This collection from NRICH provides activities to help learners think and work like a mathematician. Tasks have students exploring, questioning, working systematically, visualizing, conjecturing, explaining, generalizing and justifying. Activities are listed under strategies and processes.

This problems is an opportunity to explore triangular numbers in the familiar context of decorating a birthday cake with a number of candles corresponding to a child's age. The problem lends itself to systematic strategies and multiple representations. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

This lesson is to teach the problem-solving strategy using the CUBES acronym. The students will use digital photos to create real-life story problems of their own and practice using the CUBES strategy to solve the problems they create as well as those of their peers.

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.

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 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.

In this open investigation, students look for connections between shape and number by generating star patterns (regular n-grams) inside a circle. Ideas for implementation, extension and support are included along with a printable sheet (pdf) of circles with marked circumferences.

This shunting puzzle asks students to use a siding to allow two trains to pass one another on a single track. The difficulty is that the siding length is limited. Teaching suggestions, a printable page, and a solution are included.