Continuum. A Mathematics Manipulatives. Hands on Heads on: The effective use of mathematics manipulative materials


 Arron Welch
 2 years ago
 Views:
Transcription
1 Hands on Heads on: The effective use of mathematics manipulative materials A Mathematics Manipulatives Continuum Geoff White Paul Swan Linda Marshall
2 Mathematics materials likely to be found in a primary school What is a mathematics manipulative? A manipulative material is an object(s) that can be handled by an individual in a sensory manner during which process, conscious and unconscious thinking will be fostered. Consequently, a mathematics manipulative object(s) would lead to an awareness and development of concepts and ideas linked with mathematics and they would most likely be purpose designed. The members of the research team sought an allembracing definition, but such a definition eluded them. With careful consideration, it was decided that there are tools (such as a calculator), teaching tools (demonstration models) and teaching aids (fraction charts); generally these were not considered as mathematics manipulative materials. Within the general definition, structured and unstructured mathematics manipulative materials were recognised. Needless to say, throughout the education literature many definitions of mathematics manipulative materials have been offered. Mathematics materials Hands On: Heads On A Mathematics Manipulatives Continuum 2 Abacus looped (2, 3, 6 loops) threeprong (different styles but same principle) Attribute Blocks and support materials Beads & Threading Laces Bead Frame (Counting frame) Centicube and support materials such as baseboards Clocks  variety; both digital and analogue Classroom Kit (see page 14) Coloured rods (Cuisenaire) Construction Materials (ensure comprehensive collections of a few varieties; eg. Knex, Mobilo, Interstar, etc) Counting materials Cotton reels, cubes (variety), popsticks, counting sticks Cubes  1 cm, 2 cm Wood or plastic (See Unifix, Multilink (Gain), Centicube, etc) Dominoes  a variety of types Fractions  a wide variety; eg. fraction games & fraction cakes. Fraction Kits  eg. Wainwright Fraction Kits Geoboard  5 x 5, 10 x 10 pins Geometric models (solid) and hollow, such as, Power Solids Johnstone Number Line MAB (Multibase Arithmetic Blocks) or Base 10 blocks and a variety of support material Matrix Games What s in the Square?, What Else is in the Square? and similar products Measurement Materials (see page 13) Mira (Geoflector, Geo mirror) Mirrors Number Board (1100)  variety Pattern Blocks Peg board and pegs (variety) Puzzles: geometric, pentomino, soma cube, tangram etc Scales Kitchen scales, bathroom scales Balance Scales Pan Balance Spring Scales/Balance Assorted mass sets (see also page 13) Tangrams Tessellation Pack The Brick Sorting Materials  farm animals, dinosaurs, frogs, teddies etc. Unifix cubes  (Constructo cubes, Simfit, Stack cubes) Unit Blocks (Project Blocks) Welford Blocks 2D to 3D Shapes Interlocking shapes create a net which form a solid. There is a large number of materials in this genre. Here are some examples: Polydron, Lokko, Klikko, Clixi, GeoFit, Geo Shapes and Mini Geofix ( a smaller version) A Range of Games Many schools have a wide variety of games available, stored in both classrooms and storerooms. It is recommended that students benefit from learning the skills of a few good games rather than being introduced to a wide range.
3 Schoolwide use of mathematics manipulatives M athematics manipulatives do not teach on their own; rather they open pathways to learning. There is a tendency to use the materials as demonstration pieces  Look at this, see how it works!. Rather, the success of their use lies in the threeway interaction between the student, the teacher and the materials. By focussing on the materials, the teacher leads the student to insights which they develop through language and interactions with the teacher and their peers. The materials act as a catalyst to learning. At the end of the process, the materials have not changed, but it is a fair assumption that the learner (and maybe the teacher) will have done so. Revisit earlier experiences. Teacher The Mathematics Learning Experience Developmental considerations are essential for success. Experience has shown that by carefully managing the use of manipulative materials, the creation of a developmentally focussed mathematics program can be achieved. Mathematics Manipulatives A common myth affects the use of mathematics manipulatives in the classroom: once exposed to a material, children have learned all that material has to offer. A person interacts with a material with a different mindset at different times. These different reactions widen the experience the learner develops. For example, ideas fostered by the use of Pattern Blocks in early childhood classes will later translate into formal fractions concepts in the middle and upper primary classes. Likewise, formal symmetry ideas will have been demonstrated practically as students experiment with the Pattern Blocks. In summary, it is more effective to start an idea with children and carry it through. What is started must be continued. The planned use of manipulatives provides the basis for a continuum of experiences for the student throughout the school. Frequently, the childcentred early childhood experiences are abandoned too rapidly and are replaced by an almost oneway process: teacher to student. Unfortunately, the three way interaction no longer seems appropriate. 3
4 Categories of mathematics manipulatives K ey Materials Many mathematical concepts can be developed and strengthened by the frequent use of these materials. It is suggested they visit a classroom for 3 weeks every term. Appropriate manipulative materials are suggested on the sequence presented on the following page. (Note: Experience has shown that a three week time span is appropriate to maintain students interest.) R otated or shared Materials Substantial quantities of a material, housed in adequate containers, are circulated amongst the classrooms on a preplanned basis. In the primary school, experience has shown that three weeks is a most satisfactory period of time and these items may visit on more than one occasion per year and be suitable for several classes; for example, children will benefit from a regular exposure to Geoshapes in Years 49. Materials need to be both readily available (not in some distant storeroom) and stored in portable containers. C lassroom Kit One of the main problems mentioned by teachers is the need to have certain items on hand at all times. As well, classrooms need to be fitted out with some vital teaching support items, such as, analogue and digital clocks, thermometers, an accurate balance scale (not a kitchen scale) and suitable weather or observation charts. All of these materials play a part in the mathematical experience. A suggested list of suitable items is listed later. M aterials kept in the Mathematics Storeroom Usually, these materials are items or collections required for special presentations or they are too bulky to be housed in a classroom. These items could include Johnstone number lines and some measurement materials such as trundle wheels. A detailed list of materials is provided so classroom teachers can plan for the appropriate use of certain materials. The aim is to rely on the storeroom as little as possible. 1. Plan sufficient quantities for groups of 46 children. 2. Purchase a lot of a little: rather than a little of a lot. 3. When increasing or replacing stock, ensure the same quality and style of product is obtained. (Keep a copy of the invoice in order to identify items.) 4
5 A suggested mathematics manipulatives continuum K Kindergarten Children need to have constant access to sand and water play, this could continue into Preprimary and Year 1/2 environments. In the playground, children have access to a wide variety of kinaesthetic skill activities at all times. Consider this an essential for any Early Childhood program. Unit (Project) Blocks are a key material for a sound Early Childhood experience: children need constant access to this material. (Each Early Childhood teaching area could allocate a dedicated space for Block Play.) We must be careful not to overexpose children to the same materials. Key Materials Rotated Materials PP PrePrimary 1 Year 1 2 Year 2 The Brick Number, Pattern, Working Mathematically Additional Brick components may be introduced. Unifix Use the blocks only. As the children gain experience a range of support material will be introduced. Pattern Blocks Different aspects of this material will be featured at various levels. What s in the Square? (Concepta) Begrippen Construction materials Johnstone number lines Attribute Blocks Geoshapes/Polydron Geoboards 34 Years 3 & Years 5, 6, 7 Coloured Rods MAB (Base 10) Becomes a Rotated Material at this level. Before introducing MAB, children will experience trading activities with Place Value boards and Popsticks. Centicube Geoshapes/Polydron Tangrams, Pentominoes etc Fraction Kits There will be special collections of materials, such as Mira, which are used infrequently but are important experiential materials. CLASSROOM KITS: A kit of appropriate material is allocated to each classroom (initially, a teaching block). Contents of the kit will vary according to the classroom level. Every room could be fitted out with an analogue and digital clock, large thermometer, an accurate balance scale and a form of magnification. A larger collection of calculators may be allocated; one per teaching unit or kept in the storeroom. Carefully consider whether an item needs to be on hand at all times. Use materials to provide variety in the classroom. 5
6 The Brick The Brick is a component of The Little Architect Construction Set, a collection of different plastic shapes designed to construct housetype models. Designed by Fab Caponio of Moorabbin, Melbourne, Victoria; The Brick is moulded in highgrade plastic and is very durable. Some additional pieces from the construction set, such as endcaps, halfbricks and faces may be added to make an even more versatile manipulative. First introduced to schools in 1980, the successful use of The Brick has been demonstrated in many early childhood classrooms, but a wide range of mathematical ideas may be generated from its use. It is recommended that children right through the primary school have a chance to explore with the material. Appropriate for use at all levels of Primary School Allow children to become familiar with the material; do not push formal mathematical ideas. Children will be familiar with The Brick, but free play/exploration needs to be fostered still. The Brick can be used in a similar fashion to Unifix. However, in contrast to Unifix, The Brick may be joined in a variety of ways, providing a 3dimensional attribute to the materials. Unifix can be joined in a linear fashion only. Easy joining techniques, provide the possibility of creating a range of different shapes. Create classification activities after What s in the Square? has been introduced. 6 Students create a wide range of patterns and designs; many of which have a strong mathematical structure Tower structures provide an experience in 3D modelling. Creating various ranges of colour combinations (2, 3, and 4 colours). Experience has shown that upper primary students enjoy using The Brick, making it one of the most versatile manipulative materials available. Requirements: 4000 pieces per class/group
7 Unifix In the early 1950s, the invention of polyethylene plastic enabled a wide range of teaching materials to be designed and manufactured. The Unifix cube is modelled on a wooden block in which a hole through the centre enabled a child to thread a number of them on a lace. This joining principle was changed to an interlocking joiner which allowed any number of the cubes to be joined end to end. Possibly to match the tenness of the number system, ten colours were moulded. A welldeveloped support material program is offered; included are Number Line tracks, Grids, Place Value Trays and Number Indicators. This system is modelled on the work of the famous American early childhood educator, Catherine Stern, who published Children Discover Arithmetic in Appropriate for use at all levels in Early Childhood Unifix materials are especially suitable for use in developing: Number awareness Four operations Pattern making Early algebra ideas While young children may be not aware of any mathematical formula, the search for and discovery of a rule for building different stacks arouses enthusiasm. Try these: Using the same three colours (say, red, green and white) each time, how many different 3 stacks can be made? Now, use four colours: how many different stacks can be made? Allow children time to work at this problem. Usually, we make this challenge early in the week and suggest to the children that all solutions be finished by (say) 11:30 am on Friday. Gathering around the solution table the children can review all the submitted ideas. Without providing a definitive solution to these, the next challenge is set. Using 2 colours each time, how many different stacks of three can be made? Using Unifix cubes with trading activities. Developing mathematics with Unifix by Swan and White is a definitive teaching guide. You will find the children s pondering exciting! Note: many ideas can be reinforced using The Brick; likewise, many ideas developed with The Brick can be reinforced using Unifix cubes. Unifix Support Materials Requirements: 2000 pieces per class/group 7
8 Pattern Blocks In the early 1960s, a group of scientists, physicists, mathematicians and teachers collaborated to create the Elementary Science Study. Some of the scientists who developed the original atomic bomb resigned when they realised the terrifying power it released. Rather than continue, they put energy into encouraging children to think so that the bomb would never be used again. At the same time, it may be considered as an offspring of the confidence and optimism of those in the science community. Of course, this is a simplified version, but many innovations were created and appropriate class lessons were developed. Interestingly, some of the creations would be classified as mathematics material today, but they served the same purpose  encouraging children to think. Pattern Blocks are one such creation. The acceptance by the primary school population was almost immediate and they are produced in most westernised countries. Appropriate for use at all levels of Primary School It is recommended that children experience Patterns Blocks at all levels of the primary school. As the children gain experience, new insights will emerge as they manipulate the material. When developing some measurement concepts, such as area, use the blocks very sparingly. They were not designed for this purpose. A classroom table or arrangement of two desks to allow seating for four children, allows a wide variety of activities and solutions to be carried out in the classroom at the same time. Children can share ideas while the teacher can easily check the wide range of thinking. We suggest a small but firm board is used on which to build models  they can be moved at the end of a session. Design and Pattern: a never ending range of possibilities Symmetry, Tessellations Geometry: angles, shapes 8 When using Pattern Blocks, always have the camera on hand. Some of the creations might never appear again! Pattern Blocks could be sorted into individual sets, so the children can take a set home. We have found that parents enjoy exploring the blocks. Developing mathematics with Pattern Blocks by Swan and White is a definitive teaching guide. Requirements: 2000 pieces per class/group (8 sets of 250 pieces) Measurement concepts Number concepts Reflections in a hinged mirror.
9 Coloured Rods (Cuisenaire) In 1953, Professor Caleb Gattegno (Cattegno) met George Cuisenaire, an innovative Belgian teacher. Over the previous quarter of a century, Cuisenaire was using, with success, a range of coloured sticks to aid the teaching/learning of arithmetic to children. Immediately, Cattegno saw the potential of these rods and a year later, in Britain, he established the Cuisenaire Company to distribute the material. Within a short time, Cuisenaire rods were used throughout the western world. One might say, The rest is history! Today, countless boxes, crates and cartons of Cuisenaire rods lie idle in storerooms or, as in many cases, have been dumped or destroyed. A new generation of teachers has little or no knowledge of the rods. It will be in the interests of the achievement of the students to find the rods and revive their appropriate use. New knowledge and understanding of how children learn mathematics can justify the revival of this most versatile material that gave children a rich concrete experience in mathematical exploration. Appropriate for use in Junior Primary to Lower Secondary School Coloured Rods are especially suitable for use in developing: Number awareness Fractions understanding Number bonds Partitioning Early Algebra Ideas It is time we revisit Cuisenaire Rods in order to give children a rich concrete experience in discovering mathematical ideas. (It was not the Cuisenaire rods that were unsuccessful!) Fraction Ideas Requirements: 1 container (250 pieces) per 34 students; that is, 8 containers per class group 9
10 MAB  Base Ten Blocks MAB (Multibase Arithmetic Blocks) were introduced to Australian teachers by Professor Zoltan Dienes as part of the Adelaide Project of Initially, students were introduced to blocks in Bases 3, 4, 5 and 6. Dienes argued, quite correctly, that these smaller denominations were easier for young children to handle because he was concerned that the students understood the Number System before being introduced to Base Ten. Around this time, the Mathematics Education craze which came to be known as The New Maths swept the country unsuccessfully. Embedded in this new program was a heavy emphasis on work in bases other than 10 and converting them to Base Ten. This proved impractical and was abandoned. Other than Base 10 blocks, MAB in bases other than 10 was abandoned. Generally, today Base Ten blocks have been reduced to a material primarily used for demonstration purposes. A wide range of support materials are marketed and include magnetic MAB and place value arrows. The inherent developmental features of the blocks are ignored, both in print and practice. Appropriate for use in Middle Primary to Junior Secondary School Introduce this material after extensive Tactile Trading experience and introduction to Base 10 using bundling with pop sticks and Place Value charts Develop a common terminology throughout the school. Base Ten Blocks are especially suitable for use in developing: Four operations (After a thorough Trading experience) Value relations eg. If a long has a value of 100; what is the value of the cube? Decimal system Decimal fractions (use with Coloured Rods to develop Percentage ideas) The effectiveness of Base Ten Blocks is lost if they are used purely as a demonstration piece and are taken out of the hands of children. Appropriate containers contain 40+ Flats, 40+ longs and about 50 minis. This will provide enough for a group of 4 children. Important Tip: Make sure all your materials are the same dimensions. Some schools have mixed imperial with metric MAB and this causes problems when the children match up the pieces. Developing mathematics with Base Ten by Swan and White is a definitive teaching guide. 10
11 Centicube (Centifit) The increase in interest in Mathematics Education in the 1960s encouraged the development of a wide range of teaching materials. In Britain, E.S. Perry, home of the Osmiroid pens, created the quality suite of Osmiroid educational materials. The Super Beamer Balance was designed for use by young children and Centicube, the 1 cm³ interlocking cube which weighed 1 gram (near enough), was moulded. For years, it was promoted as an essential handson item for use in the teaching of mathematics. Because of its success, manufacturers in several countries copied it but tight patent laws beat such opposition until the mid1980s. Now, there are several lookalikes but, unfortunately, most are incompatible with the original and other brands of 1 cm cubes. There is nothing more frustrating than working with materials that are not compatible. So, warning, when your school chooses a 1 cm cube, make sure the same model is purchased when you resupply, or you may simply start over again. A wide range of printed support material may be found in older mathematics resources collections. Appropriate for use in Upper Primary to Junior Secondary School Centicube is especially suitable for use in developing: Spatial Investigations 3D modelling to isometric drawings spatial visualisation Measurement activities: volume, capacity, mass, etc. These 1 cm³ plastic cubes are suitable for creating threedimensional shapes. Weighing a gram (with a 5% tolerance), the mathematical attributes of these cubes may be applied to many measurement topics. These are not really suitable for use in Early Childhood classrooms. It is a fair comment that, initially, fingers become sore after using the cubes. It is recommended that students are permitted to play freely with them. Prealgebra challenges Work out how many Centicube cubes are used to make each model. Is there a rule which would work if the base was 12 x 12, not 10 x 10? See inside a cube 2 Bar  3 Bar Investigations By joining a 2 bar and a 3 bar; create as many different shapes as possible. Requirements: Centicubes come in containers of 1000 cubes. In most circumstances, one container for 4 to 6 students will be adequate. There is a wide range of support materials for ideas. 11
12 Shared Materials (Early Childhood) D evelopmental Play (Construction type materials) Mobilo Lego or Coko Construction (Clever) Sticks Interstar and a range of extras Kapla Blocks Junior Engineer These are samples of the many construction kits available. Limit the choice but make sure you have good quantities of each item. W idening the range of mathematical experiences Geoboards A small set of simple geoboards (5x5 pins) will provide students with geometric shape experiences. Pegboards Beneficial for creating number patterns and bonds. Colour Cubes Ideal for additional patterning experience. These are listed as samples of suitable materials: preference may be shown for other materials, especially those already on hand. W orking Mathematically Concepta & similar products What s in the square? Introduce matrix logic at an early stage Attribute Blocks and support materials. Children need to experience this material on a regular basis. After being taught how to use these materials, children will be competent to use them without a lot of teacher supervision. Important thinking skills are strengthened with their use. S orting and classification materials Is there an end to the list of both commercial and noncommercial materials that may be used for sorting? Regularly vary items for sorting, but have a sorting area as a permanent fixture in the classroom. Buttons Keys Bears Rocks Water play and sand play are considered a natural part of early childhood classrooms: why can t all children in this area continue their kindergarten experience? Unit (Project) Blocks are available in most kindergartens. Consider extending their availability to all early childhood grades. The mathematical experience is invaluable. Light boxes and mirror reconstructions will be another vital developmental play area. 12
13 Rotated/Shared Materials (Middle to Upper Primary) W orking Mathematically Students who have not been introduced to matrix logic principles need to become familiar with What s in the Square? and What Else is in a Square?. Attribute Blocks will visit classrooms on a regular basis. A wide variety of activities and challenges may be offered to students in upper primary classes Attribute Blocks W idening the range of mathematical experiences Geoboards As an introduction to perimeter and area as well as geometrical concepts, the geoboard is available in square, circle and isometric form. Mira Probably most appropriately used in middle primary and lower secondary classes, this is a valuable aid to teach symmetry. Also include flexible and hinged mirrors. Geo Shapes There is a wide variety of this genre of construction material, for example: Polydron, Clixi, Polyfit, Lokko, Googolplex, Klikko. Any of these materials provide a sound geometrical experience. Tessellation Tessellation pack: a variety of tessellating shapes. Mosaics: while used in the early childhood classrooms more sophisticated applications may be offered. M easurement Materials Appropriate collections of measurement materials are best stored in large plastic containers that may be moved easily to a classroom. Many measurement items will be placed permanently in the classroom see Class Kit Materials. A Checklist of Measurement Materials (with suggested minimum numbers of each item) Bow calliper x 4 Graduated calliper x 4 Metre rule x 8 (Metline Metre and Quadrat Links make a suitable substitute) Tape measure 20 m x 2 Tape measure 2 m x 10 Rulers 30 cm x 10 Trundle Wheel x 2 Constructo Straws, Orbit Using straws and connectors, three dimensional shapes may be created. Orbit is more sophisticated. Construction Materials Some of the materials used in the Early Childhood classrooms could visit the middle primary classes, for example: Mobilo, Kapla blocks, Gears, Knex, etc. Balance scale x 4 Kitchen scale x 2 Bathroom scale x 2 Spring scales a variety Masses (weights): plastic, metal A variety of geometric puzzles Pentominoes Soma Cubes Tangrams and other similar items. Think About! Classrooms have access to water and/or sand to support activities in mass and volume. Pliable clay or plasticine will be accessible at all times. Litre Set Volumetric shapes Graduated cylinders Measuring cups and spoons Measuring jugs Displacement jug Geometric Solids Access to a sand and/or water tray is recommended. 13
14 (Suggested) Items to be included in Classroom Kits The need for teachers to search for manipulative materials was a common complaint. As a compromise, a Classroom Kit is suggested. Each classroom has a collection of frequently used items allocated to the room for the school year. This list is limited but it will be supported by the Key and Rotated materials which are delivered to the classroom on regular intervals. L ower Primary Classroom Kits Playing cards, dominoes, dice, popsticks and counters are used frequently to support the development of number understanding. A Balance Scale is always on hand: children benefit from workingout balancing arrangements. A large Thermometer enables a constant check on the temperature. Encourage children to keep records. All children will have their own calculators. Play Money on hand means a shop can operate. MiddleUpper Primary Classroom Kits Items more appropriate for older children will be included in this kit. Most of what is included in the Early Childhood kit will still be used. Geometric puzzles, such as Pentominoes, Soma Cubes and Tangrams may be included. Digital vs analogue clocks One or two games, such as Numero or Tantrix, are played as focus games in a classroom; that is, children learn how to play the game with skill. For symmetry work (a constant interest for children) it is recommended that Mira and a small collection of mirrors be included. Some teachers recommend that real money (especially coins!) be used instead of play money. Many classroom teachers recommend that in each classroom both an analogue and a digital clock be installed permanently. Children will have experience of using both clocks. An idea: in one week all the time readings are spoken in analogue terms; the next week, all the times are spoken or recorded in digital terms. Also you can have the occasional week using 24hour time. By having the two clocks sidebyside, children become efficient at reading both clocks, appreciating the different notations. Older children may become responsible for time allocations in the classroom. 14
15 A sample Key Materials Rotation Plan Staff members would receive this plan at the beginning of the school year. Early Childhood Middle Primary Upper Primary Term 1 PreP Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Weeks 13 Weeks 46 Weeks 79 (10) The Brick Pattern Blocks Unifix Unifix The Brick Pattern Blocks Pattern Blocks Unifix The Brick Coloured Rods Pattern Blocks Coloured Rods Pattern Blocks Coloured Rods Pattern Blocks Centifit Measure ment Materials MAB Base 10 MAB Base 10 Centifit Measure ment Materials Measure ment Materials MAB Base 10 Centifit A similar plan is created for Terms 2, 3 and 4. Items in each rotation will depend on the equipment in the school. It is recommended that all small collections are collated into one (or two) large collections. Older children can be made responsible for the change over of materials. Items such as The Brick and Pattern Blocks may become Rotated/Shared materials in the Middle and Upper sections of the primary school. Mathematics manipulatives in action Support materials and teacher resources may travel with the containers. Students handle the containers of manipulative materials with ease. 15
16 Thank you! Many teachers and students have contributed to the creation of this booklet. The sharing of ideas and the consequent development of those ideas is happening in many classrooms; as well, children are continually making important contributions to our overall experience of the use of manipulatives in mathematical learning. Many schools have a legacy of the acquisition of manipulative materials, much of this legacy being located in storerooms. We hope this booklet will encourage you to explore the storerooms and cupboards of your school; amongst the variety of materials there will be items which will have a worthwhile place in any mathematics manipulative materials organisational plan. As a means of helping children develop mathematical understandings, the use of concrete materials or mathematics manipulatives such as Pattern Blocks and MAB have been advocated since the early 1960 s. Arising from this notion, is the often used flimsy justification that the children are involved in hands on learning. A research team from Edith Cowan University decided to examine the extent to which mathematics manipulatives are being used, how they are being used and the outcomes associated with their use. This document has been produced in response to some of the findings in the research. As well, based on the data collected, research papers have been presented by various members of the team in different educational conferences throughout the world. Many teachers participating in this research expressed interest in learning how to manage and organise mathematics manipulative materials, not only in their own classroom but also throughout the school. Hence the genesis of A Mathematics Manipulatives Continuum. The research team acknowledges the support of our research partners: the Association of Independent Schools of Western Australia (AISWA), Edith Cowan University and RIC Publications. Edith Cowan University 2009 All rights reserved This document may be photocopied in its entirety for educational purposes. Written by: Geoffrey White, Dr Paul Swan, Linda Marshall Graphic Design: Kinyon Design Key photography: Alisha Hughes Further information: This copy distributed to schools with the compliments of : R.I.C. Publications Pty. Ltd. 16
