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Patterns & Algebra: 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 Patterns & Algebra
Section 3: Content Issues in Learning About Patterns & Algebra
Section 4: Developing Symbol Sense
Section 5: Problem Solving in Patterns & Algebra
Section 6: Communication in Patterns & Algebra
Section 7: Assessment and Evaluation in Patterns & Algebra
Section 8: Differentiating Instruction in Patterns & Algebra

Section 1: Introduction

There are no WEBCONNECTS in Section 1 of the Patterns & Algebra Background and Strategies book.

Section 2: Instructional Issues Around Teaching Patterns & Algebra

Technology Resources (p. 32)

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 Patterns & Algebra 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.

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 Patterns & Algebra

Patterns: Appropriate Technology (p. 60)

Braid Pattern Applet provides an applet where students can select the number of braid strands and then alter the braid by lengthening or shortening individual strands. Ask students to describe and compare the diagonal patterns in the various braids they create.

Creating, Describing, and Analyzing Patterns is an NCTM site with three pattern activities. Making Patterns includes an interactive figure for creating, comparing, and viewing multiple repetitions of a pattern core. In Describing Patterns, examples of various ways that students might interpret a pattern (such as colour, shape, and size) are given. Extending Pattern Understandings demonstrates ways in which students begin to create a grouping that can be repeated and begin to relate two patterns.

This site allows students to use Cuisenaire Rods  (or integer bars) to create, describe, extend, and compare repeating patterns. Use Start the Integer Bars Applet. Patterns can be created using attributes of size, colour, and orientation by dragging the rods into the grid and rotating them as needed.

This site allows students to use Pattern Blocks to create, describe, extend, and compare repeating patterns. Use Start the Pattern Java Program. Patterns can be created using attributes of shape, colour, and orientation by dragging the blocks into the grid and rotating them as needed.

The Square Grid Pattern Applet provides an applet where students can create different patterns on grids by changing the number of blue squares in the grey grid and the location of the blue squares. The theory of creating specific patterns is well beyond elementary math, but students will enjoy creating different patterns at random. Ask them to describe the patterns they create.

Virtual Manipulatives offers a wide range of applets. Of interest when working with repeating patterns is Colour Patterns in which students complete repeating colour patterns.  Number Patterns is another applet, where students complete non-repeating number patterns. Many of the number patterns involve integers.

Algebra: Appropriate Technology (p. 70)

Creating, Describing, and Analyzing Patterns is an NCTM site with three pattern activities. Making Patterns includes an interactive figure for creating, comparing, and viewing multiple repetitions of a pattern core. In Describing Patterns, examples of various ways that students might interpret a pattern (such as colour, shape, and size) are given. Extending Pattern Understandings demonstrates ways in which students begin to create a grouping that can be repeated and begin to relate two patterns.

Fibonacci Number Puzzles offers a range of puzzles involving the Fibonacci numbers. Introduce students to this number pattern, 0, 1, 1, 2, 3, 5, 8, 13, 21, …, and ask them to determine the pattern rule (add the two previous numbers to get each subsequent number) and extend it (34, 55, 89, 144, 233, 377, 610, 987, …) before introducing them to this site.

This site shows patterns created by figurate numbers—triangular numbers, square numbers, and so on to octagonal numbers. Students can extend the patterns for any of these. They should be able to determine the pattern rules for triangular numbers and square numbers. 

FunBrain Games offers many games. Of interest here is Number Cracker. Access it by using the link to All Games… and then selecting from the Number Games list. In the game, students determine the missing number in non-repeating number patterns. A range of difficulty levels is offered.

Number Tricks presents a number trick and an algebraic explanation of why it works. Other tricks are presented for students to try and to explain, and then they are asked to create a trick of their own and explain why it works.

Online Math Games for Kids offers two games for students to practise extending non-repeating patterns. Under Middle School Math Games, both Patterns 1 (geometric patterns) and Patterns 2 (number patterns) present several terms and options for the next term for students to select.

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets on the topic of number patterns.

Section 4: Developing Symbol Sense

There are no WEBCONNECTS in Section 4 of the Patterns & Algebra Background and Strategies book.

Section 5: Problem Solving in Patterns & Algebra

Sources of Other Problems (p. 104)


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 Patterns & Algebra

Mathematics Vocabulary and Symbols (p. 118)

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 Patterns & Algebra

 Other Resources (p. 144)

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 Patterns & Algebra

Strategies for Motivated and Gifted Learners (p. 157)

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 Patterns & Algebra

Section 1: Introduction

How PRIME Complements Curriculum (p. 4)

Curriculum correlations that relate CAMET (Council of Atlantic Ministers of Education and Training) Kindergarten to Grade 6 curriculums to the 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 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 Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Section 2: Phases of Development in Patterns & Algebra

Supporting Students in Phase 3, How Parents Can Help (p. 48)

This site allows students to use Cuisenaire Rods (or integer bars) to create, describe, extend, and compare repeating patterns. Use Start the Integer Bars Applet. Patterns can be created using attributes of size, colour, and orientation by dragging the rods into the grid and rotating them as needed.

FunBrain Games offers many games. Of interest here is Number Cracker. Access it by using the link to All Games… and then selecting from the Number Games list. In the game, students determine the missing number in non-repeating number patterns. A range of difficulty levels is offered.

Geometric Patterns shows several geometric tessellations.

Islamic Geometric Patterns shows several geometric patterns that are original creations and follow ancient Islamic geometric patterns.

Online Math Games for Kids offers two games for students to practise extending non-repeating patterns. Under Middle School Math Games, both Patterns 1 (geometric patterns) and Patterns 2 (number patterns) present several terms and options for the next term for students to select.

Pattern Blocks allows students to use pattern blocks to create, describe, extend, and compare repeating patterns. Use Start the Pattern Java Program. Patterns can be created using attributes of shape, colour, and orientation by dragging the blocks into the grid and rotating them as needed.

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets on the topic of number patterns.

Virtual Manipulatives offers a wide range of applets. Of interest when working with repeating patterns is Colour Patterns. Students complete repeating colour patterns.

Supporting Students in Phase 4, How Parents Can Help (p. 60)

All You Ever Wanted to Know About Pascal's Triangle explains how Pascal’s Triangle and many of its patterns are formed.

Fibonacci Number Puzzles offers a range of puzzles involving the Fibonacci numbers. Introduce students to this number pattern, 0, 1, 1, 2, 3, 5, 8, 13, 21, …, and ask them to determine the pattern rule (add the two previous numbers to get each subsequent number) and extend it (34, 55, 89, 144, 233, 377, 610, 987, …) before introducing them to this site.

This site shows patterns created figurate numbers—triangular numbers, square numbers, and so on to octagonal numbers. Students can extend the patterns for any of these. They should be able to determine the pattern rules for triangular numbers and square numbers. 

FunBrain Games offers many games. Of interest here is Number Cracker. Access it by using the link to All Games… and then selecting from the Number Games list. In the game, students determine the missing number in non-repeating number patterns. A range of difficulty levels is offered.

Number Tricks presents a number trick and an algebraic explanation of why it works. Other tricks are presented for students to try and to explain, and then students are asked to create a trick of their own and explain why it works.

Online Math Games for Kids offers two games for students to practise extending non-repeating patterns. Under Middle School Math Games, both Patterns 1 (geometric patterns) and Patterns 2 (number patterns) present several terms and options for the next term for students to select.

The BBC Bitesize Maths site offers a number of interactive activities, fact sheets, tests, and printable worksheets on the topic of number patterns.

Sissa’s Reward presents the Sissa’s Reward problem to be solved. It has links to similar problems.