Directed Numbers Adding Subtracting Demonstration This resource provides

Directed Numbers – Adding & Subtracting – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

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Tim’s cauldron is filled with ice cubes & fire cubes. The temperature is 5°C. − 10 − 5 0 5 10

If we add a fire cube … 5 + +1 = 6 − 10 − 5 0 5 10

If we subtract 8 fire cubes … 6 − +8 = − 2 − 10 − 5 0 5 10

Try these! Subtract 7 fire cubes … 3 − +7 = − 4 Subtract 7 fire cubes … 2 − +7 = − 5 Subtract 4 fire cubes … 0 − +4 = − 4 Subtract 4 fire cubes … − 2 − +4 = − 6 Subtract 9 fire cubes … − 8 − +9 = − 17

Try these! Subtract 7 fire cubes … 3 − +7 = − 4 Subtract 7 fire cubes … 2 − +7 = − 5 Subtract 4 fire cubes … 0 − +4 = − 4 Subtract 4 fire cubes … − 2 − +4 = − 6 Subtract 9 fire cubes … Subtracting a positive number is simple subtraction! − 8 − +9 = − 17

If we add an ice cube … 5 + − 1 = 4 − 10 − 5 0 5 10

If we add 2 ice cubes … 4 + − 2 = 2 − 10 − 5 0 5 10

If we add 6 ice cubes … 2 + − 6 = − 4 − 10 − 5 0 5 10

If we add 2 ice cubes … − 4 + − 2 = − 6 − 10 − 5 0 5 10

Try these! Add 6 ice cubes … 5 + − 6 = − 1 Add 6 ice cubes … 3 + − 6 = − 3 Add 5 ice cubes … 0 + − 5 = − 5 Add 5 ice cubes … − 2 + − 5 = − 7 Add 9 ice cubes … − 9 + − 9 = − 18

Try these! Add 6 ice cubes … 5 + − 6 = − 1 Add 6 ice cubes … 3 + − 6 = − 3 Add 5 ice cubes … 0 + − 5 = − 5 Add 5 ice cubes … − 2 + − 5 = − 7 Add 9 ice cubes … Adding a negative number means subtraction! − 9 + − 9 = − 18

If we subtract 5 ice cubes … If we subtract coldness it must get hotter! 5 − − 5 = 10 − 5 0 5 10

If we subtract 4 ice cubes … 5 − − 4 = 9 − 10 − 5 0 5 10

If we subtract 6 ice cubes … 0 − − 6 = 6 − 10 − 5 0 5 10

If we subtract 8 ice cubes … − 5 − − 8 = 3 − 10 − 5 0 5 10

Try these! Subtract 3 ice cubes … 5 − − 3 = 8 Subtract 3 ice cubes … 4 − − 3 = 7 Subtract 4 ice cubes … 0 − − 4 = 4 Subtract 4 ice cubes … − 4 − − 4 = 0 Subtract 12 ice cubes … − 7 − − 12 = 5

Try these! Subtract 3 ice cubes … 5 − − 3 = 8 Subtract 3 ice cubes … 4 − − 3 = 7 Subtract 4 ice cubes … 0 − − 4 = 4 Subtract 4 ice cubes … − 4 − − 4 = 0 Subtract 12 ice cubes … Subtracting a negative number means addition! − 7 − − 12 = 5

Tim’s Temperature Cauldron What is the temperature of each cauldron? = ____ A = ____ ① = ____ What is the temperature of the cauldron? If you subtract 2 fire cubes , what is the new temperature? (Cross out the fire cubes) Write this as a calculation: B What is the temperature of the cauldron? If you add 3 ice cubes , what is the new temperature? (Draw the cubes) Write this as a calculation: C What is the temperature of the cauldron? If you subtract 5 ice cubes , what is the new temperature? (Cross out the ice cubes) Write this as a calculation: Write a rule to describe the calculation in each question: Question A, Question B & Question C.

