onthedrawingboard.weebly.comonthedrawingboard.weebly.com/.../order_for_developing_n…  · Web viewPrompt the inclusion of ‘one more’ or ‘one less’ to a ten-frame and see

The following tables outline the order for developing number concepts:

ONE-DIGIT NUMBERS: 0 – 9…the basis for all numbers (Booker, p. 87)

MATCH: WORDS - SYMBOLS - OBJECTS

Check ‘meaning’ for number words. Match words to objects and symbols. Use ten-frames to specifically show how one number builds on and links to other numbers. Use counters or Unifix cubes in a doubles-based pattern. Booker, pp.89 – 92.

1 – 4 Use ten-frames to show structured patterns. Use counters or Unifix cubes in a doubles-based pattern. Booker, p.89.

0

Contrast with 1 – 4, using a ten-frame and empahasising that zero is not nothing, but ‘none of something’. Booker, p.90.

5 – 9 Use ten-frames to show structured patterns. Use counters or Unifix cubes in a doubles-based pattern.

SYMBOLS & WORDS 0 - 9 As soon as possible, students should learn to write number symbols and words. Booker, p.91.

5 five

SEQUENCE NUMBERS 0 – 9 Use ten-frames and Unifix to practise, review and reinforce the meaning of each one-digit number, including zero. Counting involves: ordered sequence, one-to-one match of number words to object, knowing that last number tells ‘how many’. Students should also be able to subitise to 5. Booker, p.94.

I would introduce a basic 0 – 9 number line here, to help students visualise the 0 – 9 sequence AND to familiarise students with the number line tool which will be useful later.

ONE MORE & ONE LESS Prompt the inclusion of ‘one more’ or ‘one less’ to a ten-frame and see the corresponding change in number symbol and word. Booker, p. 94.Could consolidate this by checking their 0 – 9 number line.

COMPARE & SEQUENCE NUMBERS

Booker, p.98.

(1) Compare groups of objects to answer, “Which has more?”- Objects with Objects- Objects with Symbols- Symbols with Symbols

(2) Recognise greatest, middle or least numbers.(3) Order several numbers.

ORDINAL NUMBERS Regular cases: fourth, sixth, seventh, eighth, ninth …then,Irregular cases: fifth, third, second, first. Booker, p.100.

COUNTING ON & BACK Use ten-frames, begin at a certain number and count on as counters are added or count back as counters are removed. Booker, pp. 96-98.

All NEW numbers are generated from those learned above. Go to TWO-DIGIT NUMBERS

TEN CONCEPT‘TEN’ CONCEPT Use ten-frame to show that ten ones make one ten. This is crucial for meaningful

development of larger numbers. Students should write the number name and symbol.

10 ten

MULTIPLES OF TEN Make visual groups of ten (e.g. train carriages – see Booker, p.104). Link to ‘names’ but not written form yet. Introduce the multiples whose names stem from regular language first:9t, 8t, 7t, 6t, 4tThen introduce the multiples whose names stem from the ordinal numbers:fif t, thir tLastly, introduce ‘twenty’ – linking to ‘two’ and ‘twin’. Booker, p. 104-5.

I think number lines could be used here for ordering multiples of ten.

TWO-DIGIT NUMBERS: 20 – 99

TENS & ONES

Using ten-frames, students count the number of full ten-frames (e.g. 4t) and the number of ones in the last ten-frame (7), then say these numbers together (4t7).Booker, p. 105.

PLACE VALUE CHARTS

SEE - Booker, pp. 106 – 108

Focus is on Materials, Language AND Recording:(i) Tens and Ones (before …)(ii) Tens and No Ones.

TEEN NUMBERSBooker, pp.106 – 108

Focus on materials and recording first. Then irregular language.

TEEN NUMBERS based on NUMBER NAMES 19, 18, 17, 16, 14

TEEN NUMBERS based on ORDINAL NAMES 15, 13

TEEN NUMBERS with NO ‘TEEN’ to indicate ten 12, 11

COMPARING, SEQUENCING & ORDERING 2-DIGIT NUMBERS

Once all two-digit numbers are known, including the teens, ‘further processes such as comparing, sequencing and counting on and back can be built up … Whereas the single-digit numbers are ordered or compared by simply knowing the number sequence, two-digit numbers demand a more systematic analysis … the key is PLACE VALUE … an efficient comparison strategy requires that the tens digits be compared first; if they are the same it is then necessary to compare the ones digits. The development of this process should also begin with materials and link through language to the number symbols only when the children understand what is needed’ (Booker et al., 2010, p.112).

COMPARE MATERIALS with MATERIALS

Using bundling sticks/ base-10 materials/ Unifix Cubes/ paddle-pop sticks … provide two combinations of tens and ones to represent two different numbers. “Which is greater?”

‘or’

COMPAREMATERIALS with SYMBOLS

‘or’ 48

COMPARESYMBOLS with SYMBOLS

15 ‘or’ 73

Note: The word ‘or’ is used at this stage [ The > symbol is not introduced until place value for 4-digit numbers is learned]

Next, the 0 – 99 chart is introduced …

INTRODUCE0 – 99 BOARD

increases by ones

I think this is where we could introduce SKIP COUNTING - highlight lines of numbers on chart to show number

patterns/sequences and practise skip counting. The link below is to online interactive 0-99 and 0-100 charts:

http://www.abcya.com/interactive_100_number_chart.htm

Could also use 0 – 99 chart to make skip counting number lines: to ‘skip count by twos, fives and tens starting from zero’ ACMNA012. for ‘identifying numbers that are represented on a number line and placing numbers on a

prepared number line’ ACMNA013.

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s by

tens

(1) Sequence numbers : before, after one more, one less 10 more, ten less ordinal names.

(2) Consolidate counting : Count on by ones Count back by ones Count on by tens Count back by tens

NOTE:

The arrangement of the numbers in the 0 – 99 chart means the three-digit number 100 has no place. In Booker, 100 is the first number of the next unit in the numeration system (p.113). However, there is also a 1-100 chart at the link mentioned above. 100 may not even need to be a part of Term 1 Mathematics planning. If so, see Booker p.113 for further teaching sequences.