Angle measure. Although

angle measure did not appear until later in the instructional sequence, foundational skills related to

angle measure were developed from the beginning of the sequence, such as angle categorizations and discussions focused on what was being measured.

To quantify the notion of apparent distance between stars, an

angle measure is used.

The results of horizontal

angle measures calibrations are given in Figs.

The instruction begins with an activity that aims at constructing a coherent concept of

angle measure. We should ask students to position the transparent model so that the skewer is vertical with the circular protractor face up, and mark the point two radians to the right of the dot using a string and the radian ruler (see Figure 3(a)) whose scale matches that of the transparent model (one radian is equal to the radius of the model) and another point one radian above the dot.

Several days into the Shape Makers unit on quadrilaterals, students were using the measured shape makers, which display both

angle measure and side length and instantaneously update these measurements when the shape makers are manipulated.

Students use properties that they already know to formulate definitions, for example, for squares, rectangles, and equilateral triangles, and use them to justify relationships, such as explaining why all squares are rectangles or why the sum of the

angle measures of the angles of any triangle must be 180.

The second excerpt from the data-analysis unit is a conversation about

angle measure. Of the four conversations presented in this article, this one is the closest approximation to my vision of how I wanted these conversations to sound when I began these lessons.

7.In mathematics, what type of

angle measures more than 180 degrees but less than 360 degrees?

If calibration of horizontal

angle measures can be realized implementing different types of horizontal precise rotary tables (of different accuracy) available in industry, calibration of vertical angle measurements is a serious problem since very special instrumentation is needed for this task.

The octagon problem is a rich mathematical task requiring deductive reasoning that incorporates several geometric concepts including regular polygons,

angle measures of a regular polygon, transformations (reflection, rotation, and dilation), scale factors, properties of right isosceles triangles, and properties of quadrilaterals.

Impedance measures of R and Xc were used to calculate phase

angle measures. Significance tests to test for nonzero slopes were done on each fish by using a standardized major axis (SMA) test and between fish by using the Bartlett-corrected likelihood ratio (LR) test for differences in the slopes.

They began to notice the

angle measures that were different in the two figures, and one student began to see the parallelogram as a rectangle plus two right triangles.

The tangent of the gliding

angle measures the ratio of drag to lift, so [c.sub.D] can be calculated.

After introducing the concept of angle measurement and modeling how to measure angles, the teacher could have students work in small groups to measure angles related to objects around the room and label the angles with the appropriate classification according to their

angle measures. After the small group practice, individual students could be given a set of different triangles or quadrilaterals.