MATH RESOURCES AVAILABLE FOR LOAN
MATH RESOURCES AVAILABLE FOR LOAN These are materials that were used by Shirley Hamilton as the district math specialist. These materials are now available for you to check out and have in your classroom
More informationMotcombe and Milton on Stour Fractions progression Developed Spring Fractions Progression
Objectives/Activities Year R Key Vocabulary fair, sharing, the same, different, whole, equal, altogether, double, half. 1. Understanding fairness Finding equal and unequal groups. Realising when two groups
More informationYear 1 Maths Expectations
Times Tables I can count in 2 s, 5 s and 10 s from zero. Year 1 Maths Expectations Addition I know my number facts to 20. I can add in tens and ones using a structured number line. Subtraction I know all
More informationIntermediate Phase New DaybyDay Planning Pack MATHEMATICS
Intermediate Phase Planning Pack MATHEMATICS Contents: Work Schedules: Page Grade 4 2 Grade 5 4 Grade 6 5 Lesson Plans: Grade 4 6 Grade 5 21 Grade 6 36 Milestones: Grade 4... 52 Grade 5 57 Grade 6 62 Rubrics:
More informationLEGO Math Activities
LEGO Math Activities By Teri Ann Berg Olsen www.littlebrickschoolhouse.com The first educational manipulatives designed to suit a child s development were invented by Friedrich Fröebel (17821852), founder
More informationthe NJCCCS. By providing a positive approach, we will build confidence to attain
MATH PHILOSOPHY In order to become lifelong problem solvers with an understanding of the relevance to real life situations, our students need to have a solid foundation of math which will meet the NJCCCS.
More informationExplore Create Understand
Explore Create Understand Bob Ansell Contents Introduction 3 What is Polydron? 4 Polydron in the classroom 6 Creating the right environment Polydron in Mathematics 7 Early Years 1  Continue these patterns
More informationNumeracy and mathematics Experiences and outcomes
Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different
More informationEureka Math Tips for Parents
Eureka Math Tips for Parents Sums and Differences to 10 In this first module of, students make significant progress toward fluency with addition and subtraction of numbers to 10. They are presented with
More informationNumeracy Targets. I can count at least 20 objects
Targets 1c I can read numbers up to 10 I can count up to 10 objects I can say the number names in order up to 20 I can write at least 4 numbers up to 10. When someone gives me a small number of objects
More informationCourse Title: Math Grade Level: Fourth
Course Title: Math Grade Level: Fourth Math  Fourth Page 1 2.1 Numbers, Number Systems and Number Relationships: A. Use expanded notation to represent whole numbers or decimals. B. Apply number theory
More informationEveryday Mathematics Grade K3. Parent Resource Guide
Everyday Mathematics Grade K3 Parent Resource Guide . Dear Parents, In this booklet you will find information about the mathematics curriculum taught in our district for grades kindergarten through fourth
More informationMath syllabus Kindergarten 1
Math syllabus Kindergarten 1 Number strand: Count forward and backwards to 10 Identify numbers to 10 on a number line Use ordinal numbers first (1 st ) to fifth (5 th ) correctly Recognize and play with
More information1 st What is mathematics?
s 1 st What is mathematics? What is a number? How is math being discovered or invented? What should be learned in a math course? What should be learned about understanding numbers? What math knowledge
More informationYear 2 Maths Objectives
Year 2 Maths Objectives Place Value COUNTING COMPARING NUMBERS IDENTIFYING, REPRESENTING & ESTIMATING NUMBERS count in steps of 1, 2, 3, and 5 from 0, and in tens from any twodigit number, forward or
More informationAbercrombie Primary School Progression in Calculation 2014
Abercrombie Primary School Progression in Calculation 204 What you need to know about calculations Mathematics will be at the core of your child s schooling from the moment they start to the moment they
More informationLevel Descriptors Maths Level 15
Level Descriptors Maths Level 15 What is APP? Student Attainment Level Descriptors APP means Assessing Pupil Progress. What are the APP sheets? We assess the children in Reading, Writing, Speaking & Listening,
More informationGRADE 5 UNIT PLANS LINKED TO THE BIG IDEAS
GRADE 5 UNIT PLANS LINKED TO THE BIG IDEAS STRAND: Patterning and Algebra TERM: 1 First Instructional Strand Patterns and Relationships 1. Experience with a wide variety of patterns helps students recognize
More informationYear 8  Maths Autumn Term
Year 8  Maths Autumn Term Whole Numbers and Decimals Order, add and subtract negative numbers. Recognise and use multiples and factors. Use divisibility tests. Recognise prime numbers. Find square numbers
More informationChellaston Infant School School Lane, Chellaston DERBY, DE73 6TA. MATHEMATICS POLICY Reviewed by Numeracy team Spring 2012
Chellaston Infant School School Lane, Chellaston DERBY, DE73 6TA Acting Headteacher: Lindsay Galley Telephone: 01332 700298 admin@chellastoni.derby.sch.uk MATHEMATICS POLICY Reviewed by Numeracy team Spring
More informationSchool Subject Week 25
Grade 8th Topic: Overview/Description School Subject Week 25 Central Tendency & Charts and Graphs Find mean, median, mode; make predictions and draw conclusions by analyzing scatter plots Focus: Find mean,
More informationFOURTH GRADE NUMBER SENSE
FOURTH GRADE NUMBER SENSE Number sense is a way of thinking about number and quantity that is flexible, intuitive, and very individualistic. It grows as students are exposed to activities that cause them
More informationCHARLESTON CUSD #1 MATH CURRICULUM GRADE KINDERGARTEN
CHARLESTON CUSD #1 MATH CURRICULUM GRADE KINDERGARTEN Kindergarten Math Assessment Framework Skill / Concept Standards Timeline Classroom Connections Assessment Number Sense /Computation Reading, Writing,
More informationCurriculum overview for Year 1 Mathematics
Curriculum overview for Year 1 Counting forward and back from any number to 100 in ones, twos, fives and tens identifying one more and less using objects and pictures (inc number lines) using the language
More informationGuidelines for using the Abacus Mathematics Programme. within the National Curriculum
Guidelines for using the Abacus Mathematics Programme within the National Curriculum 1. The National Curriculum, NNS and Abacus The National Numeracy Strategy has provided a scheme of work to ensure that
More informationMaths Level Targets. This booklet outlines the maths targets for each sublevel in maths from Level 1 to Level 5.
