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Dear Parents and Caregivers
This document was created in order to support the wonderful work you do with your child at home. It has bothered me that there is so much jargon surrounding Numeracy and maths because it makes it so much harder for parents to access and understand the new way that we teach maths. I have attempted to rewrite and explain the process more thoroughly so that we may work closer together toward improving your childs understanding and enjoyment of mathematics.
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
What is the Number Framework?
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
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:
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.
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
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:
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.
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.
Stages 0-3 (Counting from One):
Your child recalls:
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
Your child knows:
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 ...
Stage 4 (Advanced Counting):
Your child recalls:
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, 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
Your child knows:
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?
Stage 5 (Early Additive)
Your child recalls:
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
Your child knows:
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
Your child rounds
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.
Stage 6 (Advanced Additive)
Your child recalls:
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
Your child knows:
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
Your child rounds:
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
Stage 7 (Advanced Multiplicative)
Your child recalls:
Division facts up to the 10 times tables e.g. 728
Fraction to decimal to percentage conversions and vice versa for halves, thirds, quarters, fifths and tenths e.g. = 0.5 = 50%
Your child knows:
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. 5= 25, "25 = 5
Your child identifies:
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
Your child knows:
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
Your child rounds
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)
Stage 8 (Advanced Proportional)
Your child recalls
Fraction to decimal to percentage conversions for given fractions and decimals e.g. 9/8= 1.125 = 112.5%
Your child knows
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. 2= 8, 5= 125
Your child identifies
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
Your child knows
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
Your child rounds
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 HYPERLINK "http://www.nzmaths.co.nz" 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 childs learning!
Erin Freeman 2008
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