Fractions: TG4A Unit 5 p Express, interpret, read, draw and mark mixed numbers on a number
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1 The foundations of fractions are laid in Inspire Maths 1 by analyzing parts and whole using the part-whole strategy. This appears throughout IM1A and IM1B. Fractions: TG2B Unit 12 p56 Key concepts: Understanding fractions by using shapes to represent one whole with denominators up to 12 and write fractions with denominators up to 12 from given shapes. Fractions: TG3B Unit 14 p116 - Numerator and denominator: Fractions: TG4A Unit 5 p Express, interpret, read, draw and mark mixed numbers on a number line and as region models (translating pictorial representations of mixed numbers to symbolic and vice versa). Fractions (1): TG5A Unit 3 p116 - Identifying and differentiating like and unlike fractions: Fractions: TG6A Unit 4 p106 - Four operations with fractions - Dividing by a proper fraction: dividing a whole number by a proper fraction, dividing a proper fraction by a proper fraction - Using model drawing as a concept to represent fraction contexts: - Understanding equivalent fractions using a fraction strip (paper) to show equal parts and write equivalent parts of a given fraction with the help of a model drawing: - Express, interpret, read, draw and mark improper fractions on a number line and as region models (translating pictorial representations of improper fractions to symbolic and vice versa): - part: TG1A p32 - whole: TG1A p32 - Adding unlike fractions by making a systematic list of the multiples of the denominator and by drawing a model: Ratio: TG6A Unit 5 p145 - Ratio and fraction: write and express ratio by comparing and analyzing parts and wholes (values): (1) - Write equivalent fractions of a given fraction using the multiplying/dividing factor technique expressing in its simplest form. - Subtracting unlike fractions by making a systematic list of the multiples of the denominator and by drawing a model 1 Progression chart Fractions, percentages and decimals Oxford University Press
2 Progression of Key Concepts in Inspire Maths Inspire Maths 1 Inspire Maths 2 Inspire Maths 3 Inspire Maths 4 Inspire Maths 5 Inspire Maths 6 - Compare and order two or more fractions with the same denominator using rectangular strips or model drawings of the same size: - Comparing fractions using the equivalent fraction method: - Conversion of fractions relating improper fractions to mixed numbers and converting between the two by separating an improper fraction into a whole and part of a whole, or by division, or by multiplication: - Adding related fractions (the related fractions are changed to like fractions first). - Compare and order two or more fractions with different denominators using rectangular strips or model drawings of the same size. - Adding and subtracting like fractions. - Solving word problems by recalling and applying part-whole and adding on concepts in addition of two fractions using model drawing. Recalling and applying part-whole and taking away concepts in subtraction of fractions using model drawing. - Subtracting related fractions (the related fractions are changed to like fractions first). - Adding and subtracting fractions: add two or three related fractions, subtract two related fractions, subtract a fraction from a whole number: - Fractions and division: a whole number when divided by another whole number can result in a whole number with or without a remainder, a proper fraction or a mixed number: - Converting fractions to decimals: converting tenths, hundredths and thousandths, converting using long division, converting improper fractions and mixed numbers 2 Percentage: TG6A Unit 6 p197 - numerator: TG3B p116 denominator: TG3B p116 equivalent faction: TG3B p117 simplest form: TG3B p122 portion: TG3B p123 common denominator: TG3B p126 common numerator: TG3B p127 express: TG3B p129 - Adding mixed numbers with or without regrouping (1) (2) fractions: TG2B p56 equal part: TG2B p56 Progression chart Fractions, percentages and decimals (2) - Finding percentages: express a fraction or a decimal as a percentage and vice versa, analyze the parts and whole to express the percentage giving the number of parts: - - Comparing ratios: Oxford University Press
3 - unequal: TG2B p56 - whole: TG2B p57 - fractional parts: TG2B p61 - fractions (one-half to one-twelfth): TG2B p61 - fraction story: TG2B p67 - like fractions: TG2B p74 - Fractions of a set: - Subtracting mixed numbers with or without regrouping - unitary method: TG6A p175 Decimals (1): TG4B Unit 9 p6 - Understanding tenths: Fractions (2): TG5A Unit 4 p168 - Product of proper fractions: multiplying two fractions is the same as finding the fractional part of another fraction; conceptualizing the meaning of multiplying two proper fractions with concrete representation; use of the cancellation (simplification) method to compute the product of two proper fractions; exploring and comparing the product of two whole numbers and the product of two proper fractions - Understanding hundredths - Understanding thousandths - Comparing and ordering decimals 3 Progression chart Fractions, percentages and decimals Oxford University Press
4 - Rounding decimals to the: nearest whole number nearest tenth nearest hundredth: (1) - Product of an improper fraction and a proper or improper fraction: - Product of a mixed number and a whole number: - Fractions and decimals: expressing a fraction (whose denominator is a factor of 10 or 100) as a decimal and express a decimal as a fraction in its simplest form: (2) - Dividing a fraction by a whole number: 4 Progression chart Fractions, percentages and decimals Oxford University Press
5 Decimals (2): TG4B Unit 10 p77 - Refer to addition and subtraction progression document - Refer to multiplication and division progression document - mixed number: TG4A p137 - simplify: TG4A p141 - cancellation: TG4A p141 - improper fraction: TG4A p142 - conversion: TG4A p146 (3) Decimals: TG5B Unit 7 p2 p28 - Converting fractions to decimals: converting tenths and hundredths, converting thousandths - Using a calculator Decimals: TG5B Unit 7 p6 Refer to multiplication and division progression document Measurement: TG5B Unit 8 p53 - Converting a measurement from a larger unit to a smaller unit - Converting a measurement from a smaller unit to a larger unit 5 Progression chart Fractions, percentages and decimals Oxford University Press
6 Percentage: TG5B Unit 10 p108 - Per cent - Converting more fractions to percentages - Percentage of a quantity - unlike fractions: TG5A p116 - proper fractions: TG5A p116 - per cent: TG5B p108 6 Progression chart Fractions, percentages and decimals Oxford University Press
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