Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Georg Cantor's first set theory article wikipedia , lookup
Location arithmetic wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Surreal number wikipedia , lookup
Large numbers wikipedia , lookup
Positional notation wikipedia , lookup
Real number wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Unit 1: Number I Core ( 20 lessons) Syllabus Main Learning Objectives Reference Suggested Teaching Activities Resources/Extra material References from Pimentel and Wall Core IGCSE Mathematics Second Editions unless stated otherwise 9.1 9.2 9.3 NEW Notation and meaning for is an element of , is not an element of, is a subset of , is a proper subset of , universal set U, empty set or { }, complement of A, A’, number of elements in A, n(A) Sets in descriptive form {x } or as a list. NEW Venn diagrams with at most three sets. 9.4 New Find intersection and union of sets by using Venn Diagrams. 1.1 RECAP (A) Know the vocabulary and notation for different sets of numbers: natural numbers N (N = 0,1,2,3…), primes, squares, integers Z, rational numbers Q, irrational numbers, real numbers R RECAP Irrational Numbers Be able to determine if a number is irrational or not 1.1 Use Venn Diagrams to illustrate the relationship between the different sets of numbers (this will be a NEW approach) Calculator/ Non calc. activity Old IGCSE ref. Worksheet Not on old IGCSE Worksheet Not on old IGCSE Not on old IGCSE Worksheet Mention these sets when introducing Venn diagrams –see above Non Calc Ex. 1.9 (p. 8) GDC 1.1 RECAP Prime Numbers. Be able to determine if a number is prime. 1.3 RECAP (A) Know how to determine Prime Factors, the Highest Common Factor, Multiples, Lowest Common Multiple RECAP (A)Be able to add, subtract, multiply, divide and apply the use of brackets appropriately with whole numbers, manually. Understand the meaning of the word product. Investigating- working systematically, listing outcomes Investigating – working systematically Investigating – working systematically, elimination RECAP (A) Be able to find equivalent fractions and be able to convert fractions from improper to mixed number form. 1.2 Paper 3 Paper 3 Paper 3 1.2 1.2 RECAP (A) Be able to convert fractions from improper to mixed number form. Sieve of Eratosthenes, prime factor trees, use of 1 – 100 number grids. When finding factors of a number try to find the factor pair. The Four Fours Problem. Use four 4s and any combination of operations to create all the numbers between 1 and 20 Triples. Biggest number Prime Numbers A visual presentation of equivalence is helpful. Students will need to be shown how to use the GDC to input and manipulate fractions ie 2 ½ is input as 2 + 1÷2 Ex. 1.5 (p. 6) Ex. 1.6 (p. 6) Ex. 1.7 (p. 7) Ex. 1.8 (p. 7) Ex. 7.1 (p. 44) Non Calc Non Calc Worksheet – copy on maths server Worksheet Worksheet– copy on maths server Ex. 7.2 (p. 46) Ex. 4.3 (p.26) Non Calc Non Calc 1.2 1.2 1.2 1.2 1.2 1.2 RECAP(A)Be able to add and subtract fractions with the same and different denominators and when written as improper fractions and/or mixed numbers RECAP(A) Be able to multiply and divide fractions when written as improper fractions and/or mixed numbers. Be able to find the reciprocal of a fraction (or a whole number!) NEW(A) Be able to divide by a fraction and then another fraction. Divide a whole number by a fraction. Multiply a whole number by a fraction RECAP (A) Convert from fractions to decimals and vice-versa RECAP(A)Be able to add and subtract with integers, manually. A visual presentation of adding with different denominators, for example, is helpful. Ex. 7.3 (p. 47) Non Calc A visual presentation of the equivalence of dividing by a fraction and multiplying by its denominator is helpful. Ex. 7.4 (p.48) Non