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Look at the section on Number to Algebra for ideas on how to introduce Algebra Tiles.
Expressions with algebra tiles
Expressions with algebra tiles
This activity introduces expressions with unknown variables and constant terms.
Also available expressions with variable -10<x <10
Ask students to match the models to the statements. Ideally they should already be familiar with base blocks and algebra tiles.
Next move the change x slider above to show that x is variable and the units are constant.
The expressions can be manipulated using Mathsbot to highlight the distributive property 2(x+3) = 2x + 6.
Using the rectangle representation links to the area model for multiplication and division and highlights the common factor of 2.
Equal expressions
Equal expressions
Move the slider to change the value of x. When does 3x + 2 = x + 6?
When is 3x+2 > x+6?
When is 3x+2 < x+6?
Algebra tiles and graphs
Algebra tiles and graphs
Making connections between the bar model and the graph model.
Change the number bars, size of constant term and position using the sliders.
Compare expressions
Compare expressions
Compare 3x and x+3
Change the value of x by moving the sliders
Equations and graphs
Equations and graphs
Solve equations and inequalities by moving the slider and comparing the bar model to the graph.
Solving Linear Equations
Solving Linear Equations
Algebra tiles do not show equality and inequality.
Before using algebra tiles to solve equations represent equality and inequality using a bar model or a dynamic model like equal expressions above.
Balance/elimination method
Balance/elimination method
Add multiples of x’s, -x’s, 1’s or -1’s to both expressions to isolate x on one side of the equation.
This method will always work and leads to the standard balancing method.
3 - x + x = x - 4 + x
3 + 4 = 2x - 4 + 4
Simultaneous Equations
Simultaneous Equations
Change x and y until the bars are equal.
Simultaneous equations by elimination
Simultaneous equations by elimination
The elimination method is clear to see using algebra tiles and zero pairs when the coefficients have opposite signs.
2x + y = 7
x - y = 2
Add the two equations together to get the image below.
3x + y - y = 9
The zero pair highlights the elimination.
3x = 9
x = 3
Substitute into 2x + y = 7
6 + y = 7
y = 1
x = 3 and y = 1
From here you can move on to multiplying one and then both equations before eliminating by adding the equations.
Difficulties and misconceptions start when the coefficients are the same sign.
Method 1 – subtracting the two equations or finding the difference
Method 1 – subtracting the two equations or finding the difference
Method 2 – elimination using zero pairs
Method 2 – elimination using zero pairs
Method 2 also avoids the difficulties that arise in questions that involve subtracting negatives.
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