Do-Nows involving Triangles
NJ CCCS 4.2, 4.5
Use these daily, one at a time, as a do-now activity.
Objective: Students will be able to prove that the sum of the measures of the angles in any triangle is 180 degrees.
Number 1
Give each group a parallelogram figure. Children work in groups to solve. How many degrees are the sum total of the measures of the four angles? How can you prove it? Students will eventually write this as statements and reasons. (Answer: 360 degrees. Students may draw a diagonal line dividing the figure into two triangles and add the sum of the measures of the angles of both triangles. There are other proofs as well that can be accepted.)
Number 2
Draw adjacent supplementary angles on a white board for each group. Students will describe what they see. (Answer: A straight line intersected by another creating two angles.) Within the group, another student will show how to create two triangles by adding two more lines. Then the students identify all angles and label them. They will discover how to find the measure of each angle within the triangle.
Objective: Students will identify triangles as acute, equiangular, obtuse, or right. To identify triangles as scalene, isosceles, or equilateral.
Number 1
Provide students with straws, wood craft sticks, straight plastic strips, or pieces of wood doweling in various lengths. Have students create triangles with three equal-length sides, two equal-length sides, and no equal-length sides and comment on what happens to the angles within the triangle with these variations. They write in their journals about each variation and what they discover about the sides and the angles.
Number 2
Provide students with newspapers, magazines, and other supplies that they can look at in groups. Students find triangles used as graphs, illustrations or decorations in newspapers and magazines. They measure the lengths of the sides and use lines to compare the sides of each triangle. They name the triangles by the lengths of their sides.
Number 3 (Extended Number 2 or give as a more challenging concept)
As students measure the sides of triangles, have them note which type(s) are prevalent. They analyze why each type of triangle was perferred in a given ad or graph. For example, does the context call for the symmetry of an equilateral or an isosceles triangle? Does a scalene triangle draw the eye more because of its irregularity?
Number 4
Students work in groups to create "impossible triangles." First they must experiment with sides of different lengths. Can they construct a triangle with sides of 2, 3, and 5 inches. (Answer-no) 3, 4, and 8 inches? (Answer-no) 3, 4, and 6 inches? (Answer-yes) They then write combinations that will work and shuffle them in with those that will not. Each group will read combinations and another group will guess which sides can form triangles. They will discover, from their observations, a rule about triangles. (In any triangle, the sum of the lengths of any two sides is greater than the length of the third side.)
Objective: Students will be able to identify triangles that are congruent. To identify triangles that are similar.
Number 1
Students are given several quadrilaterals and asked to fold each one once to form two triangles. They answer: What do you notice about the two triangles?" (Answer-A parallelogram, square, rectangle, and rhombus form two identical triangles. A trapezoid forms two triangles that are not the same size or angles.)