Maths Level Targets This booklet outlines the maths targets for each sublevel in maths from Level 1 to Level 5. Expected National Curriculum levels for the end of each year group are: Year 1 Year 2 Year
More informationFor use with Discovering Secondary Mathematics
For use with To all secondary school teachers SUB Oxford University Press are the publishers of the following courses among many others: Test it & Fix it: KCSE Revision series Head Start English Kiswahili
More informationMaths Targets Year 1 Addition and Subtraction Measures. N / A in year 1.
Number and place value Maths Targets Year 1 Addition and Subtraction Count to and across 100, forwards and backwards beginning with 0 or 1 or from any given number. Count, read and write numbers to 100
More informationIn mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
More informationMultiplying Fractions by a Whole Number
Grade 4 Mathematics, Quarter 3, Unit 3.1 Multiplying Fractions by a Whole Number Overview Number of Instructional Days: 15 (1 day = 45 60 minutes) Content to be Learned Apply understanding of operations
More informationThe Effects of Mathematics Manipulatives on Middle Childhood Students. Angela Johnson. Ohio Dominican University
The Effects of Mathematics Manipulatives on Middle Childhood Students Angela Johnson Ohio Dominican University Effects of Mathematics Manipulatives 2 Introduction Using manipulatives is often beneficial
More informationTasks to Move Students On
Maths for Learning Inclusion Tasks to Move Students On Part 1 Maths for Learning Inclusion (M4LI) Tasks to Move Students On Numbers 1 10 Structuring Number Maths for Learning Inclusion (M4LI) Tasks to
More informationLesson 3 Compare and order 5digit numbers; Use < and > signs to compare 5digit numbers (S: Bonds to 100)
Abacus Year 5 Teaching Overview Autumn 1 Week Strands Weekly summary 1 Number and placevalue (NPV); and order 5digit Read, write, compare Written addition numbers, understanding and subtraction the placevalue
More informationUsing manipulatives to teach elementary mathematics
ABSTRACT Using manipulatives to teach elementary mathematics Matthew Boggan Mississippi State University Sallie Harper Mississippi State University Anna Whitmire Mississippi State University The purpose
More informationGrades K 8. Scope and Sequence. Math K 4. Intermediate 3 5. Courses 1 3
Grades K 8 Scope and Sequence 4 Intermediate 3 5 Courses 1 3 K 4 4 Scope and Sequence The Scope and Sequence for the K 4 mathematics series is intended to help educators view the progression of mathematical
More informationRead and write numbers to at least 1000 in numerals and in words.
Year 1 Year 2 Year 3 Number, place value, rounding, approximation and estimation Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Count, read and write
More informationAlgebra MATHEMATICS MANIPULATIVES RESOURCE GUIDE
Algebra MANIPULATIVES MATHEMATICS RESOURCE GUIDE AlgeBlocks helps students master algebra concepts with a handson system that includes instructional resources and threedimensional manipulatives. By
More informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More informationFirst Steps in Mathematics Measurement Diagnostic Tasks Student Worksheets
First Steps in Mathematics Measurement Diagnostic Tasks Student Worksheets Understand Units Direct Measure Indirect Measure FIRST041 First steps in Mathematics: Measurement First Steps in Mathematics:
More informationIn a range of practical and play contexts the child explores and solves problems involving doubling, utilising his or her own methods.
FOLTE Multiplication Policy Reception Children to count by rote in 2s to 20, 5s to 50 and 10s to 100. Doubling Children to solve problems using doubling. In a range of practical and play contexts the child
More informationLevel 1  Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3
Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels
More informationToronto Catholic District School Board Mathematics Continuum Kindergarten to Grade 8
Toronto Catholic District School Board Mathematics Continuum Kindergarten to Grade 8 The Math Continuum Effective planning means beginning with the end in mind. It clarifies for teachers students, the
More informationCedar Road Primary School Maths No Problem Calculation Policy
Cedar Road Primary School Maths No Problem Calculation Policy 201617 Textbooks and workbooks The textbooks allow teachers and pupils to explore each topic in real depth. From the 2500 handdrawn illustrations
More informationYear 4 Mathematics Student Portfolio Summary
Year 4 Student Portfolio Summary WORK SAMPLE PORTFOLIOS These work sample portfolios have been designed to illustrate satisfactory achievement in the relevant aspects of the achievement standard. The
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More informationAnnotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.
