Coordinates, polygons and shape properties

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선생님을 위해: Coordinates, polygons and shape properties(Primary Maths, Grade 5)을(를) 위한 바로 쓸 수 있는 수업 슬라이드, 복습 노트 — 수업에 사용하거나, 학생들이 실시간 게임으로 즐기는 인터랙티브 클래스 활동으로 진행하세요.

수업 노트

The Coordinate Plane

A coordinate plane is a flat surface with two number lines that cross at a right angle.
The x-axis is the horizontal (left-right) number line.
The y-axis is the vertical (up-down) number line.
The origin is the point where the two axes meet. Its coordinates are (0, 0).
Each point on the plane is named by an ordered pair like (3, 5). The first number is the x-coordinate (how far right), the second is the y-coordinate (how far up).
We only use the first quadrant in Grade 5, so all coordinates are positive (or zero).

Plotting and Reading Points

To plot a point, start at the origin. Move right along the x-axis by the first number, then move up by the second number.
For example, (4, 2) means move 4 steps right and 2 steps up.
To read a point, look at where it is. The x-coordinate is how far right from the origin, and the y-coordinate is how far up.
Always write coordinates in brackets with a comma: (x, y).
Points on the x-axis have y = 0, like (3, 0). Points on the y-axis have x = 0, like (0, 5).

Using Coordinates in Problems

You can use coordinates to describe where things are on a map or grid.
For example, a treasure at (2, 3) is 2 steps right and 3 steps up from the origin.
To find the distance between two points on the same horizontal line, subtract the x-coordinates.
To find the distance between two points on the same vertical line, subtract the y-coordinates.
Always check that your answer makes sense by looking at the grid.

Polygons and Their Sides

A polygon is a flat shape with straight sides that close up.
Polygons are named by the number of sides they have.
A triangle has 3 sides.
A quadrilateral has 4 sides.
A pentagon has 5 sides.
A hexagon has 6 sides.
An octagon has 8 sides.

Classifying Triangles

Triangles can be classified by their sides.
An equilateral triangle has all three sides equal.
An isosceles triangle has two sides equal.
A scalene triangle has no sides equal.
Triangles can also be classified by their angles: acute (all angles less than 90°), right (one angle exactly 90°), and obtuse (one angle more than 90°).
The sum of the angles in any triangle is always 180°.

Classifying Quadrilaterals

A quadrilateral is any 4-sided polygon.
A rectangle has four right angles and opposite sides equal.
A square has four equal sides and four right angles.
A rhombus has four equal sides but not necessarily right angles.
A parallelogram has opposite sides parallel and equal.
A trapezoid has at least one pair of parallel sides.
A square is also a rectangle and a rhombus because it has all their properties.

Shape Properties and Missing Values

Use the properties of a shape to find missing angles or sides.
In a triangle, if you know two angles, subtract their sum from 180° to find the third.
In a rectangle, opposite sides are equal, so if one side is 5 cm, the opposite side is also 5 cm.
In a square, all sides are equal, so if one side is 3 cm, all sides are 3 cm.
In a parallelogram, opposite angles are equal, and adjacent angles add up to 180°.

Transformations: Reflection and Translation

A translation slides a shape without turning or flipping it.
When you translate a shape, every point moves the same distance and direction.
A reflection flips a shape over a line, like a mirror.
The line you flip over is called the line of reflection.
After a reflection, the shape is the same size and shape, but it is reversed.
You can use a grid to help you move or flip shapes accurately.

슬라이드

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연습 문제

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1.What is the name of the point where the x-axis and y-axis meet?
Easy
- AOrigin
- BVertex
- CCenter
- DIntersection
2.In the ordered pair (3, 5), which number is the x-coordinate?
Easy
- A3
- B5
- CBoth
- DNeither
3.The point (0, 0) is called the origin.
Easy
True or false?
4.Which point is located at (2, 4) on a coordinate grid?
Easy
- A2 units right and 4 units up
- B4 units right and 2 units up
- C2 units left and 4 units up
- D4 units left and 2 units up
5.Which of the following are polygons? (Select all that apply)
Medium
- ATriangle
- BCircle
- CSquare
- DRectangle
- EPentagon
6.Match each polygon with its number of sides.
Easy
- Triangle
- Quadrilateral
- Pentagon
- 3 sides
- 4 sides
- 5 sides
7.Order these shapes from fewest sides to most sides.
Medium
- Triangle
- Square
- Pentagon
- Hexagon
8.Every square is also a rectangle.
Medium
True or false?

