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Negative Numbers in Context
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Foundational skills
Recognise negative temperature
\[ \text{Example: } -5^\circ\text{C} \]
Understand that a negative temperature means below zero or below freezing.
Recognise negative money
\[ \text{Example: } -\text{£}30 \]
Understand that a negative bank balance means owing money or being in debt.
Recognise negative position
\[ \text{Example: Floor } -2 \]
Understand that a negative floor number means below ground level.
Identify colder (neg vs neg)
\[ -8^\circ\text{C} \text{ or } -3^\circ\text{C?} \]
Recognise that the more negative temperature is colder.
Identify colder (pos vs neg)
\[ 2^\circ\text{C} \text{ or } -4^\circ\text{C?} \]
Recognise that negative temperatures are colder than positive temperatures.
Temperature – reading
Read negative thermometer
\[ \text{Example: } -7^\circ\text{C} \]
Read a negative value from a thermometer diagram.
Read thermometer crossing zero
\[ -10 \dots 0 \dots 10 \]
Read a value from a thermometer that shows both positive and negative values.
Temperature – decrease resulting in negative
Temp drop (pos to neg)
\[ 4^\circ\text{C} \text{ falls by } 9^\circ\text{C} \]
Work out the temperature after a decrease that crosses zero into negative values.
Temp drop (neg to more neg)
\[ -3^\circ\text{C} \text{ falls by } 5^\circ\text{C} \]
Work out the temperature after a decrease when already negative.
Temperature – increase from negative
Temp rise (stay neg)
\[ -7^\circ\text{C} \text{ rises by } 4^\circ\text{C} \]
Work out the temperature after an increase when starting from negative.
Temp rise (neg to pos)
\[ -6^\circ\text{C} \text{ rises by } 10^\circ\text{C} \]
Work out the temperature after an increase that crosses zero from negative to positive.
Temperature – finding the change
Change (both pos)
\[ 3^\circ\text{C} \rightarrow 11^\circ\text{C} \]
Find the increase in temperature when both values are positive.
Change (both neg)
\[ -9^\circ\text{C} \rightarrow -4^\circ\text{C} \]
Find the increase in temperature when both values are negative.
Change (neg to pos)
\[ -5^\circ\text{C} \rightarrow 3^\circ\text{C} \]
Find the increase in temperature when crossing from negative to positive.
Drop (pos to neg)
\[ 6^\circ\text{C} \rightarrow -4^\circ\text{C} \]
Find the decrease in temperature when crossing from positive to negative.
Temperature – difference
Difference (neg vs neg)
\[ \text{Diff: } -2^\circ\text{C} \text{ and } -9^\circ\text{C} \]
Calculate the positive difference between two negative temperatures.
Difference (pos vs neg)
\[ \text{Diff: } -7^\circ\text{C} \text{ and } 5^\circ\text{C} \]
Calculate the positive difference between a negative and positive temperature.
Money
Interpret balance
\[ -\text{£}45 \rightarrow \text{owes?} \]
Convert a negative balance into a positive amount owed.
Spending (pos to neg)
\[ \text{£}25 \text{ – spend } \text{£}40 \]
Work out bank balance after spending more than available.
Spending (neg to more neg)
\[ -\text{£}20 \text{ – spend } \text{£}15 \]
Work out bank balance after spending when already in debt.
Deposit (stay neg)
\[ -\text{£}35 \text{ + deposit } \text{£}20 \]
Work out bank balance after deposit when in debt.
Deposit (neg to pos)
\[ -\text{£}30 \text{ + deposit } \text{£}50 \]
Work out bank balance after deposit that clears debt and leaves positive balance.
Floors and lifts
Lift up (stay below)
\[ -3 \text{ up } 2 \]
Work out the new floor after a lift goes up from a basement level.
Lift up (to above)
\[ -2 \text{ up } 5 \]
Work out the new floor after a lift goes up from basement to above ground.
Lift down (to below)
\[ 3 \text{ down } 5 \]
Work out the new floor after a lift goes down from above ground to basement.
Floors travelled
\[ -2 \rightarrow 4 \]
Work out the number of floors between a basement level and above ground.
Sea level and depth
Dive deeper
\[ -12\text{m} \text{ down } 8\text{m} \]
Work out new depth after descending further below sea level.
Ascend (stay under)
\[ -25\text{m} \text{ up } 10\text{m} \]
Work out new depth after rising towards the surface.
Ascend to surface
\[ -18\text{m} \text{ up } 18\text{m} \]
Work out position after rising exactly to sea level.
Depth difference
\[ -8\text{m} \text{ and } -23\text{m} \]
Find the vertical distance between two underwater positions.
Other contexts
Golf scores
\[ -3 \rightarrow +2 \]
Work out the change in golf score (under/over par) between two points.
Timeline BC/AD
\[ 45 \text{ BC} \rightarrow 30 \text{ AD} \]
Work out the number of years spanning BC (negative) and AD (positive) dates.
Special cases
Multi-step temp
\[ -4 \text{ rise } 9 \text{ fall } 5 \]
Solve a problem with multiple temperature changes.
Multi-step money
\[ -\text{£}40 \text{ earn } \text{£}65 \text{ spend } \text{£}30 \]
Solve a problem with multiple money transactions.
Find start temp
\[ ? \text{ rise } 7 \rightarrow 3 \]
Work backwards to find the original temperature before a change.
Find change
\[ -6 \rightarrow 2 \]
Work out the direction and size of change between two temperatures.
Timer (Optional)
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