Work sample portfolio summary WORK SAMPLE PORTFOLIO Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Each portfolio is an example
More informationPROBLEM SOLVING, REASONING, FLUENCY. Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value. Measurement Four operations
PROBLEM SOLVING, REASONING, FLUENCY Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value Addition and subtraction Large numbers Fractions & decimals Mental and written Word problems,
More informationBridging Documents for Mathematics
Bridging Documents for Mathematics 5 th /6 th Class, Primary Junior Cycle, PostPrimary Primary PostPrimary Card # Strand(s): Number, Measure Number (Strand 3) 25 Strand: Shape and Space Geometry and
More informationMathematics K 6 continuum of key ideas
Mathematics K 6 continuum of key ideas Number and Algebra Count forwards to 30 from a given number Count backwards from a given number in the range 0 to 20 Compare, order, read and represent to at least
More informationSenior Phase Grade 9 Today Planning Pack MATHEMATICS
M780636110304 Senior Phase Grade 9 Today Planning Pack MATHEMATICS Contents: Work Schedule: Page Grade 9 2 Lesson Plans: Grade 9 4 Rubrics: Rubric 1: Recognising, classifying and representing numbers 19
More informationAssessment for Learning Explain how you solved this problem. equipment to show your solution? STRAND CODE Year 2 Objectives Year 2 Year 2
BLOCK A Speaking and listening objectives for the block Explain how you solved this problem. Speak with clarity and Does everyone understand how the problem was Unit 1 intonation when reading and reciting
More informationComparing Fractions and Decimals
Grade 4 Mathematics, Quarter 4, Unit 4.1 Comparing Fractions and Decimals Overview Number of Instructional Days: 10 (1 day = 45 60 minutes) Content to be Learned Explore and reason about how a number representing
More informationMath vocabulary can be taught with what Montessorians call the Three Period Lesson.
Full Transcript of: Montessori Mathematics Materials Presentations Introduction to Montessori Math Demonstrations ( Disclaimer) This program is intended to give the viewers a general understanding of the
More informationMATHEMATICS  SCHEMES OF WORK
MATHEMATICS  SCHEMES OF WORK For Children Aged 7 to 12 Mathematics Lessons Structure Time Approx. 90 minutes 1. Remind class of last topic area explored and relate to current topic. 2. Discuss and explore
More informationShape: Area and Perimeter:
Number: Odd and Even Investigation Y3 & Y4 investigated calculations with odd and even numbers. What happens when you add the numbers 4 + 2 =? is the answer odd or even, does this work for every pair of
More informationYear 6 Maths Objectives
Year 6 Maths Objectives Place Value COUNTING COMPARING NUMBERS IDENTIFYING, REPRESENTING & ESTIMATING NUMBERS READING & WRITING NUMBERS UNDERSTANDING PLACE VALUE ROUNDING PROBLEM SOLVING use negative numbers
More informationJust want the standards alone? You can find the standards alone at
K Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 201213 school year. This document is designed to help North Carolina
More informationShape and Space. General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships.
Shape and Space General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships. Elaboration Instructional Strategies/Suggestions KSCO:
More informationAnnotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.
Work sample portfolio summary WORK SAMPLE PORTFOLIO Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Each portfolio is an example
More informationFOREWORD. Executive Secretary
FOREWORD The Botswana Examinations Council is pleased to authorise the publication of the revised assessment procedures for the Junior Certificate Examination programme. According to the Revised National
More informationKINDERGARTEN UNIT PLANS LINKED TO THE BIG IDEAS
UNIT PLANS LINKED TO THE BIG IDEAS STRAND: Number Sense and Numeration TERM: 1 Section: B Counting 1. Counting includes both the recitation of a series of numbers and the conceptualization of a symbol
More informationNational Curriculum 2014 Numeracy Objectives Number Number and Place Value Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Number Number and Place Value Pupils should be taught to and backwards, beginning with 0 or 1, or from any given number 0, and in tens from any number, forward and backward 50 and 100; find 10 or 100 more
More informationSOLVING PROBLEMS. As outcomes, Year 1 pupils should, for example: Pupils should be taught to:
SOLVING PROBLEMS Pupils should be taught to: Choose and use appropriate number operations and ways of calculating to solve problems As outcomes, Year 1 pupils should, for example: Understand and use in
More informationCommutative Property Grade One
Ohio Standards Connection Patterns, Functions and Algebra Benchmark E Solve open sentences and explain strategies. Indicator 4 Solve open sentences by representing an expression in more than one way using
More informationCHAPTER 1: PATTERNS AND ALGEBRAIC THINKING
CHAPTER 1: PATTERNS AND ALGEBRAIC THINKING Algebra skills are essential for your future students. Why? Here are just a few reasons: Mathematics, and especially algebra, is the language of science and modern
More informationYear 3 End of year expectations
Number and Place Value Count in 4s, 8s, 50s and 100s from any number Read and write numbers up to 1000 in numbers and words Compare and order numbers up to 1000 Recognise the place value of each digit
More informationGRADE 2 MATHEMATICS. Students are expected to know content and apply skills from previous grades.
GRADE 2 MATHEMATICS Students are expected to know content and apply skills from previous grades. Mathematical reasoning and problem solving processes should be incorporated throughout all mathematics standards.
More informationISAT Mathematics Performance Definitions Grade 4
ISAT Mathematics Performance Definitions Grade 4 EXCEEDS STANDARDS Fourthgrade students whose measured performance exceeds standards are able to identify, read, write, represent, and model whole numbers
More informationSupport Booklet for. Student Name: Coach Name(s): Start Date: What does the student want to achieve from this programme?
Support Booklet for Student Name: Name(s): Start : What does the student want to achieve from this programme? Target End : Sarah Emson Page 1 Why and Who? Using Turn Tables Using Turn Tables Individual
More informationMinnesota Academic Standards
A Correlation of to the Minnesota Academic Standards Grades K6 G/M204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley
More informationUnit 1: Family Letter
Name Date Time HOME LINK Unit 1: Family Letter Introduction to Third Grade Everyday Mathematics Welcome to Third Grade Everyday Mathematics. It is part of an elementary school mathematics curriculum developed
More informationGrades K 5 Scope and Sequence. Your #1 Choice for WorldClass Mathematics! Deep Math Understanding. RealWorld Problem Solvers.
