NA5-9: Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
Elaboration on this Achievement Objective
This means students will recognise the features of tabular, graph and equation representations of linear and quadratic relationships. This includes connecting constant first or second order difference in tables with linear and quadratic relations respectively, with the graph (linear and parabolic) and standard equation forms (y = mx + c and y = a x 2 + bx + c) for such relations. For example, given the spatial pattern below students can use a table, graph or equation to represent the relation and solve problems.
This includes finding both a recursive and direct (functional) rules and using them to find further terms using a spreadsheet or calculator, for example:
Students should also use these tabular and graphic representations for other relationships, such as simple exponential and step relations, but it is acceptable for them to use recursive rules for these more difficult relations.
Teaching resources for this Achievement Objective
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Five
Number and Algebra
This unit integrates student learning in the mathematics and science learning areas. Students will be developing their use of rates and ratios, exploring linear relationships using tables and graphs, in the context of chemical reactions involving acids and bases. SI units of measure are used to...
Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in an investigation of parabolas in a practical context.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Five
Number and Algebra
Problem solving activities
Level Five
Number and Algebra
The purpose of this unit is to engage the student in applying their knowledge and skills of algebra to solve problems within the context of electrical circuits.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series.
Level Three
Level Four
Level Five
Number and Algebra
This counting collections activity engages students in finding the number of squares of any size on a chessboard.
Level Five
Number and Algebra
Units of Work
This unit explores the fact that the properties that hold for multiplication and division of whole numbers also apply to fractions (commutative, associative, distributive, and inverse). The operations of multiplication and division are developed using a length model (Cuisenaire rods). While the size...
Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in recognising non-linear patterns, in this case a quadratic relationship. Students might use tables, graphs and equations to represent the relationship between sides of a polygon and the number of diagonals for the polygon.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Five
Integrated
Units of Work
This measurement unit concerns Pick’s Rule which applies to finding areas of polygons where all the vertices are lattice points, (in this application, the nails on geoboards). The unit centres on finding linear patterns.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Five
Number and Algebra
Units of Work
In this large range of activities some basic concepts in algebra are developed. The intention of this unit is not to teach skills in isolation, but rather to use each activity for developing all the concepts, with opportunities for discussion and consolidation.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Five
Number and Algebra
Units of Work
Techniques for drawing linear graphs are introduced via whole number problem situations where the focus is on the solutions rather than the technique. Only linear equations of the form ax±by=c are graphed by finding two or more points on the line. No attempt is made to link these equations by...
Level Five
Number and Algebra
Units of Work
In this unit students represent a quadratic relationship using spatial patterns, tables, graphs and equations, recognising the key features of a parabola, and finding unknowns from the graph of a parabola and from simple quadratic equations. Procedural fluency and conceptual understanding are...
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Five
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practice number properties.
Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in using algebraic equations, graphs and/or tables to solve a problem.
Level Five
Integrated
Problem solving activities
Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in evaluating powers of whole numbers and generalise the repeating sequence in the ones digit of those powers.
Level Five
Number and Algebra
Units of Work
In this unit procedural fluency and conceptual understanding are developed together. Students will be representing quadratic relationships, particularly using graphs and equations. Quadratic functions are used to model phenomena such as paths of projectiles, stopping distances and profits to...
Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in using their knowledge of linear relationships to solve a problem.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra activity from the Figure It Out theme series.