This brief article relates the legend of young Gauss and the summing of consecutive numbers. Readers are asked to apply the method and they are shown a general solution. A link to a printable page is provided as well as links to related topics.

This activity helps students become familiar with positional words and develop systematic thinking. Students use the clues provided to arrange six colored squares in an array, either on paper or with the interactive Flash applet that is provided. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support and a printable sheet (doc). Students may be asked to create a similar problem for others to solve.

This activity allows students to explore reflective symmetry. They are asked to color a given arrangement of triangles in symmetric patterns using specific numbers of colors. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets

This short assessment is a great way to take stock of your communication style and its consequences. As written, this is appropriate for older youth or adults, including parents. However, the questions can easily be re-written to speak in the language of your group, whatever their age. Have individuals share in pairs or triads. Debrief by asking what new information or insight assessment offers.

In this investigation students explore the concept of ratios and their relationship with factors and multiples. Given an assortment of cogs (gears) with different numbers of teeth, solvers are asked to find which pairs allow for each tooth of one to fit into every gap of the other, and to form conjectures regarding which pairs would work generally. The problem is well-suited for group work. The Teachers' Notes page offers suggestions for implementation, key questions, student sheets, and links to articles, videos, and an interactive Cog Environment (cataloged separately).

This problem gives children an opportunity to explore an increasing pattern and then generalize the results with a rule. Students begin with a single counter, surround it by a ring of other counters and then each new ring is surrounded with more counters. Solvers record results as they replicate the pattern and make predictions about many counters there will be in any given ring. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support.

Solvers of this problem apply number sense and logical reasoning to determine the numbers of cows and sheep in each of five fields by using clues about how many cows and sheep can be seen by each animal. The problem includes questions for getting started, suggestions for implementation and differentiation, a printable student page, and sample solutions.

This activity asks students to recognize differences in shapes and sort them. They are given a set of 15 shape cards that they can sort by the criteria of color, size and shape. Ideas for implementation, extension and support are included along with a printable sheet of the cards.

In this article the author suggests three ways teachers can support learners to become confident and competent problem solvers. Each suggestion is discussed in detail with links to NRICH tasks and articles to provide further understanding of this complex process. The article can also be downloaded as a PDF.

This article offers advice to educators on developing learners' collaboration skills through problem solving. The author presents six categories of tasks, each of which addresses a set of teamwork skills (e.g. listening, sharing, reflecting) and includes several tasks which could serve as the vehicle. Links to the tasks, printable materials, and other resources are included.

This 13-page article presents eight aspects to consider when creating a classroom culture that supports problem solving. The article identifies each of the eight aspects and then goes into more detail suggesting activities that can be done in the classroom to promote more student discourse and problem solving. Throughout the article are links to supportive math activities, research articles and professional development activities.

This article helps educators answer questions about geometric thinking and the activities that develop it. It outlines the 3 levels of thinking about shape and space and the 5 phases of activities known as the van Hiele model. The tangram puzzle provides a vehicle for describing these phases and the types of thinking students achieve in each one. The article concludes with a suggestion about followup activity.

This problem demonstrates the power of the 100 square (Hundred Chart) in helping children to recognize number properties and in beginning to reason carefully and form conjectures. Students look at sums of numbers located in a certain configuration within squares of the grid. There is a link to a printable hundred chart.

This collection of 6 games develops place value, operation sense and fluency, estimation, and strategic thinking. It is played on paper with a 6- or 9-sided die (printable pdf game sheets included). Players choose a game grid with empty cells representing the digits of a computation (addition, subtraction, multiplication, or division). They take turns rolling a die and placing the resulting number in a cell on their own grids. The goal is to create a sum/difference/product/quotient that is closest to a target number. Variations include using a decimal point and scoring options. Teachers' Notes include suggestions for introducing the game, discussion questions, support suggestions, and a link to a more challenging extension (Countdown, cataloged separately).

This activity gives students an opportunity to discuss the quantities involved in statements about measurements or statistics and may involve estimation, calculation and/or research. Ideas for implementation, extension and support are included.

This game for two or more players tests students' knowledge of the uses of various measuring tools. An interactive spinner picturing 8 tools that measure the attributes of length, weight, volume, angle and time determines the players' movement on a game board. Students must explain their reasoning about their choices of tool applications. A printable page is available.

This problem helps learners become more familiar with odd and even numbers and addition facts within five. By challenging them to justify their findings, it also develops reasoning and communication skills. The problem displays 9 dominoes and asks the student to sort them according to parity, and then into pairs totaling 5 pips. It poses questions that stimulate thinking about basic number concepts. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to an interactive Dominoes Environment (cataloged separately).

This problem requires students to have a good understanding of fractions and challenges children to visualize 3D shapes. Students are asked how to divide a doughnut into eight equal pieces using only three cuts. The Teachers' Notes page includes rationale, suggestions for implementation, discussion questions, and ideas for extension with a link to a worksheet and support.

This article describes the progression from halves, to thirds and fourths, as well as fair sharing as a means of teaching more abstract fractions to young students. Throughout the article activities are suggested to support the learning, as well as a link to a six-minute video which shows two children working on a difficult sharing situation practically with a teacher who questions appropriately to get the thinking going. Two of the activities mentioned in the article, "Happy Halving" and "Bowl of Fruit" are cataloged separately.

In this problem students practice basic addition and subtraction skills along with logical reasoning to satisfy three interdependent conditions. Solvers use the clues provided to determine the number of eggs in each of three baskets. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, a PowerPoint presentation, and vocabulary cards (pdf).