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Measurement
 
 

WEBCONNECTS, or Internet links, are described in the margin of the Background and Strategies Book and the Guide to the Developmental Map. These links extend the discussion from the books to the Internet.

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Background and Strategies Webconnects
Guide to the Developmental Map Webconnects

Background and Strategies Table of Contents

Section 1: Introduction
Section 2: Instructional Issues Around Teaching Measurement
Section 3: Content Issues in Learning About Measurement
Section 4: Developing a Sense of Size
Section 5: Problem Solving in Measurement
Section 6: Communication in Measurement
Section 7: Assessment and Evaluation in Measurement
Section 8: Differentiating Instruction in Measurement

Section 1: Introduction

Connections to Other Subject Areas (p. 6)

Body Proportions in Art offers a connection between measurement and visual arts—average adult body and facial proportions. It lists and shows diagrammatically the ratio of other body parts to the head and the position of facial parts. As well, it offers a link to Leonardo da Vinci’s drawing of the human figure.

Building a Scale Model City offers a connection between measurement and social studies and visual arts?many aspects of city living and scale models. It shows how students in Grades 5 and 6 use simulation software, Sim City 2000, to create skyscrapers. It offers advice on getting started, lesson plans, and links to various tall structures.

Measurements in Our Neighborhood offers a link between measurement and social studies?how measurements are used daily by everyone all around us. It uses field trips and discussions. The K to Grade 1 project deals with these big ideas:  most people measure in their daily lives; there are many different types of measuring tools; many things in our surroundings need to be measured; measurement is essential to finding answers in many fields of study; and there are standard and non-standard units of measurement.

Measuring Plant Growth, from Math Forum, offers a link between measurement and science?a bean plant project. It outlines the process and offers follow-up activities.

Measuring Shadows, from eThemes, offers a link between measurement and science?lengths of shadows. It provides links to sites which explain why shadow lengths change; how to determine the height of an object using shadows, a stick, and ratios; offer an interactive activity that lets students change the location of the sun and see how that changes shadow lengths; and provide instructions for conducting experiments with shadows.

Off the Scale, from NCTM Illuminations Lessons, offers a link between measurement and social studies using maps and solving problems involving scale. While the lesson uses maps of students’ “home state” and Imperial units, it can be adapted to maps of students’ “home province or territory” and metric units.

Section 2: Instructional Issues Around Teaching Measurement

Technology Resources (p. 36)

BBC Bitesize offers interactive activities, information summaries, and

quizzes. Metric units are used throughout. However, money is not in dollars and cents because this is from Britain.

Math Central, from the University of Regina, features teaching resources including links to activities, mathematics glossaries, and Quandaries and Queries.

Mathematically Sane provides links to balanced, research-based information about mathematics teaching and learning.

The Math Forum, from Drexel University, features Ask Dr. Math and an Internet Mathematics Library. It offers both student and teacher areas with links to Web sites with activities and problems. Some of our direct links are Measuring Plant Growth and Short vs Tall.

Math Playground offers varied and abundant practice of math skills for students in Grades K–6, including Logo Park.

The National Council of Teachers of Mathematics (NCTM) site provides information about the organization, its conferences, and its publications. Principles and Standards for School Mathematics is available online here as are problems, activities for home and school, applets, and lessons.

 

The National Library of Virtual Manipulatives for Interactive Math, from Utah State University, is a source of applets for learning mathematics. It is categorized by grade level and strand. Measurement Virtual Manipulatives is our link to NLVM`s Measurement applets. NOTE: Units are Imperial and some metric, using American spelling, er, rather than re, and money illustrated is US dollars.

NCTM Illuminations provides activities and resources that are appropriate for teachers at various grade levels to use as they reflect on, plan for, and implement NCTM Standards–based mathematics education in their classrooms. NOTE: Units are Imperial and some metric, using American spelling, er, rather than re. Some of our direct links are Get the Turtle to the Pond Lesson and Shape Cutter.

Section 3: Content Issues in Learning About Measurement

The Metric System of Measurement (p. 43)

How Many? discusses the base units and the derived units of SI (International System)

International System of Units from NIST discusses SI base units for the seven base quantities well as historical background of SI.

SI Metric offers definitions of the seven base units.

Linear Measurement: Appropriate Technology (p. 58)

Bed Length uses a poem to introduce an activity about the use of non-standard units and the need for a standard unit.