더 많은 문제

9.Which statement is true?
Medium
- AAll rectangles are squares.
- BAll squares are rectangles.
- CAll rhombuses are squares.
- DAll parallelograms are rectangles.
10.Match each ordered pair to the correct point on the coordinate grid.
Medium
- (2, 3)
- (3, 2)
- (1, 4)
- Point A
- Point B
- Point C
11.Which of the following are true statements about squares and rectangles? (Select all that apply)
Medium
- AEvery square is a rectangle.
- BEvery rectangle is a square.
- CA square has four right angles.
- DA rectangle has four equal sides.
- EA square is a quadrilateral.
12.The point (5, 0) lies on the x-axis.
Medium
True or false?
13.Which of the following ordered pairs are in the first quadrant? (Select all that apply)
Medium
- A(3, 4)
- B(-2, 5)
- C(0, 3)
- D(6, -1)
- E(2, 2)
14.Match each polygon to its number of sides.
Medium
- Triangle
- Quadrilateral
- Pentagon
- 3
- 4
- 5
15.Which point is at (3, 5) on a coordinate grid?
Medium
- A3 units right and 5 units up from the origin
- B5 units right and 3 units up from the origin
- C3 units left and 5 units up from the origin
- D5 units left and 3 units up from the origin
16.The point (0, 4) lies on the y-axis.
Easy
True or false?
17.A square is also a rectangle.
Easy
True or false?
18.Which of these is NOT a polygon?
Medium
- ACircle
- BTriangle
- CPentagon
- DHexagon
19.A triangle has vertices at (1, 2), (5, 2), and (1, 5). What type of triangle is it?
Medium
- ARight triangle
- BEquilateral triangle
- CIsosceles triangle
- DScalene triangle
20.Which of the following is the correct ordered pair for the origin?
Easy
- A(1, 1)
- B(0, 0)
- C(0, 1)
- D(1, 0)
21.On a coordinate grid, a point is plotted at (3, 8). What is the x-coordinate of this point?
Medium
- A3
- B8
- C5
- D11
22.Which of the following shapes has exactly 5 sides?
Medium
- APentagon
- BHexagon
- CQuadrilateral
- DTriangle
23.Which of the following is NOT a polygon?
Medium
- ACircle
- BSquare
- CTriangle
- DHexagon
24.What is the name of the horizontal line on a coordinate grid?
Easy
- Ax-axis
- By-axis
- Corigin
- Dquadrant
25.What is the name of the vertical line on a coordinate grid?
Easy
- Ax-axis
- By-axis
- Corigin
- Dquadrant
26.What are the coordinates of the point where the x-axis and y-axis meet?
Easy
- A(0, 0)
- B(1, 1)
- C(0, 1)
- D(1, 0)
27.Which ordered pair names a point that lies on the y-axis?
Easy
- A(0, 5)
- B(5, 0)
- C(3, 3)
- D(2, 7)
28.The point (3, 0) lies on the x-axis.
Easy
True or false?
29.The point (0, 4) is on the x-axis.
Easy
True or false?
30.Which of the following ordered pairs have an x-coordinate of 2? (Select all that apply)
Easy
- A(2, 3)
- B(3, 2)
- C(2, 5)
- D(5, 2)
- E(2, 2)
31.Match each ordered pair to its correct description.
Medium
- (0, 0)
- (4, 0)
- (0, 4)
- origin
- on the x-axis
- on the y-axis
32.Order the following points from left to right on the coordinate grid.
Easy
- (3, 1)
- (1, 3)
- (5, 2)
33.Which of these is the correct way to write the coordinates of a point?
Easy
- A(x, y)
- B(y, x)
- C[x, y]
- D{x, y}
34.The point (2, 3) is the same as the point (3, 2).
Easy
True or false?
35.A rectangle has vertices at (1, 1), (1, 4), (5, 1), and (5, 4). What is the length of the longer side?
Medium
- A3 units
- B4 units
- C5 units
- D6 units
36.What is the name for a polygon with 6 sides?
Easy
- Ahexagon
- Bpentagon
- Coctagon
- Dheptagon
37.What is the name for a polygon with 8 sides?
Easy
- Aoctagon
- Bhexagon
- Cpentagon
- Ddecagon
38.Which of the following are quadrilaterals? (Select all that apply)
Easy
- Asquare
- Btriangle
- Crectangle
- Dpentagon
- Erhombus
39.A rectangle is always a square.
Easy
True or false?
40.A square is always a rectangle.
Easy
True or false?
41.Fill in the blanks with the correct words.
Easy
The horizontal axis is called the ____ and the vertical axis is called the ____.
42.A rectangle has vertices at (1, 2), (1, 5), (4, 2), and (4, 5). What is the length of the longer side?
Medium
43.What is the name for a quadrilateral with all sides equal and four right angles?
Hard
44.What is the x-coordinate of the point (4, 7)?
Easy
45.Complete the sentence.
Easy
The two axes on a coordinate grid are called the ____ and the ____.
46.Fill in the blank with the correct word.
Easy
A polygon with four sides is called a ____.
47.A rectangle has vertices at (2, 1), (2, 6), (7, 1), and (7, 6). What is the length of the longer side?
Medium
48.What is the y-coordinate of the point (6, 2)?
Easy
49.A point is plotted at (3, 8). What is the x-coordinate of this point?
Easy
50.What is the distance (in units) between the points (2, 3) and (2, 9) on a coordinate grid?
Easy
51.A rectangle has vertices at (1, 2), (1, 5), (4, 2), and (4, 5). What is the perimeter of the rectangle?
Easy
52.A square has vertices at (0, 0), (4, 0), (4, 4), and (0, 4). What is the area of the square?
Medium
53.Explain why a square is also a rectangle. Use the properties of both shapes in your answer.
Hard
54.A rectangle has vertices at (1, 2), (1, 5), (4, 2), and (4, 5). What is the length of the longer side?
Medium
- A2
- B3
- C4
- D5
55.What is the x-coordinate of the point (4, 7)?
Easy
- A6
- B3
- C4
- D5
56.A rectangle has vertices at (2, 1), (2, 6), (7, 1), and (7, 6). What is the length of the longer side?
Medium
- A5 units
- B6 units
- C7 units
- D4 units
57.What is the y-coordinate of the point (6, 2)?
Easy
- A3
- B1
- C4
- D2
58.A point is plotted at (3, 8). What is the x-coordinate of this point?
Easy
- A5
- B2
- C3
- D4
59.What is the distance (in units) between the points (2, 3) and (2, 9) on a coordinate grid?
Easy
- A6 units
- B7 units
- C8 units
- D5 units
60.A rectangle has vertices at (1, 2), (1, 5), (4, 2), and (4, 5). What is the perimeter of the rectangle?
Easy
- A13 units
- B12 units
- C11 units
- D14 units
61.A square has vertices at (0, 0), (4, 0), (4, 4), and (0, 4). What is the area of the square?
Medium
- A17 square units
- B18 square units
- C15 square units
- D16 square units

