Stage/No: C02
Length: 4 weeks
CF Outcomes: 6, 7, 8, 18
Levels: 3, 4, 5, 6
Due out: available now

{slider=Publishing}

C02S: Number
4 week module
Old ISBN: 1876800216
New APN: 9781876800215

{slider=CF Outcomes}

This information is found in the wrap around pages of the teachers module. It details the Curriculum Framework Outcomes addressed in the module.

Outcomes 1 & 2 should be an inherent part of all mathematics lessons.

1. Show a disposition to use mathematics to assist with understanding new situations, solving problems and making decisions, showing initiative, flexibility and persistence when working mathematically and a positive attitude to their own continued involvement in learning and doing mathematics.

2. Appreciate that mathematics has its origins in many cultures, and its forms reflect specific social and historical contexts, and understand its significance in explaining and influencing aspects of our lives.

Outcomes 3, 4 & 5 "Working Mathematically" are an integral part in the design of every module. These outcomes determined the three stage learning process developed in each module.

3. Call on a repertoire of general problem-solving techniques, appropriate technology and personal and collaborative management strategies when working mathematically.

4. Choose mathematical ideas and tools to fit the constraints in a practical situation, interpret and make sense of the results within the context and evaluate the appropriateness of the methods used.

5. Investigate, generalise and reason about patterns in number, space and data, explaining and justifying conclusions reached.

Outcomes 6, 7 and 8 from "Number" and 18 from "Algebra" are specific to this module.

6. Read, write and understand the meaning, order and relative magnitudes of numbers, moving flexibly between equivalent forms.

7. Understand the meaning, use and connections between addition, multiplication, subtraction and division.

8. Choose and use a repertoire of mental, paper and calculator computational strategies for each operation, meeting needed degrees of accuracy and judging the reasonableness of results.

18. Read, write and understand the meaning of symbolic expressions, moving flexibly between equivalent expressions.

{slider=Student Outcomes}

This information is found in the wrap around pages of the teachers module. It details the major student outcomes that should have been developed during the module.

### Major Student Outcomes

During this module students should have been developing the following outcomes:

Working mathematically outcomes at levels 3, 4, 5 and 6 are interwoven with the structure of these modules.

### Number:

N6a.3 [N3.1a]: Reads, writes, says, counts with and compares whole numbers into the thousands, money and familiar measurements.

N6b.3 [N3.1b]: Reads, writes, says and understands the meaning of unit fractions, flexibly partitioning and rearranging quantities to show equal parts.

N6a.4 [N4.1a]: Reads, writes, says, counts with and compares whole numbers into the millions and decimals.

N6b.4 [N4.1b]: Reads, writes, says and understands the meaning of fractions. The student estimates the relative size and order of readily visualised fractions and shows equivalence between them.

N6a.5 [N5.1a]: Reads, writes, says and understands the meaning, order and relative magnitude of whole and decimal numbers and negative integers.

N6b.5 [N5.1b]: Reads, writes, says and understands the meaning, order and relative magnitude of fractions, straightforward ratios and percentages and knows the more common equivalences between them.

N6.6 [N6.1]: Reads, writes, says and understands the meaning, order and relative magnitude of positive and negative rational numbers, ratios, familiar rates and numbers expressed with integer powers.

N7.4 [N4.2]: Understands the meaning, use and connections between the four operations on whole and decimal numbers, and uses this understanding to choose appropriate operations (whole multipliers and divisors) and constructs and completes equivalent statements.

N7.5 [N5.2]: Understands the meaning, use and connections between the four operations on whole, decimal and fractional numbers, and uses this understanding to choose appropriate operations, including those in which fractional and decimal multipliers and divisors are required.

N8.3 [N3.3]: Adds and subtracts whole numbers and money, multiplying and dividing by one-digit whole numbers, using mainly mental strategies for doubling, halving, adding to 100 and additions and subtractions derived readily from basic facts.

