Download Advanced Counting (Stage 4)

Advanced
Counting
(Stage 4)
to
Early
Additive
(Stage 5)
I am learning to…
Solve + and
– problems
by:
Using doubles,
e.g. 8 + 7 =  as 7 + 7 = 14, 14 + 1 = 15
or 8 + 8 = 16, 16 – 1 = 15
Going through tens,
e.g. 28 + 6 =  as 28 + 2 = 30, 30 + 4 = 34.
Joining and separating tens and ones,
e.g. 34 + 25 = (30 + 20) + (4 + 5) = 59.
Solve x and
÷ problems
by:
Using repeated addition,
e.g. 4 x 6 as 6 + 6 = 12, 12 + 12 = 24.
Using doubling and halving
e.g. 3 x 10 = 6 x 5
Using addition to predict the result of
division.
e.g. 20 ÷ 4 = 5 because 5 + 5 = 10 and
10 + 10 = 20
Find a unit
fraction of:
A set using addition facts,
1
e.g. of 12 is 4 because 4 + 4 + 4 = 12
3
A shape using fold symmetry,
e.g.
Early
Additive
(Stage 5)
to
Advanced
Additive
(Stage 6)
I am learning to…
Solve + and –
problems by
using:
Place value partitioning (100’s, 10’s, 1’s),
e.g. 724 – 206 =  as 724 – 200 = 524,
524 – 6 = 518.
Rounding and compensating,
e.g. 834 – 479 =  as 834 – 500 + 21 = 355.
Reversibility
e.g. 834 – 479 =  as 479 +  = 834.
Solve x and ÷
problems by:
Doubling and halving,
e.g. 24 x 5 = 12 x 10 = 120.
Rounding and compensating
e.g. 9 x 6 is (10 x 6) – 6 = 54
Using reversibility
e.g. 63 ÷ 7 =  as 7 x  = 63.
Solve
Finding a fraction of a set using multiplication
problems
and division,
with fractions
1
and ratios by: e.g. 5 of 35 using 5 x 7 = 35.
Renaming improper fractions using
multiplication
15
1
e.g.
as 5 (sing 5 x 3 = 15)
3
3
Advanced
Additive
(Stage 6)
to
Advanced
Multiplicative
(Stage 7)
I am learning to…
Solve + and –
problems by:
Partitioning fractions and using simple equivalent
fractions,
3 5
3 2
3
3
e.g. + =  as ( + ) + = 1 .
4 8
4 8
8
8
Using place value partitioning, reversibility, and
rounding and compensating with decimals,
e.g. 2.4 – 1.78 =  as 1.78 +  = 2.4
or 2.4 – 1.8 + 0.02 = 0.62.
Recognising equivalent operations with integers,
e.g. +5 - -3 =  as +5 + +3 = +8.
Solve x and ÷
problems
with whole
numbers by:
Using place value partitioning (100’s, 10’s, 1’s),
e.g. 7 x 56 =  as 7 x 50= 350, 7 x 6 = 42,
350 + 42 = 392.
Using rounding and compensating,
e.g. 92 ÷ 4 =  as 25 x 4 = 100 so 92 ÷ 4 = 25 – 2
Using proportional Adjustment,
e.g. 81 ÷ 3 =  as 81÷ 9 = 9, so 81 ÷ 3 = 3 x 9
Solve
problems
with fractions
by:
Finding fractions of whole numbers by using
multiplication and division.
5
1
e.g. of 24 as of 24 = 4, 5 x 4 = 20 or 24 – 4 = 20
6
6
Solving division problems that have fraction answers,
24
4
e.g. 24 ÷ 5 =
=4 .
5
5
Converting common fractions, decimals and
percentages.
3 75
e.g. =
= 75% = 0.75
4 100
Advanced
Multiplicative
(Stage 7)
Advanced
Proportional
(Stage 8)
to
I am learning to…
Solve + and –
problems by:
Partitioning fractions and using equivalent fractions,
3
2
3 2
9 8
1
e.g. 2 - 1 = 1 + ( - ) = 1 + (
)=1
.
4
3
4 3
12 12
12
Combining different proportions.
e.g. 25% of 36 combines with 75% of 24 gives 45% of
60 (27 out of 60)
Solve x and ÷
problems
with fractions
and decimals
by:
Using standard place value, reversing, and
compensating from tidy numbers,
e.g. 0.7 x 3.9 =  as 0.7 x 3 = 2.1,
0.7 x 0.9 = 0.63, and 2.1 + 0.63 = 2.73.
Converting from fractions to decimals to
percentages,
e.g. 80% of 53 =  as 8 x
1
x 53 = 8 x 5.3 = 42.4.
10
Creating common denominators,
e.g.
or
Solve
problems
with
fractions,
ratios and
proportions
by:
3 3 9
x =
5 4 20
2 1
8
3 8
2
÷ =  as
÷
= =2 .
3 4
12 12 3
3
Using common factors to multiply between and within
ratios,
e.g. 8:12 as :21 as 8:12 = 2:3 (common factor of 4)
so 2:3 = 14:21 (multiplying by 7).
Partitioning percentages,
e.g. 65% of 24 =  as 50% of 24 is 12, 10% 24 is 2.4,
5% is 1.2, 12 + 2.4 + 1.2 = 15.6