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# division

## Solving multi-step equations

• Units of Work
• Number and Algebra
• Level Four

The purpose of this unit of five lessons is to support students as they read, write and solve multistep equations that include variables that stand for fixed values. Importantly, students also come to see that a variable can be interpreted in other ways, including representing a quantity that varies in relation to another quantity.

This is the ninth in a series of algebra units focusing on using symbols and expressions to think mathematically. It complements the content of algebra student e-ako 15 and 16.

This unit follows:

• Numerals and Expressions, in which numerals are explored, and the operations of addition and subtraction are introduced through the recording of number expressions.
• Equality and Equations, in which the concept of an equation as an ‘object that balances’, is introduced.
• Inequality symbols and relationships, in which these symbols are introduced and explored ≠, <, >.
• Number families and relationships. This explores families of facts, the inverse relationship of addition and subtraction and of how to use these operations in problem solving situations.
• Multiplication and division relationships develops understanding of the symbols for and operations of multiplication and division, of their inverse relationship, and of how to use these operations in problem solving situations.
• The order of operations further develops understanding of how number operations behave, and recognises that there is a need for rules to guide us in the order in which we carry out these operations, in problem solving situations.
• A study of number properties explores the way numbers and operations behave in a more formal way, and introduces variables.
• Unknowns and variables: Solving one-step equations develops an understanding of variables and how to solve equations in both a ‘common sense’ and formal way.

## Unknowns and variables: Solving one-step equations

• Units of Work
• Number and Algebra
• Level Four

The purpose of this unit of four lessons is to support students as they read and record equations in which letters (or variables) represent an ‘as yet unknown’ amount. This idea is initially introduced in unit seven and is built upon here.

This is the eighth in a series of algebra units focusing on using symbols and expressions to think mathematically. It complements the content of algebra student e-ako 13 and 14.

This unit follows:

• Numerals and Expressions, in which numerals are explored, and the operations of addition and subtraction are introduced through the recording of number expressions.
• Equality and Equations, in which the concept of an equation as an ‘object that balances’, is introduced.
• Inequality symbols and relationships, in which these symbols are introduced and explored ≠, <, >.
• Number families and relationships. This explores families of facts, the inverse relationship of addition and subtraction and of how to use these operations in problem solving situations.
• Multiplication and division relationships develops understanding of the symbols for and operations of multiplication and division, of their inverse relationship, and of how to use these operations in problem solving situations.
• The order of operations further develops understanding of how number operations behave, and recognises that there is a need for rules to guide us in the order in which we carry out these operations, in problem solving situations.
• A study of number properties explores the way numbers and operations behave in a more formal way, and introduces variables.

The unit that follows this unit is:

## A study of number properties

• Units of Work
• Number and Algebra
• Level Three

The purpose of this unit of three lessons is to develop the students’ deeper understanding of the way numbers behave, to enable them to use everyday language to make a general statement about these behaviours, and to understand the symbolic representation of these ‘properties’ of numbers and operations.

This is the seventh in a series of algebra units focusing on using symbols and expressions to think mathematically. It complements the content of algebra student e-ako 11 and 12.

This unit follows:

• Numerals and Expressions, in which numerals are explored, and the operations of addition and subtraction are introduced through the recording of number expressions.
• Equality and Equations, in which the concept of an equation as an ‘object that balances’, is introduced.
• Inequality symbols and relationships, in which these symbols are introduced and explored ≠, <, >.
• Number families and relationships. This explores families of facts, the inverse relationship of addition and subtraction and of how to use these operations in problem solving situations.
• Multiplication and division relationships develops understanding of the symbols for and operations of multiplication and division, of their inverse relationship, and of how to use these operations in problem solving situations.
• The order of operations further develops understanding of how number operations behave, and recognises that there is a need for rules to guide us in the order in which we carry out these operations, in problem solving situations.

The units that follow this unit are:

## The order of operations

• Units of Work
• Number and Algebra
• Level Three

The purpose of this unit of three lessons is to develop the students’ understanding of how number operations behave, to recognise that there is a need for rules to guide us in the order in which we carry out these operations, and to interpret and apply these rules in problem solving situations.

This is the sixth in a series of algebra units focusing on using symbols and expressions to think mathematically. It complements the content of algebra student e-ako 10.

This unit follows:

• Numerals and Expressions, in which numerals are explored, and the operations of addition and subtraction are introduced through the recording of number expressions.
• Equality and Equations, in which the concept of an equation as an ‘object that balances’, is introduced.
• Inequality symbols and relationships, in which these symbols are introduced and explored ≠, <, >.
• Number families and relationships. This explores families of facts, the inverse relationship of addition and subtraction and of how to use these operations in problem solving situations.
• Multiplication and division relationships develops understanding of the symbols for and operations of multiplication and division, of their inverse relationship, and of how to use these operations in problem solving situations.

The units that follow this unit are:

## Multiplication and division symbols, expressions and relationships

• Units of Work
• Number and Algebra
• Level Three

The purpose of this unit of five lessons is to develop understanding of the symbols for and operations of multiplication and division, of their inverse relationship, and of how to use these operations in problem solving situations.

This is the fifth in a series of algebra units focusing on using symbols and expressions to think mathematically. It complements the content of algebra student e-ako 8 and 9.

This unit follows:

The units that follow this unit are:

## The Great Divide: A Mathematical Marathon

• Other
• Number and Algebra
• Level Two

This is an activity based on the picture book The Great Divide: A Mathematical Marathon

## 365 Penguins

• Other
• Number and Algebra
• Level Two

This is an activity based on the picture book 365 Penguins

## Dividing fractions

• Units of Work
• Number and Algebra
• Level Three

The purpose of this series of lessons is to develop understanding of the operation of division with fractions.

This unit supports teaching and learning activities in the Student Fractions e-ako 11 and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages.

This is the sixth in a series of units developing fractional understanding. This unit builds on these previous units of work:

The unit that follows is:

## Multiplying fractions

• Units of Work
• Number and Algebra
• Level Three

The purpose of this series of lessons is to develop understanding of the multiplication of fractions.

This unit supports teaching and learning activities in the Student Fractions e-ako 10 and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages and in Book 8 Teaching Number Sense and Algebraic Thinking.

This is the fifth in a series of units developing fractional understanding. This unit builds on these previous units of work:

## Addition, subtraction and equivalent fractions

• Units of Work
• Number and Algebra
• Level Three

The purpose of this series of lessons is to develop understanding of equivalent fractions and the operations of addition and subtraction with fractions.

This unit supports teaching and learning activities in the Student Fractions e-ako 7 and 7+, 8 and 8+, 9 and 9+, and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages.

This is the fourth in a series of units developing fractional understanding. This unit builds on these previous units of work: