This exploratory problem provides students a way to consolidate their understanding of halving and halves and gives students experience of mathematical proof. The students are given multiple images of squares split in half. The goal is to prove how they are correctly halved and to think of other ways to split a square into two halves. The Teachers' Notes page offers rationale, suggestions for implementation along with a PowerPoint presentation, discussion questions, ideas for extension and support, and printable (pdf) worksheets of the problem.

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).

This brief article describes some methods of indirect measurement that have been applied throughout history to the problem of estimating the height of tall trees. Several methods involving scaling, angles, ratios, and tools are discussed.

This brief article describes the development of money used for commerce from the ancient practice of bartering and commodity trading to the present day's use of coinage and bank notes. The origins of minting coins and the functions of banks are also discussed. Links to other sources on money history are included.

This brief article describes Samuel Morse and the code first used by telegraph operators in the 19th century. The time intervals used in transmissions are detailed, and there is a connection between the code and letter frequencies in the English alphabet. Included is a link to a printable page and a Morse Code font for Windows.

In this investigation, students visualize and compare volumes in solids composed of unit cubes and look for patterns in the measurements. They work systematically to organize and analyze the results. Ideas for implementation, extension and support are included.

In this set of addition and subtraction word problems students are encouraged to find their own way to solve the problems. This enables students to discover the strengths and weaknesses of different solution methods and to see how multiple methods all arrive at the same answer. Included with the problem set are tips for getting started, the solutions, a teacher resource page, and a printable student page.

This activity provides an opportunity for students to work on spatial visualization and number sense together. Learners are presented with a hundred grid and told there is another printed on the reverse side. They must work out the unseen numbers for several positions on the grid. Ideas for implementation, extension and support are included along with a printable sheet of grids.

This problem challenges children to make sense of information presented by applying their knowledge of number properties and to make and test conjectures based on that information. Students try to determine the secret number property or rule by examining the numbers that fit the rule and the numbers that don't fit the rule. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support and a link to an interactivity of the game.

In this lesson activity students create visual representations for the data presented in the book, "If the World Were a Village" by David J Smith and Shelagh Armstrong. Students are challenged to create different representations and reason why one representation may be better than another. Suggested representations are pictographs, bar graphs, and tables. The activity includes the problem, teacher notes, hints, and solution suggestions.

When a flood is forecast for the Red River of the North, community leaders, emergency responders, and residents around Fargo, North Dakota, and Moorhead, Minnesota, can gauge their need for preparation by accessing visualizations showing the extent, depth, and timing of expected flooding.

This activity helps students develop a sense of the relative size of quantities in the categories of temperature, speed, time duration and loudness. Learners rank their estimates of given measures in order from least to greatest and justify their decisions. Students are encouraged to do research and carry out experiments when possible. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and links to related activities.

This problem presents students with a situation in which the probability of an event must be determined. Students make a prediction about the probability of Kaia's father wearing the same tie during one week and simulate the event with an experiment to confirm their prediction with the experimental probability. Additional resources for the teacher are provided along with a printable version of the problem.

This Java applet game allows children to think strategically in an engaging context: the goal is for the two frogs and two toads to change places on the lily pads. The challenge is to do this in as few slides and jumps as possible. Students will need to work very systematically and may also want to develop their own recording system.

This problem provides an interesting context to consolidate addition of fractions and requires students to develop and analyze different strategies and explain their findings. Students are asked to find a general method for expressing unit fractions (fractions which have numerators of one) as the sum of two different unit fractions. They also explore whether all unit fractions can be written like this in more than one way. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

In this problem students practice addition and subtraction (and possibly multiplication) while developing systematic work strategies. Given two types of ladybirds, each with either 4 or 7 spots, learners explore ways of combining them to achieve different total numbers of spots. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and links to related games.

This brief article describes the number sequence of Leonardo of Pisa (Fibonacci), and its connecton to the golden ratio and rectangle. Links to related topics and a link to a printable page are included.

This collection of division word problems prompts learners to use a variety of methods of division. Allowing learners to choose their own method to solve the word problems enables them to see the strengths and weaknesses of various methods and to see why certain methods might be better for specific problems. Included with these problems is the solution, teacher resource page, tips on getting started, and a printable student page.

This activity allows students to investigate line symmetry and reflections. Using a mirror, students locate the lines of symmetry. in a square and then proceed to find other shapes by reflecting parts of the square. Ideas for implementation, extension and support are included along with a printable worksheet of squares (.doc)

This problem provides students the opportunity to explore fractions in a practical context as well as identify and explain patterns and justify their ideas. Solvers are shown a sequence of five squares shaded light blue and dark blue and are asked to find what fraction of the total area of each square is covered by light blue. They are also asked to work out what the next two squares would look like if they followed the pattern. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.