National Numeracy Project: framework for Years 1, 2 and 3
Victoria Neumark explains what's involved and gives examples of the classroom work involved
Taking examples from the three strands for Years 1,2,3 we find that each set of basic activities is arranged so that there is some stress on vocabulary, more and less difficult activities for differentiation and opportunity for summarising.
Within the strand Numbers and the Number System, for the topic of place value and ordering, a subsidiary objective, for example, is "understand the vocabulary of comparing and ordering numbers, including ordinal numbers to denote position".
For this the framework suggests: For Year 1: Understand and use in a practical context the terms how many, as many as, the same number as, equal toImore than, fewer than, greater than, less than, smaller than, larger thanI most, fewest, greatest, least, smallest, largest I order, first, last, before, after, next, between, half-way between.
And the ordinal numbers: first, second, third, fourthI Answer: who is the first, last, third I in this queue?
What is on the fifth page of this book?
Point to the seventh bead in this line.
What is the 12th letter of the alphabet?
For Year 2: Understand and read the terms as for Year 1 above.
What position is the fourth white bead?
What day of the month is it?
Write today's date What date is your birthday?
For Year 3: Understand, read and write the terms as for Year 1 above What position is the sixth black bead?
What colour is the 19th bead?
In the Calculations strand, the topic understanding division has one objective as "understand the question of division and associated vocabulary".
For Year 1: Share out objects, for example, share 6 crayons equally between 2 or sort 6 cubes into 2 equal piles Group objects in pairs or threes and count how many groups. For example, pair off: the children in a class, some socks, and then count how many pairs; or, starting from 0, count how many hops of 2 are needed to reach 8, or how many hops of 3 are needed to reach 12.
Understand and use in practical contexts: one each, two each..., share, left over...
Respond to oral or written questions like: Share 8 between 2. How many lots of 3 make 9?
How many pairs can you make from 6 socks?
Make as many different rectangles as you can from 12 square tiles, describing them, for example, as 3 long and 4 wide For Year 2: Understand the operation of division as: sharing equally; repeated subtraction.
6 V 2 can mean sharing equally: for example, if 6 sweets are shared equally between 2 people they are given out as "one for you, one for you..." etc or it can mean how many sets or groups of 2 can be made from 8: for example, the number of people who can have 2 sweets each is worked out by giving out the 8 sweets two at a time; or starting from 0, four hops of five are needed to reach 20.
Understand and read: one each, two each..., share, divide, remainder, divided by... and read and write the division sign V .
Begin to understand that: division by 1 leaves a number unchanged.
Respond to oral or written questions like: Share 18 between 2 Divide 6 by 3, How many lengths of 2 cm can you cut from 10cm of tape?
How many horses have 20 horseshoes between them?
Complete written questions: with quick mental recall: 6 V 2 = n 20 V n = 2 * V 10 = 3 using counters (or sharing) or a number line (for repeated subtraction) , then mental strategies 16 V 4 = n 24 V n = 6 * V 3 = 8 Make as many different rectangles as you can from 24 square tiles.
For Year 3: Understand the operation of division as: sharing equally; repeated subtraction 20 V 5 can mean sharing equally, for example if 20 plums are shared equally between 5 people they are given out "one for you, one for you.. ."
or it can mean how many sets of 5 can be made from 20: for example the number of people who can have 5 plums each is worked out by giving out the 20 plums two at a time.
Understand, read and write: share, divide, remainder, divided by, the division sign V, and understand that 12 means one divided into two equal parts.
Develop understanding that: division by 1 leaves a number unchanged; a number cannot be divided by zero.
Begin to understand that multiplication is the inverse of division (multiplication reverses division).
Respond to oral or written questions like Share 18 between 2 Divide 25 by 5 How many lengths of 10 cm can you cut from 80 cm of tape? Is 35 a multiple of 5?
Complete written questions: with quick mental recall 16 V 2 = n 60 V n = 6 * V 5 = 7 using counters (or sharing) or a numebr line (for repeated subtraction), then mental strategies 16 V 4 = n 24 V n = 6 * V 3 = 8 using a calculator 76 V 2 = n 54 V n = 18 * V 9 = 30 Make as many different rectangles as you can from 36 square tiles.