Get the Turtle to the Pond Lesson, from the NCTM Illuminations Lessons site, offers a creative problem-solving activity where students use directional language as well as estimating length and angle measure to enter a sequence of LOGO commands to help the turtle get to the pond.

Max’s Challenge uses a poem to introduce using non-standard units and invites students to send in information about what they measured and the lengths they found.

Measure, from Math Forum, is an applet where students measure a specific integer bar using other integer bars as non-standard units.

Miss Nelson …, from Math Forum, uses a story to introduce an activity about the use of non-standard units.

MSW Logo provides links to Logo software and Logo activities.

Perimeter Explorer allows students to determine the perimeters of randomly generated rectangles or irregular shapes on a grid by counting.

Player Heights allows students to sort players by comparing their heights by moving the players around.

Reading a Ruler randomly generates lengths along a ruler for students to measure. There are three levels of difficulty – to nearest centimetre, to nearest half centimetre, and to nearest millimetre. NOTE: American spelling, er, rather than re, is used.

Short vs Tall, from Math Forum, is an applet where students compare the height of an integer bar when it is oriented vertically and horizontally.

Area: Appropriate Technology (p. 78)

Area Explorer allows students to determine the areas of randomly generated rectangles or irregular shapes by counting grid squares.

Geoboard is an applet that allows students to create shapes using bands on a geoboard. They can create shapes of specific areas or create shapes and find the areas.

Shape Cutter, from the NCTM Illuminations Tools site, allows students create shapes, decompose them, and recompose them to make other shapes. They can determine areas by counting grid square. As well, students can create parallelograms, decompose them, and recompose them to make rectangles to explore how the same area formula applies to both shapes.

Capacity, Volume, and Mass: Appropriate Technology (p. 78)

Fermi Questions, from Math Forum, offers volume, mass, and capacity problems for students to investigate.

Greater Than, Less Than, Or Equal To outlines an activity where students sort rocks by estimated mass, and then measure them to check.

Heavy or Light provides pictures of common items for students describe as heavy or light and to compare with other items.

How High?, from NLVM, offers an interactive activity about the conservation of volume.

Measure, from BBC Bitesize, offers an interactive activity about measuring the length of a parcel and weighing it to determine the postage required. As well, it has Revision Bite, which is a summary of measuring length, measuring mass, measuring capacity, reading scales, 12-hour and 24-hour time, and units of time; and an interactive quiz. NOTE: postage is in p (pence) and ml and l are used instead of mL and L.

Weight (not Mass) calculates weight on other planets, the moon, and other places in the universe as well as discussing the difference between weight and mass.

Time, Temperature, and Money: Appropriate Technology (p. 118)

Analog and Digital, from NLCM, tells the current time on an analog and a digit clock. Students can set the time on one clock and the other clock changes to the same time. Showing seconds is an option.

Clock Wise is an analog clock applet where times are randomly generated and students record the time or students enter a time and the clock changes to that time.

e-Clock allows students to change an analog clock by increasing or decreasing by  the hour, half hour, quarter hour, 5 minutes, or minute. The analog clock changes and the time can be displayed in words and digitally.

Elapsed Time randomly generates start and end times. Students can determine the elapsed time either by advancing a clock or doing mentally. The clocks can be displayed as analog or digital. There are three levels of difficulty.

Match Clocks shows times on an analog clock and student change the time on a digital clock to match.

Reading a Thermometer offers a non-interactive opportunity for students to read thermometers and make comments about the temperature.

Same Time is a memory game where students find two cards telling the same time.

Telling Time offers links to many sites about telling time for students and teachers.

Time for Time is a resource about time for students and teachers. It includes interactive practice clocks, games, and quizzes.

What Time …, from NLVM, shows time on one analog clock and students change the time on a second analog clock to show what time it will be in so many hours and minutes.

Worksheet Creator is a resource that randomly generates worksheets for telling time and putting hands on clocks. Both can be to the hour, half hour, quarter hour, or minute.

Angles: Appropriate Technology (p. 126)

Angles, from BBC Bitesize, offers an interactive activity about turning a hose to spray things in a playground. As well, it has Revision Bite, which a summary of angles as a measure of turn, types of angles, adding up angles, using a protractor, and perpendicular and parallel lines; and an interactive quiz.

Angle Measure provides students with angles to measure when they are displayed with a protractor or angles to estimate when they are displayed without a protractor.

