Stage 4 Unit: Integers
Integers
Syllabus Content pp 58
NS4.2
Key Ideas
Compares, orders and calculates with integers
Perform operations with directed numbers
Simplify expressions involving grouping symbols and
apply order of operations
Working Mathematically Outcomes
Questioning
Asks questions that
could be explored
using mathematics in
relation to Stage 4
content
Applying Strategies
Analyses a
mathematical or reallife situation, solving
problems using
technology where
appropriate
Communicating
Uses mathematical
terminology and
notation, algebraic
symbols, diagrams,
text and tables to
communicate
mathematical ideas
Knowledge and Skills
Students learn about

recognising the direction and magnitude of an
integer

placing directed numbers on a number line

ordering directed numbers

interpreting different meanings (direction or
operation) for the + and – signs depending on the
context

adding and subtracting directed numbers

multiplying and dividing directed numbers

using grouping symbols as an operator

applying order of operations to simplify expressions

keying integers into a calculator using the +/– key

Using a calculator to perform operations with
integers
Casino HS Stage 4 unit - integers
Reasoning
Identifies relationships
and the strengths and
weaknesses of different
strategies and
solutions, giving
reasons
Reflecting
Links mathematical
ideas and makes
connections with, and
generalisations about,
existing knowledge
and understanding in
relation to Stage 4
content
Working Mathematically
Students learn to
interpret the use of directed numbers in a real world
context eg rise and fall of temperature
(Communicating)
construct a directed number sentence to represent a real
situation (Communicating)
apply directed numbers to calculations involving money
and temperature (Applying Strategies, Reflecting)
use number lines in applications such as time lines and
thermometer scales (Applying Strategies, Reflecting)
verify, using a calculator or other means, directed
number operations eg subtracting a negative number is
the same as adding a positive number (Reasoning)
question whether it is more appropriate to use mental
strategies or a calculator when performing operations
with integers (Questioning)
Background Information
Complex recording formats for directed numbers such as raised
signs can be confusing. The following formats are
recommended.
-2 – 3 = -5
-3 + 6 = 3
-3 + (-4) = -3 – 4 = -7
-2 – (-3) = -2 + 3 = 1
Brahmagupta, an Indian mathematician and astronomer (c 598
– c 665 AD) is noted for the introduction of zero and negative
numbers in arithmetic.
-3.25 + 6.83 = 3.58
Technology
Links
Resources
Language
Casino HS Stage 4 unit - integers
Learning experiences and assessment activities
Learning Experiences
At the end of Stage 3, students are able to order, read and
write numbers of any size using place value. They can
interpret and express numbers using expanded notation and
locate position on the number line (including negative
numbers). They select and apply appropriate mental written
or calculator strategies for addition, subtraction,
multiplication and division of whole numbers and use formal
written algorithms (limited in the case of multiplication to
two digits and for division to a single-digit divisor).
In Stage 4, they begin to extend their knowledge of number
properties and relationships.
 Maths Net 7 Quinlan, Clarke and Abrahams
pge 357
A variety of useful and relevant games
i) indoor cricket
ii) dice games
iii) trading cards
iv) number line games
v) coloured dice

Magic squares with integers
Casino HS Stage 4 unit - integers
Assessment Activities
Assessment activity
Focus: Directed Numbers
Topic: Positive and Negatives Game
Individual/group
Task:
• The game is simple
• The Game Board is basically a number line.
• I found that this simple game gave the students plenty of practice
evaluating things like --2, -+2, +-2
• Positive and negative direction is reinforced.
minutes
Unit
Lloyd Stagg (Viniculum Vol 40(2) pp16)
Possible prompts to assist student engagement
Suggested Materials
 Game to be played in pairs
 Class competition
You will need per pair of students
• A game board (Instructions below)
• A marker or token for each person
(pencils or erasers will do)
• Two dice
• Sticky tape and scissors
• 5mm graph paper to make two cubenets to cover each dice (or use small circle
stickers.)
Outcomes
Perform operations with directed numbers
Simplify expressions involving grouping symbols and apply order of operations
Preparing the dice
• One die is covered with the numbers-3, +3, 2, +2, -1, +1 (perhaps on opposite aces)
• The other die (or coin) faces are covered equally with + and - signs
Constructing the Game Board
1. Use the full width of an A4 landscape page
(i.e. a workbook turned side on)
2. Place a ruler across the page and draw a line
down both sides of the ruler.
3 Beginning at one edge of the page, mark off
the ruled lines every 2cm.(the last one will be
narrower)
4. Fill in the numbers from 7 through zero to +7 as shown
Playing the game
Casino HS Stage 4 unit - integers
1. Pairs take turns to roll both dice
2. The die with faces marked + and - is placed in front [to
of] of the die marked-3, +3, -2, +2, -1, +1 so you have, for
example [reading the uppermost face of each die]:
the left
3. The overall value of both dice is determined (the above example is evaluated as -2)
4. The player who rolled the dice moves his/her marker according to the overall value of their roll.
(In the above example it would be left two squares).
5. The winner of a game is the first player to move off the board at either end.
6. A tournament between two players is played on a first-to-win-three games basis.
7. The class can play a round robin.
Challenge and Extensions
Currently this game is essentially a luck-race (as described in Gough, J. (2001). Learning to Play —
Playing to learn: Mathematics Games That Really Teach Mathematics, Mathematical Association of
Victoria, Brunswick). The similar one-dimensional race-game Snakes and ladders is he classic luckrace. How could the rules, and perhaps the playing equipment, be changed to make it a proper
"game", where players have some (occasional) scope for choice, and where the choices made by
one player in his or her turn can possibly affect the available choices of the next player's turn?
(Hint: consider Ludo, as a classic race game that is a real "game".)
Can you adapt the idea of this game so players move their counters across the 2-D graph board?
Criteria for judging quality of performance
The student may demonstrate the following:



Feedback
Students will receive:



Casino HS Stage 4 unit - integers
Stage _ Unit: __________
(Topic)
Syllabus Content pp __
(outcome reference)
Key Ideas
Working Mathematically Outcomes
Questioning
Applying Strategies
Knowledge and Skills
Students learn about
Casino HS Stage 4 unit - integers
Communicating
Reasoning
Working Mathematically
Students learn to
Reflecting
Background Information
.
Technology
Links
Resources
Language
Casino HS Stage 4 unit - integers
Learning experiences and assessment activities
Learning Experiences
Casino HS Stage 4 unit - integers
Assessment Activities
Assessment activity
Focus:
Topic:
Individual/group
Task:
•
minutes
Unit
Possible prompts to assist student engagement

Outcomes
Criteria for judging quality of performance
The student may demonstrate the following:



Feedback
Students will receive:



Casino HS Stage 4 unit - integers
Suggested Materials