Numeracy

Your child's e-portfolio will contain assessment data from the [|Numeracy Project]. At Fairfield Intermediate we gather data on both the Knowledge Domain and the Strategy Domain (read below for more information). The IKAN assessment tests their knowledge and the GLOSS test determines the strategy stage. Students' progress is carefully monitored as the year progresses using formative assessment and conferencing.

Below you will find curriculum expectations based on a longitudinal study and information explaining the Numeracy Project.



The shaded parts in the documents above are indications of the expected levels of achievement. The expectation is that by the end of the year the majority of students will be working at this stage, with most of the accompanying knowledge known, and students close to being ready to work at the next stage. A range of achievement is normal and expected at each year level. These expectations, and the indications of when to consider students to be “At Risk”, “Cause for Concern” or “High Achievers”, are a guide only. They are intended to assist principals and teachers in setting high yet attainable expectations, and develop teaching and learning programmes for all students at each year level in their school. These expectations are for schools with everything in place for numeracy teaching and learning. Some schools take two years of professional development before everything is in place, others take longer. The Years One to Eight percentages come from the longitudinal study by Tagg, A. and Thomas, G. (2007) Do they continue to improve? Tracking the progress of a cohort of longitudinal students, In //Findings from the New Zealand Numeracy Development Projects 2006.// Wellington: Learning Media.

__**Support Information**__
All Numeracy goals that I set (with assistance from you and your child) are based on the knowledge component of the ‘Number Framework’ as it is called. I will explain further… The Number Framework is intended to help teachers, parents and students understand the stages of learning of number knowledge and understanding. There are two sections to the Number Framework. The Strategy section describes the processes or methods students use to solve problems involving numbers - how they work things out. The Knowledge section describes the key items about number that children know and can recall quickly for example, times tables. The two sections are linked, with children requiring knowledge to improve their strategies, and using strategies to develop new knowledge. The Strategy section of the Number Framework describes a series of stages that children progress through as they develop their understanding of a range of strategies for solving number problems. There are eight stages altogether, with the first three often grouped together: There are three areas, or 'domains' within the Strategy section, which describe a child's ability to solve different types of problems (additive, multiplicative and proportional). Your child is likely to be learning a broad range of strategies in their classroom mathematics programme. One of the ways that you can most easily support them is to help them develop the knowledge that they will need to be able to use these strategies. The Knowledge section is usually broken down into five areas, referred to as 'domains': Numeral Identification, Number Sequence and Order, Grouping/Place Value, Basic Facts, and Written Recording. Grouped into 3 domains: Below is all the knowledge (from the Basic Facts and Groupings and Place Value domains) your child needs to know at each of the 8 stages. It is **absolutely vital** that your child learns everything in the previous stage before moving to the next. There is some advice on learning times tables (that you will note does not have to be known until stage 5/6) attached also. Recall means that your child can answer related questions quickly and without hesitation. Knowing means understanding the concept.
 * What is the Number Framework?**
 * The Strategy Section**
 * **Stage 0-3: Counting from One** - children can solve problems by counting from one, either using materials or in their head.
 * **Stage 4: Advanced Counting** - children can solve problems by counting in ones, or by skip counting, starting from numbers other than one.
 * **Stage 5: Early Additive** - children can solve simple problems by splitting up and adding together the numbers in their head.
 * **Stage 6: Advanced Additive** - children use a range of different methods to solve more challenging problems in their head.
 * **Stage 7: Advanced Multiplicative** - children use a range of different methods to solve multiplication and division problems in their head.
 * **Stage 8: Advanced Proportional** - children can solve complicated problems involving fractions, decimals and percentages using a combination of methods.
 * The Knowledge Section**
 * **Number Identification and Order** - activities to help children learn to read numbers and know the order of numbers.
 * **Place Value** - activities to help children learn how 10s, 100s, 1000s, tenths, hundredths, thousandths etc are used.
 * **Number Facts** - activities that will help children learn their addition, subtraction, multiplication and division facts.

Your child recalls: Your child knows:
 * Stages 0-3 (Counting from One):**
 * Addition and subtraction facts to five e.g. 2+1, 3+2, 4-2 …
 * Doubles to ten e.g. 3+3, 4+4, 2+2
 * Groupings within 5 e.g. 2 and 3, 4 and 1
 * Groupings with 5 e.g. 5 and 1, 5 and 2, 5 and 3, …
 * Groupings within 10, e.g. 5 and 5, 6 and 4 ...

Your child recalls: Your child knows:
 * Stage 4 (Advanced Counting):**
 * Addition and subtraction facts to 10 e.g. 4+3, 6+2, 7-3 …
 * Doubles to 20 and corresponding halves e.g. 6+6, 9+9, ½ of 12 …
 * “Ten and” facts e.g. 10+4, 10+3, 7+4 …
 * Multiples of ten that add to 100 e.g. 30+70, 40+60, 80+20 …
 * Groupings with 10 e.g. 10 and 2, 10 and 4
 * Groupings within 20 e.g. 12 and 8, 13 and 7, 6 and 14
 * The number of tens in a decade e.g. how many tens are there in 40? 30?

