This problem reinforces a learner's understanding of factors and multiples. Students are presented with the hundred grid or parts of the grid where specific numbers have been shaded and must find out which factors have been chosen in order to produce the shading. A link to a spreadsheet which shades the squares according to the chosen factors, can be used by students to check their hypotheses. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

This website has thousands of free mathematics enrichment materials for teachers and learners from ages 5 to 19 years. All the resources are designed to develop subject knowledge, problem-solving, and mathematical thinking skills. The website is updated with new material on the first day of every month with fifteen problems and a number of games, articles and other resources. All are tagged with curriculum content links and challenge levels. Past issues, as far back as November 1999, can be accessed by a link on the home page.

The problems in this NRICH collection utilize simple mathematical concepts with an emphasis on the thinking process. These problems have been categorized by strategies and process skills with an aim at helping learners develop their mathematical thinking skills.

This simple game with 5 variations develops place value understanding and strategic thinking. It is played on paper with a 6- or 9-sided die (printable pdf game sheet included). Two players take turns rolling a die and placing the resulting number in one of their four cells, representing the places of a 4-digit number. In the basic version the player who creates the larger number wins. Variations include aiming for the smaller number or a predetermined target number, using a decimal point, placing numbers in an opponent's cells, and several scoring options. Teachers' Notes include suggestions for introducing the game, support suggestions, and a link to a more challenging extension (Dicey Operations, cataloged separately).

This web page provides instructions for a basic form of Nim, an ancient game that develops strategic thinking. Starting with a total of 7 counters, two players take turns removing one or two at a time. The player who takes the last counter wins. The game of Nim is very adaptable. This page includes questions that encourage players to generalize a winning strategy as well as a link to another page describing several of variations.

This problem provides an opportunity for students to practice counting and to represent and record findings in different ways: "Noah saw 12 legs walk by into the Ark. How many creatures did he see?" Multiple solution possibilities encourage students to be systematic in their strategies. The Teachers' Notes page offers suggestions for implementation, discussion questions, and an idea for extension.

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 non-fiction book report.

This activity promotes algebraic thinking of equivalency as well as giving children practice in addition and subtraction. Students see weights on each side of a balance, and are asked to find ways they can hang a weight or two weights to balance the bar. An interactive balance allows student to explore the different ways weights can be added to balance or equalize the bars. A more challenging problem,"Getting the Balance" is cataloged separately. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.

This activity helps children become more familiar with horizontal and vertical number lines (0 through 10) and how to use them for addition. It can be used to introduce subtraction as the inverse of addition and the use of an unknown number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, printable number lines (pdf), and a link to a related game, Incey Wincey Spider (catalogued separately).

In this activity students are asked to relate the numbers 1- 20 to rectangular shapes. Learners use unit squares or cubes to sort numbers by their 'shapes,' either squares, rectangles or sticks (rectangles of unit width). Ideas for implementation, extension and support are included.

This problem, based on the story of Goldilocks and the Three Bears, provides a context for children to apply ratio and proportion concepts as well as fraction computation skills. Using the given size relationships among the bears, solvers determine the sizes of various objects in the bears' house. The Teachers' Notes page offers suggestions for implementation, key questions, ideas for extension and support, a printable pdf of the problem, and links to related problems.

This number puzzle helps children develop fluency with pairs of numbers that sum to 10 while applying logic and spatial-visualization skills. Users arrange 9 small triangles within a large one so that the numbers on the matching edges total 10. Students can use the interactive Flash applet or the printable (pdf) triangles provided. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to related games (cataloged separately).

In this problem learners explore square numbers and the relationships between them while practicing basic number skills. By applying a systematic strategy they determine three numbers that satisfy the conditions of the scenario. There are links to hints and a solution page; Teachers' Resources include suggestions for implementation, reflection, and differentiation.

The author of this article uses four NRICH investigations to illustrate how a teacher might extend the results of students' work as a springboard for developing deeper mathematical understanding. He models good prompting, e.g., "Tell me what you notice about the result" and "I wonder what would happen if ...", and warns against trying to lead students' thinking. [The problems discussed are cataloged separately.]

This problem provides an opportunity for students to reason about ratio and proportion in the realistic context of mixing a fruit drink from concentrate. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to related problems (Blackcurrantiest is cataloged separately).

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 describes a Big6 lesson focused on organizing information.

This webpage for parents and caregivers describes the various types of resources available at NRICH, a project at the University of Cambrige: rich problems, strategy games, posters, and articles on mathematically gifted children. There are links to these resources and more.

In this brief article British math teacher Jenny Murray describes how she organizes fun sessions for children and parents to work together on math puzzles, games, and problems.

In this fraction activity students are presented with various situations in which they must determine what fraction of the pizza each person would receive. The activity is built around simple fractions and designed so that students record their results and determine a pattern for dividing fractions among a set of people. In addition to the activity, a solution, teacher resource page, and printable page are provided.

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 is an information literacy lesson plan for young children.