teacher, to meet the individual needs of students whilst taking into account their preferred learning styles 2.2 Select and implement activities to support understanding of numbers, use of number computations, measurement and numerical data 2.3 Record students’ progress in accordance with program/school guidelines 2.4 Maintain student confidentiality at all times

3. Support student numeracy programs

3.1 Implement support strategies, under direction of supervising teacher, to accommodate student’s ability according to education guidelines and program specifications 3.2 Encourage the development of self-reliance in numeracy through positive feedback

Performance Evidence

The candidate must show evidence of the ability to complete tasks outlined in elements and performance criteria of this unit, manage tasks and manage contingencies in the context of the job role. There must be demonstrated evidence that the candidate has completed the following tasks: • analysed what at least two students are doing when working mathematically

and applied an appropriate model of learning to develop the students’ numeracy skills

• implemented numeracy support programs to support at least two students who may be at various levels, as directed by the teacher

• maintained and completed workplace records • communicated with a range of students, including:

• active listening • giving clear directions and/or instructions

• consulted with the teaching team and other education support workers on workplace procedures and new approaches to accommodate individual student requirements.



Topic Area One Apply developmental and learning approaches to basic numeracy skills under supervision of teacher.

Performance Criteria:

1.1 Identify the skills and knowledge required by students to make meaning of numbers and basic computations 1.2 Identify numeracy processes that are relevant and appropriate to the student’s ability and year level according to specified guidelines and practices of the school 1.3 Identify links between mathematical/numeracy processes and maths support strategies 1.4 Apply learning models and language to meet student needs

Student Notes: An important role that SLSO play within the educational environment is supporting students who are experiencing difficulties with numeracy. This unit will examine some of the support strategies available to SLSO in the classroom and small numeracy groups and will also provide a clearer picture of how students develop skills in this area.

The approach that a teacher or SLSO takes to the instruction of numeracy and mathematics can help form the future attitude that a student will carry with them throughout their life around the concept of mathematics. Many people have had poor experiences with maths and carry a burden of fear or unhappiness about it.

As a SLSO you need to understand your own feelings about maths and work with your learner/s to find a positive and achievable approach to teaching and learning in this area of the curriculum. To this end, the concepts of explicit and discovery learning are offered as a way of approaching the barriers that some students may feel towards maths.



Activity 1

Class Discussion - How do you feel about Maths?

1. What do you think of when we say the word ‘Mathematics’?

2. How did you feel about maths at school? Talk about your classes, teachers, and parents. What did you like/dislike?

a) What happened if you didn’t understand something in maths classes?

b) What areas of maths make you feel most fearful?

c) What areas of maths do you feel most confident about?

After considering your answers to the above, answer the following:

a) When you work with your students do you pass on your attitudes about maths? Are they positive or negative?

b) What words do you use that point to the attitudes that you share with the students?

c) What does your body language say?

d) How can you consciously try to be positive about how you help students approach challenges and frustrations in their maths work?

e) What do you say?

f) What do you do?



What is numeracy?

“Numeracy involves using mathematical ideas efficiently to make sense of the world. While it necessarily involves understanding some mathematical ideas, notations and techniques, it also involves drawing on knowledge of particular contexts and circumstances in deciding when to use mathematics, choosing the mathematics to use and critically evaluating its use. Each individual’s interpretation of the world draws on understandings of number, measurement, probability, data and spatial sense combined with critical mathematical thinking.”

(DEC NSW 2015)

The role of literacy and language in numeracy

People use a shared language for thinking and talking. Mathematical language including symbols, graphs, and tables and diagrams plays an important part in the acquisition of ideas and concepts. Students need to be able to think mathematically and to express their ideas clearly and logically to achieve success in mathematics.

Language also provides a link between concrete examples and abstract representations. For example, a student who doesn’t understand the term ‘divided by’ or recognise the ‘÷’ symbol may be able to take twenty lollies and share them equally between five children. However, they are unlikely to successfully complete a text book exercise of division sums.

Students also need to be able to use and understand the appropriate mathematical terminology to benefit from discussing; describing and justifying (identified as key competencies) what they are doing in cooperative learning groups, which are often used to reinforce mathematical instruction.

The vocabulary of maths can be classified into three different groups:

1. Words that mean the same as they do in ordinary language – these words present little difficulty, but do need to be used appropriately with the correct context. For example, equal and more.

2. Words that are used only in mathematics – these words need to be explicitly taught simultaneously with skill and concept teaching to avoid confusion. For example, numeral and equilateral.



3. Words that have different meaning form what they do in ordinary language – these words are most difficult for students to grasp because of confusion between the different meanings. For example, times, from, face.

This situation is further complicated by the fact that:

• One skill or operation can be described by a variety of words. For example, minus, take away and subtract may be used at different times to refer to the one operation, and

• Students may make faulty generalisations about verbal cues in written problems or fail to read the whole problem, relying on cue words. For example, compare the use of more in the following problem:

Hamit delivered 28 newspapers on Sunday and 40 newspapers on Monday. How many more papers did he deliver on Monday?

Hamit delivered 40 newspapers on Monday. He delivered 12 more than that on Sunday. How many papers did he deliver on Sunday?

Both problems have more as a key or cue word. However, in the first example, subtraction was the required operation, whereas in the second example, addition was required.

There are several strategies that can be used to reinforce student’s use and understanding of mathematical terminology, including:

Words in context

The most important strategy to use in teaching mathematical vocabulary is to teach the words in context. Students need many opportunities to become competent users of mathematical language by building up knowledge about the language of the topic at the same time as they are learning the skills and processes involved.

Restrict vocabulary

The variety of terms used for any one skill, idea or concept should be restricted until the student has mastered one term. SLSO need to check with their classroom teachers about the preferred terminology, and use this consistently with students.



Cooperative grouping

When students work in supervised, cooperative groups, they are able to practice the skills that have been taught and use the appropriate language to discuss what they are doing. This enables students to clarify their thinking and consolidate their understanding of mathematical concepts. It also helps to bridge the gap between the school learning environment and real-life use of the concepts.

