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).

In this math investigation students must determine how two people can share the food items for a picnic equally. The problem involves dividing whole numbers by two and using fractions to divide items equally. The problem is accompanied by a Teachers' Resource page that includes suggestions for approaching the problem, questions, extension ideas, and tips for support.

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.

The Big6 is a six-stage model to help anyone solve problems or make decisions by using information. Students can use this model to guide them through the research process. This resource guides students through writing a fiction book report.

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.

The Big6 is a six-stage model to help anyone solve problems or make decisions by using information. Students can use this model to guide them through the research process. The Super3 is a simplified version of the model for younger students. This worksheet uses the familiar Flat Stanley project to guide students through the Super3.

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 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.

These 10 strategy games from around the world develop spatial skills and strategic thinking. Two of them include interactive versions, but all can be played with simple materials indoors or out.

This article highlights a number of mathematical strategy games that are available on the NRICH website. Most have interactive versions but also can be played offline. The author explains their value in the classroom, offers suggestions for implementation and extension, and provides links to the games and to other related articles.

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 problem consolidates children's understanding of halving in a spatial context and will help them to develop their powers of visualization. The students are given four different shapes and the goal is to divide them each into two parts that are exactly the same. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, a link to an extension activity, Same Shapes (cataloged separately), and a link to a simpler activity, Halving (cataloged separately).