The road bends, The length of the road bends

### 1.1. Knowledge to remember

– Understand and recognize bends.

– Understand how to calculate the length of a bend.

- The curve ABCD consists of three straight segments: AB, BC and CD.
- The length of the bend line ABCD is the sum of the lengths of the segments AB, BC, CD: 2cm + 4cm + 3cm = 9cm.

### 1.2. Math forms

**Form 1: Draw bendy lines as required**

Connect the non-collinear points with straight lines in the appropriate order to create a crooked line.

**Form 2: Calculate the length of the bend.**

The length of the bend is calculated as the sum of the lengths of the straight segments of that bend.

**Form 3: Read the name of the winding road shown in the figure.**

I read the names of the endpoints of the line segments in the bend, in the direction connecting the points from left to right or from right to left.

### 1.3. Solving Textbook Exercises page 103

**Lesson 1**

Connect the points to get a curved line including:

__Solution method__

Use a straightedge to connect the given points to form a curved line.

__Solution guide__

It can be concatenated in a variety of ways, such as the following:

**Lesson 2**

Calculate the length of the bend (according to the sample):

**Form: **The length of the MNPQ bend is:

3 + 2 + 4 = 9 (cm)

Answer: 9cm.

__Solution method__

Calculate the sum of the lengths of the given line segments (same unit of measure)

__Solution guide__

The length of the bend ABC is:

5 + 4 = 9 (cm)

Answer: 9cm.

**lesson 3**

A piece of copper wire is bent into a triangle as shown in the figure. Calculate the length of the copper wire.

__Solution method__

The length of that copper wire is equal to the sum of the lengths of the three sides of the triangle.

__Solution guide__

The length of the copper wire is:

4 + 4 + 4 = 12 (cm)

Answer: 12cm.

**Attention:**

The length of the string can be calculated by another way: 4 × 3 = 12(cm)

### 1.4. Solving Textbook Exercises page 104

**Lesson 1**

a) A curved road consists of two straight segments of lengths 12cm and 15cm respectively. Calculate the length of that bend.

b) A folded segment consists of three straight segments with lengths 10dm, 14dm and 9dm, respectively. Calculate the length of that bend.

__Solution method__

a) Find the sum of the lengths of the two given line segments.

b) Find the sum of the lengths of the three given line segments.

__Solution guide__

a) The length of the bend is:

12 + 15 = 27 (cm)

b) The length of the bend is:

10 + 14 + 9 = 33 (dm)

Answer: a) 27cm; b) 33 dm.

**Lesson 2**

The snail crawls from A to D (as shown). How many decimeters must the snail crawl?

__Solution method__

Calculate the total length of line segments AB; BC and CD.

__Solution guide__

The number of decimeters that a snail has to crawl is:

5 + 2 + 7 = 14 (dm)

Answer: 14 dm.

**lesson 3**

Write the names of the bends in the following figure, knowing:

a) That winding road consists of three straight segments.

b) That winding road consists of two straight segments.

__Solution method__

List and name the bends.

__Solution guide__

a) The curve is: ABCD or DCBA.

b) The winding road is: ABC; BCD.

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