Displays

Charts can be displayed around the room reminding students of the mathematical meaning of words. The charts should include illustrations and examples of how the word should be used. SLSO can assist in the preparation of teaching aids.



Activity 2

The language of Maths

1. Why is it important for students to have a good understanding of the mathematical language associated with the skill or concept that they are learning?

2. Identify two (2) words (not those given in the topic notes) for each of the following categories:

Words that mean the same as they do in ordinary language

Words that are used only in maths

Words that have a different meaning from what they do in ordinary language



3. Complete the following chart by placing the words / phrases in the correct columns:

+ - X ÷ =

the same as the sum of how many?

Less makes divide

Equals add plus

Join bunches of difference

Is equal to multiply remove

Minus altogether and

Times total rows of

Groups of take away subtract



The K-10 Mathematics Syllabus

The K-10 Mathematics Syllabus replaces the previous K-6 and 7-10 syllabii. The K–10 syllabuses are inclusive of the learning needs of all students. Particular advice about supporting students with special education needs, gifted and talented students, and students learning English as an additional language or dialect is included in the syllabuses.

To support students in the development of mathematics skills it is important to have an overview of the syllabus and how it operates.

Introduction: Click on the link below to watch the Powerpoint: Guide to the new Mathematics K-10 syllabus

http://syllabus.bos.nsw.edu.au/mathematics/mathematics-k10/guide-to-the-new-syllabus/

The following notes are adapted from the NSW Mathematics K-10 syllabus (DEC NSW 2015)

The Mathematics K-10 syllabus is divided as follows:

Working Mathematically

Students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning

Content is organised by strands and substrands:

Number and Algebra

Students develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation

Measurement and Geometry

Students identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems

Statistics and Probability

Students collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements





http://syllabus.bos.nsw.edu.au/mathematics/mathematics-k10/




Supporting Students in Mathematics with Special Education Needs

The Mathematics K–10 Syllabus recognises that students learn at different rates and in different ways. By using the teaching and learning cycle (assessing, planning, programming, implementing and evaluating), teachers can ensure that the individual learning needs of all students are considered and a learning environment is created that supports students to achieve the outcomes of the syllabus.

Teachers should undertake regular and ongoing assessment to ensure students are making sufficient progress and to identify any difficulties they may be experiencing in their learning.

The following figure illustrates one method of planning and programming that incorporates the principles of assessment:



Most students with special education needs will access learning experiences based on the regular syllabus outcomes and content. However, they may require additional support, including adjustments to teaching, learning and assessment activities.

All decisions regarding curriculum options for students with special education needs should be made within the collaborative curriculum planning process.

When programming for students with special education needs, appropriate teaching procedures and strategies should be selected. Students who are experiencing difficulties generally benefit from:

new material presented in small steps additional explanation pre-teaching of expected prior knowledge, strategies and skills

necessary for learning new related concepts repeated modelling guided practice extensive independent practice explicit teaching of learning strategies (cognitive and metacognitive

strategies) additional teaching and learning experiences at each phase of learning

(acquisition, fluency, maintenance, generalisation) instructional scaffolding.

The Mathematics K–10 Syllabus is organised into a Working Mathematically strand and three content strands: Number and Algebra; Measurement and Geometry; and Statistics and Probability.

The syllabus is written with the flexibility to enable students to work at different stages in different strands. For example, students could be working on Stage 4 content in one strand and Stage 3 content in another.

Find further information about the organisation of content in the Mathematics K–10 Syllabus.

In particular, students with special education needs may experience difficulties in Mathematics in relation to:

insufficient background knowledge and/or lack of fluency with key facts, concepts, strategies and procedures

understanding the symbols and language specific to mathematics selecting an appropriate strategy to address a problem, remembering

steps in a strategy and/or reflecting on their use of the strategy understanding critical features of a concept and/or generalising key

facts, concepts, strategies and procedures to other contexts remembering key facts, concepts, strategies and procedures.



Students with special education needs may require a range of adjustments and assistance in order to develop numeracy skills and apply these across a range of contexts. Suggestions for supporting students with special education needs in Mathematics include:

providing multiple opportunities for practice, review, discussion and application

use of visual scaffolds to aid memory developing knowledge, skills and understanding that move from simple

to complex using examples and non-examples to illustrate a concept modelling mathematics-specific language developing understanding of mathematics-specific language through

the use of synonyms, definitions and meanings of prefixes presenting content in smaller, more manageable steps additional demonstration of key facts, concepts, strategies and

procedures additional guided practice, independent practice and feedback using instructional scaffolding, such as modelling, cues, partial

solutions and teacher questioning demonstrating cognitive strategies to support problem-solving, such as

visualising, verbalising, self-questioning, highlighting key information and procedural prompts

providing opportunities for metacognitive strategies, such as self-instruction, self-questioning and self-monitoring

providing written procedures for problem-solving pre-teaching prior expected learning of key facts, concepts, strategies

and procedures necessary for new learning explicit teaching of alternative uses of everyday language in the

context of mathematics.

YEARS 7–10 LIFE SKILLS

For some students with special education needs, particularly those students with an intellectual disability, it may be determined that the Years 7–10 Life Skills outcomes and content can provide a more meaningful program.

For more information in relation to teaching Mathematics to students with special education needs, refer to the following support documents:

Mathematics K–6 Support Document for Students with Special Education Needs

http://k6.boardofstudies.nsw.edu.au/go/mathematics/support-students-special-needs/

http://k6.boardofstudies.nsw.edu.au/go/mathematics/support-students-special-needs/



Activity 3

1. In small groups, click on the following link to browse the online interactive syllabus:


Use the navigation on the left side to look at:

• Outcomes • Content • Syllabus elements • Support materials • Special education needs

2. In your group, click on the following link to look at some Sample Units. Discuss your findings within your group.

http://syllabus.bos.nsw.edu.au/support-materials/sample-units/

3. In your group, click on the following link to browse the online Mathematics K-6 Support Document for Students with Special Education Needs. Discuss your findings within your group.

http://k6.boardofstudies.nsw.edu.au/wps/portal/go/mathematics/support-students-special-needs

4. Under Implementation, look at and discuss the information about Adjustments:

http://k6.boardofstudies.nsw.edu.au/wps/portal/go/mathematics/support-students-special-needs/implementation/adjustments

