__Longbeach School – Maths Intentions__The following intentions have been selected as the key competencies required for the Number strand of the New Zealand Mathematics Curriculum. The Number strand involves calculating and estimating, using appropriate mental, written and machine calculation methods in flexible ways.

These ‘intentions’ are divided into 2 parts:

*Knowledge and Strategies.*The

*Knowledge*component is the ‘base knowledge’ about numbers that is required before the numbers can be applied to solve problems. The

*Strategies*component describes the methods that are used to solve the problems.

__Knowledge - One to one counting__Say, read and write all the numbers in the range 0 – 10

Say the forwards and backwards number sequences up to 10

Order the numbers in the range 0 – 10

__Strategies - One to one counting__Count a set of objects in the range 1 – 10

Form a set of objects in the range 1 – 10

__Knowledge - Counting from One on Materials__Say, read and write all the numbers in the range 0 – 20

Say the forwards and backwards number sequences up to 20

Say the number before or after a given in the range 0 – 20

Order the numbers in the range 0 – 20

__Strategies - Counting from One on Materials__Solve simple addition & subtraction problems to 20 by counting all the objects

Count all the objects by creating groups of 10

__Knowledge - Counting from One by Imaging__Recall groupings within 5 and 10 – e.g. 2 + 3 and 6 + 4

Recall doubles to 10 – e.g. 2 + 2, 5 + 5

Record the results of counting and operating using symbols, pictures and diagrams

Say the forwards and backwards skip counting sequences in the range 0 – 20 for 2s & 5s

Explain the fractions ½ and ¼

__Strategies - Counting from One by Imaging__Solve simple add & sub problems by counting all the objects mentally

Count objects by imaging groups of 10

Solve simple mult & div problems by counting all the objects

Find ½s & ¼s of shapes and objects – e.g. ½ a bar of chocolate

Find ½s & ¼s of sets of objects to 20 by equal sharing

__Knowledge - Advanced Counting__Say the forwards and backwards number sequences in the range 0 – 100, at least

Say the before and after a given number in the range 0 – 100, at least

Recall the doubles to 20, and the corresponding ½s - e.g. 4 + 4= & ½ of 14=7

Record the results of mental add & sub using equations

Say the forwards and backwards skip counting sequences in the range 0–100 for 2s & 5s

Identify the symbols for ½s, ¼s, 1/3s and 1/5s

Recall the number of tens in decades up to 100 – e.g. four 10s in 40

__Strategies - Advanced Counting__Solve simple add problems by counting on in their head from the largest number

Solve simple sub problems by counting back in their head from the largest number

Solve add & sub problems by counting on in ones and tens - e.g. 43 + 32 as 53, 63, 73, 74, 75

Solve mult problems by skip counting in 2s,5s & 10s – e.g. 4 x 5 as 5,10,15,20

Find simple fractions of shapes or sets, staring with ½s and ¼s by using materials or imaging

__Knowledge - Early Additive__Identify and order all of the numbers in the range 0 – 1000

Say the forwards & backwards number sequences by 1s, 10s, 100s in the 0 - 1000

Say the number 1, 10, 100 less or more than a given number

Recall the number of 10s & 100s in numbers up to 5 digits

Recall add and sub facts to 20

Round 3 digit whole numbers to the nearest 10 or 100

Say the forwards & backwards skip counting sequences in the range 0 – 100 for 2s, 3s, 5s and 10s

Recall groupings of 2 to 20, 5 to 50 & 10 to 1000 – e.g. 8 groups of 2 in 17

Instantly recall the mult and div facts for multiples of 2,5,& 10

Record the results of mult and div calculations using equations and diagrams

Order fractions with like denominators e.g.1/4 and ¾

**Strategies - Early Additive**Solve add and sub problems mentally from known basic facts –

e.g. 8 + 7 as 8 + 8 – 1 or (5 + 3) + (5 + 2) as 5 + 5 + 5

Solve add and sub problems with 2 and 3- digit numbers using grouping of 10 –

e.g. 43 + 25 as 40 + 20 + 3 + 5 or 39 + 26 as 40 + 25

Use repeated add or sub to solve simple mult and div problems – e.g. 4 x 6 as 6 + 6 + 6 + 6 or 16 ÷ 4 as 4, 4, 4, 4

Find a fraction of a set by skip-counting, repeated add or known basic facts – e.g. 1/3 of 12 as 4 + 4 + 4 = 12 so 4 is 1/3 of 12

__Knowledge - Advanced Additive__Identify and order the numbers in the range 0 – 1 000 000

Say the forwards & backwards number sequences by 1s, 10s, 100s in the 0 – 1 000 000 including finding numbers 10, 100, 1000 more or less than a given number

Recall groupings within 1000 e.g. 240 + 760

Carry out column addition and subtraction with whole numbers up to four digits

Recall groupings of 2s, 3s, 5s & 10s that are in numbers to 100 including remainders

Instantly recall all the basic multiplication facts to the twelve times

Identify decimals to 3 places

Read the symbols for any fraction

Order fractions ½, ¼, 1/3, 1/5 and 1/10

Recall the number of 1/10s & 1/100s in decimals to 2 places

Round decimals with 2 decimals places to the nearest whole number

Record the results of mental calculations using mult and div equations and diagrams

__Strategies - Advanced Additive__Choose appropriately from a full range of strategies to solve add & sub problems mentally such as: Compensation e.g. 632- 179 as 632 – 180+1,

Place Value e.g. 273 - 106 as 273 – 100 - 6

Equal additions e.g. 754 – 529 as 755 – 530 and so on.

