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Number & Operations: WebConnects
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.

The links listed direct to sites outside of Nelson Education Ltd. which implies neither responsibility for, nor approval of, the information contained in those other Web sites on the part of Nelson Education Ltd. You may close the new browser window to return to Nelson or simply return to http://www.prime.nelson.com.

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 Number and Operations
Section 3: Content Issues in Learning About Number and Operations
Section 4: Developing Number Sense
Section 5: Problem Solving in Number and Operations
Section 6: Communication in Number and Operations
Section 7: Assessment and Evaluation in Number and Operations
Section 8: Differentiating Instruction in Number and Operations

Section 1: Introduction

There are no WEBCONNECTS in Section 1 of the Number and Operations Background and Strategies book.

Section 2: Instructional Issues Around Teaching Number and Operations

The Importance of Context (p. 10) 

goENC.com is an online K–12 math and science subscription resource centre. It lets you search for integrated children’s literature and math books – listing the title, grade level, cost, and a brief description of content of related books. The books can be ordered online from goENC.com.

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.

Technology Resources (p. 29)

goENC.com is an online K–12 math and science subscription resource centre. PRIME links you directly to their home page.

Math Central, from the University of Regina, features a Mathematics Glossary, Quandaries and Queries, and links to Web sites with math activities.

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

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

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.

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. Virtual Manipulatives is our link to its many Number and Operations applets.

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.

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets. It also offers games. Number games require knowledge from strands other than number, and questions about imperial/metric conversions may be asked.

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.

Section 3: Content Issues in Learning About Number and Operations

Small Numbers: Appropriate Technology (p. 40)

Counting Down offers practice in counting backward, or down, from 20. A number is given and students are asked for the next number if counting down.

Dart Game, from the BBC Number Time site, involves number recognition to 9 and doubling numbers to 9 at the first level. The higher levels involve adding and multiplying by 2.

FunBrain Games offers many games. Two of interest are Connect the Dots and One False Move. Access them by using the link to All Games and then selecting from the Top Games list. The first is a counting game with options to count by 1s, 5s, and backward by 1s from 30. The second is an ordering game with options for least to greatest and greatest to least. Only the easiest level uses numbers from 1 to 100; the other levels use integers.

Mend the Number Square is a game from the BBC Number Time site. Students place missing numbers in a 100 chart.

Online Math Games for Kids offers numerous games for students to practise number and operations skills. Of interest here are Dogs Counting, Order Numbers, and Money Games under Elementary Math Games.

Printable Small Number Worksheets, from the BBC Number Time site, offers printable worksheets for students to practise working with numbers up to 20 by inserting missing numbers and re-ordering numbers.

Snakes and Ladders is a game from the BBC Number Time site. Students roll a die and move along a 100-chart game board riddled with snakes and ladders.

Addition and Subtraction: Appropriate Technology (p. 48)

The Addition and Subtraction Flashcards site provides practice adding and subtracting facts to 20 or to 100, separate or mixed, using flashcards. It also has basic multiplication fact flashcards. 

Students can use Cuisenaire Rods to model addition and subtraction. Use Start the Integer Bars Applet. The numerical values of the rods can be turned on, and rods can be created to 20. Students can place rods end to end to add and then check their answer by placing the rod that has the numerical value of the sum to see if it is the same length as the end to end rods. Similarly, they can place one rod under another to subtract and then check their answer by placing the rod that has the numerical value of the difference to see if it matches the difference in the lengths of the rods.

Online Math Games for Kids offers numerous games for students to practise number and operations skills. Of interest here are the addition and subtraction games under Elementary Math Games.

The BBC Number Time site offers printable addition and subtraction practice worksheets that are found under each of the following titles: Add and take away, Number ladders, Making numbers, and Number stories.

Test the Toad is a game from the BBC Number Time site. Students practise addition and subtraction facts to 15, using a number line (numbered people).

Virtual Manipulatives offers a wide range of applets. Of interest when adding and subtracting are Number Line Arithmetic and Number Puzzles. The former models adding and subtracting sums to 20 using jumps on a number line. In the latter, students arrange numbers 1 to 9 in a diagram so that they add to a given value.