5. Click on the following link to choose a specific Case Study for your group to look at in detail. Each group will then report the ideas they found to the class.

http://k6.boardofstudies.nsw.edu.au/wps/portal/go/mathematics/support-students-special-needs/case-studies


http://syllabus.bos.nsw.edu.au/support-materials/sample-units/









Topic Area 2 Implement a numeracy support program

Performance Criteria:

2.1 Provide a numeracy support program as directed by the teacher, to meet the individual needs of students whilst taking into account their preferred learning styles 2.2 Select and implement activities to support understanding of numbers, use of number computations, measurement and numerical data 2.3 Record students’ progress in accordance with program/school guidelines 2.4 Maintain student confidentiality at all times

Student Notes:

Concepts and thinking strategies

It is important for SLSOs to understand the terms, ‘concepts’ and ‘thinking strategies’ that are referred to throughout this document. Therefore, a brief description of these terms is included at this point.

Teaching concepts

Mathematical attributes or properties can be grouped as concepts because of common features than can be identified in the members of the group. For example, a shape that has four sides of equal length and four right angles fits the concept of a square.

Concepts are helpful in teaching mathematics because they enable new skills to be related to skills that have been learned earlier. Y identifying the sameness through a set of examples and non-examples of a concept, students are able to generalise their thinking to other members of the concept set. For example, when teaching the concept of a square, teachers and SLSOs can demonstrate and describe the features of objects that are, and are not squares, by using and describing concrete objects



that are squares and are not squares. This may commence with activities as simple as sorting or grouping.

When learning concepts, students need to be given many opportunities to find and work with examples and non-examples of the concept. In this way, they are able to generalise their knowledge and understanding about mathematical attributes and properties into a concept to identify other untaught examples of the concept.

Thinking strategies

The ways that students think mathematically in order to solve mathematics tasks are referred to as mathematical thinking strategies. The Working Mathematically strand of the mathematics curriculum involves the development of students’ thinking strategies. The following scenario demonstrates the need for students to use effective thinking strategies.

Two students were asked to solve the addition sum: 12 + 14 = ___.

Chris wrote: 12 + 14 = 25, Thomas wrote 12 + 14 = 26.

The students were asked to explain how they reached their answers.

Chris’s explanation

Teacher: Can you tell me how you did this sum?

Chris: I just did it in my head

Teacher: Did you count?

Chris: No. I didn’t need to.

Thomas’s explanation

Teacher: Can you tell me how you did this sum?

Thomas: Well, I added 10 to 12 and then added 4.

In this explanation, it is clear that Chris did not use a counting strategy to solve the task. However, Thomas used the base ten strategy reasoning that 12 + 10 = 22, so he could add ten and then add the remain 4 units from 14 to equal 26.

Students need to be given encouragement and guidance to develop increasingly more efficient strategies. One of the difficulties in getting students to use more complex strategies is that although less efficient strategies are slower, they do work. Therefore, some students prefer to use the less efficient strategy than to take risks and experiment with



more abstract strategies which will ultimately demand less effort and time.

For example, when asked to do the sum: 56 + 74 = ____, Tony a year four student, counted out 74 counters. Once he had 74 counters he had to recount each one, this time beginning his count at 57. Although Tony finally arrived at the correct answer, this was an extremely inefficient and time consuming strategy.



Approaches to Mathematics Instruction

Two common approaches that have been adopted to teach mathematics are discovery learning and direct instruction.

Discovery learning

Discovery learning is an approach which encourages students to gain knowledge and skills by exploring concepts. Teachers often use this approach by placing students in small groups to experiment with mathematical ideas and concepts. It can be a valuable learning experience when all students are actively involved. However, for some students with disabilities and learning difficulties it is important to determine whether they are achieving the desired learning outcomes, and are actively engaged in the activities.

When students learn by discovery, they need to have a certain amount of prior knowledge, be self-motivated learners and be able to use effective thinking strategies to solve problems. Students with learning difficulties or disabilities that cause difficulties with learning may not have these skills and therefore may not benefit from this approach.

It is also important to note that some students may have the prior knowledge and skills, but may have difficulty generalising it across different situations. SLSO can assist students in this process by providing verbal, gestural or physical prompts and cues during the lesson.

Direct Instruction

Direct instruction is an effective approach used to teach specific skills. It involves the explicit teaching of the skill using a structured, systematic approach to program design and instruction. As in discovery learning, direct instruction uses students’ everyday experiences and real-life examples to teach skills.

In order for students with learning difficulties to master mathematical concepts, direct instruction that is accompanied by many opportunities for success by practicing the skills, is required in structured learning situations.

Several steps need to be followed to ensure that students learn using this approach.

Deciding what needs to be taught

It is important that students are ready to learn a new skill before being expected to do so. For example, a student who cannot count objects should not be expected to add numbers. They will need to master the skill of counting objects first. Decisions regarding he students’ programs will be made by the teacher and, where applicable, the students’ learning



support team. SLSO assist in the implementation of the program that has been designed by classroom teachers.

Demonstrating of modelling the skill or strategy

Teachers and SLSOs need to demonstrate a skill or strategy ensuring that the students are watching. In order to teach the skill and/or strategy correctly, SLSO should consult with teachers to ensure that they are using the same technique and terminology as that used by the teacher.

SLSOs who use modelling techniques should:

• make sure the students are listening before the demonstration begins and that they attend throughout the demonstration

• use cues and prompts to draw students’ attention to key features

• keep the demonstration short and ensure that students model the skill or strategy immediately after the demonstration

• repeat the demonstration as often as is required

• allow many opportunities for rehearsal and practice of the modelled response

• give demonstrations using a variety of materials and in a range of contexts

• encourage students to become independent by fading the number of steps demonstrated, the type of assistance provided (e.g. progress from physical to gestural to verbal prompts) and the amount of assistance given is a set time frame

• Give frequent and sincere praise and encouragement.