Tim’s Temperature Cauldron ② Use the cauldrons to answer the calculations (cross out or add cubes). a) b) 2 − (+2) = 0 d) c) − 3 − (+2) = − 5 e) − 2 + (+3) = 1 g) f) − 6 + (− 3) = − 9 h) 5 − (− 4) = 9 j) 4 + (− 6) = − 2 − 7 − (− 3) = − 4 1 + (+3) + (− 2) = 2 i) − 8 + (− 8) = − 16 k) − 4 − (+6) = − 10 − 7 − (− 8) + (+3) = 4 l) − 8 − (− 2) = − 6 You may want to rewrite these calculations to solve them in stages. m) 4 − (− 2) + (− 4) = 2 n) − 6 + (− 2) − (− 3) + 2 = − 3 o) − 5 − − 3 + 4 − − 3 = 5 p) 6 + 5 − 12 − − 3 + − 8 = − 6

Tim’s Temperature Cauldron What is the temperature of each cauldron? +3 = ____ A ① − 4 = ____ +1 = ____ What is the temperature of the cauldron? 4 If you subtract 2 fire cubes , what is the new temperature? (Cross out the fire cubes) Write this as a calculation: B 4 − +2 = 2 What is the temperature of the cauldron? 4 If you add 3 ice cubes , what is the new temperature? (Draw the cubes) Write this as a calculation: C 4 1 4 + − 3 = 1 − 2 What is the temperature of the cauldron? If you subtract 5 ice cubes , what is the new temperature? (Cross out the ice cubes) Write this as a calculation: 2 − − 5 = 3 Write a rule to describe the calculation in each question: Question A, Question B & Question C. Answers

Tim’s Temperature Cauldron ② Use the cauldrons to answer the calculations (cross out or add cubes). a) b) 2 − (+2) = 0 d) c) − 3 − (+2) = − 5 e) − 2 + (+3) = 1 g) f) − 6 + (− 3) = − 9 h) 5 − (− 4) = 9 j) 4 + (− 6) = − 2 − 7 − (− 3) = − 4 1 + (+3) + (− 2) = 2 i) − 8 + (− 8) = − 16 k) − 4 − (+6) = − 10 − 7 − (− 8) + (+3) = 4 l) − 8 − (− 2) = − 6 You may want to rewrite these calculations to solve them in stages. m) 4 − (− 2) + (− 4) = 2 n) − 6 + (− 2) − (− 3) + 2 = − 3 o) − 5 − − 3 + 4 − − 3 = 5 p) 6 + 5 − 12 − − 3 + − 8 = − 6 Answers

Tim’s Temperature Cauldron What is the temperature of each cauldron? = ____ A B C = ____ Tim’s Temperature Cauldron What is the temperature of each cauldron? ① = ____ What is the temperature of the cauldron? = ____ A = ____ If you subtract 2 fire cubes , what is the new temperature? (Cross out the fire cubes) Write this as a calculation: B What is the temperature of the cauldron? If you add 3 ice cubes , what is the new temperature? (Draw the cubes) Write this as a calculation: What is the temperature of the cauldron? C What is the temperature of the cauldron? If you subtract 5 ice cubes , what is the new temperature? (Cross out the ice cubes) Write this as a calculation: Write a rule to describe the calculation in each question: Question A, Question B & Question C. = ____ What is the temperature of the cauldron? If you subtract 2 fire cubes , what is the new temperature? (Cross out the fire cubes) What is the temperature of the cauldron? ① Write a rule to describe the calculation in each question: Question A, Question B & Question C.

Tim’s Temperature Cauldron ② Use the cauldrons to answer the calculations (cross out or add cubes). a) b) 2 − (+2) = 0 d) c) − 3 − (+2) = − 5 e) − 2 + (+3) = 1 g) h) 5 − (− 4) = 9 j) 4 + (− 6) = − 2 a) − 7 − (− 3) = − 4 f) − 6 + (− 3) = − 9 k) − 4 − (+6) = − 10 b) 2 − (+2) = 0 d) 1 + (+3) + (− 2) = 2 i) − 8 + (− 8) = − 16 Tim’s Temperature Cauldron ② Use the cauldrons to answer the calculations (cross out or add cubes). − 3 − (+2) = − 5 e) − 2 + (+3) = 1 g) 5 − (− 4) = 9 l) − 8 − (− 2) = − 6 j) 4 + (− 6) = − 2 − 7 − (− 3) = − 4 f) − 6 + (− 3) = − 9 h) − 7 − (− 8) + (+3) = 4 You may want to rewrite these calculations to solve them in stages. c) 1 + (+3) + (− 2) = 2 i) − 8 + (− 8) = − 16 k) − 4 − (+6) = − 10 − 7 − (− 8) + (+3) = 4 l) − 8 − (− 2) = − 6 You may want to rewrite these calculations to solve them in stages. m) 4 − (− 2) + (− 4) = 2 n) − 6 + (− 2) − (− 3) + 2 = − 3 o) − 5 − − 3 + 4 − − 3 = 5 p) 6 + 5 − 12 − − 3 + − 8 = − 6

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk