# NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.

Elaboration on this Achievement Objective

This means students will describe the function rule for a linear relationship as well as recognise recursive relationships where more complex relationships are involved. For example, given the pattern of fish made with matchsticks and counters below, students should be able to represent the relationships in a table and graph and use these representations to predict the terms in the sequence:

Counters | 1 | 2 | 3 | 4 | 5 |

Matchsticks | 8 | 14 | 20 | 26 | 32 |

Level Four students should be able to:

- give linear rules connecting the variables (for example, "the number of matchsticks is the six times the number of counters plus two", or "take one off the number of fish, multiply that number by six then add eight")
- extend the graph or table of a linear relationship to predict further co-ordinate pairs, recognising that constant difference (add six in the fish pattern) is associated with points that lay on a line
- use recursive methods to predict further members of a sequence where the relationship is non-linear. For example, the sequence of triangular numbers:

| |||||||||||||||||||||

+2 | +3 | +4 | +5 |

Recursive means finding what is added to or subtracted from one term to get the next.

Teaching resources for this Achievement Objective

This is a level 4 algebra activity from the Figure It Out theme series.

identify a number pattern from the pattern

Figure It Out activities

Number and Algebra

Level Four

This is a level 3 and 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

generalise that repeated addition equates to multiplication use a rule to describe a pattern

Figure It Out activities

Number and Algebra

Level Three

This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a diagram or table to find a pattern use a rule to describe a pattern

Figure It Out activities

Number and Algebra

Level Four

This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

explore triangular number patterns

Figure It Out activities

Number and Algebra

Level Four

This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a table to find a numbr pattern use an equation to describe a patter

Figure It Out activities

Number and Algebra

Level Four

use a table to find a rule for a geometric pattern write the rule for relationship as a linear equation

Figure It Out activities

Number and Algebra

Level Four

This is a level 3-4 activity from the Figure It Out series. A PDF of the student activity is included.

Figure It Out activities

Number and Algebra

Level Four

Identify the possible outcomes of an event Follow a logical argument Write a rule for the pattern Interpret information and results in context (logic, be systematic)

Problem solving activities

Statistics

Level Four

In this unit we are paying close attention to the general rule of a pattern for the first time. We look at odd and even numbers as well as multiples of small numbers. We also look at squares and cubes of numbers and see that it is possible to make more than one pattern from the same three initial...

continue a pattern use a table of values be able to find the general rule for simple patterns

Units of Work

Number and Algebra

Level Four

This is a level 4 algebra strand link activity from the Figure It Out series. A PDF of the student activity is included.

use a table to find a rule for a geometric pattern write a rule to describe a relationship

Figure It Out activities

Number and Algebra

Level Four

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series. A PDF of the student activity is included.

Students will: measure, record, and average data for 2 variables (number of marbles and bungy cord stretch) plot a scatter graph using appropriate scales (independent variable on x-axis [number of marbles]; dependent variable [overall length] on y-axis) use tables and graphs to identify patterns/...

Figure It Out activities

Statistics

Level Three

use a rule to describe a pattern

Figure It Out activities

Number and Algebra

Level Four

use a graph to show a relationship

Figure It Out activities

Number and Algebra

Level Four

write a rule to describe a pattern use a rule to make predictions

Figure It Out activities

Number and Algebra

Level Four

Express rules in words See more than one rule for a given pattern Devise and use problem solving strategies to explore situations mathematically

Problem solving activities

Number and Algebra

Level Four

This counting collections activity engages students in finding the number of squares of any size on a chessboard.

Number and Algebra

Level Three

To provide a set of learning tasks that integrate across the strands of the New Zealand Mathematics Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson , especially if students need more time to become...

Session One Use systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists. Session Two Use tables, graphs and word rules to represent growing patterns. Session Three Draw cube models using plan views. Session Four Draw cube models using isometric projections....

Number and Algebra

Level Four

This is a level 4 algebra strand activity from the Figure It Out series. It also has an achievement objective from the Level 4 Number strategies and knowledge substrand. A PDF of the student activity is included.

use a table or double number line to find a linear relationship

Figure It Out activities

Number and Algebra

Level Four

complete a table to find a pattern use a linear equation to describe a relationship

Figure It Out activities

Number and Algebra

Level Four

find and use rules in number patterns

Figure It Out activities

Number and Algebra

Level Four

The unit is designed as a simple introduction to systems of linear equations. Students solve problems in which they meet two constraints to find a single solution. Both constraints can be expressed as linear equations.

Identify and find values for variables in context. Identify linear relationships in context. Represent linear relationships using tables, graphs and simple linear equations. Draw strip diagrams to represent linear equations and ratios. Solve problems in which two or more conditions must be met.

Units of Work

Number and Algebra

Level Four

This is a level 4 algebra activity from the Figure It Out series. A PDF of the student activity is included.

draw and interpret graphs of linear relationships.

Figure It Out activities

Number and Algebra

Level Four

This is an activity based on the short illustrated novel Fibonacci’s Cows

Students will be able to identify examples of natural and human made structures that represent the Fibonacci sequence. Students will be able to explain the relationship between members of the sequence and how the next number is generated. Students will explore the Golden Ratio and the Golden Angle...

Picture book activities

Number and Algebra

Level Four

These are level 3 number problems and level 4 number and algebra problems from the Figure It Out series. A PDF of the student activity is included.

use proportions to solve problems (Problem 2) find patterns in a series of equations (Problem 3) solve problems using addition facts (Problem 4)

Figure It Out activities

Number and Algebra

Level Four

use a formula to continue a pattern

Figure It Out activities

Number and Algebra

Level Four