mr barton maths

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Adding and Subtracting Negative Numbers

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Foundational skills
Understand adding a negative
\[ 3 + (-5) \rightarrow \text{Left} \]
Recognise that adding a negative number means moving left.
Understand subtracting a negative
\[ 2 – (-4) \rightarrow \text{Right} \]
Recognise that subtracting a negative number means moving right.
Rewrite adding a negative
\[ 7 + (-3) \rightarrow 7 – 3 \]
Convert an addition of a negative number into an equivalent subtraction.
Rewrite subtracting a negative
\[ 5 – (-2) \rightarrow 5 + 2 \]
Convert a subtraction of a negative number into an equivalent addition.
Subtracting to cross zero
Subtract to get negative (small)
\[ 3 – 7 = -4 \]
Subtract a larger number from a smaller positive number.
Subtract to get negative (large)
\[ 12 – 19 = -7 \]
Subtract a larger number from a smaller positive number with larger values.
Subtract from zero
\[ 0 – 8 = -8 \]
Subtract a positive number from zero.
Adding positive and negative
Add pos + neg (result positive)
\[ 9 + (-4) = 5 \]
Positive has greater absolute value.
Add pos + neg (result negative)
\[ 3 + (-8) = -5 \]
Negative has greater absolute value.
Add pos + neg (result zero)
\[ 6 + (-6) = 0 \]
Add opposites.
Add neg + pos (result positive)
\[ (-5) + 12 = 7 \]
Positive has greater absolute value.
Add neg + pos (result negative)
\[ (-11) + 4 = -7 \]
Negative has greater absolute value.
Adding two negatives
Add two negatives (small)
\[ (-3) + (-5) = -8 \]
Add two negative integers.
Add two negatives (larger)
\[ (-8) + (-13) = -21 \]
Add larger negative integers.
Subtracting – positive minus negative
Positive minus negative (small)
\[ 4 – (-3) = 7 \]
Subtract a negative from a positive.
Positive minus negative (large)
\[ 12 – (-7) = 19 \]
Subtract a negative from a positive (larger).
Subtracting – negative minus positive
Negative minus positive (more neg)
\[ (-4) – 5 = -9 \]
Subtract a positive from a negative.
Negative minus positive (larger)
\[ (-7) – 12 = -19 \]
Subtract a larger positive from a negative.
Subtracting – negative minus negative
Neg minus Neg (result negative)
\[ (-9) – (-4) = -5 \]
Result remains negative.
Neg minus Neg (result positive)
\[ (-3) – (-8) = 5 \]
Result becomes positive.
Neg minus Neg (result zero)
\[ (-7) – (-7) = 0 \]
Subtracting number from itself.
Missing number problems
Add: Positive + □ = Result
\[ 8 + \Box = 3 \]
Find negative missing addend.
Add: Negative + □ = Result
\[ (-6) + \Box = -2 \]
Find missing number (pos/neg).
Sub: □ – Positive = Negative
\[ \Box – 7 = -3 \]
Find start number.
Sub: Negative – □ = Result
\[ (-5) – \Box = -9 \]
Find missing subtrahend.
Multiple operations
Add 3 integers
\[ 5 + (-8) + 3 \]
Includes at least one negative.
Mixed add/sub with negatives
\[ 4 – 7 + 2 \]
Crossing zero.
Mixed ops with multiple negatives
\[ (-3) + (-4) – (-2) \]
Includes subtracting a negative.
Four integers
\[ 2 – 5 + 8 – 6 \]
Mixed operations.
Decimals – adding
Pos + Neg Decimal (Positive)
\[ 4.5 + (-2.3) \]
Result is positive.
Pos + Neg Decimal (Negative)
\[ 2.4 + (-5.7) \]
Result is negative.
Add two negative decimals
\[ (-3.2) + (-4.6) \]
Result is more negative.
Decimals – subtracting
Pos – Neg Decimal
\[ 5.8 – (-2.4) \]
Result is positive addition.
Neg – Pos Decimal
\[ (-3.5) – 2.7 \]
Result is more negative.
Neg – Neg Decimal
\[ (-6.4) – (-2.9) \]
Mixed result.
Special cases
Add opposites
\[ 15 + (-15) \]
Number + its opposite.
Difference between pos and neg
\[ 7 – (-7) \]
a – (-a).
Subtract from negative to get 0
\[ -12 + \Box = 0 \]
Additive inverse.
Timer (Optional)
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