Data Management And Probability Grades 4 To 6-Books Pdf

Data Management and Probability Grades 4 to 6
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Management,and Probability,Grades 4 to 6,A Guide to Effective Instruction. in Mathematics,Kindergarten to Grade 6, Every effort has been made in this publication to identify mathematics resources and. tools e g manipulatives in generic terms In cases where a particular product is used. by teachers in schools across Ontario that product is identified by its trade name in the. interests of clarity Reference to particular products in no way implies an endorsement of. those products by the Ministry of Education,Introduction 1. The Pleasure of Mathematical Surprise and Insight 1. Working Towards Equitable Outcomes for Diverse Students 2. Accommodations and Modifications 3,The Mathematical Processes 6. Addressing the Needs of Junior Learners 8, Learning About Data Management and Probability in the Junior Grades 10.
The Big Ideas of Data Management and Probability 11. About Big Ideas 11, About the Teaching and Learning of Data Management and Probability 13. Big Ideas and Tiered Instruction 14, The Big Ideas of Data Management and Probability in Grades 4 to 6 16. Collection and Organization of Data 20,Overview 20. Example Favourite TV Shows 20, Method 1 Matching Questions With Methods of Data Collection. and Organization 21,Method 2 Extending the Problem 24.
Data Relationships 26,Overview 26,Example The Masses of Backpacks 26. Method 1 Understanding Data Relationships 27, Method 2 Exploring Data Relationships Through Project Based Learning 30. Probability 31,Overview 31,Example The Sum of Two Number Cubes 31. Method 1 Experimental Probability 32,Method 2 Theoretical Probability 34. References 36,Learning Activities 37,Introduction to the Learning Activities 39.
Grade 4 Learning Activities 41,Too Much TV, Collection and Organization of Data Data Relationships 41. Heads or Tails,Probability 55,Grade 5 Learning Activities 68. Daily Physical Activity, Collection and Organization of Data Data Relationships 68. Lost Socks,Probability 81,Grade 6 Learning Activities 93. Paper Airplane Contest, Collection and Organization of Data Data Relationships 93.
Rock Paper Scissors,Probability 104,Appendix Guidelines for Assessment 115. Glossary 119,Introduction, Data Management and Probability Grades 4 to 6 is a practical guide that teachers will find. useful in helping students to achieve the curriculum expectations outlined for Grades 4 to 6. in the Data Management and Probability strand of The Ontario Curriculum Grades 1 8. Mathematics 2005 This guide provides teachers with practical applications of the principles. and theories that are elaborated in A Guide to Effective Instruction in Mathematics. Kindergarten to Grade 6 2006, The first part of the guide provides a detailed discussion of the three big ideas or major. mathematical themes in Data Management and Probability and provides a discussion of. mathematical models and instructional strategies that have proved effective in helping. students understand the mathematical concepts related to each big idea The guide emphasizes. the importance of focusing on the big ideas in mathematical instruction to achieve the goal. of helping students gain a deeper understanding of mathematical concepts At the end of the first. part of the guide is a list of references cited, The second part of the guide provides sample learning activities for Grades 4 5 and 6 that. illustrate how a learning activity can be designed to. focus on an important curriculum topic, involve students in applying the seven mathematical processes described in the mathematics.
curriculum document, develop understanding of the big ideas in Data Management and Probability. At the end of the second part of the guide is an appendix that discusses assessment strategies. for teachers There is also a glossary that includes mathematical and other terms that are. used in the guide,The Pleasure of Mathematical Surprise and Insight. Young children enter school mathematically curious imaginative and capable They have. to learn to be otherwise Papert 1980 The aim of this resource is to help consolidate. and extend junior students mathematical capacity and their potential for mathematical. growth by providing ideas and classroom activities that draw their attention to relationships. embedded in the big ideas of the Data Management and Probability strand in the Ontario. mathematics curriculum and that offer them opportunities to experience the pleasure of. mathematical surprise and insight Gadanidis 2004, The activities in this resource incorporate the ideas and practice of classroom teachers The. activities have been field tested in Ontario classrooms and feedback from practising. teachers has been used to create the final versions The chapter The Big Ideas of Data. Management and Probability pp 11 19 discusses the big ideas on which the activities. have been built and contains additional ideas for classroom activities. The teaching of mathematics around big ideas offers students opportunities to develop a. sophisticated understanding of mathematics concepts and processes and helps them to. maintain their interest in and excitement about doing and learning mathematics. Working Towards Equitable Outcomes for Diverse Students. All students whatever their socio economic ethnocultural or linguistic background must. have opportunities to learn and to grow both cognitively and socially When students can. make personal connections to their learning and when they feel secure in their learning. environment their true capacity will be realized in their achievement A commitment to. equity and inclusive instruction in Ontario classrooms is therefore critical to enabling all. students to succeed in school and consequently to become productive and contributing. members of society, To create effective conditions for learning teachers must take care to avoid all forms of. bias and stereotyping in resources and learning activities which can quickly alienate. students and limit their learning Teachers should be aware of the need to provide a variety. of experiences and to encourage multiple perspectives so that the diversity of the class is. recognized and all students feel respected and valued Learning activities and resources for. teaching mathematics should be inclusive providing examples and illustrations and using. approaches that recognize the range of experiences of students with diverse backgrounds. knowledge skills interests and learning styles, The following are some strategies for creating a learning environment that acknowledges.
