Stage 6 Strategy and Knowledge

1. STAGE 6 Addition & Subtraction Profile Sheet
Adapted from NZ Maths Planning Sheets Moving from Early Additive to Advanced Additive Stage 5-6
STRATEGY KNOWLEDGE
(Key Idea #1) Begin to using the
number line to solve change unknown
problems.
Identify all of the numbers in the range 0 -
1 000 000.
(Key Idea #2) Know that 10 tens
make one hundred and 10 hundreds
make one thousand.
Say the forwards and backwards whole
number word sequences by ones, tens,
hundreds, and thousands in the range
0 – 1 000 000.
F
B
Find numbers that are 10, 100, and
1 000 more than a given number.
Find numbers that are 10, 100, and
1 000 less than a given number.
(Key Idea #3) Solve addition and
subtraction problems using place value.
Read decimals with tenths
Order decimals with tenths.
(Key Idea # 4) Solve addition and
subtraction problems by using rounding
and compensating.
Count forwards and backwards in tenths.
(Key Idea #5) Know addition and
subtraction are inversely related.
Recall groupings within 1000, e.g., 240 +
760.
(Key Idea # 6) Solve subtraction
problems with the mental strategy of
equal adjustments.
Record the results of mental calculation
using addition equations and diagrams
(Key Idea # 7) Choose wisely the best
strategy for solving a problem.
Record the results of mental calculation
using subtraction equations and diagrams.
(Key Idea # 8) Use the standard
written form to solve addition &
subtraction problems.
Carry out column addition and subtraction
with whole numbers of up to four digits.
Round whole numbers to the nearest ten,
hundred, or thousand.
Adapted from Team Solutions Student Profiles and NZ Maths Planning Sheets by Emma Watts

2. STAGE 6 Multiplication & Division Profile Sheet
Adapted from NZ Maths Planning Sheets Moving from Early Additive to Advanced Additive Stage 5-6
STRATEGY KNOWLEDGE
Use times five facts to work out times
six, seven, and four facts (using the
distributive property).
Recall groupings of twos, threes, fives,
and tens that are in numbers to 100
and the resulting remainders.
Use times ten facts to work out times
nine facts (using the distributive
property).
Recall all the multiplication and division
facts for 2, 3, 5, 10 x tables.
×
÷
Change the order of the factors to
make a multiplication problem easier,
e.g. 26 x 3 = 3 x 26
Recall groupings of 10 and 100 that can
be made from a four-digit number.
Find out how many ones, tens, hundreds
and thousands are in all of a whole
number.
Recall multiplication facts for squares
to 100.
Use two times facts to work out three,
four, six, and eight times facts (using
doubling and the distributive property).
Record the results of mental
calculation using multiplication and
division equations and diagrams.
Multiply by tens, hundreds, thousands,
and other multiples of ten.
Solve sharing problems by reversing
multiplication facts.
Solve “How many equal sets of ?”
problems by reversing multiplication
facts.
Solve problems using a combination of
addition, subtraction, multiplication
and division mental strategies.
Adapted from Team Solutions Student Profiles and NZ Maths Planning Sheets by Emma Watts

3. STAGE 6 Ratios & Proportions Profile Sheet
Adapted from NZ Maths Planning Sheets Moving from Early Additive to Advanced Additive Stage 5-6
STRATEGY KNOWLEDGE
Find fractions of a set using
multiplication and division.
⅓ of 21 is 7 ( ⅓ × 21 = 7 )
Identify decimals to three places.
Use symmetry to find fractions of
continuous shapes like lengths, circles,
and rectangles.
Identify symbols for any fraction,
including tenths, hundredths,
thousandths, and those greater than 1.
Solve division problems that have
fraction answers using halving.
Say the forwards and backwards word
sequences for halves, quarters, thirds,
fifths, and tenths.
F
B
Create equivalent ratios by repeated
copying.
Say the decimal number word
sequences, forwards and backwards, in
tenths and hundredths.
F
B
Measure how many times a unit
fraction goes into a whole number.
How many quarters are in five?
(5 ÷ ¼ = 20)
Order unit fractions for halves,
quarters, thirds, fifths, and tenths.
Rename improper fractions as mixed
numbers using materials with
multiplication, and position improper
fractions on a number line.
Recall the number of tenths and
hundredths in decimals to two places.
Round decimals with up to two places to
the nearest whole number.
Adapted from Team Solutions Student Profiles and NZ Maths Planning Sheets by Emma Watts

4. STAGE 6 Algebraic Thinking Profile Sheet
Adapted from NZ Maths Planning Sheets Moving from Early Additive to Advanced Additive Stage 5-6
STRATEGY
Find relationships in repeating and sequential patterns and represent the
relationships using additive and simple multiplicative rules.
Find relationships in patterns and ordered pairs, and describe the
relationships using word rules, tables, and graphs.
Use a rule to create a pattern.
Interpret relationships shown in equations using the properties of
operations and understanding of the equals sign.
Adapted from NZ Maths Planning Sheets by Emma Watts