Calculating Angles  is a non-interactive worksheet about measuring angles on a clock face, types of angles, and reading a protractor.

Get the Turtle to the Pond Lesson, from the NCTM Illuminations Lessons site, offers a creative problem-solving activity where students use directional language as well as estimating length and angle measure to enter a sequence of LOGO commands to help the turtle get to the pond.

Image Tool allows students to draw an angle using three points and the angle measure is given. The angles can be changed by moving any of the three points.

Match provides an opportunity for students to match angle terms and their meanings.

MSW Logo provides links to Logo software and Logo activities.

Protractor allows students to move a protractor to gain experience positioning and reading a protractor in order to measure angles.

Types of Angles allow students to view acute and obtuse angles and identify given angle measures by type.

Section 4: Developing a Sense of Size

There are no WEBCONNECTS in Section 4 of the Measurement Background and Strategies book.

Section 5: Problem Solving in Measurement

Sources of Other Problems (p.162 )

Figure This, an NCTM site, offers problems called Challenges for Families, with hints. Problems are indexed by title and by math topic (see Math Index). Both quick answers and full solutions are provided.

Math Mountain offers many problems for students in Grades 2–3 and 4–5 with hints and solutions. It also has links to its archived problems and to many Web sites with math problems, puzzles, and tips.

NRICH, from University of Cambridge, focuses on a different topic each month. It offers many problems on the topic at various levels. Students are invited to submit solutions. As well, links to archived problems are provided.

Problem of the Week, from the Columbus State University, offers weekly problems such as Elementary Math Brain Teaser and Middle School Madness and invites students to submit answers. Those who answer correctly get their names posted. Students can also submit answers to past problems.

Puzzle Corner, from the AIMS (Activities Integrating Math & Science) Education Foundation, offers over 100 interesting puzzles that can help students learn to enjoy puzzles and the mathematics behind them. The puzzles are categorized by type, such as dissecting, and are listed in order of increasing difficulty within each category. Solutions are available.

Word Problems for Kids, from St. Francis Xavier University, offers challenging, non-traditional problems for students in Grades 5–12. In addition to answers, hints are available.

Section 6: Communication in Measurement

Reading Opportunities in Mathematics (p. 178)

The Mathematics Council of the Alberta Teachers' Association (MCATA) Mathematics and Literature site lists children’s literature books for three math strands—number concept, shape and space, and data analysis—and general reference. The information provided includes author, title, publisher, and date.

Mathematics Vocabulary and Symbols (p. )

A Math Dictionary for Kids has definitions with examples in student-friendly language.

The Mathematics Glossary – Middle Years has definitions from the Saskatchewan Education document Mathematics 6–9: A Curriculum Guide for the Middle Level. The definitions were designed to be meaningful to middle-level mathematics teachers. Some definitions have examples.

The Math Dictionary offers concise definitions to mathematical terms. Some definitions have links to illustrated examples.

Section 7: Assessment and Evaluation in Measurement

 Other Resources (p. 204)

GAP, the Great Assessment Picture book, is 12 chapters, each a Word document, covering many aspects of assessment.

The Math Problem Solving Rubric is a five-criteria, four-level problem solving rubric for teachers.

Section 8: Differentiating Instruction in Measurement

Strategies for Motivated and Gifted Learners (p. 218)

Aunty Math offers challenging problems for students in Grades K–5. Students are invited to submit their solutions. There are options for more difficult or easier problems as well as tips for teachers and parents.

Dare to Compare offers questions for students in Grades 4 and 8 math (and science). The questions are from the Trends in International Mathematics and Science Study (TIMSS). Students can select the number of questions they want to try. Answers are provided.

Figure This, an NCTM site, offers problems called Challenges for Families, with hints. Problems are indexed by title and by math topic (see Math Index). Both quick answers and full solutions are provided.

MATHCOUNTS is a coaching and competition program for middle school. Even without registering your school to participate, you can take advantage of several free problem-solving features. There is a problem of the week, with the solution provided the next week, links to archived problems, and links to Web sites with math problems.

Math Mountain offers many problems for students in Grades 2–3 and 4–5 with hints and solutions. It also has links to its archived problems and to Web sites with math problems, puzzles, and tips.

Math Olympiads for Elementary and Middle Schools offers contests for Grades 4–6 and 7–8. Before registering a team of students, you can view a sample test at each level online. There is also a problem of the month, with the solution provided the next month.