Use pencil and paper or calculators to work out add & sub answers where numbers are large or untidy

Solve mult and div problems from other facts known using a variety of strategies such as: Doubling e.g. 4 x 6 as 2 x 6 x 2

Rounding e.g 19 x 4 as 20 x 4 – 4

Reversing e.g. 56 ÷ 8 as 8 x ? = 56

Multiply by 10s, 100s and 1000s

Solve division problems by equal sharing

Use a variety of mult and div strategies to solve problems that involve finding a fraction of a whole amount e.g. 1/3 of 27 as 27 ÷ 3 = 9

Use mult and div to compare the size of fractions, especially fractions > 1

Use repeated halving and multiplication facts to solve divisions that have fraction answers e.g. 7 ÷ 4 = 1 + ½ + ¼ = 1 ¾

Use mult and div to create equivalent ratios e.g. 2:3 as 10:15, and to solve simple ratio problems

__Knowledge - Advanced Multiplicative__Read and order decimals to 3 places

Say the forwards and backwards decimal sequences by 1000ths, 100ths, 10ths,

Round decimals with 2 decimal places to the nearest 10th

Recall the number of groupings of 10s, 100s and 1000s that can be made from a 7 digit number

Carry out a short written algorithm for mult and div of a 3 digit-whole number by a single-digit number

Recall equivalent fractions for ½s, 1/3s, ¼s, 1/5s & 1/10s

Recall fraction ? decimal ? percentage conversions for 1/2s, 1/3s, 1/4s, 1/5s & 1/10s

__Strategies - Advanced Multiplicative__Use a broad range of mental strategies to solve add & sub problems with whole numbers and decimals such as:

Tidy numbers e.g. 3.1 – 2.79 as 3.1 – 2.79 + 0.01

Place value e.g. 3.06 + 2.7 as 3.06 + 2 + 0.7

Reversibility e.g. 6.7 – 4.9 as 4.9 + ? = 6.7

Equal additions e.g. 4.2.- 2.8 as 4.4 – 3.0

Add and subtract related fractions using part-whole knowledge e.g. 2/3 + 5/6 = 4/6 + 5/6 = 9/6 = 1 3/6 or 1 ½

Solve problems that involve the ordering and add & sub of integers e.g. 5 - 3 =

Use a pencil and paper or a calculator to add and subtract decimals and whole numbers where the numbers are difficult or untidy

Use a broad range of mental strategies to solve mult & div problems with whole numbers such as:

Compensation from tidy numbers e.g. 252 ÷ 9 as 270 ÷ 9 = 30 so 252 ÷ 9 =28

Place Value e.g.7 x 56 as (7 x 50) + (7 x 6)

Reversibility e.g. 84 ÷ 7 as 7 x ? = 84

Proportional adjustment e.g. doubling and halving i.e. 24 x 6 as 12 x 12

Splitting factors e.g. 544 ÷ 16 as 544 ÷ 2 ÷ 2÷ 2 ÷ 2 = 34

Solve division problems that have remainders and express the answer in a fraction or decimal e.g. 76 ÷ 5 = 151/5 or 15.2

Use mental strategies based on multiplying & dividing to solve problems with fractions, decimals, percentages and ratios such as:

Place value e.g. 6 x 3.4 as (6 x 3) + (6 x 0.4)

Compensating from tidy numbers e.g. 2.9 x 6.3 as 3 x 6.3 = 18.9 . so 18.9 - .0.63 = 18.27

Using unit fractions e.g.5/8 of 72 as 1/8 of 72 = 9 so 5 x 9 = 45

Find the general rules for finding unknown numbers of a repeating sequence e.g. 1, 3, 7, 15 = ( x 2 + 1)

Solve problems that have one or more unknowns’ e.g. (2 x?) + ? = 16

**Knowledge - Advanced Proportional**Order fractions, decimals and percentages

Recall the number of 10ths, 100ths and 1000ths in numbers with 3 places

Know what happens when a whole number or decimal is multiplied or divided by 10, 100 or 1000

Recall fraction ? decimal ? percentage conversions for 1/8s, 1/10s & 1/20s

Carry out column add & sub equations of decimals up to 3 decimal places

Carry out short mult & div equations of decimals by a single digit number

Carry out whole number multiplication of 4-digit numbers by a 2-digit numbers

Order positive and negative decimal numbers

Recall the Prime numbers to 50

Recall the fact’s squares and square roots

Recall simple powers of numbers e.g. 3n

__Strategies - Advanced Proportional__Choose appropriately from a full range of mental strategies to problems with fractions, decimals, ratios, rates, and proportions such as:

Applying reversibility e.g. 13.6 ÷ 0.4 as 0.4 x ? = 13.6

Applying equivalency e.g. 28/42 = ?% as 28/42 ? 4/6 ? 2/3 = 66.6.%

Finding proportional relationships e.g.12:15 = ?:25 as 12 is 4/5 of 15 so 20 is 4/5 of 25

Convert ratios to proportions e.g. 3:5 of 96 as 3:5 is 3/8 so 3/8 of 96 is 36

Calculating rates e.g. 75 km/h means 300km will take 4 hours

Adding fractions with different denominators e.g. 2/3 + ¾ = 8/12 + 9/12

Solve problems involving the multiplication of integers

Solve problems with powers, the multiplication of powers and finding square roots

Solve problems that involve letters as unknowns e.g. r = (4 x t) + 1, r = 51 what is t?