(adapted from Cole and Chan 1990:208)

Concrete to abstract

The use of concrete materials is important in mathematics teaching and learning for the following reasons:

• The manipulation of concrete materials aids concept and skill development and enhances understanding of processes

• Structured games provide opportunities for students to practise and consolidate skills and encourage speed in mental calculation. Additionally, there is potential for developing spatial visualisation skills in an enjoyable way.

• Puzzles and strategy games develop problem-solving, spatial and organisational skills



• Students’ use of materials provides them with opportunities to talk and write in English or other languages about their mathematical experiences.

(Mathematics K-6 Syllabus, NSWDSE, 1989:32)

The early stages of mathematical skill development should follow a sequence of concrete to abstract. When a new skill is introduced students should be given the opportunity to work with concrete materials and real-life examples and gradually move to more abstract representations of the skill.

Concrete materials include and toy, peg, coin, counter or other item that the student can easily move around on a table or floor.

Some students with an intellectual disability will remain at the concrete stage of learning into secondary school, or continue to use concrete materials to perform basic mathematical operations into their adult life.

Calculators

Students who are experiencing difficulties in mastering basic operations may be taught to use a calculator to perform these tasks. In this way, they can be helped to become independent in many real life situations. However, time must be spent teaching students how to use the calculator properly.

A calculator can:

• Provide the correct answer quickly and accurately

• Focus attention on the problem

• Give confidence

• Provide motivation

• Act as a catalyst for new learning

• Serve as an assessment tool

• Extend students’ facility with numbers

Guided practice

Once the skill or strategy has been demonstrated and modelled students need to have immediate and adequate guided practice at performing the skill or strategy until they had mastered it.

During guided practice, students should be asked questions that prompt them to use previously acquired and newly taught skills and strategies. Work should be checked after each attempt to ensure that the skill is not practised incorrectly due to a lack of understanding. The worksheet on



the following page is an example of an activity that can be started off with some help but once the learner ‘gets the hand of it’ should be able to continue on their own.

Independent Practice

When the skill or strategy is mastered students need further opportunities for repetition through independent practice to increase their fluency. Written pen and paper tasks, games and oral recall may be used to develop fluency. For example:

• Textbook exercises and worksheets encourage progression from concrete to abstract thinking

• Board games or dice games can be used to practise counting skills

• Chanting tables to a rhythm helps students to recall multiplication tables.

Examples of activities

On the following pages are some different examples of games and/or activities that help to reinforce learning.



Eratosthenes Sieve

Named after the Greek Mathematician Eratosthenes, the sieve provides a very efficient method for finding prime numbers.

A prime number is a number that cannot be divided by any smaller number, other than one. Eratosthenes was a Greek scientist who lived 200 years before Christ. He found out how to find the prime numbers.

To find all the prime numbers between 1 and 100, follow these directions:

1. Put a ring around 2. Count by 2s, crossing out every number you land on.

2. Using a different colour, put a ring around the next uncrossed number which is a 3. Count by 3s, crossing out every number that you land on

3. Using a different colour, put a ring around the next uncrossed number which is a 5. Count by 5s, crossing out every number you land on

4 Using a different colour, put a ring around the 7. Count by 7s, crossing out every number you land on.

Following this pattern, you should now find that the numbers uncrossed are the prime numbers less than 100. Check this by seeing is any number will go into it (other than itself and one).

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100



Crossnumber Puzzle 1

2 3

4

5

6 7

8 9

10

11 12

13

Clues down Clues across

1. 253 – 82 2. 17 + 6

3. 12 x 9 4. 9 x 8

6. 17 x 3 5. Number of cents in ½ of $1.00

7. 2 x 29 6. 110 ÷ 2

8. 3 sixes plus 2 8. number of cents in $21.81

9. 25 – 6 10. number of 2s in 60

10. Cost of 3 pencils at 12c each

11. 12 x 8

12. Multiply 8 by itself 13. 100 – 12



Tables Sheet 2x

2x0=0

2x1=2

2x2=4

2x3=6

2x4=8

2x5=10

2x6=12

2x7=14

2x8=16

2x9=18

2x10=20

2x11=22

2x12=24

3x

3x0=0

3x1=3

3x2=6

3x3=9

3x4=12

3x5=15

3x6=18

3x7=21

3x8=24

3x9=27

3x10=30

3x11=33

3x12=36

4x

4x0=0

4x1=4

4x2=8

4x3=12

4x4=16

4x5=20

4x6=24

4x7=28

4x8=32

4x9=36

4x10=40

4x11=44

4x12=48

5x

5x0=0

5x1=5

5x2=10

5x3=15

5x4=20

5x5=25

5x6=30

5x7=35

5x8=40

5x9=45

5x10=50

5x11=55

5x12=60

6x

6x0=0

6x1=6

6x2=12

6x3=18

6x4=24

6x5=30

6x6=36

6x7=42

6x8=48

6x9=54

6x10=60

6x11=66

6x12=72

7x

7x0=0

7x1=7

7x2=14

7x3=21

7x4=28

7x5=35

7x6=42

7x7=49

7x8=56

7x9=63

7x10=70

7x11=77

7x12=84

8x

8x0=0

8x1=8

8x2=16

8x3=24

8x4=32

8x5=40

8x6=48

8x7=56

8x8=64

8x9=72

8x10=80

8x11=88

8x12=96

9x

9x0=0

9x1=9

9x2=18

9x3=27

9x4=36

9x5=45

9x6=54

9x7=63

9x8=72

9x9=81

9x10=90

9x11=99

9x12=108

10x

10x0=0

10x1=10

10x2=20

10x3=30

10x4=40

10x5=50

10x6=60

10x7=70

10x8=80

10x9=90

10x10=100

10x11=110

10x12=120

11x

11x0=0

11x1=11

11x2=22

11x3=33

11x4=44

11x5=55

11x6=66

11x7=77

11x8=88

11x9=99

11x10=110

11x11=121

11x12=132

12x

12x0=0

12x1=12

12x2=24

12x3=36

12x4=48

12x5=60

12x6=72

12x7=84

12x8=96

12x9=108

12x10=120

12x11=132

12x12=144



Tables Game

The aim of this game is to practice your tables so that doing other maths becomes easier for you.

Materials needed:

Tables sheet } needed to play the game

Game sheet }

Results Graph sheet – used to record results and begin developing graphing skills.

