Core Concept 1.4
Simplifying and manipulating algebra
188.8.131.52 Understand and recognise that a letter can be used to represent a specific unknown value or a variable
The dynamic representations below use dynamic algebra tiles.
Moving the slider changes the value of x.
The example above is from the NCETM Secondary PD material
Ask students to match the models to the statements. (open in Desmos and turn the expressions on and off using the control panel on the left).
Next move the change x slider above to show that x is variable and the units are constant.
What would the value of each expression be is x = 5?
What do you notice when x = 4
When is 3x+2 = 2(x+3)?
When is 3x+2 < 2(x+3)?
When is 3x+2 > 2(x+3)?
When is 2x+5 = 3x+2?
When is 2x+5 < 3x+2?
When is 2x+5 > 3x+2?
Move the slider to change the value of x.
Open in Desmos by clicking edit graph on Desmos on the bottom right corner of the image.
The red tiles represent -1. In this representation -6 is placed underneath the positive tiles to represent zero pairs.
Which is bigger? 3x or x+3
Combing the dynamic representation with the graphical representation allows students to see connections.
When you move the slider you can see when
3x > x+3
3x = x+3
3x < x+3
Arrange these cards in order.
Here students can see base x when x varies.
These can be used to support students understanding of the card sort activity above.
184.108.40.206 Understand that relationships can be generalised using algebraic statements
220.127.116.11 Understand how to use the distributive law to multiply an expression by a term such as 3(a + 4b) and 3p2(2p + 3b)
In this dynamic representation you can change the values of a,b, c and x
18.104.22.168 Use the distributive law to find the product of two binomials
a) 3(x + 5)
a) 3(x - 5)
22.214.171.124 Understand that an additive relationship between variables can be written in a number of different ways
3m - 2n + r = V
3m - 2n + r + 2n = V + 2n
3m + r = V + 2n
3m - 2n + r + 2n -3m = V + 2n -3m
r = V + 2n - 3m
3m - 2n + r + 2n - r = V + 2n - r
3m = V + 2n -r