This brief article on Archimedes describes some of his practical inventions, his love of pure mathematics, and his quirkiness. Many links to related topics are included as well as a link to a printable page.

This flash applet provides students with an activity to become more familiar with factors and multiples. The challenge is to arrange the four number cards (1, 2, 3 and 21) on a square of the grid to make as many different diagonal, vertical or horizontal lines as possible. The number card can be placed on a square of the grid if the square is the same number, a multiple of that number and or a factor of that number. Users have the ability to change the difficulty level. The Teachers' Notes page offers rationale, suggestions for implementation, key discussion questions, ideas for extension and support.

This problem helps learners improve their knowledge of factors, especially those in the usual multiplication tables, and encourages the problem solving strategy of trial and error. The goal of the game is to go around the track in as few moves as possible, keeping to the rules that a player can move any number of spaces which is a factor of the number the player is on, except 1. There is a "training" track to play on initially to see the rules in action and then a more complicated track for players to use. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support.

This problem offers opportunities for students to reinforce their understanding of factors and multiples and provides them the chance to justify their solutions. The goal is for the students to create number chains of four whole numbers that can range from 2 to 100 and each consecutive number is a multiple of the previous number. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support, and a link to a spreadsheet for students to experiment with placing numbers in specific boxes in the chain.

This puzzle, played with cards on a board (downloadable file), provides an interesting context in which students can apply their knowledge of number properties. Students attempt to arrange 25 numbers and 10 property headings into a 5 by 5 grid so that each number satisfies two conditions. Properties addressed include primes, square and triangular numbers, specific sets of multiples and factors, and parity. It can be worked individually or in small groups cooperatively. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to an article, "Using Games in the Classroom" (catalogued separately).

This series of problems requires students to apply their knowledge of area and perimeter to find the optimal area given a specified amount of fencing. The problems progress in difficulty as new elements are added to the situation, therefore changing the outcome. This page includes tips for getting started, solution, teachers resource page, and a printable problem page.

This problem reinforces addition fact fluency, develops reasoning, and encourages working systematically. Solvers determine which seven cards, out of a set of 15 numbered cards 1-15, are used to satisfy the given sums of each consecutive pair of cards. The resource includes hints for getting started, printable copies of the problem and number cards, suggestions implementation and differentiation, discussion questions, and sample student solutions.

This problem with multiple solutions provides an opportunity for students to practice subtraction while developing logical thinking and systematic record-keeping strategies. Given a pyramid of six circles, solvers are challenged to arrange the numbers 1 - 6 so that each number is the difference between the two numbers just below it. Children may use pencil and paper or the interactive Flash applet provided. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, work sheets (pdf), and a link to a more challenging version.

This activity gives students the chance to explore area and perimeter in a problem solving setting. Nine differently-sized squares need to be tiled into a rectangular frame of unknown proportions. Three prompts of solving strategies are provided. Ideas for implementation, extension and support are included along with a printable sheet of the problem.

In this problem students study motion along a path and the properties of a parallelogram. Students must navigate back to a starting point after traveling three legs in cardinal directions on a compass. Ideas for implementation, extension and support are included.

This problem helps develop an understanding of the relationship between the part and the whole. Given a square figure divided into smaller triangles, students are asked to use the pattern to divide the square into two halves, three thirds, six sixths, and nine ninths. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of of the problem.

This open-ended problem requires students to use the pattern of triangles on the given figure to divide the square into halves, thirds, sixths, and ninths. The problem asks students to find the part of the whole that is squares or triangles and then determine how these shapes represent each fraction of the whole. Included with this problem are teacher notes with suggestions for introducing the problem, discussion questions, support suggestions, and a printable version of the square.

This problem with multiple solutions is an opportunity for students to practice finding equivalent fractions using a visual fraction bar model. The goal is for the student to develop a deep understanding of equivalent fractions using the model in order to determine a rule for finding equivalent fractions without a model. A Teacher's Note page, hints, possible solutions, and a printable page are provided.

This problem provides students an opportunity to find equivalent fractions and carry out some simple additions and subtractions of fractions in a context that may challenge and motivate students. Users need to download, print, and cut-out the fraction jigsaw. Then, they must arrange the square pieces right-side up so that the edges that touch contain equivalent fractions. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

In this problem students use a visual representation of fractions to compare fractions. Students are given two fractions and using the fraction wall they must compare them and find the difference between them. A Teacher's Notes page, hints, solutions, and printable pages are provided. The goal of this problem is for students to compare the two fractions given by using the visual fraction wall or their knowledge of equivalent fractions and subtracting fractions.

This problem gives students practice in calculating with fractions, using factors and multiples, finding equivalent fractions, logical reasoning, and working systematically. Students use clues to determine the total number of discs in a game and the fraction represented by each color. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of the problem.

This Nim-like interactive Flash game provides an opportunity to practice basic addition and subtraction while developing strategic thinking through generalization and by applying knowledge of factors and multiples. It can be played against the computer or a friend. Players take turns adding a whole number from 1 to 4 to a running total. The player who hits the target of 23 wins. Computer settings allow changing the target number, the range of numbers to add, who goes first, and whether the player reading the target wins or loses. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for support, and links to related games.

This problem encourages children to identify and describe a pattern and to extend the pattern into a general rule. Using an applet, learners try to discover the number of garlic cloves being planted if the arrangement into various rows always finds that there is one left over. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for support and extension.

In this activity, students explore number decomposition and the powers of two. They play a number guessing game, and by the presence or absence of the secret number on each of six cards, the number can be found. An applet has the computer play the trick with the learner. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for support and extension.

This class activity is designed to introduce young learners to the concept of tree diagrams. This class activity requires learners to organize data about the individual student's physical characteristics(gender, hair and eye color) utilizing connecting cubes. The activity includes a follow up activity, questions, tips on getting started, a teacher resource page, and a printable version of the problem.