This activity helps students develop concepts and language related to position by experimenting with the size and relationships between two circles in a qualitative way. They use terms such as outside, touching and overlapping. The Teachers' Notes page includes suggestions for implementation and discussion questions. Students then can move to a follow-up activity, 3 Rings, cataloged separately.

This activity helps students develop concepts and language regarding the size and positional relationship possibilities of three circles in the plane in a qualitative manner. They use terms such as overlapping, inside, and touching as they work systematically to find all possible arrangements. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension. This activity can be a follow-up to "2 Rings" cataloged separately.

The phenomenon that launches this unit is a cell phone call to a student in the class, where the caller on speaker phone asks “How are you hearing me?”. Over the course of the unit, students discover the patterns with waves. Then use that understanding to explain ultrasound medical imagining technology and ultimately how cell phones work. Cell phone communication is operationalized by the engineering challenge of communicating a three letter signal by first coding a spreadsheet to digitize the signal in binary (ASCII), then transmit the digital signal using light and sound (AM and FM), then receive and decode the signal to complete the communication. This project models the sending and receiving of a text message.

This problem introduces repeated doubling in the context of a plant with branches that split into 2 more branches every week. The problem lays the foundation for understanding exponential growth and lends itself to a variety of representations. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

This activity reinforces the concepts of area and perimeter and their independent relationship. Students analyze and compose shapes made from unit squares that satisfy area and perimeter specifications. Ideas for implementation, extension and support are included along with printable sheets and shape cards.

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 organized under specific strategies and processes.

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.

In this creative thinking activity students must determine how many combinations can be made when putting three beads into bags. To complete the activity students must create their own recording system to make sure they are not repeating solutions and they have found all possible solutions. Included in this resource are teacher’s notes with suggestions for introducing the activity, discussion questions, support suggestions, and a printable version.

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 problem provides an opportunity for students to develop problem solving skills while applying skip-counting and exploring the concepts of multiples and factors within 20. It is posed in the context of toppings on cookies ("biscuits" in the UK) and lends itself to multiple representations. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and downloadable handouts.

In this problem students explore the concept of proportion by comparing the relative strengths of different mixes of juice flavor and water in a visual context. Given four mixtures represented by purple and white rectangles, students order the drinks from strongest to weakest flavor and explain their reasoning. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.

This problem requires a sound understanding of the fraction relationship between part and whole and can be used for finding fractions of numbers and quantities. Students are given the fractional amount of apples in a fruit bowl and the specific number of other fruit in the bowl in order to figure out how many apples are in the bowl. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension, a link to a worksheet which provides student support, and a downloadable pdf of the puzzle.

This problem introduces children to algebra by looking for a pattern and generalizing with a rule. Students explore in how many different ways can a stick of 6, 7 or 8 different colored interlocking cubes be broken into two parts. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and an idea for support and extension.

This brief article describes the historical methods of marking and measuring time. Among the instruments and methods discussed are sundials, water clocks, celestial motions, and mechanical clocks. Included are descriptions of the sources of inaccuracies of these methods. Links to related resources and a separate page of pedagogical notes are provided.

This problem promotes logical thinking and introduces learners to the trial and error (guess and check) problem solving strategy, especially with the interactive provided. In this problem children need to understand the difference between having a certain number of brothers and the number of boys in a family to answer the question, "How many children are there in the Brown family?" The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a down loadable worksheet for students to table their trials.

This problem helps children begin to understand the various properties of common geometric solid shapes. It also promotes naming, discussion and experimentation concerning their features, and requires them to justify their ideas. It asks students to judge the stability of nine configurations made from six common solids. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets.

This activity gives students practice naming and using shape and color attributes to create patterned sequences. The first challenge asks students to use attribute differences to extend a sequence. A second, more open-ended challenge asks students to maximize the length of their sequences under a further constraint. An interactive applet is provided as an alternative to physical manipulatives. The Teachers' Notes page includes suggestions for implementation and discussion questions.

This hands-on activity helps students develop spatial sense and scaling concepts. Students use interlocking cubes to build first a chair and then a table of appropriate size for the chair. The student goes on to build two other sets of chairs and tables to make three different sizes in all. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension.

In this activity students develop fraction concepts by reasoning about what choices they would make in order to get the most chocolate. Students determine how much candy they would receive as they enter one at a time and sit at one of three tables holding different amounts of candy which get shared equally. The activity includes the problem, tips for getting started, a teacher resource page, and a printable page of the problem.

This is an activity to teach conflict resolution strategies. In groups of three, one student clenches his/her fist. As a team the other two students need to figure out a way to unclench this student’s fist. Give them thirty seconds to figure it out.