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Multiplication and Division
Multiplication as Scaling
Area and Bar Models
Area Models for Multiplication
Click and drag the coloured Dienes blocks over the shaded area to count the number of 0.1's, 0.01's, 0.001's and 0.0001's.
Area and Grid Models
Division with Dienes and Area Model
These representations for base 10 use the same colours as algebra tiles for ones, x and x squared including red tiles for negatives.
Quadratic Expressions with Algebra Tiles
(ax + b)(cx + d)
Negatives are represented by red tiles and make zero pairs. In the three models above and left, you can vary the size of a, b, c, d and x.
Difference of Two Squares
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.
Completing the square model to the left allows students to see the structure of the general form of x^2+bx + c = (x+b/2)^2 - (b/2)^2 + c.
(b/2)^2 and -(b/2)^2 make a zero pair.
Dynamic Algebra Tiles
Dynamic Variable x
Linear Expressions with Dynamic Algebra Tiles
Compare expressions with algebra tile representations using the dynamic 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.
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. See Core concept 4.1: Sequences for examples.