Calc These manipulations of fractions are essential foundation for later work on algebraic fractions. Fraction Action worksheet Non Calc Ex. 7.5 (p.48) Ex. 7.6 (p.49) Ex. 1.1 (p. 1) Ex. 1.2 (p. 2) Non Calc/Calc Non Calc Ex. 1.3 (p. 3) Dividing is not covered in these exercises see Worksheet Negative Numbers 1 Non Calc Familiarise students on how to do this on the GDC This is a key topic and impacts later on algebra if it is not mastered at this stage!! Introduce the topic by playing “walk the plank” see DM for details. RECAP(A)Be multiply and divide and Students will need to be shown apply the use of brackets appropriately how to use the GDC to input and with integers, manually. Apply manipulate integers ie using (-) directed number in practical situations button not minus button. 1.2 RECAP(A) Apply directed number in practical situations 1.2 RECAP (A) Be able to add, subtract, multiply, divide and apply the use of brackets appropriately with decimals, manually. 1.2 RECAP (A) Apply decimals in practical situations Investigating – being systematic, drawing a picture Investigating – using a table, looking for patterns, making predictions, testing them, making generalisations RECAP Convert from percentages to decimals to fraction and vice-versa Paper 3 Paper 3 1.8 Diagonals Worksheet Negative Numbers 2 Decimals Worksheet 1 (there are some speed tests at the end of this worksheet which might be fun!) Decimals Worksheet 2 Worksheet Digit Sum Worksheet Ex. 4.4 (p.27) Ex. 4.5 (p.27) 1.8 RECAP Calculate a fraction of a quantity Use this as an introduction to finding a % of a quantity. Ex. 4.2 (p. 25) 1.8 RECAP Calculate a % of a quantity Practice calculating 5%, 10%, 20%, 50% etc mentally. Ex. 11.2 (p. 71) 1.8 RECAP Express one quantity as a percentage of another Use statistics that are taken from the class eg what % of the class live in Sha Tin? Use two-way tables to gather the data eg gender v how you get to school Ex. 11.3 (p.72) Non Calc Non Calc Non Calc Non Calc for simple cases Non Calc for simple cases Non Calc for simple cases Non Calc for simple cases 1.8 RECAP Calculate % increase or decrease 1.5 RECAP(A) Ratio – write equivalent ratios. RECAP(A) Ratio - divide a quantity in a given ratio 1.5 1.5 NEW Use the unitary method for direct proportion and understand common measures of rate NEW Recognise what the graph of direct proportion looks like. Know that the rate is the gradient of the straight line graph 1.5 NEW Use the unitary method for inverse proportion NEW Recognise what the graph of inverse proportion looks like. Paper 3 Investigating – collecting data, constructing, proving RECAP(A) Rounding to a degree of accuracy or number of decimal places RECAP(A) Rounding to a number of significant figures. 1.11 1.11 1.11 RECAP(A) Rounding to enable estimation Ensure when calculating % increase and decrease that students use x 1.05 to increase by 5% etc ICT–mymaths–Number – Percent – compound interest Ex. 11.4 (p.74) Non Calc for simple cases Ex. 10.3 (p. 64) Non Calc Ex. 10.4 (p.65) Non Calc Ensure that students graph situations of direct proportion. Eg Total wage v hours worked. Use the GDC to plot these points. Note that the gradient for direct proportion represents the rate. ICT – mymaths – Number – Ratio and Proportion - Higher Ensure that students graph situations of inverse proportion eg Time v Speed to cover a constant distance. Use the GDC to plot these points. ICT – mymaths – Number – Ratio and Proportion Higher Ex. 10.1 (p.62) Ex. 10.2(p.64) Non Calc for simple cases What is the Golden Ratio? Worksheet Note that for IGCSE and IB where not stated, students must round all answers correct to 3 sf GDC Ex. 10.5(p.67) Non Calc for simple cases GDC Ex. 8.1 (p. 51) Ex. 8.2 (p. 52) Ex.8.3 (p. 52) Non Calc Ex. 8.4 (p. 53) Non Calc Non Calc