The teacher:

1. the teacher will write on the board:

5 10 15 20 25 30 35 40 45 50 55 60

2. During the game, the teacher will cross off one number every 5 seconds to let you know how long it has taken for you to do the activity. When you finish, look to the board and write down on your sheet the time that you took.

The student:

The teacher will tell you what table is being done today. When they say

“START” you write down only the answers to the table. Work as fast and as accurate as possible. You can use the Tables Sheet to help you. The aim is to be accurate and to improve your speed.

Correcting answers:

A student or teacher can either read out the answers for everyone to mark their own work or the group can say out loud, the whole sum for each answer e.g. everyone says 3x0=0, 3x2=6, 3x4=12 etc. This is a good way of practicing saying the tables and covering a variety of learning styles: read/copy/write; listening/saying.



Tables Sheet 2x

2x0=0

2x1=2

2x2=4

2x3=6

2x4=8

2x5=10

2x6=12

2x7=14

2x8=16

2x9=18

2x10=20

2x11=22

2x12=24

3x

3x0=0

3x1=3

3x2=6

3x3=9

3x4=12

3x5=15

3x6=18

3x7=21

3x8=24

3x9=27

3x10=30

3x11=33

3x12=36

4x

4x0=0

4x1=4

4x2=8

4x3=12

4x4=16

4x5=20

4x6=24

4x7=28

4x8=32

4x9=36

4x10=40

4x11=44

4x12=48

5x

5x0=0

5x1=5

5x2=10

5x3=15

5x4=20

5x5=25

5x6=30

5x7=35

5x8=40

5x9=45

5x10=50

5x11=55

5x12=60

6x

6x0=0

6x1=6

6x2=12

6x3=18

6x4=24

6x5=30

6x6=36

6x7=42

6x8=48

6x9=54

6x10=60

6x11=66

6x12=72

7x

7x0=0

7x1=7

7x2=14

7x3=21

7x4=28

7x5=35

7x6=42

7x7=49

7x8=56

7x9=63

7x10=70

7x11=77

7x12=84

8x

8x0=0

8x1=8

8x2=16

8x3=24

8x4=32

8x5=40

8x6=48

8x7=56

8x8=64

8x9=72

8x10=80

8x11=88

8x12=96

9x

9x0=0

9x1=9

9x2=18

9x3=27

9x4=36

9x5=45

9x6=54

9x7=63

9x8=72

9x9=81

9x10=90

9x11=99

9x12=108

10x

10x0=0

10x1=10

10x2=20

10x3=30

10x4=40

10x5=50

10x6=60

10x7=70

10x8=80

10x9=90

10x10=100

10x11=110

10x12=120

11x

11x0=0

11x1=11

11x2=22

11x3=33

11x4=44

11x5=55

11x6=66

11x7=77

11x8=88

11x9=99

11x10=110

11x11=121

11x12=132

12x

12x0=0

12x1=12

12x2=24

12x3=36

12x4=48

12x5=60

12x6=72

12x7=84

12x8=96

12x9=108

12x10=120

12x11=132

12x12=144



The Game Sheet Rule:

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Correct:

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Rule:

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Rule:

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Rule:

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Rule:

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Rule:

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Rule:

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Rule:

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Rule:

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1= Time:

Correct:

/20

What table were you best at? _______

What was your fastest time? ________



Results Graph

Write the table that you did along the top of the graph

20

19

18

17

16

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14

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9

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1

Name:

Date:



Survival Maths and adjusting the syllabus for learners with special needs

For students with disabilities and learning difficulties, it may be necessary to prioritise the mathematical skills that they realistically need to function effectively in society. These skills are known as survival maths skills.

According to Westwood (1993:169), ‘parents and employers agree that the key areas for functional numeracy are: counting, tables, use of the four basic operations, money management, time and measurement.’ The following areas have been suggested as the core content of essential maths that is basic to the needs of school leavers:

• Basic numbers

• Money

• Measurement; and

• Problem-solving

In most cases, students with moderate or severe intellectual disabilities will have individual programs (IEP). Other students will access the regular class program, but with adaptations and modifications.

High school students who have an intellectual disability are able to study a Life Skills Mathematics course that is specifically designed to meet their individual learning needs. Life skills courses are recognised by the NSW Board of Studies as accredited courses for both the School Certificate and Higher School Certificate qualification.

Assessment of numeracy skills

Careful assessment of students’ strengths, areas of need and interests helps to answer the fundamental questions of teaching:

- What do the students currently know?

- What do the students need to know?

- How will I help them learn this?

Teachers gather a variety of evidence about students’ achievements over time. They use this evidence to make balanced judgements about students’ progress as they work toward achievement of knowledge, skills and understanding of mathematical concepts and ideas. SLSOs are able to assist classroom teachers to collect this evidence.



Assessment of learning

‘Assessment for learning in mathematics is designed to enhance teaching and improve learning. It is assessment that gives students opportunities to produce the work that leads to development of their knowledge, skills and understanding.

Assessment for learning involves teachers in deciding how and when to assess student achievement, as they plan the work students will do, using a range of appropriate assessment strategies including self-assessment and peer assessment.

Teachers of mathematics will provide students with opportunities in the context of everyday classroom activities, as well as planned assessment events, to demonstrate their learning.

In summary, assessment for learning:

• Is an essential and integrated part of teaching and learning

• Reflects a belief that all students can improve

• Involves setting learning goals with students

• Helps students to know and recognise the standards they are aiming for

• Involves students in self-assessment and peer assessment

• Provides feedback that helps students to understand the next steps in learning and plan how to achieve them

• Involves teachers, students and parents reflecting on assessment data’

(NSW DET 2002 Mathematics K-6 syllabus)

SLSOs may be asked to:

1. Observe students

Observing students as they work through maths activities can provide clues about the processes that the students are using as they complete set tasks and solve problems. Things to look for:

• Approaches to the task. Does the student take a systematic approach?

• Sequencing of steps to complete the task. Is the student following the steps that s/he has been taught to use?



• Signs of frustration and anxiety indicating that the task may be too difficult.