Your child recalls: Your child knows: Your child rounds
 * Stage 5 (Early Additive)**
 * Addition facts to 20 and subtraction facts to 10 e.g. 7+5, 8+7, 9-6 …
 * Multiplication facts for the 2, 5 and 10 times tables and the corresponding division facts
 * Multiples of 100 that add to 1000 e.g. 400+600, 700+300 …
 * Groupings within 100 e.g. 49 and 51, 35 and 65
 * Groupings of two in numbers to 20 e.g. 8 groups of 2 in 16
 * Groupings of five in numbers to 50 e.g. 9 groups of 5 in 45
 * Groupings of ten that can be made from a 3 digit number e.g. tens in 763 is 76, tens in 745 is 74, tens in 342 is 34
 * Number of hundreds in centuries and thousands e.g. 8 hundreds in 800, 40 hundreds in 4000
 * 3 digit whole numbers to the nearest 10 or 100 e.g. 561 rounded to the nearest 10 is 560 and to the nearest 100 is 600.

Your child recalls: Your child knows: Your child rounds:
 * Stage 6 (Advanced Additive)**
 * Addition and subtraction facts up to 20 e.g. 9+5, 14-6 …
 * Multiplication basic facts up to the 10 times tables (10x10) (please refer to information about teaching times tables) and some corresponding division facts
 * Multiplication basic facts with tens, hundreds, and thousands, e.g. 10x100=1000, 100x100= 10 000
 * Groupings within 1000 e.g. 240 and 760, 492 and 502 …
 * Groupings of 2, 3, 5 and 10 that are in numbers to 100 and finds the resulting remainders e.g. 3s in 17 is 5 with 2 remainder, 5s in 48 is 9 with 3 remainder
 * Groupings of 10 and 100 that can be made from a 4 digit number e.g. tens in 4562 is 456 with 2 remainder, hundreds in 7894 is 78 with 94 remainder
 * Tenths and hundredths in decimals to 2 places e.g. tenths in 7.2 is 72, hundredths in 2.84 is 284
 * Whole numbers to the nearest 10, 100, or 1000
 * Decimals with up to 2 decimal places to the nearest whole number e.g. rounds 6.49 to 6, 19.91 to 20 …

Your child recalls: Your child knows: Your child identifies: Your child knows: Your child rounds
 * Stage 7 (Advanced Multiplicative)**
 * Division facts up to the 10 times tables e.g. 72÷8 …
 * Fraction to decimal to percentage conversions and vice versa for halves, thirds, quarters, fifths and tenths e.g. ½ = 0.5 = 50%
 * The divisibility rules for 2,3,5,9 and 10 e.g. 471 is divisible by 3 since 4+7+1=12
 * Square numbers to 100 and the corresponding roots e.g. 5²= 25, √25 = 5
 * Factors of numbers to 100, including prime numbers e.g. factors of 36= {1,2,3,4,6,9,12,18,36}
 * Common multiples of numbers to 10 e.g. 35, 70, 105 … are common multiples of 5 and 7
 * The groupings of numbers to 10 that are in numbers to 100 and finds the resulting remainders e.g. sixes in 38, nines in 68
 * The groupings of ten, one hundred, and one thousand that can be made up from a number of up to seven digits e.g. tens in 47 562, hundreds in 782 345, thousands in 5 678 098
 * Equivalent fractions for halves, thirds, quarters, fifths, tenths with denominators up to 100 and up to 1000 e.g. 1 in 4 is equivalent to 25 in 100 or 250 in 1000
 * Whole numbers and decimals with up to two places to the nearest whole number or tenth e.g. rounds 6.46 to 6.5 (nearest tenth)

Your child recalls Your child knows Your child identifies Your child knows Your child rounds
 * Stage 8 (Advanced Proportional)**
 * Fraction to decimal to percentage conversions for given fractions and decimals e.g. 9/8= 1.125 = 112.5%
 * Divisibility rules for 2,3,4,5,6,8 and 10 e.g. 5632 is divisible by 8 since 632 is divisible by 8, 756 is divisible by 3 and 9 as its digital root is 9
 * Simple powers of numbers to 10 e.g. 2³= 8, 5³= 125
 * Common factors of numbers to 100, including highest common factor e.g. common factors of 48 and 64 = {1,2,4,6,16}
 * Least common multiples of numbers to 10 e.g. 24 is the least common multiple of 6 and 8
 * The number of tenths, hundredths and one-thousandths that are in numbers of up to 3 decimal places e.g. tenths in 45.6 is 456, hundredths in 9.03 is 903, thousandths in 8.502 is 8502
 * What happens when a whole number or decimal is multiplied or divided by a power of 10 e.g. 4.5 x 100, 67.3 ÷ 10
 * Decimals to the nearest 100, 10, 1, 1/10, or 1/100 e.g. rounding 5234 to the nearest 100 gives 5200

Advice for learning times tables:
 * Rote, rote, rote
 * When your child is ready to learn their times tables then they must learn this knowledge off by heart and maintain it!!

Hints and games for learning knowledge:
 * Make flashcards
 * Display equations in everyday places (e.g. times tables on the toilet door!)
 * Play a ball game where each bounce is a times table answer
 * Have family math competitions
 * Use a timer to measure how long it takes to recite and record. Make graphs showing the results
 * Make up songs to encourage memorisation
 * Use CD ROMs designed to improve mathematic skills (check to make sure they are not learning anything above the stage they are at).
 * Internet sites such as [|www.nzmaths.co.nz] which have support material for families (click on the families button)
 * Have your child teach Numeracy games such as Boggle, Number Hangman, Traffic Lights, and Bowl a Fact to the family and then host a tournament.

Remember to have fun and if you need any other support or information please do not hesitate to ask. I am very happy to sit down and explain any of the concepts above and to guide you with other activities to support your child’s learning!

Erin Freeman 2009