# 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

## Strategy

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.

Model a sequence of squares with sides measuring 1 matchstick, 2 matchsticks, 3 matchsticks.

Students then make the next two squares of the pattern. The perimeter of a square is the distance all the way around. Create a table showing the perimeter of each of the squares.

Length of one side of square (in matchsticks) Perimeter of square (in matchsticks)
1 4

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

#### Discuss

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

2. Use coloured counters to show various patterns for students to identify and describe.

• 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:

No Equation Independent variable Dependent variable
5 t = 3x2 + 2x - 5 enter answer enter answer
8 3x + 2y - 9 = 0 enter answer enter answer
9 x - 3y - 5 = 0 enter answer enter answer

Identifying the Independent and Dependent variables in an equation (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.

 x y -1 0 1 2 3 4 -2 0 2 4 6 8

The rule is y is always double x.

The equation is y = 2x

 a b -1 0 1 2 3 4 -4 0 4 8 12 16

The rule is __________________________

The equation is ______________________

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

 x y -1 0 1 2 3 4 3 5 7 9 11 13
• 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
 a b -1 0 1 2 3 4 -1 3 7 11 15 19
• When a = ______ b = ______________
• When a = ______ b = ______________
• When a = ______ b = ______________
• So the equation is _________________

Determine the rule and write the equation worksheet 2 (PDF 40.92KB)

## References

### 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.