Grades K 5 Scope and Sequence Your #1 Choice for WorldClass Mathematics! Deep Math Understanding. RealWorld Problem Solvers. Grade K Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Math in Focus : Singapore
More informationNational Curriculum Levels
National Curriculum Levels How do they work? 1 The National Curriculum Levels A few parents have asked for an explanation of the levelling system within the National Curriculum. From Year 1 onwards, then
More information1 How do I make a number?
st What is a number? 1 How do I make a number? Why do we need to count? What are some ways we count? NUMBER SENSE GEOMETRY & SPATIAL SENSE Place value and number relationships reads and writes numerals
More informationYear 1 maths expectations (New Curriculum)
Year 1 maths expectations Counts to and across 100, forwards and backwards, beginning with 0 or one, or from any given number Counts, reads and writes numbers to 100 in numerals; counts in multiples of
More informationMathematics in Indigenous Contexts. Aboriginal Art: the School Mural
Mathematics in Indigenous Contexts Aboriginal Art: the School Mural Planning of Unit Purpose How Crawford Public School is now. This will be used for 25 th anniversary of school. 20 th of September. Possibilities
More informationCreated specifically for the needs of early math learners in Grades K 2
For Grades K 2 Real learning, real math, really fun! Created specifically for the needs of early math learners in Grades K 2 Developed by a highly experienced team of teachers, educational writers, animators,
More informationMathematics standards
Mathematics standards Grade 2 Summary of students performance by the end of Grade 2 Reasoning and problem solving Students represent and interpret mathematical problems by using numbers, objects, signs
More informationYear 2 Maths Objectives
Year 2 Maths Objectives Counting Number  number and place value Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward Place Value Comparing and Ordering Read and write
More informationProgression in reading scales.doc 1
Progression in reading Y1 Y6 Renewed Framework Y2 Read the numbered divisions on a scale, and interpret the divisions between them (e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions
More informationTeaching programme: Reception
Teaching programme: Reception Counting and recognising numbers 2 8 2 2, 3 4, 5 5 6 7 7 8 Counting Say and use the number names in order In familiar contexts such as number rhymes, songs, stories, counting
More informationSt Paul s First School Numeracy Update
St Paul s First School Numeracy Update Concrete vs abstract When we were children, maths consisted of learning all the important steps and rules. We were not given manipulatives, nor an explanation for
More informationAdd and subtract 1digit and 2digit numbers to 20, including zero. Measure and begin to record length, mass, volume and time
Year 1 Maths  Key Objectives Count to and across 100 from any number Count, read and write numbers to 100 in numerals Read and write mathematical symbols: +,  and = Identify "one more" and "one less"
More informationMaths Nonnegotiables
Maths Nonnegotiables Arithmetic must be taught on a daily basis. Its focus should be developing mental strategies fluency. Times tables should be a key mental maths focus in year 3 4. The new curriculum
More informationINFORMATION FOR PARENTS AND CARERS TARGETS IN MATHEMATICS
Emerging towards the expected Year 1 level I can share 6 objects between 2 children. I can write and use numbers (less than 10) in role play. I can compare bigger than and smaller than in role play. I
More informationData and Measure Progress Ladder
Data and Measure Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths
More informationSecond edition. Student's Book 3. Laurie Sealy and Sandra Moore
CARIBBEAN Primary MATHEMATICS Second edition Student's Book 3 Laurie Sealy and Sandra Moore BRIGHT SPARKS SB3 prf4.indd 1 Macmillan Education Between Towns Road, Oxford, OX4 3PP A division of Macmillan
More informationISBN13 Catalog or other # Grade Copyright Publication Contract Level(s) Date Date Price EVERYDAY MATH KINDERGARTEN
Date: 4/14/15 Publisher Name: McGrawHill School Education LLC State Evaluation and Adoption of Instructional Materials for: Category 1: Mathematics Grades K2 Submit via email in.xls (Excel Format only)
More informationYear 5 Mathematics Programme of Study Maths worksheets from mathsphere.co.uk MATHEMATICS. Programme of Study. Year 5 Number and Place Value
MATHEMATICS Programme of Study Year 5 Number and Place Value Here are the statutory requirements: Number and place value read, write, order and compare numbers to at least 1 000 000 and determine the value
More informationSenior Phase Grade 8 Today Planning Pack MATHEMATICS
M780636110236 Senior Phase Grade 8 Today Planning Pack MATHEMATICS Contents: Work Schedule: Page Grade 8 2 Lesson Plans: Grade 8 4 Rubrics: Rubric 1: Recognising, classifying and representing numbers...22
More informationIngleby Manor Scheme of Work : Year 7. Objectives Support L3/4 Core L4/5/6 Extension L6/7
Autumn 1 Mathematics Objectives Support L3/4 Core L4/5/6 Extension L6/7 Week 1: Algebra 1 (6 hours) Sequences and functions  Recognize and extend number sequences  Identify the term to term rule  Know
More informationUnderstanding the Progression of Math Courses in NEISD
Understanding the Progression of Math Courses in NEISD According to House Bill 1 (HB1), students in Texas are required to obtain credits for four courses in each subject area of the foundation curriculum
More informationMathematics Principles and practice
Mathematics Principles and practice What can learning in mathematics enable children and young people to achieve? Mathematics is important in our everyday life, allowing us to make sense of the world around
More informationGeometry and Measurement
Geometry and Measurement (Developmentally Appropriate Lessons for K5 Students) Amanda Anderson Title I Teacher Lincoln Elementary aanderson@bemidji.k12.mn.us Executive Summary This 10day unit plan is
More informationMathematics Improving your Key Stage 3 test result
Mathematics Improving your Key Stage 3 test result A booklet of helpful hints, tips and a revision checklist Contents Page Why are KS3 tests important? 2 The Mathematics test explained 2 How can you support
More informationAn Australian Microsoft Partners in Learning (PiL) Project
An Australian Microsoft Partners in Learning (PiL) Project 1 Learning objects  Log on to the website: http://www.curriculumsupport.education.nsw.gov.au/countmein/  Select children Select children  This
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationBig Ideas in Mathematics
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
More informationRTI MATH RESPONSE TO INTERVENTION
RTI MATH RESPONSE TO INTERVENTION Lakeshore offers the best in learning materials for intervention in math. In Stock and Ready to Order (800) 7784456 Fax (800) 5375403 LakeshoreLearning.com Lakeshore
More informationVirginia Standards of Learning: Math K 2. Pixie
How to read the Pixie Standards Correlations The Pixie Standards Correlations include information on how you and your students can use Pixie to meet your K2 language arts and math standards. Since you
More information