If students make an error as you are observing them it is helpful to ask yourself the following questions:

1. Why did the student get this item wrong?

2. Can the student get the correct answer if allowed to use concrete materials, count on fingers or use a number line?

3. Can the student explain what s/he did? Ask the student to work through the example step by step. At what point does the student make the error?

(adapted from Westwood, 1993:153)

2. Administer informal tests

Class teachers often design informal tests that are based on the class program. These tests are given on a regular basis to determine students’ understanding of topics and content areas that have been previously taught.

SLSOs may assist in administering tests. However, they need to discuss their role with the class teacher to determine the amount and type of support that should be provided to the student in the testing situation.

3. Discuss work with students

Discussion between teachers or SLSOs and students can reveal a great deal about the student’s level of confidence, skill and understanding. Listening carefully to students as they verbalise their thoughts while working through a task is a good way of discovering their thinking processes and where any mistakes may have been made.

There are a number of things to keep in mind during discussions with students:

• Ask open questions (that require more than yes no answers). For example:

• How did you ...?

• What does ... mean?

• Why does ...?



• Allow sufficient time for the student to respond after a question is posed

• Encourage the student to take the lead in the discussion. Let the student explain what they are doing without interruptions

4. Collect work samples

Classroom teachers are able to use work samples to make decisions regarding the need for remedial teaching, consolidation, promotion or extension.

‘Teachers’ judgements regarding students’ achievement of an outcome, are based on knowledge of the student’s progress over time. It is not based solely on a single work sample’ (NSW DET, 1998:5)

SLSOs can assist students to maintain portfolios and collect work samples that indicate the students’ level of understanding, difficulties experienced and the quality and quantity of work completed.

Once SLSOs have assisted with monitoring and assessing students’ progress in the classroom they need to communicate their findings to classroom teachers who are then responsible for planning and adapting the students’ programs accordingly.

Teachers may ask SLSOs to use a checklist or written proforma to record their findings. However, it may be more beneficial and convenient to meet and discuss the results. Decisions regarding feedback to the classroom teacher will depend upon:

• Reasons for the assessment

• Time and availability

• Preferences of the teacher and

• Skills of the SLSO

Student progress can be assessed in many ways and the selection of the method and materials may depend on many factors, however, some of the ‘possible sources of information for assessment purposes include the following:

• Samples of students’ work

• Explanation and demonstration to others

• Questions posted by students

• Practical tasks such as measurement activities

• Investigations and/or projects



• Students’ oral and written reports

• Short quizzes

• Pen and paper tests

• Comprehension and interpretation examples of students’ work

• Explanation and demonstration to others

• Questions posted by students

• Practical tasks such as measurement activities

• Investigations and/or projects

• Students’ oral and written reports

• Short quizzes

• Pen and paper tests

• Comprehension and interpretation exercises

• Student produced work samples

• Teacher/student discussions or interviews

• Observation of students during learning activities, including listening to students’ use of language

• Observation of students’ participation in a group activity

• Consideration of students’ portfolios

• Students’ plans for and records of their solutions of problems

• Students’ journals and comments on the process of their solutions.’

(NSW DET 2002. Mathematics K-6 syllabus)



Strategies to teach problem solving

The goal of teaching problem solving strategies in mathematics is to assist students to apply their knowledge, skills and understanding of maths concepts to real life situations.

Students with learning difficulties or disabilities that cause difficulties with learning often have limited strategies for solving problems. They may not understand the problem or may not be able to decide which information is relevant. Irrelevant information containing numerical expressions can be particularly confusing. Additionally, they may select an incorrect or inefficient strategy for a specific problem.

There are five (5) skills involved in solving problems efficiently. They are:

1. Decoding ability – can the student read the problem?

2. Comprehension – can the student understand the specific mathematical terminology?

3. Transformation – can the student understand the everyday language in the problem?

4. Process skills – can the student perform the mathematical operation required to reach the correct solution?

5. Encoding – can the student make up the answer?

To assist students to develop these skills SLSOs are able to:

• Model and demonstrate the appropriate use of problem solving strategies

• Provide guided practice with plenty of prompts and cues to students as they learn to use the strategy

• Encourage students to trial new, more efficient strategies

• Monitor and evaluate students’ progress as they become more independent I the use of problem solving strategies

Steps to problem solving

Four steps that students can follow to solve maths problems are:

1. Understand the problem

2. plan how to solve the problem

3. try a solution

4. check the problem and its solution



Students need to be given a teaching sequence of modelling, guided practice and independent practice with correction and feedback as they progress through the stages of development in each step of this problem solving strategy.

Step 1: Understand the problem

Understanding the problem is about visualising a picture of the problem. To do this students need to isolate key words in the problem and to ignore irrelevant information. Teachers and SLSOs can model finding key words in mathematical problems. For example, the key words in this problem are in italics:

Jenny’s mother took her shopping with $200 to buy some new clothes. They bought a shirt for $15.00, a pair of shorts for $30.00 and a jacket for $75.00. How much did they spend?

Once the key words have been identified, students who are learning to solve word problems can be taught to create a graphic representation of the problem. This strategy is recommended because as well as assisting comprehension, many everyday number problems are concrete in nature and can be readily represented.

In the above problem, a quick whiteboard sketch or a line drawing would be useful to assist the students to visualise the problem.

Step 2: Plan how to solve the problem

Although drawing a picture is often chosen as the strategy, students can be also taught to use other types of graphical representations that are more appropriate and efficient for specific problems. They can make lists, charts, tables, graphs and patterns. For example, in the problem used above, this list would be most helpful:

ITEMS COST

Shirt $15.00

Shorts $30.00

Jacket $75.00

Students can now discuss what they can learn from the list. This part of planning a solution may be done as a whole class, in small groups or individually with the teacher or SLSO.

An important part of planning a solution is deciding which operation is applicable to the problem. This is a critical decision that students with learning difficulties and disabilities may need guidance with for some time.

Useful questions to ask students at this stage would be:



• What can we do to find out the total cost of the three things Jenny bought?

• Will the answer be more than $75.00? Why do you think that?

