Hot Blocks and Cold Blocks 1 hot block

Hot Blocks and Cold Blocks +1 hot block -1 cold block -n cold bar Click to add text +n hot bar

+ 1 4 Zero Pairs - 1 4 +1 +x² -1 +5 +7 -7 +3 -3 -5 +a +1 +3 p -a -1 -3 p

Show me 0 in four different ways +1 +1 -1 -1 +1 +1 +1 -1 -1 -1 +1 +1 -1 -1

Subtracting negative from positive +5 +4 +1 +1 +1 -1 -1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 0 - -1 = +1

Subtracting negative from positive +5 +4 +1 +1 +1 -1 -1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 0 - -2 = +2

Subtracting negative from positive +5 +4 +1 +1 +1 -1 -1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 0 - -3 = +3

Subtracting negative from positive +5 +4 +1 +1 -1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 0 - -4 = +4

Subtracting negative from positive +5 +4 +1 +1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 1 - -1 = +2

Subtracting negative from positive +5 +4 +1 +1 +1 -1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 1 - -2 = +3

Subtracting negative from positive +5 +4 +1 +1 -1 -1 -1 +3 +2 +1 0 -1 -2 -3 -4 -5 1 - -3 = +4

Bar Model 0 - -15 = +15 -15

1 - -15 = +16 +1 +15 -15 2 - -15 = +17 +1 +1 +15 -15

10 - -15 = +25 +10 +15 -15 30 - -15 = +45 +30 +15 -15

positive subtract negative +a - -b = a + b +a +b -b

If you subtract a negative - - the temperature goes up (+a) – (- b) when will the value of this expression be positive, negative, zero? (-a) – (- b) when will the value of this expression be positive, negative, zero?

Subtracting Positives +5 +4 +3 +1 +2 -1 0 +1 -1 -2 -3 -4 -5 0 - +1 = -1

Subtracting Positives +5 +4 +3 +2 -2 +2 +1 0 -1 -2 -3 -4 -5 0 - +2 = -2

Subtracting Positives +5 +4 +3 +3 +2 -3 0 +1 -1 -2 -3 -4 -5 0 - +3 = -3

Subtracting Positives +5 +4 +3 +n +2 -n 0 +1 -1 -2 -3 -4 -5 0 - +n = -n

Bar Model 1 - +5 = -4 +1 +5 -5 2 - +5 = -3 +1 +1 +5 -5

Bar Model 2 - +20 = -18 +1 +1 +20 -20

Bar Model 3 - +57 = -54 +3 +57 -57

Bar Model a - +b = a + - b +a +b -b

If you subtract a positive - + the temperature goes down (+a) – (+ b) when will the value of this expression be positive, negative, zero? (-a) – (+ b) when will the value of this expression be positive, negative, zero?

Subtracting + and - - + 3 - - 8 2 - - y Hotter or Colder? - - 2 - - 0. 2 - - 5 - + 7 - + mn - + ½

Subtracting + and - -a- - c m-+ n -1 - + 3 -2 - - 8 Hotter or Colder? 1 - - 0. 2 3 - - 5 x-- y 4 - - 2 3 - + 7 ¾ - + ½

Positive or Negative? -7 - - 2 3 - -2 -5 - -12 -4 - 7 8 - 2 2 - 9 -245 - 157 -4 m - 2 m 172 - -87 7 a - -2 a

Subtraction to Addition 3 - -1 = 4 +1 +1 3 + 1 = 4 +1 +1 -1 a - -b +a a + b +b -b +a +b

Subtraction to Addition -a - -b -a + b +b -a +b -b -a -a - -b +b -a -b -a + b +b -a

Subtraction to Addition a - +b a + -b +a +b -b a - +b +a +a -b a + - b +b -b +a -b

Subtraction to Addition -a - +b -a + -b +b -a -b

Show me that these questions have the same answer. . . 3 – +1 = 2 +3 3 + -1 = 2 +1 -1 +3 -1 Subtract is the same as adding the opposite

5 – +2 = 5 + -2 = 3 5 subtract pos 2 is the same as 5 add opp 2 6 - +3 = 6 + -3 = 3 6 subtract pos 3 is the same as 6 add opp 3 7 - +5 = 7 + -5 = 2 7 subtract pos 7 is the same as 7 add opp 5 321 - +156 = 321 + -156 = 165 321 subtract pos 156 is the same as 321 add opp 156 t – +t = t + -t = 0 t subtract pos t is the same as t add opp t 5 t – +3 t = 5 t + - 3 t = 2 t 5 t subtract pos 3 t is the same as 5 t add opp 3 t

-3 – +5 = - 3 + -5 = -8 opp 3 subtract pos 5 is the same as opp 3 add opp 5 -2 – +7 = -2 + -7 = -9 opp 2 subtract pos 7 is the same as opp 2 add opp 7 -4 – +9 = -4 + -9 = -13 opp 4 subtract pos 9 is the same as opp 4 add opp 9 -t – +t = -t + - t = -2 t opp t subtract pos t is the same as opp t add opp t -2 t – +8 t = -2 t + -8 t = -10 t opp 2 t subtract pos 8 t is the same as opp 2 t add opp 8 t

5 – -2 = 5 + +2 = 7 5 subtract opp 2 is the same as 5 add pos 2 6 - -3 = 6 + +3 = 9 6 subtract opp 3 is the same as 6 add pos 3 7 - -5 = 7 + +5 = 12 7 subtract opp 7 is the same as 7 add pos 5 321 - -156 = 321 + +156 = 477 321 subtract opp 156 is the same as 321 add pos 156 t – -t = t + +t = 2 t t subtract opp t is the same as t add pos t 5 t – -3 t = 5 t + +3 t = 8 t 5 t subtract opp 3 t is the same as 5 t add pos 3 t

Equivalent expressions a - + b -a - + b a - - b -a - - b a - b -a + - b

a and b are positive integers -a + b -a - b always positive negative when b < a positive when a > b negative when a < b always negative positive when b > a

a and b are positive integers -a + b positive when b > a negative when b < a a + b always positive -a - b always negative a - b negative when a < b positive when a > b