A2 🧱 Algebra Builder Tools
1D, 2D and 3D Variables
Select Base 𝑥 and compare variables in 1D, 2D and 3D.
1D representations show variables and constants as a length. This is perfect for perimeter problems at GCSE.
1D models can also be represented as vectors with magnitude and direction. More on this comes in terms and expressions.
2D representations show variables and constants as an area. They are more commonly known as Algebra Tiles.
They provide an area model for work on quadratic expressions and link to the grid model for multiplication.
3D representations show variables and constants as a volume.
Expand three brackets and compare with the cuboid. Switch to 2D to look at each face.
The three tools below will be used in later units.
Perimeter Model
Algebra Tiles
Algebra Blocks
Place Value Tables (not available in the student tools)
What would happen to the digits in the table if I multiplied the expression by 𝑥?
Have a play with different bases and look at what is the same and what is different compared to place value, multiplying and dividing in Base 10.
How would you add and subtract using the column method in different bases? How does it compare with base 10? Can you do the same with Base 𝑥?
How could you use this to stretch and challenge students and strengthen conceptual understanding of procedures for the four operations and place value?