 Recognise odd and even numbers up to 1000, and some of their properties, including the outcomes of sums or differences of pairs of odd/even numbers

Examples of what pupils should know and be able to do
Explore and give examples to satisfy these statements.
 The last digit of an even number is 0, 2, 4, 6 or 8.
 After 1, every second number is odd.
 If you add two odd numbers the answer is even.
 Primary mathematics exemplification: Properties of numbers
Probing questions
 Are all numbers ending in 4 even?
 How do you know if a number is even?
 If I divide an even number by 2 will I always get a wholenumber answer? What if I divide an odd number by 2?
What if pupils find this a barrier?
 Explore properties of odd and even numbers: for example, an odd number + an odd number will make an even number.
 Make links between even numbers and multiples of two.
 Use Mathematics ITP: Number grid (SWF60 KB) Attachments to look at patterns.
 Describe and extend number sequences: count on or back in tens or hundreds, starting from any two or threedigit number

Examples of what pupils should know and be able to do
First with and then without a 1–100 grid:
 count on in tens from 30 … from 26
 count on in 40s from 30 … from 27.
Without a grid:
 count back in 20s from 140 … from 153
 count back in 30s from 160 … from 145.
Counting in tens
Respond to questions such as:
 Count on and back in tens, crossing 100.
 Count on 40 in tens: from 30, from 27, from 480, from 652…
 Count back 40 in tens:from 80, from 72, from 590, from 724…
 Count on in tens from 36 to 76. How many tens did you count?
 Count back in tens from 84 to 34. How many tens did you count?
Counting in hundreds
Respond to questions such as:
 Count on or back 400 in hundreds: from 500, from 520, from 570…
 Count on in hundreds from 460 to 960. How many hundreds did you count?
 Count back in hundreds round the circle of children, starting at Jo with 970. Who will say 370?
 Describe these sequences: 256, 356, 456, 556… 421, 431, 441, 451… Write the next three numbers in each sequence.
Use, read and begin to write: odd, even, sequence, predict, continue, rule, relationship…
Count from 0 or 1 in steps of two to about 50. Count back again.
Respond to questions such as:
 Is 74 odd or even? How do you know?
 Test whether 75 is odd or even. Now try all the numbers from 75 to 95. What do you notice?
 Ring the odd numbers: 65 70 77 88 91 94
 Continue these sequences: 35, 37, 39, 41… 68, 66, 64… Describe each pattern
 What odd number comes before 91? After 69?
Make general statements about odd or even numbers such as:
 an even number ends in 0, 2, 4, 6 or 8
 an odd number ends in 1, 3, 5, 7 or 9
 if you add two even numbers the answer is even
 if you add two odd numbers the answer is even.
Respond to questions such as:
 Count on from any small number in steps of 2, 3, 4, 5, 10 or 100, and then back.
 Use a number grid computer program to display multiples of 2, 5, 10… on a $10\times 10$ grid, and describe the patterns made.
 Take a $5\times 5$ number grid. Count on in threes from 1. Colour numbers you land on. What do you notice?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 If you went on, would 28 be in your sequence? Or 40? How do you know?
What would happen if you started at 2? Would the pattern be the same?
Now try a $6\times 6$ number grid. Try steps of 4 and 5.
 2, 7, 12, 17… 78, 76, 74, 72… Describe each pattern. What is the rule? What are the next three numbers in each sequence?
 Fill in the missing numbers in this sequence: 5, 9, □, 17, 21, □, □
Create sequences with a given constraint: for example, make a sequence which has the numbers 7 and 16 in it.
Use, read and begin to write: multiple.
Recognise that multiples of:
 100 end in 00
 50 end in 00 or 50
 10 end in 0
 5 end in 0 or 5
 2 end in 0, 2, 4, 6, 8
Respond to questions such as:
 Ring the numbers which are multiples of 5: 15 35 52 55 59 95
 Count in 50s to 1000, then back to zero. Write three different multiples of 50.
 What is the multiple of 10 before 140? What is the multiple of 100 after 500? What is the next multiple of 5 after 195?
Probing questions
 If you count in tens from 42, which digit changes? Why doesn't the ones digit change?
 If you start with 93 and count back in tens, what would be the smallest number you would reach on a 1–100 grid? Would 14 be one of the numbers you say? Why not?
 What do you notice when I subtract 10 from a number? Can you explain?
What if pupils find this a barrier?
 Give pupils a 1–100 grid and ask them to start from 5 and chant all the numbers moving vertically down the column. What is the same and what is different about these numbers? Why?
 Start at 92 and move vertically up. What is happening now?
 Repeat for different numbers.
 Continue without the grids, counting on and back in tens and hundreds. Make this a regular feature of prestarters for lessons.
Mathematics ITP: Number grid (SWF60 KB) Attachments is useful for counting on and back in tens.
 Mathematics ITP: Counting on and back (SWF26 KB) Attachments
 Mathematics ITP: Number line (SWF39 KB) Attachments
 Mathematics ITP: Place value (SWF18 KB) Attachments
Attachments
Related downloads
 Mathematics ITP: Number grid
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 60 KB ]
 Mathematics ITP: Counting on and back
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 26 KB ]
 Mathematics ITP: Number line
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 39 KB ]
 Mathematics ITP: Place value
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 18 KB ]
 Download all [ 82 KB ]