Greater Whole Numbers: Appropriate Technology (p. 68)

Base Ten Blocks is a site that allows students to create numbers to 999 using base ten blocks. Use Start the Base 10 Blocks Java Program. Students regroup a greater place value to a lesser one using a hammer icon (to break apart) and regroup a lesser place value to a greater one using a glue icon (to attach). They move more than one block at a time using a lasso icon.

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets. Of interest here are those for The number system.

Virtual Manipulatives offers a wide range of applets. Of interest when working with place value of whole numbers is Chip Abacus. Here students model numbers to 999 by placing coloured chips in a place value chart. They regroup by exchanging 1 hundred chip for 10 ten chips, for example.

Addition and Subtraction Algorithms: Appropriate Technology (p. 81)

Base Ten Blocks is a site that allows students to add and subtract numbers to 999 using base ten blocks. Use Start the Base 10 Blocks Java Program.  When adding, students regroup a lesser place value to a greater one using a glue icon (to attach). Subtraction is takeaway where students create the minuend and take away the subtrahend, regrouping a greater place value to a lesser one using a hammer icon (to break apart) when needed.

H.B. Meyer, from Germany, has 4 by 4 magic squares which are addition puzzles. Rather than students completing magic squares, suggest they display a “quick” solution for a general, a panmagic, a centralsymm., and then a mirrorsymm. magic square to determine the addition rule that applies to each.

Online Math Games for Kids offers numerous games for students to practise number and operations skills. Of interest here are the addition and subtraction games under Middle School Math Games.

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets. Of interest here are those for Addition and Subtraction. When prices are used, they are in British currency.

Virtual Manipulatives offers a wide range of applets. Of interest when using addition and subtraction algorithms are Base Block Addition and Base Block Subtraction. Students find sums to 9999 by modelling the addends using base ten blocks and regrouping as needed. They find differences with minuends to 9999 using a one-to-one comparison between blocks in the minuend and subtrahend to remove blocks, regrouping where needed. Note: this applet refers to minuends and subtrahends as positive and negative numbers respectively.

Multiplication and Division Algorithms: Appropriate Technology (p. 97)

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets. Of interest here are those for Multiplication and Division.

Virtual Manipulatives offers a wide range of applets. Of interest when multiplying and dividing are Number Line Arithmetic, Rectangular Multiplication, and Rectangular Division. Number Line Arithmetic models multiplying and dividing products to 50 using jumps on a number line. In number line multiplication, for 6 × 8, for example, both 8 jumps of 6 and 6 jumps of 8 are shown. Rectangular Multiplication relates three different models to area. In Rectangular Division, students can select a quotient and a divisor, and see the quotient displayed as a rectangle and the remainder as a column beside the rectangle.

Number Theory: Appropriate Technology (p. 102)

H.B. Meyer, from Germany, has a sieve of Eratosthenes that can be used to determine prime numbers to 400.

 

Virtual Manipulatives offers a wide range of applets. Of interest when studying number theory is Sieve of Eratosthenes. This can be used to determine prime numbers to 200.

Fractions: Appropriate Technology (p. 116)

Fraction Bars allows students to use fraction bars to model and compare fractions. Use Start the Fraction Bars Applet. This program also allows for conversion among fractions, decimals, and percents.

Fraction Pointer presents students with fractions located on a number line for them to model as part of a circle or part of a square by creating the number of equal sections needed and colouring the correct number of them.

The Fraction Track site by NCTM provides the applet for the game Fraction Track. It explains how to play the game as well as how to use it in class.

This site allows students to use Pattern Blocks to model and compare fractions. Use Start the Pattern Java Program. Students move blocks into the grid area and rotate them as needed.

Virtual Manipulatives offers a wide range of applets. There are three of interest when studying fractions. Fractions—Naming models simple fractions for students to identify. Fractions—Parts of a Whole allows students to model simple fractions as parts of a circle or parts of a square. Fractions—Visualizing directs students to model simple fractions by creating the number of equal parts needed and colouring the correct number of them. 

Decimals: Appropriate Technology (p. 130)

Base Ten Blocks allows students to add and subtract two decimal numbers given to the same place of the form xx.x, x.xx, or 0.xxx using base ten blocks. However, an appropriate place value mat is not available. Start the Base 10 Blocks Java Program. When adding, students regroup a lesser place value to a greater one using a glue icon (to attach). Subtraction is takeaway where students create the minuend and take away the subtrahend, regrouping a greater place value to a lesser one using a hammer icon (to break apart) when needed.

Fraction Bars allows students to use fraction bars to model, compare, and convert among fractions, decimals, and percents. Use Start the Fraction Bars Applet.

Virtual Manipulatives offers a wide range of applets. Of interest when adding and subtracting decimals is Base Block Decimals. Students add and subtract two decimals given to the same place ranging from xxx.x to x.xxx. They find sums by modelling the addends using base ten blocks and regrouping as needed. They find differences using a one-to-one comparison between blocks in the minuend and subtrahend to remove blocks, regrouping where needed. Note: this applet refers to minuends and subtrahends as positive and negative numbers respectively.

Section 4: Developing Number Sense

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

Section 5: Problem Solving in Number and Operations

Sources of Other Problems (p. 170)
This site offers Brain Teasers each week for students in Grades 3–4, 5–6, and 7–8. The next week it gives the answers. The problems and answers stay on the site for three weeks.

An NCTM site entitled Figure This offers problems called Challenges for Families, with hints. Problems are indexed by title and by math topic. 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 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.

Math Contest, from 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.

The Math Forum, from Drexel University, offers a problem of the week which is free. The next week, the answer is posted. Access to their library of problems of the week requires a paid membership.

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 Number and Operations

Mathematics Vocabulary and Symbols (p. 183)

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 69: 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 Number and Operations

 Other Resources (p. 210)

The Kid-Friendly Problem Solving Rubric is a seven-level problem solving rubric in student language.

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

Principles for Fair Student Assessment is a set of guidelines for fair assessment generally accepted by professional organizations within Canada.

Section 8: Differentiating Instruction in Number and Operations

Strategies for Motivated and Gifted Learners(p. 224)

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.

This site offers Brain Teasers each week for students in Grades 3–4, 5–6, and 7–8. The next week it gives the answers. The problems and answers stay on the site for three weeks.

Explore Your Knowledge 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. 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.

Math Contest, from Columbus State University, offers weekly problems such as Elementary Math Brain Teaser and Middle School Madness. Students are invited 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 Number
Section 3: Phases of Development in Operations

Section 1: Introduction

How PRIME Complements Curriculum (p. 4)

Curriculum correlations that relate APEF (Atlantic Provinces Educational Foundation) Kindergarten to Grade 6 curriculums to the Number Developmental Map and the Operations Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Curriculum correlations that relate Ontario Kindergarten to Grade 6 curriculums to the Number Developmental Map and Operations Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Curriculum correlations that relate WNCP(Western and Northern Curriculum Protocol) Kindergarten to Grade 6 curriculums to the Number Developmental Map and Operations Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Section 2: Phases of Development in Number

Supporting Students in Phase 5, How Parents Can Help (p. 70)

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.

This site offers Brain Teasers each week for students in Grades 3–4, 5–6, and 7–8. The next week it gives the answers. The problems and answers stay on the site for three weeks.

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

An NCTM site entitled Figure This offers problems, called Challenges for Families, with hints. Problems are indexed by title and by math topic. Both quick answers and full solutions are provided.

Game Wheel, from the BBC Education Maths File site, offers games involving number concepts as well as games from other math strands.

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 Contest, from 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. 

Online Math Games for Kids offers numerous games for students to practise number and operations skills. Of interest here are the number and operation games under Middle School Math Games.

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 3: Phases of Development in Operations
 
There are no WEBCONNECTS in Section 3 of the Number and Operations Guide to Using the Developmental map book.