Year 6AC9M6SP01

Cross-Sections and the Four Quadrants

Compare the parallel cross-sections of objects and recognise their relationships to right prisms. Locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane.

Read this first

Slice a prism straight across and every slice looks the same.

The four quadrants are made by the two axes crossing.

Words you need

Cross-section: The face you see when you slice through.
Prism: A solid with the same shape all the way along.
Quadrant: One of the four parts of the plane.

Worked example

e.g. Plot (3,2) and (-3,2). What is different?

Start at the origin, where the axes cross.
For (3,2), go 3 right and 2 up.
For (-3,2), the minus means go 3 left instead.
Both are 2 up, but on opposite sides.

A minus in the first number means left. A minus in the second means down.

Practice

The pictures fade as you go. By the last few you are on your own.

1Where is (-2,-4)?with a picture

Answer2 left and 4 down.

2What is the cross-section of a cylinder?with a picture

AnswerA circle.

3A point moves from (2,3) to (2,-3). What changed?with a hint

Need a hint?

Look at the second number.

AnswerIt moved down, across the x axis.

4What is the cross-section of a triangular prism?with a hint

Need a hint?

Look at the end face.

AnswerA triangle.

5Which quadrant has both numbers negative?on your own

AnswerThe third, bottom left.

6A point moves from (1,1) to (4,1). Describe the move.on your own

Answer3 to the right.

7Why does a prism have the same cross-section all along?on your own

AnswerIts shape does not change from end to end.

Think about it

What happens to a point when the first number turns negative?

One good answerIt flips to the other side of the vertical axis.

How does a cross-section help identify a solid?

One good answerIt shows the shape that repeats all the way through.

Common mistakes

Thinking a minus always means down.

A minus in the first number means left.

Slicing a prism at an angle.

A cross-section is a straight cut across.