and values the diversity of students and enables them to participate fully in the learning. experience, providing mathematics problems with situations and contexts that are meaningful to all. students e g problems that reflect students interests home life experiences and cultural. backgrounds and that arouse their curiosity and spirit of enquiry. using mathematics examples drawn from diverse cultures including Aboriginal peoples. using children s literature that reflects various cultures and customs as a source of mathe. matical examples and situations, understanding and acknowledging customs and adjusting teaching strategies as necessary. Data Management and Probability Grades 4 to 6, For example a student may come from a culture in which it is considered inappropriate. for a child to ask for help express opinions openly or make direct eye contact with an. considering the appropriateness of references to holidays celebrations and traditions. providing clarification if the context of a learning activity is unfamiliar to students. e g describing or showing a food item that may be new to some students. evaluating the content of mathematics textbooks children s literature and supplementary. materials for cultural or gender bias, designing learning and assessment activities that allow students with various learning. styles e g auditory visual tactile kinaesthetic to participate meaningfully. providing opportunities for students to work both independently and interdependently. with others, providing opportunities for students to communicate orally and in writing in their home.
language e g pairing an English language learner with a first language peer who also. speaks English, using diagrams pictures manipulatives sounds and gestures to clarify mathematical. vocabulary that may be new to English language learners. For a full discussion of equity and diversity in the classroom as well as a detailed checklist. for providing inclusive mathematics instruction see pages 34 40 in Volume 1 of A Guide to. Effective Instruction in Mathematics Kindergarten to Grade 6 2006. The term accommodations is,used to refer to the special tea. Accommodations and Modifications ching and assessment strategies. human supports and or indi, The learning activities in this document have been designed for vidualized equipment required. to enable a student to learn, students with a range of learning needs Instructional and assess. and to demonstrate learning, ment tasks are open ended allowing most students to participate Accommodations do not alter the.
fully in learning experiences In some cases individual students provincial curriculum expectations. for the grade, may require accommodations and or modifications in accordance. Modifications are changes made, with their Individual Education Plan IEP to support their in the age appropriate grade. participation in learning activities level expectations for a subject. in order to meet a student s,learning needs These changes. PROVIDING ACCOMMODATIONS,may involve developing expecta. Students may require accommodations including special strate tions that reflect knowledge and. skills required in the curriculum, gies support and or equipment to allow them to participate in.
for a different grade level and or, learning activities There are three types of accommodations increasing or decreasing the. number and or complexity of the, Instructional accommodations are adjustments in teaching strate regular grade level curriculum. expectations, gies including styles of presentation methods of organization. Ontario Ministry of Education, or the use of technology or multimedia 2004 pp 25 26. Introduction, Environmental accommodations are supports or changes that the student may require in the.
physical environment of the classroom and or the school such as preferential seating or. special lighting, Assessment accommodations are adjustments in assessment activities and methods that. enable the student to demonstrate learning such as allowing additional time to complete. tasks or permitting oral responses to test questions. Some of the ways in which teachers can provide accommodations with respect to math. ematics learning activities are listed in the following chart. Instructional Accommodations, Vary instructional strategies using different manipulatives examples and visuals e g concrete. materials pictures diagrams as necessary to aid understanding. Rephrase information and instructions to make them simpler and clearer. Use non verbal signals and gesture cues to convey information. Teach mathematical vocabulary explicitly,Have students work with a peer. Structure activities by breaking them into smaller steps. Model concepts using concrete materials and computer software and encourage students to use. them when learning concepts or working on problems. Have students use calculators and or addition and multiplication grids for computations. Format worksheets so that they are easy to understand e g use large size font an uncluttered. layout spatial cues such as arrows colour cues, Encourage students to use graphic organizers and square grid paper to organize ideas and written. Provide augmentative and alternative communications systems. Provide assistive technology such as text to speech software. Provide time management aids e g checklists, Encourage students to verbalize as they work on mathematics problems.