복습 노트

## Coordinates, Polygons and Shape Properties – Revision Notes ### The Coordinate Plane - The **coordinate plane** is a flat surface with two number lines that cross at a right angle. - The **x-axis** is the horizontal (left-right) number line. - The **y-axis** is the vertical (up-down) number line. - The point where the axes meet is called the **origin**. Its coordinates are (0, 0). - A point is named by an **ordered pair** like (x, y). The first number is the x-coordinate (how far right), the second is the y-coordinate (how far up). - We only use the **first quadrant** (where both numbers are positive). - Example: To plot (3, 2), start at the origin, move 3 steps right, then 2 steps up. ### Polygons - A **polygon** is a flat shape with straight sides. - Polygons are named by their number of sides: - 3 sides: triangle - 4 sides: quadrilateral - 5 sides: pentagon - 6 sides: hexagon - 8 sides: octagon ### Triangles and Quadrilaterals - **Triangles** can be classified by their sides: - **Equilateral**: all three sides equal, all angles 60°. - **Isosceles**: two sides equal, two angles equal. - **Scalene**: no sides equal. - **Quadrilaterals** have four sides. They include: - **Square**: all sides equal, all angles 90°. - **Rectangle**: opposite sides equal, all angles 90°. - **Rhombus**: all sides equal, opposite angles equal. - **Parallelogram**: opposite sides parallel and equal. - **Trapezoid**: at least one pair of parallel sides. - A square is also a rectangle and a rhombus because it has all their properties. ### Transformations - **Reflection**: flipping a shape over a line (like a mirror). The shape keeps its size and shape. - **Translation**: sliding a shape without turning or flipping it. Every point moves the same distance and direction. ### Finding Missing Angles or Sides - Use the properties of shapes: - The sum of angles in a triangle is 180°. - The sum of angles in a quadrilateral is 360°. - In a rectangle or square, all angles are 90°. - In a parallelogram, opposite sides are equal, and opposite angles are equal. - Example: If a triangle has angles 50° and 60°, the third angle is 180° − 50° − 60° = 70°. ### Key Formulas - Sum of interior angles of a polygon with n sides: \( (n - 2) \times 180° \) - Perimeter of a rectangle: \( P = 2 \times (l + w) \) (l = length, w = width) - Area of a rectangle: \( A = l \times w \) - Area of a triangle: \( A = \frac{1}{2} \times b \times h \) (b = base, h = height)

