Geometry Standard:

• " The study of geometry in grades 3-5, should be active. It requires the use of visual images and concrete materials. Students sort, build, model, trace, measure, and construct. They make and test conjectures and justify their thinking. This exploration requires access to a variety of concrete tools such as graph paper, rulers, compasses, pattern blocks, geoboards, and geometric solids"
  (The 3-5 Geometry standard).
  

Measurement Standard:

• "In grades 3-5 students expand their knowledge of and facility with measurement by examining additional attributes (e.g., area, volume, and angle size)..."
  (The 3-5 Measurement standard).
• "Formulas for measuring perimeter, area and volume should emerge as students have opportunities to measure, record information, and look at patterns"
  (The 3-5 Measurement standard).
  

Reasoning and Proof Standard:

• "During these grades they (students) learn to assess claims on the basis of an examination of evidence. Students learn that several examples are not sufficient to establish the truth of a conjecture. They learn that they need to consider a range of possible examples and to reason about the general properties and relationships they find across examples"
  (The 3-5 Reasoning standard).
• "A classroom climate that encourages students to put forth their own ideas for examination is very important to the development of mathematical reasoning. Both teachers' and students' statements should be open to questions, reactions, and elaborations from others in the classroom. Students need to know that being able to explain and justify their thinking is important, and should begin to learn how to detect fallacies in others' thinking. This mind-set is established when they have opportunities to apply their reasoning skills and when justifying their thinking is an expected component of mathematics discussions. Students need a great deal of time, many experiences, and a good model and guide to develop their ability to construct valid arguments and evaluate the arguments of others"
  (The 3-5 Reasoning standard).
  

Communication Standard:

• "In grades 3-5 students expand their abilities to learn from and work with others. Their communication consists not only of conversations between student and teacher or one student with another student, but of students listening to a number of peers and joining in group discussions in order to clarify, question, and extend conjectures"
  (The 3-5 Communication standard).

References and Credits