Provide access to computers,Reduce the number of tasks to be completed. Provide extra time to complete tasks,Environmental Accommodations. Provide an alternative workspace, Seat students strategically e g near the front of the room close to the teacher in group settings with. a classmate who can help them,Reduce visual distractions. Minimize background noise,Provide a quiet setting,Provide headphones to reduce audio distractions.
Provide special lighting,Provide assistive devices or adaptive equipment. Data Management and Probability Grades 4 to 6,Assessment Accommodations. Have students demonstrate understanding using concrete materials using computer software. or orally rather than in written form,Have students record oral responses on audiotape. Have students responses on written tasks recorded by a scribe. Provide assistive technology such as speech to text software. Provide an alternative setting,Provide assistive devices or adaptive equipment. Provide augmentative and alternative communications systems. Format tests so that they are easy to understand e g use large size font an uncluttered layout. spatial cues such as arrows colour cues,Provide access to computers.
Provide access to calculators and or addition and multiplication grids. Provide visual cues e g posters, Provide extra time to complete problems or tasks or answer questions. Reduce the number of tasks used to assess a concept or skill. MODIFYING CURRICULUM EXPECTATIONS, Students who have an IEP may require modified expectations which differ from the regular. grade level curriculum expectations When developing modified expectations teachers. make important decisions regarding the concepts and skills that students need to learn. Most of the learning activities in this document can be adapted for students who require. modified expectations The following chart provides examples of how a teacher could. deliver learning activities that incorporate individual students modified expectations. Modified Program What It Means Example, Modified learning expecta The student with modified The learning activity involves. tions same activity same expectations works on the same representing a probability as a. materials or a similar activity using the fraction Students with modi. same materials fied expectations represent,the probability using an area. Modified learning expecta The student with modified The activity involves creating. tions same activity different expectations engages in the a bar graph to display data. materials same activity but uses different Students with modified. materials that enable him her expectations can use statistical. to remain an equal participant software to create the bar. in the activity graph,Introduction,Modified Program What It Means Example.
Modified learning expecta Students with modified expec Students with modified. tions different activity tations participate in different expectations work on data. different materials activities management and probability. activities that reflect their,learning expectations using. a variety of materials and,technological tools, Adapted from Education for All The Report of the Expert Panel on Literacy and Numeracy Instruction for. Students With Special Education Needs Kindergarten to Grade 6 p 119. It is important to note that some students may require both accommodations and modified. expectations,The Mathematical Processes, The Ontario Curriculum Grades 1 8 Mathematics 2005 identifies seven mathematical. processes through which students acquire and apply mathematical knowledge and skills. The mathematical processes that support effective learning in mathematics are as follows. problem solving connecting,reasoning and proving representing. reflecting communicating,selecting tools and,computational strategies.
The learning activities in this guide demonstrate how the mathematical processes help. students develop mathematical understanding Opportunities to solve problems to reason. mathematically to reflect on new ideas and so on make mathematics meaningful for. students The learning activities also demonstrate that the mathematical processes are. interconnected for example problem solving tasks encourage students to represent math. ematical ideas to select appropriate tools and strategies to communicate and reflect on. strategies and solutions and to make connections between mathematical concepts. Problem Solving Each of the learning activities is structured around a problem or an. inquiry As students solve problems or conduct investigations they make connections. between new mathematical concepts and ideas that they already understand The focus. on problem solving and inquiry in the learning activities also provides opportunities for. students to,find enjoyment in mathematics, develop confidence in learning and using mathematics. Data Management and Probability Grades 4 to 6,work collaboratively and talk about mathematics. communicate ideas and strategies,reason and use critical thinking skills. develop processes for solving problems, develop a repertoire of problem solving strategies. connect mathematical knowledge and skills with situations outside the classroom. Reasoning and Proving The learning activities described in this document provide oppor. tunities for students to reason mathematically as they explore new concepts develop ideas. make mathematical conjectures and justify results The learning activities include questions. that teachers can use to encourage students to explain and justify their mathematical thinking. and to consider and evaluate the ideas proposed by others. Reflecting Throughout the learning activities students are asked to think about reflect. on and monitor their own thought processes For example questions posed by the teacher. encourage students to think about the strategies they use to solve problems and to examine. the mathematical ideas that they are learning In the Reflecting and Connecting part of. each learning activity students have an opportunity to discuss reflect on and evaluate. their problem solving strategies solutions and mathematical insights. Selecting Tools and Computational Strategies Mathematical tools such as manipulatives. pictorial models and computational strategies allow students to represent and do math. ematics The learning activities in this document provide opportunities for students to select. tools concrete pictorial and symbolic that are personally meaningful thereby allowing. individual students to solve problems and to represent and communicate mathematical. ideas at their own level of understanding, Connecting The learning activities are designed to allow students of all ability levels to.
