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Using concrete materials to teach Mathematics Resources

The Mathematics Lesson - A suggested model There are several ways in which you can structure a mathematics lesson. One way is to divide the lesson time into four sections: 1. Warm up – Ignition (whole class) 2. Major focus – including explicit teaching, purpose, (whole class) 3. Group work (small groups, pairs, individual) 4. Reflection and conclusion (whole class) 1. Ignition-warm up(Whole class) ● Activities usually run between 5 - 10 minutes in duration. ● Activities usually involve the whole class. ● Activities should allow students at all levels to be able to participate. ● Activities may or may not be directly related to main lesson focus. 2. Main Focus - Explicit Teaching (Whole class) ● Explicit Teaching typically runs between 10 - 15 minutes in duration. ● Learning intention – WALT We are learning to... ● Numeracy reference – link maths concept to real world ● Make lesson key idea explicit WALT We are learning to ....... ● Teacher models Concrete – Visual – Abstract learning 3. Main Focus (Small Groups, pairs, individual) ● Main focus small group activities typically run between 15 - 20 minutes in duration. ● Guided/supported practice of the skill or knowledge ● Teaching and activities may target students of different levels. ● You may wish to spend more time with students using less advanced strategies. ● Provide explicit feedback on the learning - e.g ‘Well done, you found all the numbers 1-10 by looking closely at the shapes of the numbers.’ ● Good opportunity to make anecdotal observations and for students to undertake ongoing assessment tasks 4. Reflection and conclusion (whole class) ● Usually runs 10 mins in duration. ● Go back to WALT “Today we are learning to use denominators to describe fractions of different size, John could you tell us how your group activity did this.” ● Students express their understanding of the Key Idea. ● Often run out of time for reflection part of the lesson. ● Many options including writing, speaking, drawing and building.

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What: Learning intention – WALT We are learning to….. Do the students know what the point of the lesson is? What is the mathematics concept or the literacy focus for the lesson?

How can you communicate it to them in language they can access? Important for teachers to write down in day book, can be quite difficult

to articulate learning intention. Why: Connectedness – real world or school world Do the students know why they are learning this? Needs to be early in lesson after the learning intention has been communicated in order to give students a reason to engage.

- Mathematics Numeracy - English Literacy

How: Various ways to explicitly teach the concept/focus as below:

Tactile/kinaesthetic – Visual – Auditory Concrete – Pictorial(visual) – Abstract Modelled – Guided – Independent Explicit quality criteria Do the students know exactly what they are to do and how well? Make criteria visual – same place in classroom - same format What: Reflection – revisit learning intention Do the students know what they have learnt?

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Classroom number kit – these resources are ideally in each classroom to support easy access

and eliminate the need to borrow items. These items are best made available to students at all times. Note: some items listed are visual supports for use with concrete materials eg. Place value flip charts, place value arrows, hundred charts Base 10 material The most important resource in the classroom. Essential for developing understanding in place value, addition and subtraction.

Place Value Mats Clarify place value when working with base 10 material

Hundred charts Individual laminated charts

Place value flip charts

Number lines Easily made and laminated Eg. 1-10 1-25 1-50

Unifix blocks As with counters used for all number work

Place value arrows Used with base 10 material to develop place value understanding

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Counters Counting, addition, subtraction, multiplication & division, patterns & algebra, data and chance. Very useful when used with document reader for modelling concepts.

Double sided counters Used to show : - commutative property of eg. Addition Commutative means that things can move or commute - friends of ten - Number bonds for addition & subtraction - subtraction and linking subtraction to addition

6 – 2 Start with 6 red then turn over 2 counters

Bowls/cups/rings For making groups in multiplication and division

Transparent counters Used with laminated 100 charts

Number crunchers Used with counters or unifix blocks to describe number bonds

Pattern blocks Used for 2D, 3D, patterns & algebra and fractions

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School maths kits – these resources are in the school for classroom borrowing.

Fractions & Decimals 2D shapes Part/whole resources to develop understanding of denominators and equivalence.

3D objects Part/whole resources to develop early understandings of halves and quarters

Fractions/decimals/percentages flip charts To develop understanding of how they relate to each other

Patterns & Algebra

Space

2 Dimensional shapes

symmetry

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3 Dimensional objects

features & properties cross sections nets

different views

Misc.

Money

Measurement

Length Informal measurement, developing awareness for a unit of measurement

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Length Formal measurement

Area Informal measurement

Area Formal measurement

Mass Informal measurement

Mass Formal measurement

Volume Measuring the space the 3D object takes up

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Capacity Measuring what a 3D object can be filled with

Time- telling the time

Time - duration

DEC Numeracy continuum K-10 The site contain great videos which clearly demonstrate student behaviour at each level. A good understanding of the Aspect 2 will make the teaching of Mathematics much easier. See videos

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DEC Numeracy Continuum (K-6) This continuum describes the development typically

expected of most students in seven aspects :

Counting sequences

Counting as a problem solving process

Pattern and number structure

Place value

Multiplication and Division

Fraction units

Unit structure of length, area and volume

Maths 3000 - (part of ESA – Education Services Australia – Federal government)

maths300 is an exciting online resource, offering over 175 lessons ideas for mathematics teachers from 0–12.

Subscription costs

NDLRN – National Digital Learning Resources Network – (part of ESA – Education Services Australia – Federal government) The National Digital Learning Resources Network contains more than 12,000 digital curriculum resources that are free for use in all Australian schools.

Article describing Concrete – Pictorial – Abstract approach to the teaching of Mathematics

Mathematics syllabus K-6 – (Board of Studies BOS)

Current state curriculum document.

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Mathematics Sample Units of Work (BOS) Great lesson ideas.

DEC - Count Me In Too Website A wide range of resources to support the teaching of Aspect 1 – Counting sequences and Aspect 2 – Counting as a problem solving process.

DEC - Counting – On Website A wide range of resources to support the teaching of Aspect 4 - Place Value and Aspect 5 -Multiplication/Division.

DEC Publications – check in school teacher resources.

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