Using Dynamic Representations
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Number Arrays and Area Models
Multiplication and Division
Area model and 2D Dienes blocks for multiplying decimals greater than 1
All representations for 2D Dienes blocks (base 10) use the same colours as algebra tiles for ones, x and x squared including red tiles for negatives.
Algebra Arrays and Area Models
Dynamic Algebra Tiles
Completing the square
Difference of Two Squares
Completing the square model allows students to see the structure of the general form of
x2+bx + c = (x+b/2)2 -b/22 + c
b/22 and -b/22 make a zero pair.
Change a and b to change the size of the squares. The a+b and a-b labels are draggable to allow students to place them by the correct side.
Area and Bar Models
Base Blocks (3D Algebra Tiles)
Base Blocks from Base -10 to 10
Base Blocks with Negative Indices
Base blocks allow students to make the link between Dienes blocks (base 10) and algebra tiles (base x) by exposing the mathematical structure of the place value of the base system.
Dynamic Algebra Tiles
Linear Expressions with Dynamic Algebra Tiles
Compare the expressions with the dynamic algebra tile representations using the variable sliders to change x.
This representation models the x and 1 algebra tiles. The green tile, x, is a variable and can be changed with the slider under the x axis.
Equations and Inequalities
Sequences and Graphs
These dynamic Cuisenaire rods show the first 5 terms and the nth of linear sequences of the form mn+c. Connections can be make to graphical representations and y=mx+c.