connect new mathematical ideas to what they already understand The learning activity. descriptions provide guidance to teachers on ways to help students make connections. among concrete pictorial and symbolic mathematical representations Advice on helping. students develop conceptual understanding is also provided The problem solving experience. in many of the learning activities allows students to connect mathematics to real life situa. tions and meaningful contexts, Representing The learning activities provide opportunities for students to represent mathe. matical ideas by using concrete materials pictures diagrams numbers words and symbols. Representing ideas in a variety of ways helps students to model and interpret problem. situations understand mathematical concepts clarify and communicate their thinking and. make connections between related mathematical ideas Students own concrete and pictorial. representations of mathematical ideas provide teachers with valuable assessment information. about student understanding that cannot be assessed effectively using paper and pencil tests. Introduction, Communicating Communication of mathematical ideas is an essential process in learning. mathematics Throughout the learning activities students have opportunities to express. mathematical ideas and understandings orally visually and in writing Often students are. asked to work in pairs or in small groups thereby providing learning situations in which. students talk about the mathematics that they are doing share mathematical ideas and ask. clarifying questions of their classmates These oral experiences help students to organize. their thinking before they are asked to communicate their ideas in written form. Addressing the Needs of Junior Learners, Every day teachers make many decisions about instruction in their classrooms To make. informed decisions about teaching mathematics teachers need to have an understanding of. the big ideas in mathematics the mathematical concepts and skills outlined in the curriculum. document effective instructional approaches and the characteristics and needs of learners. The following chart outlines general characteristics of junior learners and describes some. of the implications of these characteristics for teaching mathematics to students in. Grades 4 5 and 6, Area of Characteristics of Implications for Teaching. Development Junior Learners Mathematics, Intellectual Generally students in the junior The mathematics program should.
Development grades provide, prefer active learning experiences learning experiences that allow. that allow them to interact with students to actively explore and. their peers construct mathematical ideas, are curious about the world learning situations that involve the. around them use of concrete materials, are at a concrete operational opportunities for students to see. stage of development and are that mathematics is practical and. often not ready to think abstractly important in their daily lives. enjoy and understand the subtle enjoyable activities that stimulate. ties of humour curiosity and interest,tasks that challenge students to. reason and think deeply about,mathematical ideas,Data Management and Probability Grades 4 to 6.
Area of Characteristics of Implications for Teaching. Development Junior Learners Mathematics, Physical Generally students in the junior The mathematics program should. Development grades provide, experience a growth spurt before opportunities for physical move. puberty usually at age 9 10 for ment and hands on learning. girls at age 10 11 for boys a classroom that is safe and physi. are concerned about body image cally appealing,are active and energetic. display wide variations in physical,development and maturity. Psychological Generally students in the junior The mathematics program should. Development grades provide, are less reliant on praise but still ongoing feedback on students.
respond well to positive feedback learning and progress. accept greater responsibility for an environment in which students. their actions and work can take risks without fear of. are influenced by their peer ridicule,groups opportunities for students to. accept responsibility for their,a classroom climate that supports. diversity and encourages all,members to work cooperatively. Social Development Generally students in the junior The mathematics program should. grades provide, are less egocentric yet require opportunities to work with others. individual attention in a variety of groupings pairs. can be volatile and changeable in small groups large group. regard to friendship yet want to opportunities to discuss math. be part of a social group ematical ideas,can be talkative clear expectations of what is.
are more tentative and unsure of acceptable social behaviour. themselves learning activities that involve all, mature socially at different rates students regardless of ability. Moral and Ethical Generally students in the junior The mathematics program should. Development grades provide, develop a strong sense of justice learning experiences that provide. and fairness equitable opportunities for, experiment with challenging the participation by all students. norm and ask why questions an environment in which all ideas. begin to consider others points of are valued,view opportunities for students to share. their own ideas and evaluate the,ideas of others, Adapted with permission from Making Math Happen in the Junior Years Elementary Teachers.


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