Teaching Algebra with Manipulatives

Chapter
11
Radical Expressions and Triangles
Teaching Notes and Overview
Mini-Project
Matching Radicals
(p. 185 of this booklet)
Use With Lesson 11-2.
Algebra Activity
The Pythagorean Theorem
(pp. 187–188 of this booklet)
Use With Lesson 11-4.
Objective Simplify radical expressions.
Materials
scissors
This activity requires students to work in pairs
to simplify radical expressions that can be
simplified. Have them write the simplification
in that box and circle it. Then have them cut
out the rectangles and match the ones that are
equivalent expressions.
Answers
A, J; B, L; C, I; D, E; E, D; F, N; G, P; H, O; I, C;
J, A; K, M; L, B; M, K; N, F; O, H; P, G
Using Overhead
Manipulatives
The Pythagorean Theorem
(p. 186 of this booklet)
Use With Lesson 11-4.
Objective Explore the relationships in a right
triangle and discover the Pythagorean Theorem.
Materials
dot paper transparency*
transparency pen*
* available in Overhead Manipulative Resources
On a dot paper transparency a right triangle is
drawn. Squares are drawn on all three sides.
Each side of each square is as long as the
corresponding side of the triangle. The areas of
the two smaller squares are found. The area of
the large square requires the use of Pick’s
Theorem. Students are guided to discover the
Pythagorean Theorem.
Answers
Answers appear on the teacher demonstration
instructions on page 186.
Objective Determine whether a triangle is a
right triangle, given the lengths of its sides.
Materials
classroom set of Algebra Activity worksheets
transparency master of Algebra Activity
calculator
grid paper
scissors*
* available in Overhead Manipulative Resources
Prior to class, you may want to cut the
transparency on the dashed lines. Using the
individual squares, explain that the area of
each large square equals the length of one of its
sides squared.
Form a right triangle using the sides from each
square as its legs. As soon as the groups have
completed Exercises 1 and 2, ask them what
they learned from completing these exercises.
Discuss the relationship between the sides of a
right triangle.
Discuss the answers to Exercises 3 and 4.
Point out that squares of three numbers that
satisfy the Pythagorean Theorem are called
Pythagorean triples. Some students may want
to find additional Pythagorean triples. Let
students use a calculator to work Exercise 5.
Answers
1. 9, 16, 25; 9 16 25 or 3 2 4 2 5 2
2. right triangle; a 2 b 2 c 2
3. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,
169, 196, 225, 256, 289, 324, 361, 400, 441,
484, 529, 576, 625, 676, 729, 784, 841, 900
4. 3, 4, 5; 5, 12, 13; 6, 8, 10; 7, 24, 25; 8, 15, 17;
9, 12, 15; 10, 24, 26; 12, 16, 20; 15, 20, 25;
18, 24, 30; 20, 21, 29
5a. 39 ft 5b. 12.5 m 5c. 145 in. 12 in.
Algebra 1—Chapter 11
© Glencoe/McGraw-Hill 183 Teaching Algebra with Manipulatives