N8.4 [N4.3]: Calculates with whole numbers, money and measures (at least multipliers and divisors to 10), drawing mostly on mental strategies to add and subtract two-digit numbers and for multiplications and divisions related to basic facts.

### Algebra:

*[*The Student Outcome Statements show two of these Algebra outcomes in the Number strand.]*

*PA18.3 [N3.4]: Recognises, describes and uses spatial patterns and patterns involving operations on whole numbers, following and describing rules for linking materials by changes in shape and size or linking terms in a sequence by multiplication or addition-based or subtraction-based strategies.

*PA18.4 [N4.4]: Recognises, describes and uses spatial patterns and patterns involving operations on whole and fractional numbers, following and describing rules for linking objects or figures by changes in size and orientation or linking successive terms in a sequence or paired quantities by a single operation.

A18b.5 [A5.1]: Uses a letter to represent a variable quantity in an oral or written expression and for linking successive terms in a sequence involving one or two operations.

A18b.6 [A6.1]: Uses and interprets basic algebraic conventions for representing situations involving a variable quantity.

### Other Strands

To a lesser degree some outcomes from other strands are also integrated into this module.

{slider=Details}

This information is found in the wrap around pages of the teachers module. It gives details about the module.

###
Module Length:

Approximately 4 weeks (16 hours). This may vary upward according to the ability and prior understandings of the students.

###
Outcomes Levels:

Includes outcomes from levels 3, 4, 5 and 6.

###
Stage/Number:

Each Integrated Maths Module has been assigned a stage and number. The stage is designed to help teachers in their sequencing of modules. The number is for identification of each module.

This module is C02, that is stage C module 2.

The content of this module is:

Operations on whole numbers

Factors and multiples

Square and cube roots

Powers

Integers and Integer operations

Cartesian plane

Rule of order

Substitution

Number generalisations

###
Language development:

The following terms (or derivations of them) are an essential part of this module:

negative

number line

horizontal axis

vertical axis

Cartesian plane

formula

substitute

prime number

factor

multiple

square number

square root

cubic number

triangular number

These terms are in bold whenever they appear in this text.

{slider=Samples}

The structure of all modules is to present materials in three stages:

### Exploration - Formalisation - Application

The files available here for downloading are a Sample Activity from the Exploration Stage of this module and a Sample Application from the Application stage of this module.

These files are available as pdf files. To view and print these files you will need a program like Adobe Acrobat Reader which is available free here.

### Downloads

These links are to the sample files:

Sample Activity

Sample Application
{slider=Unit Curriculum Links}

This information is found in the wrap around pages of the teachers module produced for Western Australian schools. It details the links to the old Unit Curriculum objectives for schools trying to adapt programmes etc.

Unit Curriculum Objectives covered are:

From Transition Mathematics 1.2

- N 1.1 Solve problems involving whole numbers, including recognition of the operation required, and use of a calculator.
- N 1.2 Approximate the results of computations involving whole numbers.
- N 1.4 Multiply and divide mentally by powers of ten and by single-digit multiples of powers of ten.
- N 1.7 Determine equivalent fractions and consolidate addition and subtraction of fractions with like denominators.
From Mathematical Development 2.4

- N 2.1 Investigate patterns in sets of whole numbers, including multiples, factors, square and cube numbers.
- N 2.2 Express whole numbers as products of factors and identify prime and composite numbers.
- N 2.3 Develop an understanding of the need for a rule of order of operations and use the convention 'Rule of Order'.
- N 2.4 Develop an understanding of negative integers.
- N 2.9 Develop an understanding of square root and determine square roots of whole numbers, using a calculator
- N 2.12 Investigate number situations and patterns which lead to generalizations, including:
- (i) the equivalence of :a+b=c and a=c-b , ab=c and b = c/a, a/b = c/d and ad = bc
- (ii) expansion of a(b+c) and
- (iii) factorization of ab + ac.

From Mathematical Development 3.4

- N 3.2 Develop an understanding of operations with negative integers.

From Mathematical Development 4.4

- N 4.7 Develop further understanding of square and cube roots, using a calculator.

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