Grade Level: Intermediate
Overview: In Math Investigations, students choose a topic involving math that interests them to investigate or research. Students make a plan detailing how they will investigate their topic. The teacher reviews and approves the plan. Students use their MATH INVESTIGATION JOURNAL to record their research. Students publish their findings and share them with the class.
Some examples are keeping track of plant heights over time, measuring the amount of daylight and its changes during a particular time period, and following temperature trends.
Resources Needed: MATH INVESTIGATION JOURNAL (Egawa and Schmidt, 1995 [revised 1997]) for each student.
( National Council of Teachers of Mathematics ) Standards Addressed:
 Content: Of the five standards that describe mathematical content students should learn, Math Investigations address (1) number and (2) operation. But the potential is there for addressing all five content standards, depending on the topic students choose.
 Process: Math Investigations address all five standards that describe the mathematical processes through which students should acquire and use their mathematical knowledge. These are: problem solving, reasoning and proof, communication, connections, and representations.
Major Concepts:
 Mathematics is a way of making sense of the world, usually through mathematical models.
 Reasoning is essential in all mathematical activity.
 We use and learn about mathematics in contexts outside of math class.
Key Math Skills:
 Plan and conduct a simple investigation that includes mathematical ideas and/or processes.
 Communicate the findings of the investigation to others. As students communicate their findings, they should be able to organize their thinking and express their mathematical ideas coherently.
 Students extend their math knowledge by considering the thinking and strategies of others.
 Use a variety of tools, techniques, and formulas to solve problems and adapt strategies to new situations. In fact, students will often make up their own tools and formulas if given the opportunity, and this could lead to very exciting mathematical activity.
 Collect, organize, and represent data to answer a question posed and investigated.
Habits of Mind:
 Respect for mathematical data
 Recognition of reasoning and proof as essential and powerful parts of mathematics
 Develop a disposition to formulate, represent, abstract, and generalize in situations within and outside mathematics.
Facilitation Plan Outline: The first time that you engage your students in Math Investigations, you will want to lay some groundwork. One possible framework is as follows:
 Begin by asking students to interview people at home about the ways they use mathematics at home or on the job.
 Facilitate a class discussion in which students share what they learned from family members. Focus on the variety of ways that math is present in our everyday lives. Record responses on chart paper.
 Ask students to brainstorm in small groups about issues or topics of interest for investigation. As they list their ideas, ask them to discuss the connection to mathematics.
 Post these lists around the room and allow students to view other groups' ideas and make comments.
 Share the MATH INVESTIGATION JOURNAL with students and discuss expectations and timelines.
 As Math Investigations begin, students might choose to work alone or with one or two partners. Even when they are working with partners, you should require all students to keep their own Math Investigation journal.
 Before picking a topic to investigate, students list three or four ideas in their journal. These may be questions, issues, or topics of interest. Some topics investigated by students have included: planning a vacation, pet ownership, building a bicycle, entering a soapbox derby, attending a sporting event, managing a budget, the currency of different countries, surveyrelated questions, designing a garden, and planning a garden.
 Students choose one question or topic to investigate. After recording their question or topic, students brainstorm on the ideas or questions that will be important to think about as they conduct their investigation. At this point, the teacher holds a conference with the individual student to review the Math Investigation topic or question.
 Ask students to think about and record what they already know about the topic and list those things they need to find out about as they conduct their investigation. This will usually take the form of a list of questions to ponder as they work through the investigation.
 Each student is then responsible for talking to other classmates and adults to expand their thinking about the topic. They record the names of people they talked to and the questions that others had regarding the investigation.
 From their notes, students list the big ideas that stand out.
 Now it is time to make an investigation plan. In the plan, students list all of the things they need to do in order to carry out the investigation. After students develop their plan, they hold a second conference with the teacher to review the plan.
 As part of the plan, they develop a work calendar outlining the timeline to completion. The time needed for investigating topics may vary according to their complexity and other factors. Inclass and outofclass time is usually allotted for working on the investigation.
 As students work on their investigations, the teacher will have opportunities to teach mini lessons to individual and small groups of students based on the types of problems that students encounter. Math content will surface, as well as the need for strategies. As the teacher works with a student who has requested assistance, she/he can invite others to join a smallgroup session in which they explore strategy or new content.
 Students record their investigative notes and problemsolving strategies on the Investigation Records pages of their journals.
 After completing the investigation, students record their conclusions or findings.
 The next step is to develop a plan for communicating their findings to others or for publishing their research. This plan might include sketches of visuals that will be used when sharing.
 On the Bibliography page, students list their interview sources, print sources, and multimedia sources.
 On the Reflections page of their journal, students record the mathematical processes and the mathematical computations they used during their investigation.
 The teacher should also ask students to think about some things that they could have investigated further during this investigation and topics they might explore during the next investigation.
 A forum is then provided to students for sharing their findings with an audience of peers. Classmates are given the opportunity to ask presenters questions and to provide feedback to the presenter.
Assessment: Student assessment is ongoing throughout the investigation. Students are assessed in content knowledge, skill development, and habits of mind displayed. The tools available for teacher information include individual student conferencing, observational notes during work time, the MATH INVESTIGATION JOURNAL, and the presentation to the class.