Step 3: try a solution

In the early stages of problem solving teachers will model various solutions to a specific problem. This reinforces for the students that it is reasonable to test out a number of solutions as they work towards finding the correct answer. With more complex problems, there may be more than one pathway to arrive at the same answer.

During guided practice students and teachers work together attempting solutions. When the students have developed sufficient skills, they will work independently at attempting their own solutions.

Step 4: check the problem and its solution

This fourth step is a difficult one for many students, and especially for those students with additional needs. Sometimes they are tentative about finding the solution, that they do not have the skills and objectivity to further analyse the problem and the solution. However, with modelling and guided practice students can be encouraged to test their solutions against what they understand about the problem.

With the given problem, for example, teachers or SLSOs may say:

Tristan, your answer is $75.00. Remember that the jacket cost $75.00 by itself. Do you think $75.00 sounds right?

Or

Tilly, you’ve written $105. Can you show us how you got that answer?

In each step of this strategy, students should be given an opportunity to explain their solutions and to listen to the strategies that their peers have used to reach their solutions. This form of cooperative learning is beneficial as it enable students to learn from their peers in a non-threatening environment. SLSOs can play an important role in guiding and monitoring group discussions and activities as students share their ideas about how to solve problems.



Activity 4

Problem solving

1. Why are graphic representations a helpful and valid aid for helping to solve problems?

2. Read the following problem and then answer the questions:

The de Bastos family had to drive 286 kilometres to get from Sydney to Canberra. They drove 150 kilometres and then stopped for 40 minutes to have lunch. How many more kilometres do they need to drive to reach Canberra?

a) Underline all the key words.

b) Write down any relevant information

c) Is any information given that could increase the difficulty of interpreting the problem? If so, what is it?

d) Which word in the problem could cause misunderstandings and why?



Getting organised to find solutions

Maths classes are an ideal opportunity to begin teaching learners how to get organised and the value of being organised. Learners with learning difficulties may have problems in this area too but with methodical practice, progress can be made.

SO what does being organised in a numeracy classroom mean?

The general rule for all learning situations including the numeracy classroom is:

Prepare - what is it that I am doing now or today? Identify the topic or thing that is being required of you or the learner.

Plan – what lists, tools, information, materials, worksheets, models of a similar task etc, do I need to help me work out what to do?

Draft – give it a go. Try working out the answer to the problem, write draft response, do a rough drawing, do a storyboard, have a first run through of the script

Edit/review – work with a partner, teacher/SLSO or a small group to see what can be done to improve your product, answer, ideas

Publish – write up your final answer, report or product, give your speech, show your film/video, perform on stage….

Other organisational things in the numeracy classroom include:

• Have concrete materials stored safely and neatly (for easy use and distribution) in one consistent place

• Have a variety of concrete materials available and sufficient for everyone in the class

• Have spare calculators and batteries in case of breakages

• Remove broken equipment for repair or disposal promptly. This is for safety reasons as well as for the self esteem of the students (and staff). Students who are surrounded by broken or tatty equipment/environments can find this very demotivating

• Have a routine for learners in what materials they are expected to supply and take out ready to begin a lesson e.g. book, pencil/pen, calculator, ruler, eraser, highlighter



Correction & Feedback

It is important to work through errors so that students know where they have gone wrong. Avoid marking work as incorrect without an explanation to the student about how and where the error occurred.

Teachers and SLSOs should ask the student to work through the whole item while they ask questions of the student to discover where the problem occurred.

When the problem has been identified, teachers and SLSOs need to demonstrate the aspect of the skill or strategy that is causing the problem and have the student model the correct response.

Students’ effort should be consistently rewarded. This means that students who are acquiring new skills receive praise and encouragement for approximations towards a correct response, not just for achievement.

The following example demonstrates the correction and feedback component of direct instruction that could be given to a student who made the error 4 x 7 = 11.

Can you read this sum?

What does this sign (points to the X) tell you to do?

No, it’s not an addition sign. Look closely at the sign. What do you have to do?

Use another example in the text or write an example such as 6 x 3 =, to demonstrate and describe the operation.

Point to the numerals and sign saying, “This sum says six times three equals”

Point to the X again and ask, What does the symbol say?

Yes, that’s right. Can you read the sum?

What does six times three equal?

Yes, that’s right!

Refer back to the original question. Point to the X and ask, What does this symbol tell you to do?

Yes, what is this sum?

Yes, that’s right. Show me how you will work it out

Four plus seven equals eleven.

Add the numbers together?



I don’t know

Times

Six times three equals

Students work with concrete materials if required to find the right answer “18”

Student models the response that is required.

Sometimes using self-correcting activities can offer the opportunity for learners to correct their own work to find out where they went wrong and correct it before it gets marked. This requires a small degree of independence and confidence on the part of the learner. These types of worksheets can also be useful with learners who feel stressed by conventional worksheets and have a high degree of fear of failing.



Activity 5

Technology in the classroom

Read the extract from an article by Linda Starr, Educators battle over calculator use: both sides claim causalities, 2002.

http://www.educationworld.com/a_curr/curr072.shtml,

Discuss the ideas in class – are they still relevant today?

What technology is available?

Some of the technology that you might use in a numeracy classroom includes:

1. Simple calculators

2. Scientific calculators

3. Abacus

4. Mobile phones: o Calculator function o Camera function to gather data such as photos and videos.

These can then be linked to a smartboard for presentation and further development

o Send pictures to a moblog for group work on a problem

Example The puzzle on the following pages is a fun way to use calculators in the classroom:

http://www.educationworld.com/a_curr/curr072.shtml



Calculator Word Puzzle

ACROSS DOWN

1 A light worker (4231 x 9)

1 Yucky muck (0.32)

5 Santa sound (2 ÷ 5)

2 Give it the O.K. (2768.9 × 20)

6 Dirty stuff (45 × 1269)

3 Don’t stand around! (2.37 − 1.47)

8 Not the stinging type (9.5 × 4)

4 Exists ( 47.3 − 28.6 + 32.3)

9 Water tube (12 × 4 × 73)

6 Come in pairs (10 609 × 5)

11 Some people open theirs too much (1970 − 43 × 27)

7 This word is slack

(1902 − 1093)

