NA4-8: Generalise properties of multiplication and division with whole numbers.
Elaboration on this Achievement Objective
This means students will generalise, which means to establish properties that hold for all occurrences. This involves the ability to look at several examples, notice what changes (variables) and what does not, use appropriate mathematical terminology and symbols to describe the pattern, and apply the generalisation to other examples. At Level Four students should be able to describe and apply the properties of multiplication and division as these operations apply to whole numbers. These properties include commutativity, distributivity, associativity, inverse and identity. This includes the ability to express generalisations using words and symbols, for example 4 x 6 = 24 so 24 ÷ 6 = 4 and 24 ÷ 4 = 6 (example) leading to a x b = c so c ÷ b = a and c ÷ a = b. This is the inverse relationship of multiplication and division.
Teaching resources for this Achievement Objective
Level Four
Number and Algebra
Picture book activities
This is an activity based on the picture book Anno’s Mysterious Multiplying Jar.
Level Four
Integrated
Rich learning activities
The purpose of this activity is to engage students in finding a pattern from multiplying dimensions and to generalise this pattern with a rule.
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 Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Number and Algebra
Secondary activities
This is a collection of activities to enhance and extend division skills and understanding.
Level Four
Number and Algebra
Secondary activities
These activities are designed to teach doubling and halving strategies.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
Level Four
Integrated
Units of Work
This unit looks at Fibonacci numbers and how they occur in nature. Fibonacci numbers provide a rich context in which to apply algebra at level 4. It is recommended that this unit be used with students that already have some experience with level 4 algebra.
Level Four
Integrated
Figure It Out activities
This is a level 4 number, algebra, and statistics activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.A PDF of the student activity is included.
Level Four
Number and Algebra
Units of Work
This unit presents a range of strategies for solving multiplication and division problems with multi-digit whole numbers. Students are encouraged to notice the structure of problems, and to anticipate which strategies might be best suited to solving them. This unit builds on the ideas presented in...
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number and algebra activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.
Level Four
Level Five
Number and Algebra
Figure It Out activities
This is a level 4 and 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Number and Algebra
Secondary activities
These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (Mikes Investigation Sheet link) and may become longer and more involved tasks with subsequent recording/reporting.
Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a problem involving investigating with whole numbers using graphical means and/or generalising.
Level Four
Number and Algebra
Picture book activities
This is a series of activities based on the novel The number devil: A mathematical adventure
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra link activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Number and Algebra
Units of Work
This unit develops students’ recognition of pattern (consistency) in equations involving multiplication and division with whole numbers.
Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to develop and practice algebraic reasoning. They follow from teaching sessions that are described below. The initial teaching episode is an attached lesson, while other teaching sessions are outlined in the...