coordinate plane: A flat surface with two number lines that cross at a right angle, used to locate points.
x-axis: The horizontal number line on a coordinate plane.
y-axis: The vertical number line on a coordinate plane.
origin: The point where the x-axis and y-axis meet, with coordinates (0, 0).
ordered pair: A pair of numbers (x, y) that gives the location of a point on the coordinate plane.
first quadrant: The part of the coordinate plane where both x and y are positive.
polygon: A flat shape with straight sides.
triangle: A polygon with three sides.
quadrilateral: A polygon with four sides.
pentagon: A polygon with five sides.
hexagon: A polygon with six sides.
octagon: A polygon with eight sides.
equilateral triangle: A triangle with all three sides equal and all angles 60°.
isosceles triangle: A triangle with two equal sides and two equal angles.
scalene triangle: A triangle with no equal sides.
square: A quadrilateral with all sides equal and all angles 90°.
rectangle: A quadrilateral with opposite sides equal and all angles 90°.
rhombus: A quadrilateral with all sides equal and opposite angles equal.
parallelogram: A quadrilateral with opposite sides parallel and equal.
trapezoid: A quadrilateral with at least one pair of parallel sides.
reflection: A flip of a shape over a line, like a mirror image.
translation: A slide of a shape without turning or flipping it.

플래시카드

What are the two number lines in a coordinate plane called?

The x-axis (horizontal) and the y-axis (vertical).

What is the point where the x-axis and y-axis meet called?

The origin. It has coordinates (0, 0).

How do you write the coordinates of a point?

As an ordered pair (x, y). The first number is the x-coordinate (horizontal), and the second is the y-coordinate (vertical).

How do you plot the point (3, 5) on a coordinate plane?

Start at the origin (0,0). Move 3 units right along the x-axis, then 5 units up. Mark the point.

What does the x-coordinate tell you?

How far to move left or right from the origin. Positive means right, negative means left.

What does the y-coordinate tell you?

How far to move up or down from the origin. Positive means up, negative means down.

In which quadrant are both x and y positive?

The first quadrant (top right).

What is a polygon?

A flat shape with straight sides that are closed. Examples: triangle, square, pentagon.

How many sides does a triangle have?

3 sides.

How many sides does a quadrilateral have?

4 sides.

How many sides does a pentagon have?

5 sides.

How many sides does a hexagon have?

6 sides.

How many sides does an octagon have?

8 sides.

What is a right triangle?

A triangle with one right angle (90°).

What is an equilateral triangle?

A triangle with all three sides equal and all three angles equal (each 60°).

What is an isosceles triangle?

A triangle with two equal sides and two equal angles.

What is a scalene triangle?

A triangle with no equal sides and no equal angles.

What is a rectangle?

A quadrilateral with four right angles. Opposite sides are equal and parallel.

What is a square?

A rectangle with all four sides equal. It is also a rhombus.

What is a rhombus?

A quadrilateral with all four sides equal. Opposite angles are equal.

What is a parallelogram?

A quadrilateral with opposite sides parallel and equal. Opposite angles are equal.

What is a trapezoid (US definition)?

A quadrilateral with at least one pair of parallel sides.

How do you reflect a shape over the y-axis?

Flip it across the y-axis. Each point moves to the opposite side, same distance from the y-axis. The x-coordinate changes sign, y stays the same.

How do you translate a shape on a coordinate plane?

Slide it without turning. Add the same number to all x-coordinates and the same number to all y-coordinates.

How do you find a missing angle in a triangle?

Add the two known angles and subtract from 180°, because the angles in a triangle always add up to 180°.

How do you find a missing angle in a quadrilateral?

Add the three known angles and subtract from 360°, because the angles in a quadrilateral always add up to 360°.

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