Number Sense and SystemsKey Concept: LogicRelated Concept: Generalisation, SimplificationGlobal Context: Orientation in time and spaceFactual Concept QuestionsWhat applications are there to negative numbers? How do you subtract a negative number from a positive number? How do you find the difference between two negative numbers? How do you order integers?
How do you represent a number below zero? Debatable Concept QuestionsWhich unit of temperature is better - Kelvin, Celcius, or Fahrenheit? What is there more of: positive numbers, or both the positive and negative numbers together? ContentDirected numbers and the number line Order Integers (positive and negative) The operations of addition and subtraction with integers (positive and negative) Understand and use the definitions of expression, formula and equation Basic algebraic notation Using variables Operations used in algebra Expand and simplify expressions with single brackets Collect like terms Substitute numbers into expressions and formulae | ## Y7 Number Sense and Systems: Directed number, collecting like terms and distributive ruleY7 Number Sense and Syste...rms and distributive rule are all the positive and negative whole numbers, including zero.Integers True or False?Write down the following statements in your exercise book and state whether they are true or false, If they are false show this by giving an example:A: (-5) + (-6) If you add two negative numbers you get a negative answerB:(-5) + (+7) If you add a negative number and a positive number you get a positive answer.C:(-5) - (+4) If you subtract a positive number from a negative number you get a negative answer.D:(-5) - (-8) If you subtract a negative number from a negative number you get a positive answer.E:(+10) - (+5) If you subtract a positive number from a positive number you get a positive number.F:(+8) - (-6) If you subtract a negative number from a positive number you get a positive answer.G:5 + (-8) = 5 - (+8)Adding a negative is like subtracting a positive. H:5 - (-8) = 5 + 8 Subtracting a negative is like adding a positive.Order of OperationsWhen there is more than one mathematical operation in a calculation we have to work in a special order. step 1: Brackets step 2: Indices step 3*: Multiplication & Division step 4**: Addition & Subtraction*step 3: work out the division and multiplication in order left to right **step 4: addition and subtraction can be calculated in any order BUT you must remember the + and - signs only applies to the number directly after it. To keep it simple and avoid mistakes work left to right. Remember: show all your workingwork clearlywork vertically - show 1 step per lineuse equals signs (one per line!)AlgebraWhere does Algebra come from? by Peter, Elie and Joonas The word and ideas about algebra comes from a book called “Compendious book on Calculation and by Completion and Balancing”.It was written by a Persian mathematician called al-Khwarizmi who lived in Baghdad in 820 AD. Algebra comes from Al-Gabr which is the arabic word which means restoration or completion and he associated it in his book with a very specific operation taking something from one side of an equation to another side of an equation. There were other people who also thought of ideas like this, like the ancient babylonians from 2000 BC, Diaphantus in 200 to 300 AD in Alexandria, then there was also Brahmagupta in india at around 600 AD. (left: picture of the book from wikipedia) Algebra is the use of letters and symbols to represent numbers. An algebraic expression is a mathematical statement using algebra. An algebraic expression can contain any number of letters and arithmetic operations. An algebraic equation is a mathematical statement where two algebraic expressions are equal, expressed using an equals sign. A formula is a general rule to calculate something, expressed algebraically. A variable is a number that is represented by a letter or symbol, often called the unknown. A term is a part of an algebraic expression that is separated by + and - signs. A constant is a number that is on its own and not attached to any variable (a number that is a term on its own). A coefficient is a number that is placed directly before a variable (multiplies the variable in the term). Simplifying algebraic expressionsexamples:
Algebraic SubstitutionAlgebraic substitution is when you replace the letters with given values. a + b = ?you need to know the values of a and b to be able to work this out.so, if a = 3 and b = 11 then we substitute the values for a and b into the expression:a + b = 3 + 11 = 143a + 4b = 3(3) + 4(11) = 9 + 44= 53 4ab = 4(3)(11)= 132Questions:If a = 4, b =5 and c= 10 evaluate the following expressions:(i) 3a + 2b - c (ii) 6(a+b) (ii) a(3-b) (iv) ab + bc (v) c - 2b (vi) abc - a - b - c |

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