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Positive and negative numbers

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CONTENTS

ITEM TYPE NUMBER
The number line Workout 38 slides
The number line Library 31 questions
Once you have registered, you can work through the slides one by one. The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account. blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.

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SAMPLE FROM THE WORKOUT

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SLIDE 1 - TASK 1

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SLIDE 2 - TASK 2

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.1]

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SOLUTION

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DEPENDENCIES

129: Square numbers
line
164: Positive and negative numbers
line
166: Sums

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CONCEPTS

ITEM
 LEV.
Number line 338.1
Negative integer (implicit) 338.1
Direction 338.1
Subtraction as addition of negative number 338.3
Negative number (explicit) 338.6
Temperature scale 338.7
Thermometer 338.7
Multiple operations with negative numbers 338.9
Difference of two numbers (implicit on number line) 339.1
Size 339.3
Distance 339.3
Sum of two differences, intervals or distances 339.4
Calculating difference from two numbers 339.6
Difference of temperature 339.8
Change of direction 340.4
+ (addition) as forwards, – (subtraction) as backwards 340.4
One dimension (implicit) 340.4
Motion as steps in one dimension 340.4
– – = + 340.9
Sequence of operations with – – (double negatives) 341.1
Bracket 341.3
Bracketed negative numbers 341.3
Iterated operations with – – 341.5
Word problems with temperature 341.7

RAW CONTENT OF THE WORKOUT

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The number line SLIDE 1 This is the number line. Fill in the two missing numbers. SLIDE 2 Now extend the number line by two squares in both directions. Mark in the new numbers. SLIDE 3 Put you pen or marker at ZERO. Count up 2 What is your number? SLIDE 4 Count up 3 Count down 4 Now count down 2 Then count down 3 SLIDE 6 This is a negative number Notes for tutors A negative sign represents both a direction and the operation of subtraction. On this website we do not use a superscript to denote a negative number. SLIDE 7 The diagram shows a thermometer ? Three temperatures have been marked onto the diagram. Mark the other temperatures from to . ? What temperature is shown on the thermometer? ? If the temperature goes up by 4 degrees from the current position, what will be the new temperature? ? If the temperature goes down by 3 degrees from the current position, what will be the new temperature? SLIDE 8 The diagram shows a thermometer ? Temperatures marked on diagram ? ? ? SLIDE 9 Work out the following ? ? ? ? ? ? ? ? ? ? SLIDE 10 ? ? ? ? ? ? ? ? ? ? SLIDE 11 Write the missing numbers onto the number lines. SLIDE 12 SLIDE 13 The word difference means the size or distance between two numbers. Example 1 The difference between 3 and 15 is 12 Example 2 The difference between -5 and 15 is SLIDE 14 Fill in the missing numbers ? ? ? ? SLIDE 15 ? ? ? ? SLIDE 16 Find the difference between ? ? ? ? ? ? ? ? ? ? SLIDE 17 Find the difference between ? ? ? ? ? ? ? ? ? ? SLIDE 18 It was a cold winter’s night! ? What was the difference of temperature between Paris and Rome? ? How many degrees warmer was Rome than Berlin? ? Between which cities was the temperature difference the greatest? SLIDE 19 It was a cold winter’s night! ? Paris and Rome: , difference: . ? Rome and Berlin: difference: . ? Rome and Moscow: difference SLIDE 20 ? What was the difference of temperature between Bethel and New York? ? How many degrees warmer was Houston than Chicago? ? Between which cities was the temperature difference the smallest? SLIDE 21 ? Bethel and New York, temperature difference = ? Houston was warmer than Chicago ? The smallest temperature difference was between Chicago and New York, and is . SLIDE 22 ? ? ? ? ? ? SLIDE 23 Solve ? ? ? ? ? ? SLIDE 24 + is forwards - is backwards Go to next to make the man walk forwards +3 SLIDE 25 Go to next to make the man change direction and walk backwards three paces SLIDE 26 minus is a change of direction. minus is to turn around and face the other way Go to next to make the man turn around SLIDE 27 Go to next to make the man turn around SLIDE 28 Go to next to make the man turn around SLIDE 29 Go to next SLIDE 30 Go to next SLIDE 31 Example Exercise ? ? ? ? ? ? SLIDE 32 ? ? ? ? ? ? SLIDE 33 We sometimes use a bracket Example Exercise ? ? ? ? ? ? SLIDE 34 ? ? ? ? ? ? SLIDE 35 ? ? ? ? ? ? SLIDE 36 ? ? ? ? ? ? SLIDE 37 ? At sunset the temperature was . Overnight, the temperature fell by 7 degrees. What was the temperature in the morning? ? The temperature in San Francisco was . It was 30 degrees warmer in Mexico City. What was the temperature in Mexico City? ? The temperature in Athens was . It was 38 degrees colder in Helsinki. What was the temperature in Helsinki? SLIDE 38 ? At sunset the temperature was . Overnight, the temperature fell by 7 degrees. What was the temperature in the morning? Answer: ? The temperature in San Francisco was . It was 30 degrees warmer in Mexico City. What was the temperature in Mexico City? Answer: ? The temperature in Athens was . It was 38 degrees colder in Helsinki. What was the temperature in Helsinki? Answer: