These materials will help you to assess pupils' progress in Algebra at level 5. The examples of what pupils should be able to do and the probing questions will help you to secure evidence of progress in relation to the assessment criteria.
 Construct, express in symbolic form and use simple formulae involving one or two operations

Examples of what pupils should know and be able to do
Use letter symbols to represent unknowns and variables.
Understand that letter symbols used in algebra stand for unknown numbers or variables and not labels, for example, ‘5a’ cannot mean ‘5 apples’.
Know and use the order of operations and understand that algebraic operations follow the same conventions as arithmetic operations.
Recognise that in the expression $2+5a$ the multiplication is to be performed first.
Understand the difference between expressions such as:
$2n$ and $n+2$
$3(c+5)$ and $3c+5$
${n}^{2}$ and $2n$
${2n}^{2}$ and ${\left(2n\right)}^{2}$
Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
Simplify these expressions:
$3a+2b+2ab$
$4x+7+3x3x$
$3(x+5)$
$12(n3)$
$m(np)$
$4(a+2b)2(2a+b)$
Substitute integers into simple formulae, for example:
Find the value of these expressions when $a=4$.
$3{a}^{2}+4$
${2a}^{3}$
Find the value of y when $x=3$
$$y=\frac{2x+3}{x}$$ $$y=\frac{x1}{x+1}$$
Simplify $p=x+x+y+y$
Write $p=2(x+y)$ as $p=2x+2y$
Give pupils three sets of cards: the first with formulae in words, the second with the same formulae but expressed algebraically, the third with a range of calculations that match the formulae (more than one for each). Ask them to sort the cards. Formulae should involve up to two operations, with some including brackets.
Probing questions
How do you know if a letter symbol represents an unknown or a variable?
What are the important steps when substituting values into this expression/formula?
What would you do first? Why?
How would you continue to find the answer?
How are these two expressions different?
Give pupils examples of multiplying out a bracket with errors. Ask them to identify and talk through the errors and how they should be corrected, for example:
$4(b+2)=4b+2$
$3(p4)=3p7$
$2(5b)=\mathrm{\u207b10}2b$
$12(n3)=9n$
Similarly for simplifying an expression.
Can you write an expression that would simplify to, for example:
$6m3n$, $8(3x+6)$?
Are there others?
Can you give me an expression that is equivalent to, for example:
$4p+3q2$?
Are there others?
What do you look for when you have an expression to simplify? What are the important stages?
What hints and tips would you give to someone about simplifying expressions? And removing a bracket from an expression?
When you substitute $a=2$ and $b=7$ into the formula $t=\mathrm{ab}+2a$ you get 18. Can you make up some more formulae that also give $t=18$ when $a=2$ and $b=7$ are substituted?
How do you go about linking a formula expressed in words to a formula expressed algebraically?
Could this formula be expressed in a different way but still be the same?
 Use and interpret coordinates in all four quadrants

Examples of what pupils should know and be able to do
Plot the graphs of simple linear functions. Generate and plot pairs of coordinates for
$y=x+1$, $y=2x$
Plot graphs such as $y=x$, $y=2x$
Plot and interpret graphs such as $y=x$, $y=2x$, $y=x+1$, $y=x1$
Given the coordinates of three points on a straight line parallel to the y axis, find the equation of the line.
Given the coordinates of three points on a straight line such as $y=2x$, find three more points in a given quadrant.
Probing questions
If I wanted to plot the graph $y=2x$ how should I start?
How do you know the point (3, 6) is not on the line $y=x+2$?
Can you give me the equations of some graphs that pass through (0, 1)? What about...?
How would you go about finding coordinates for this straight line graph that are in this quadrant?