12 A fowl animal ( 210 × 165 + 359)

8 A shocking sound (1.7 − 1.62)

13 One of these is always right (11.62 − 2.25)

9 What a pig ! (8 × 113)

14 Not profitable (92.1 − 37.03)

10 A bit fishy (10 060 − 9 327)

19 Peas or the sea (2782 + 61)

12 Set substance ( 169752 − )

21 Good to duck ( 18.45329 + )

15 Slippery stuff (7.1 × 25 × 4)

23 Spots ( 97 × 5 × 11)

16 Cry, etc. (35 × 23)

24 Don’t buy (7103 + 829 − 197)

17 A manly title ( 21296 − )

25 Grain store (0.5 × 1.43)

18 “Well?” - “Not exactly.” (257 × 3)



26 Top person (9634 − 4126)

20 Was it an adder ? (6325 + 1607 − 2418)

28 More of 12 across (40 000 − 4661)

22 Ice house (0.6903 − 0.6112)

23 Opposite to 17 down (15 × 23)

24 Only one of these (2470 × 1.5)

27 Therefore (2.451 +1.63 − 3.581)

Adapted from: TAFE NSW Access & General Education Curriculum Centre, 2005, No

Nonsense Numeracy, CD ROM.

5. Educational Applications for desktop computers, smartphones, iPads and tablets. There are many useful applications (aps) and online resources available. Talk to staff about the ones that they prefer to use with their students. Some schools may subscribe to online maths programs which students can use in class or at home. Check with your school before using them as there may be a cost involved.

o Worksheets on the internet o Specific software eg Carmen San Diego Maths Detective o Calculator function (usually in the list of Programs under

‘Accessories’) o Chat groups, wikis, blogs, moodles etc to interact with other

learners learning similar things or keep a learning journal o Wordprocessing functions to write up responses to problems o Internet functions to search for information o Spreadsheet function to use formulas and organize information

clearly or generate graphs

For further information the following links may be useful: http://www.ipadsforeducation.vic.edu.au/ http://mathseeds.com.au/apps/targeting_maths/ http://www.mathsonline.com.au/ http://www.teachingtreasures.com.au/maths/Maths_more.html

http://www.ipadsforeducation.vic.edu.au/

http://mathseeds.com.au/apps/targeting_maths/

http://www.mathsonline.com.au/

http://www.teachingtreasures.com.au/maths/Maths_more.html



http://www.education-world.com/a_curr/curr072.shtml http://www.aplusmath.com http://www.funbrain.com http://fcit.usf.edu/math/websites/math35.html http://www.abc.net.au/countusin http://www.superkids.com/aweb/tools/math

6. PDAs, XDAs and other hand held devices: o Can be used as a portable recording device for information

which is either downloaded onto a computer or processed in some other acceptable way.

o Calculator function o Word processing functions to write up responses to problems o Internet functions to search for information o Spreadsheet function to use formulas and organise

information clearly or generate graphs

http://www.education-world.com/a_curr/curr072.shtml

http://www.aplusmath.com/

http://www.funbrain.com/

http://fcit.usf.edu/math/websites/math35.html

http://www.abc.net.au/countusin

http://www.superkids.com/aweb/tools/math



The following is an example of how technology can be employed to engage students in numeracy learning:



Real Life Mathematics

When studying Maths, students may ask: ‘When will I ever need this?’ The following are some examples of the real life use of maths:

Carpenter, builder, gardener:

• Need to measure and cut timber to build houses and order the right lengths of timber from the timber yard

• Need to know volume to order concrete to pour a footing for a house or order soil or compost to fill a garden bed

• Pythagoras’ Theorem is used to calculate the length of the rafters in a roof and therefore what timber length to order

• Timber is ordered in lengths that are multiples of 0.3m i.e. 0.6m, 0.9m, 1.2m, 1.5m etc.

• Baker, pastry chef, cook, chef:

• Need to measure dry and wet ingredients using scales, measuring spoons and cups to make cakes, sauces, casseroles

• Need to sort products into portion sizes eg meat is often in 150g or 220g portion sizes

• Need to calculate the selling price of a meal i.e. three times the cost of the ingredients- 1/3 pays for the ingredients, 1/3 pays for costs such as labour, power, rent, and the last 1/3 is profit.

• Need to work out fractions eg 1/3 cup flour + ¼ cup cocoa…. How big a bowl do I need to put it in?

• Percentages: discounts for buying in bulk, % of rise in bread as it ‘proves’

• Money: paying people, paying bills etc

Nurses and medical staff:

• Measuring medicine: liquids, tablets, mg, grams • Weighing people to work out how much medicine to give them • Estimating how many sheets, towels and blankets needed for

everyone on the ward or in the hospital Pilot:

• Estimate/measure the length of the runway to make sure they stop the plane in time

• Reading timetables • Reading a roster • Reading and interpreting the navigation panel instruments



• Checking the plane is not carrying too much weight to fly safely

• Reading weather information and interpret it

At home:

• Paying bills • Cooking • Gardening • Building an extension • Putting insulation in your roof • Putting plants in a garden eg ‘you

need 5 plants to fill 1m2’ • Buying paint to paint a room ‘1L of

paint =14m2 of painted wall space’ • Mixing and spraying chemicals such as weed killer or cleaning

products • Mixing concrete to build or secure a letterbox in the ground • Reading the clock to make sure you get to an appointment on

time • Reading a timetable to catch the bus/train in time for school

or work • Buying a lottery ticket with a friend- if you win how much

does each person get • Sewing an outfit • Buying petrol for the lawn mower • Estimating how much water to put in the bath so that it

doesn’t overflow when we get in it • Estimating whether all of the shopping will fit in the boot of

the car • How many kilojoules can I eat and not get fat? • Which combination of foods will give me the right number of

kilojoules? • How can I fit all of my furniture into a room and have space to

move around?



References:

BOSTES NSW, 2015, Mathematics K-10, http://syllabus.bos.nsw.edu.au/mathematics/mathematics-k10/ Viewed 10 August 2015

DEC NSW, 2015, Mathematics, http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/numeracy/, Viewed 10 August 2015

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http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/numeracy/

http://www.educationworld.com/a_curr/curr072.shtml

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