Download Ordering, including positive and negative numbers

Ordering, including positive and negative numbers
Year 6 Spring 2
Round whole numbers to the nearest 10, 100 or 1000
Previous learning
Core for Year 6
Extension
Understand, read and begin to write these words:
Understand, read and write these words:
Understand, read and write these words:
order, more than, less than, smallest, largest, …
round, nearest, … half way between, … estimate, ...
order, more than, less than, ascending, descending, …
round, nearest, … half way between, … estimate, ...
order, more than, less than, ascending, descending, …
round, nearest, … half way between, … estimate, ...
Round four-digit numbers to the nearest 10, 100 or 1000, e.g.
Revise rounding numbers to the nearest 10, 100 or 1000, e.g.
Understand and use the rules for rounding whole numbers.
• 4836 is 5000 to the nearest 1000,
because 4836 is nearer to 5000 than 4000.
4836 is 4800 to the nearest 100,
because 836 is nearer to 800 than to 900.
4836 is 4840 to the nearest 10,
because 36 is nearer to 40 than to 30.
• To round 3627:
If the first unwanted digit is 5, 6, 7, 8 or 9, add 1 to the last
digit that you keep. Then replace all the unwanted digits by
zeros, e.g.
When rounding, round up numbers that are half way between
two multiples to the higher multiple, so:
8500 rounds up to 9000 to the nearest 1000;
7250 rounds up to 7300 to the nearest 100;
6175 rounds up to 6180 to the nearest 10.
Sketch a line from 3620 to 3630 and mark on 3627.
Ring the nearest multiple of 10.
So 3627 rounds to 3630 to the nearest 10.
Sketch a line from 3600 to 3700 and mark on 3627.
Ring the nearest multiple of 100.
So 3627 rounds to 3600 to the nearest 100.
5621 rounded to the nearest 100 is 5600;
26 900 rounded to the nearest 1000 is 30 000
Respond to questions such as:
• Round 56 275 to the nearest 100.
• How long is the rope to the nearest 10 cm? The nearest
cm? The nearest 100 cm? The nearest mm?
Sketch a line from 3000 to 4000 and mark on 3627.
Ring the nearest multiple of 1000.
So 3627 rounds to 4000 to the nearest 1000.
Estimate where four-digit numbers lie on an empty 0 to 10 000 line
Previous learning
Core for Year 6
Estimate where numbers lie on an empty 0 to 1000 line.
Estimate where numbers lie on an empty 0 to 10 000 line.
This line is marked in hundreds.
Draw an arrow to show the position for 250.
Estimate where these numbers go:
450, 220, 760, 190… Label each number.
• Now estimate the number the arrow is pointing to?
Between which multiples of 100 might it lie?
Which of these multiples is it nearer to?
Extension
• This line is marked in thousands.
Draw an arrow to show the position for 7500.
Now estimate where these numbers go:
7500, 2700, 4500, 1900… Label each number.
• Now estimate the number the arrow is pointing to?
Between which multiples of 1000 might it lie?
Which of these multiples is it nearer to?
© 1 | Year 6 | Spring TS2 | Ordering, including positive and negative numbers
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Count on and back in repeated steps, including through zero
Previous learning
Core for Year 6
Extension
Use, read and begin to write these words:
Use, read and write these words:
Use, read and write these words:
positive number, negative number, …
plus, minus, above zero, below zero, …
count on, count back, sequence, step, rule, …
positive number, negative number, integer, …
plus, minus, above zero, below zero, …
count on, count back, sequence, step, rule, …
positive number, negative number, integer, …
plus, minus, above zero, below zero, …
count on, count back, sequence, step, rule, …
Count back through zero, e.g. in steps of –1:
Count back through zero in steps of constant size, e.g.
Count back through zero in steps of constant size, e.g.
• Start at 11 and count in steps of –5:
• Start at 0.2 and count in steps of –0.1:
three, two, one, zero, negative one, negative two, …
Recognise negative answers on a calculator, e.g.
• Enter 15 – 20 on a calculator and interpret the display
as –5.
- 5.
eleven, six, one, negative four, negative nine, negative
fourteen, negative nineteen, …
nought point two, nought point one, zero, negative nought
point one, negative nought point two, …
• Start at –27 and count in steps of +2.
• Start at – 1.5 and count in steps of +0.2.
• Hayley makes a sequence of numbers starting with 100.
She subtracts 45 each time.
Write the next two numbers in the sequence.
• Ahmed makes a sequence of numbers.
He chooses a starting number and then subtracts equal
amounts each time.
The third number in his sequence is 45.
The tenth number is –32.
100
55
10
F
F
• A sequence starts at 500 and 80 is subtracted each time.
500
420
340
...
45
-32
What is the first number in the sequence?
Write the first two negative numbers in the sequence.
Order a set of positive and negative integers
Previous learning
Core for Year 6
Extension
Recognise and use positive and negative whole numbers on
a temperature scale, e.g.
Order a set of positive and negative temperatures,
e.g.
• What temperature does this thermometer show?
• Which temperature is colder: –4°C or –2°C?
• Write these temperatures in order from hottest to coldest.
92°C
37°C
–12°C
73°C
12°C
–2°C
Order positive and negative integers on a number line,
e.g.
Order positive and negative integers on a number line,
e.g.
Order a set of positive and negative numbers.
e.g.
• Fill in the missing numbers on this part of the number line.
• Draw an arrow to point to –2.
• What number is the arrow pointing to?
© 2 | Year 6 | Spring TS2 | Ordering, including positive and negative numbers
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 6
Extension
Order a set of positive and negative numbers, e.g.
Order a set of positive and negative integers, e.g.
Order a set of positive and negative integers, e.g.
•
• Put these numbers in order, least first:
• Put these numbers in order, least first:
Put these shuffled cards (from –15 to 5) in order.
–2
–8
–1
–6
–37
–4
4
29
–4
–28.
Find the difference between a positive and a negative integer, and between two negative integers, in a context such as temperature or on a number line
Previous learning
Core for Year 6
Extension
Calculate a rise or fall in temperature, e.g.
Find the difference between a positive and a negative
integer, and between two negative integers, in a context such
as temperature, e.g.
Find the difference between a positive and a negative
integer, and between two negative integers, in a context such
as a number line, e.g.
• The temperature rises by 15 degrees. Mark the new
temperature reading on the thermometer.
• The temperatures were:
• A and B are two numbers on the number line below.
inside
outside
–2°C
–7°C
What is the difference between these two temperatures?
• The temperature in York is 4°C.
Rome is 7 degrees colder than York.
What is the temperature in Rome?
• What temperature is 10 degrees higher than –8°C?
• The temperature is –3°C.
How much must it rise to reach 5°C?
• The temperature is –5 °C. It falls by 6 degrees.
What is the temperature now?
• The temperature is –11 °C. It rises by 2 degrees.
What is the temperature now?
The difference between A and B is 140.
Write the values of A and B.
• Circle two numbers with a difference of 8.
–5
• The temperature at the North Pole is –20 °C.
How much must it rise to reach –5 °C?
© 3 | Year 6 | Spring TS2 | Ordering, including positive and negative numbers
–4
–3
–2
–1
0
1
2
3
4
5
• Write two numbers with a sum of –6.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999