NRICH, from University of Cambridge, focuses on a different topic each month. It offers many problems on the topic at various levels. Students are invited to submit solutions. As well, links to archived problems are provided.

Pick's Theorem, from Ask Dr. Math at the Math Forum, offers an explanation and informal proof of Pick's theorem.

Problem of the Week, from the Columbus State University, offers weekly problems such as Elementary Math Brain Teaser and Middle School Madness and invites students to submit answers. Those who answer correctly get their names posted. Students can also submit answers to past problems.

Word Problems for Kids, from St. Francis Xavier University, offers challenging, non-traditional problems for students in Grades 5–12. In addition to answers, hints are available.

Guide to the Developmental Map Table of Contents

Section 1: Introduction
Section 2: Phases of Development in Measurement

Section 1: Introduction

How PRIME Complements Curriculum (p. 4)

The curriculum correlations will be available soon.

Section 2: Phases of Development in Measurement

Supporting Students in Phase 1, How Parents Can Help (p. 36)

Bed Length uses a poem to introduce an activity about the use of non-standard units of length and the need for a standard unit.

Heavy or Light provides pictures of common items for students to describe as heavy or light and to compare with other items.

Max’s Challenge uses a poem to introduce using non-standard units of length and invites students to send in information about what they measured and the lengths they found.

Supporting Students in Phase 3, Special Approaches for Older Students (p. 79)

Area Explorer allows students to determine the areas of randomly generated rectangles or irregular shapes by counting grid squares.

Geoboard allows students to create shapes using bands on a geoboard. They can create shapes of specific areas or create shapes and find the areas.

Perimeter Explorer allows students to determine the perimeters of randomly generated rectangles or irregular shapes on a grid by counting.

Reading a Ruler randomly generates lengths along a ruler for students to measure. There are three levels of difficulty – to nearest centimetre, to nearest half centimetre, and to nearest millimetre. NOTE: American spelling, er, rather than re, is used.

Shape Cutter allows students create shapes on a grid. They can create shapes of specific areas or create shapes and find the areas.

Supporting Students in Phase 3, How Parents Can Help (p. 80)

Angles is an interactive activity about turning a hose to spray things in a playground. As well, it has Revision Bite, which a summary of angles as a measure of turn, types of angles, adding up angles, using a protractor, and perpendicular and parallel lines; and an interactive quiz.

Angle Measure provides students with angles to measure when they are displayed with a protractor or angles to estimate when they are displayed without a protractor.

Clock Wise is an analog clock applet where times are randomly generated and students record the time or students enter a time and the clock changes to that time.

Measure is an interactive activity about measuring the length of a parcel and weighing it to determine the postage required. As well, it has Revision Bite, which is a summary of measuring length, measuring mass, measuring capacity, reading scales, 12-hour and 24-hour time, and units of time; and an interactive quiz. NOTE: postage is in p (pence) and ml and l are used instead of mL and L.

Same Time is a memory game where students find two cards telling the same time.

What Time … shows time on one analog clock and students change the time on a second analog clock to show what time it will be in so many hours and minutes.

Supporting Students in Phase 4, How Parents Can Help (p. 98)

e-Clock allows students to change an analog clock by increasing or decreasing by the hour, half hour, quarter hour, 5 minutes, or minute. The analog clock changes and the time can be displayed in words and digitally.

Fermi Questions offers volume, mass, and capacity problems for students to investigate.

How High? is an interactive activity about calculating volume and the conservation of volume.

Shape Cutter allows students create shapes, decompose them, and recompose them to make other shapes. They can determine areas by counting grid square. As well, students can create parallelograms, decompose them, and recompose them to make rectangles to explore how the same area formula applies to both shapes.

Weight (not Mass) calculates weight on other planets, the moon, and other places in the universe as well as discussing the difference between weight and mass.

Consolidating and Extending Phase 4, Instructional Focus (p. 100)

Measuring Shadows provides links to sites which explain why shadow lengths change; how to determine the height of an object using shadows, a stick, and ratios; offer an interactive activity that lets students change the location of the sun and see how that changes shadow lengths; and provide instructions for conducting experiments with shadows.

Pick's Theorem offers an explanation and informal proof of Pick's theorem.

Shape Cutter allows student to create shapes, decompose them, and recompose them to make other shapes. They can create trapezoids and parallelograms to explore how the area formula for a trapezoid is related to that for a related parallelogram.