Tile-tiled Areas: Inductive Derivation

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Explore area via tile counts.

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John Angeles

Philippines

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Froggy Jumps Tile-tiled Areas: Inductive DerivationOnline version Explore area via tile counts. by John Angeles 1 What is the formula for the area of a rectangle in terms of its length and width, using tile units? a Area = 2 × (length × width) b Area = length × width c Area = length + width 2 How can you inductively verify the area of a square using unit square tiles? a Tiles form a ring around the square b The number of tiles equals side length squared c Tiles count diagonally to get area 3 If a square has side length 5 units, how many unit tiles cover it? a 20 tiles b 25 tiles c 30 tiles 4 A rectangle 3 by 4 is tiled with unit squares. How many tiles are needed? a 7 tiles b 16 tiles c 12 tiles 5 What is the standard area unit when counting tiles on a plane? a Cubic units b Square units c Linear units 6 For a 1x1 square, what is the area in tiles? a 1 tile b 0 tiles c 2 tiles 7 If you double the side length of a square, how does the area change? a Area triples b Area multiplies by 4 c Area doubles 8 A rectangle is 2 by 7. What is its area in square units? a 21 square units b 9 square units c 14 square units 9 How many unit tiles cover a 2x2 square? a 4 tiles b 2 tiles c 8 tiles 10 Why does area scale with length when tiling with unit squares? a Because width is constant b Because perimeter increases c Because area counts how many unit tiles fit

Froggy Jumps

Tile-tiled Areas: Inductive DerivationOnline version

Explore area via tile counts.

by John Angeles

What is the formula for the area of a rectangle in terms of its length and width, using tile units?

Area = 2 × (length × width)

Area = length × width

Area = length + width

How can you inductively verify the area of a square using unit square tiles?

Tiles form a ring around the square

The number of tiles equals side length squared

Tiles count diagonally to get area

If a square has side length 5 units, how many unit tiles cover it?

20 tiles

25 tiles

30 tiles

A rectangle 3 by 4 is tiled with unit squares. How many tiles are needed?

7 tiles

16 tiles

12 tiles

What is the standard area unit when counting tiles on a plane?

Cubic units

Square units

Linear units

For a 1x1 square, what is the area in tiles?

1 tile

0 tiles

2 tiles

If you double the side length of a square, how does the area change?

Area triples

Area multiplies by 4

Area doubles

A rectangle is 2 by 7. What is its area in square units?

21 square units

9 square units

14 square units

How many unit tiles cover a 2x2 square?

4 tiles

2 tiles

8 tiles

Why does area scale with length when tiling with unit squares?

Because width is constant

Because perimeter increases

Because area counts how many unit tiles fit

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Tile-tiled Areas: Inductive Derivation

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Tile-tiled Areas: Inductive DerivationOnline version

by John Angeles

What is the formula for the area of a rectangle in terms of its length and width, using tile units?

How can you inductively verify the area of a square using unit square tiles?

If a square has side length 5 units, how many unit tiles cover it?

A rectangle 3 by 4 is tiled with unit squares. How many tiles are needed?

What is the standard area unit when counting tiles on a plane?

For a 1x1 square, what is the area in tiles?

If you double the side length of a square, how does the area change?

A rectangle is 2 by 7. What is its area in square units?

How many unit tiles cover a 2x2 square?

Why does area scale with length when tiling with unit squares?

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