Transition: Advanced Additive to Advanced Multiplicative
Achievement
Objectives
Domain: Addition and Subtraction
E
Mathematical Processes: Level Two and Three
Number and Algebra: Level Two and Three
Problem Solving: Devise and use problem solving strategies to
explore situations mathematically.
Use equipment appropriately when exploring mathematical
ideas.
Logic and Reasoning: Classify objects.
Communicating Mathematical Ideas: Devise and follow a set of
instructions to carry out a mathematical activity.
Record and talk about the results of mathematical exploration.
Explain the meaning of the digits in any whole number.
Explain the meaning of the digits in decimal numbers with up to
3 decimal places.
Order decimals with up to 3 decimal places.
Explain the meaning of negative numbers.
Express a fraction as a decimal and vice versa.
Make sensible estimates and check the reasonableness of
answers.
Mentally perform calculations that involve addition and
subtraction.
Write and solve story problems that involve whole numbers
using addition, subtraction, multiplication, or division.
Explain satisfactory algorithms for addition, subtraction, and
multiplication.
Strategies being
developed
Problem
progression
References
Knowledge being developed
Resources
Use multiplication to solve
addition and subtraction problems
where common factors can be
found,
e.g. 24 + 27 + 22 + 28 = 4  25
36 + 45 = 
as 4 × 9 + 5 × 9 = 9 × 9 =

77 - 28 = 
as 11 × 7 - 4 × 7 = 7 × 7 =

24 + 48 + 64 + 32 as
(3 + 6 + 8 + 4) × 8
= 21 × 8 = 
29 + 30 + 28 + 33 + 32 +
27 + 31 + 30 =  as 8 ×
30 = 
99 – 36 – 27 = 
as (11 - 4 – 3) × 9 = 
Teaching Addition and
Subtraction (Book 5)
Average Ability (53)
Multiple Ways to Add
and Subtract (54)
Teaching Algebraic
Thinking and Number
Sense (Book 8)
Adding Sequences (34)
Figure It Out
NS&AT3.1 Crafty
Combinations (16)
Say the forwards and backwards decimal
word sequences by thousandths,
hundredths, tenths, ones, tens, etc, starting
at any whole number..
Teaching Number
knowledge (Book 4)
Number fans (4)
Place value houses (5)
Number hangman (5)
Skip counting on the
number line (11)
Hundreds Boards
and thousands
board (16)
Figure It Out
N 3-4 Changes,
highs and lows (6)
© 2006 Crown Copyright
Numeracy Development Projects
1
CA
AC
EA
AA
AM
AP
Transition: Advanced Additive to Advanced Multiplicative
Strategies being developed
Problem
progression
References
Add and subtract fractions that have
related denominators using a range of
mental and written strategies..
See AA to AM for Ratios and Proportions
Domain: Addition and Subtraction
Knowledge being developed
E
Resources
CA
AC
EA
AA
Add and subtract decimals using a
range of mental and written strategies.
Solve addition and subtraction
problems with integers (positive and
negative numbers).
© 2006 Crown Copyright
See AA to AM for Ratios and Proportions
+
2 + +3 = 
4 + -1 = 
+
4 + -5 = 
2 + -8 = 
+
6 - +5 = 
7 - -3 = 
+
5 - -2 = 
3 - +7 = 
-
Teaching Addition and
Subtraction (Book 5)
Dollars and Bills (50)
Hills and Dales (50)
Teaching Algebraic Thinking
and Number Sense (Book 8)
6 Minus 8 Does Work (31)
Figure It Out
N3-4.1 Walking the Plank (23)
N3-4.3 The Volcanoes Erupt (20)
N3-4.3 Chilly Heights (22)
N7/8 4.4 It’s a Try (8)
N7/8 4.4 Lifting Weights (9)
N7/8 4.4 Integer Zap (10)
N7/8 4.4 Shifty Subtraction (15)
N7/8 4.6 Judo Competition (14)
Numeracy Development Projects
Say the number one-thousandth, onehundredth, one-tenth, one, and ten,
etc, before and after any given whole
number.
Order decimals to three places.
Teaching Number
knowledge (Book 4)
Number fans (4)
Skip counting on the
number line (11),
Lucky dip (13)
Teaching Number
knowledge (Book 4)
Reading decimal
fractions (8)
Card ordering (12)
Arrow Cards (13)
Rocket- Where will it
fit? (15)
Squeeze- Guess my
number (15)
Bead strings (17)
Who wins? (20)
Figure It Out
N 7/8 4.3 Going for
gold (12)
L7/8 L.1 Up the
Ladder (15)
2
AM
AP
Transition: Advanced Additive to Advanced Multiplicative
Domain: Addition and Subtraction
E
Strategies being
developed
Problem progression
References
Knowledge being
developed
Resources
Use a range of mental and
written strategies to solve
multi-step problems that
involve a combination of
addition, subtraction,
multiplication, and
division with whole
numbers.
Julie bought three tops for
$16 each and four pairs of
shorts for $13 each. How
much did her clothes cost
altogether?
Tame bought 204 cans of
softdrink for the disco. They
used 13 six-packs. How many
cans were left over?
Three girls did jobs for their
neighbours. For each job they
got paid $43, $56, $21, and
$33. They split the money
evenly between them. How
much did each girl get?
Figure It Out
BF3 Paths and Pairs (9)
BF3 Calculator Golf (18)
N3.2 Stepping Out (2)
N3.3 Strategy Strut (6)
N3.3 Worth the Work (10)
N3-4.1 Head Cases (13)
N3-4.1 Kapa Haka (14)
NS&AT3.2 Maths Detective (2)
Recall the number of
groupings of tens, hundred,
and thousands that can be
made from a number of up to
seven digits.
Teaching Number
knowledge (Book 4)
Number hangman (5)
Tens in hundreds and
more (27)
Estimating (25)
Figure It Out
N 7/8 4.2 A million grains
of rice (4)
CA
Knowledge being developed
Resources
Round whole numbers and decimals, with up to two places, to the nearest whole number, or
tenth.
Teaching Number knowledge (Book 4)
Swedish Rounding (28), Sensible rounding (28)
Figure It Out
NS 7/8 Number scavenge (6), NS 7/8 2 Time versus money
(7)
Figure It Out
NS 7/8 2 Same answer every time (11)
Carry out column addition and subtraction for whole numbers and decimals.
© 2006 Crown Copyright
Numeracy Development Projects
3
AC
EA
AA
AM
AP