Writing with algebraic notation

Students learn how to form and simplify algebraic expressions involving multiplication, addition, division and subtraction.  They use this knowledge to begin solving equations using the balance method.

This unit takes place in Year 7 Term 2 and is followed by Expressions, Equations and Formulae


Writing with algebraic notation Lessons


Prerequisite Knowledge
  • Use simple formulae
  • Generate and describe linear number sequences
  • Express missing number problems algebraically
  • Find pairs of numbers that satisfy an equation with two unknowns
  • Enumerate possibilities of combinations of two variables.

Key Concepts
  • An expression can be simplified by collecting like terms.  Like terms are those which contain the same letter symbol and equal powers.
  • Just as 2 + 2 + 2 can be written as 3 × 2, a + a + a can be written as 3 × a.  However, with algebraic notation × and ÷ symbols are not included.  3 × a is written as 3a and 3 ÷ a is written as a fraction 3/a.
  • An algebraic expression is a collection of mathematical terms with no stated value.
  • Multiplicative relationships such as xy = yx can be used to simplify some expressions.
  • The order of operations is used when substituting known values into expressions.


Working mathematically

Develop fluency

  • Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
  • Substitute values in expressions, rearrange and simplify expressions, and solve equations

Reason mathematically

  • Identify variables and express relations between variables algebraically and graphically

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Algebra

  • use and interpret algebraic notation, including:
    • ab in place of a × b
    • 3y in place of y + y + y and 3 × y
    • a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b
    • a/b in place of a ÷ b
    • coefficients written as fractions rather than decimals
  • simplify and manipulate algebraic expressions to maintain equivalence by:
    • collecting like terms
    • taking out common factors

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Solving Problems with Angles in Parallel Lines

Solving problems with angles in parallel lines is like solving a murder mystery.  One clue leads on to the next and the next until the murderer is found.  However, it doesn’t end there.  The detectives need to explain their reasoning in court using the relevant laws and procedures should the murderer plead not guilty.  If […]

Solving Two Step Equations using the Balance Method

An equation is when one expression, or term, is equal to another.  To solve an equation means to find the value of the variable (represented by a letter) that makes the two expressions equal.  There are two types of equations for secondary school mathematics, linear and none-linear.  In this blog I write about how I […]

How to Simplify Surds

When learning how to simplify surds students need to understand the difference between a rational and irrational number. Rational numbers include integers and terminating and repeating decimals. They can be written as a fraction with both the numerator and denominator as integers. An irrational number is a number which, in its decimal form does not […]