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Stage 4 - algebra - number patterns

Continue a number pattern to match a table of values; determine the rule which involves more than one operation to match a number pattern


Students can:

  • continue a number pattern to match a table of values
  • determine the rule which involves more than one operation to match a number pattern

Activities to support the strategy

Activity 1

Provide students with a collection of matchsticks. Students build a sequence of squares with different side lengths using the matchsticks.

Here is a sequence of squares with sides measuring 1 matchstick, 2 matchsticks, 3 matchsticks, etc.

Now try this with your pattern! Make the next two squares of the pattern. The perimeter of a square is the distance all the way around. Complete the table to show the perimeter of each of the squares.

Length of one side of square (in matchsticks)Perimeter of square (in matchsticks)
2enter answer
3enter answer
4enter answer
5enter answer

Predict the perimeter of a square with sides of six matchsticks.


  • If the square has sides 8 matchsticks long, what is the perimeter? 10 matchsticks long? Etc.
  • Students determine the rule to describe their matchstick pattern.

2. Use coloured counters on an overhead projector to show other patterns for students to identify and describe, e.g.

Ask students to

  • look at the pattern of counters and draw what they think the fifth and sixth shapes in the pattern would look like
  • describe the patterns they can see
  • develop an expression to show the number of counters needed for the nth shape

Activity 2

A variable is a symbol or letter which represents a number in an expression or equation. For example, "b" is a variable in the expression 3b + 5. This means, "b" can be equal to any number in this expression.

In an equation, variables can be independent or dependent. For example, in the equation c = 3b + 5, b is the independent variable (can be equal to any number) and c is the dependent variable (the value of c is determined once we know the value of b).

For example, anthropologists have developed a formula to determine the height from femur length. In cm, a man's height is given as

  • height = 2.59 x femur length + 66.4

Using pronumerals, we can use f to stand for femur length and h to stand for the man's height. The formula may then be written as

  • h = 2.59f + 66.4

The man's height depends on the length of the femur, so we say that f is the independent variable and h is the dependent variable. The formula is written with the dependent variable (h) as the subject.

1. Ask students to work through the following questions:

NoEquationIndependent variableDependent variable
1y = 3xenter answerenter answer
2h = 3k + 2enter answerenter answer
3v = u + 5tenter answerenter answer
4p = 3q - 2enter answerenter answer
5 t = 3x2 + 2x - 5enter answerenter answer
6 x + 3y = 4enter answerenter answer
73x + 2y = 9enter answerenter answer
83x + 2y - 9 = 0enter answerenter answer
9x - 3y - 5 = 0enter answerenter answer
1012m = 4n + 6enter answerenter answer

View print (PDF 104.74KB)

Discuss the answers as a class, with particular emphasis on questions 6 -10.

2. As a class, determine the rule giving the relationship between x and y in each of the following and write the corresponding equation.

Question 1

The rule is y is always double x.

The equation is y = 2x

Question 2

The rule is __________________________

The equation is ______________________

View/print (PDF 40.61KB)

3. Working in pairs, students determine the rule and write the equation for each of the following relationships.

Question 1
  • When x = 0, y = 5 = 0 + 5 = 2 x 0 + 5
  • When x = 1, y = 7 = 2 + 5 = 2 x 1 + 5
  • When x = 2, y = 9 = 4 + 5 = 2 x 2 + 5
  • So the equation is y = 2 x + 5

View print (PDF 40.61KB)

Question 2
  • When a = ______ b = ______________
  • When a = ______ b = ______________
  • When a = ______ b = ______________
  • So the equation is _________________

View/print (PDF 40.92KB)


Australian curriculum

ACMNA175: Introduce the concept of variables as a way of representing numbers using letters.

NSW syllabus

MA4-10NA: Uses algebraic techniques to solve simple linear and quadratic equations.

NSW literacy continuum

COMC13M11: Comprehension, cluster 13, marker 11: Locates and synthesises information to draw conclusions from a variety of sources.

Teacher resources

Lesson Plans and Activities

Explores triangular numbers

Exploring number patterns

Student resources

Number patterns which use a combination of operations

Numeracy Apps

Algebra Touch: Have you forgotten most of your algebra? Algebra Touch refreshes your skills using techniques only possible on your iOS device. Say you have x + 3 = 5. You can drag the 3 to the other side of the equation. Enjoy the wonderful conceptual leaps of algebra, without getting bogged down by the tedium of traditional methods. Drag to rearrange, tap to simplify, and draw lines to eliminate identical terms. Distribute by sliding terms across the sum, and Factor them back out by dragging them together. Easily switch between lessons and randomly-generated practice problems. Create your own problems or edit current ones. Current material covers: simplification, like terms, commutativity, order of operations, factorization, prime numbers, elimination, isolation, variables, basic equations, distribution, factoring out, substitution, and ‘more advanced’ mode.

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