Loci - Playground

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# Loci - Playground - PowerPoint PPT Presentation

Bill is planning the layout of a school playground. For safety reasons he has to mark part of the playground where children cannot play games. A 12m B

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## Loci - Playground

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Presentation Transcript

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Choose level of difficulty

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 1: Draw a sketch of the playground

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 2: Sketch the loci of all points 4m from corner D and shade the area within 4m of D

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 3: Sketch the loci of all points 3m from the side BC and shade the area within 3m of BC

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 4: Calculate the area that is not shaded

Fill in this table

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 5: Calculate the largest number of children that can play.

### Loci - Playground

End of Problem

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 1: Sketch a plan of the playground

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 2: Sketch the loci of all points 4m from corner D and shade the area within 4m of D

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 3: Sketch the loci of all points 3m from the side BC and shade the area within 3m of BC

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 4: Calculate the area that is not shaded

Fill in this table

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 5: Calculate the largest number of children that can play.

### Loci - Playground

End of Problem

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 1: Draw a sketch

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 2: Mark the places where children can’t play.

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 3: Calculate the area where children can play

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 4: Calculate the largest number of children that can play.

### Loci - Playground

End of Problem

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Draw a sketch.

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Sketch the areas and calculate the area where children can’t play.

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Calculate the largest number of children that can play.

### Loci - Playground

End of Problem

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Sketch the area where children can’t play

### Loci - Playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Calculate the largest number of children that can play.

End of Problem