zilongwang/ReadingBank huggingface dataset:
Baseline Data (Please include what you know about your students’ performance/skills/achievement levels at the beginning of the year, as well as any additional student data or background information used in setting your objective.) Teacher will use the Grade K Mathematics Pre Assessment to acquire baseline data. Pre-Assessments are Observation/Interview Checklists tied to Performance Tasks designed to determine the degree to which a student demonstrates particular skills that are deemed important for students to be successful in specific grade level content. Performance Level (Rounded Averages) Distinguished Command (5) Solid Command (4) Moderate Command (3) Partial Command (2) Minimal Command (1) Number of Students at each Level Preparedness Level Number of Students in Each Group (Total) Target Score on (%) Number of Students Required for “Full Attainment” Tier I (Low Level) PLD 1 and 2 Tier II (Mid Level) PLD 3 Tier III (High Level) PLD 4 and 5* * It is expected that students in Performance Level 5 maintain a level of distinguished command, making advancements within each indicator on the Observation Checklist. Scoring Plan Preparedness Group Target Score on Final Assessment Objective Attainment Level Based on Percent and Number of Students Achieving Target Score Exceptional (4) Full (3) Partial (2) Insufficient (1)
Approval of Student Growth Objective Teacher _________________ Signature_______________ Evaluator ________________ Signature _______________ Date Submitted_______________ Date Approved _______________ Results of Student Growth Objective Preparedness Group Number of Students at Target Score Objective Attainment Level SGO Score Average Objective Attainment Level Teacher ________________________ Evaluator _________________ Date _________________ _____
Look at restrictions if there is a radical in the denominator of a fraction such as: You can also investigate imaginary numbers as ways to deal with domain restrictions that may occur when performing calculations with radicals. Resources Math 20-1 (McGraw-Hill Ryerson: sec 5.1) Supporting Assessment Glossary conjugates – Two binomial factors whose product is the difference of two squares [Math 20-1 (McGraw-Hill Ryerson: page 587)] entire radical - A radical with a coefficient of 1 [Math 20-2 (Nelson: page 515)] - A statement of equality between two expressions – A general term that ultimately represents a number. An expression can consist of numbers, variables and operations on these. extraneous root – A number obtained in the process of solving an equation that does not satisfy the equation like radicals – Radicals with the same radicand and index [Math 20-1 (McGraw-Hill Ryerson: page 273)] mixed radicals - A radical with a coefficient other than 1 – Associates two or more members of a with one of the members of the set. The basic operations in mathematics are addition, subtraction, multiplication, division and exponentiation. – - Includes radical sign, radical index and radicand. – – n – x radical equation – An equation with a variable within a radicand rationalize – A procedure for converting to a rational number without changing the value of the expression [Math 20-1 (McGraw-Hill Ryerson: page 590)]
2014 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2014 Most Innovative Faculty Member, UNC School of Social Work Student Organization 2013 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2012 Most Innovative Faculty Member, UNC School of Social Work Student Organization 2012 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2011 Most Innovative Faculty Member, UNC School of Social Work Student Organization 2010 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2010 Most Innovative Faculty Member, UNC School of Social Work Student Organization 2008 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2009 Most Innovative Faculty Member, UNC School of Social Work Student Organization, 2008-2009 2007 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2008 Most Innovative and Creative Faculty Member, UNC School of Social Work Student Organization 2007 Most Supportive Faculty Member, UNC School of Social Work Student Organization 2006 Dean’s Recognition of Teaching Excellence, UNC School of Social Work 2003 “20 Under 40” promising young professionals, special focus section of the April 7, 2003 Blue Ridge Business Journal 1998 National Finalist, Cardinal Bernardin New Leadership Award, Catholic Campaign for Human Development 1994 Jane Curtis Parker Scholarship Award, UNC School of Social Work 1990 Phi Beta Kappa GRANTS
Computer Worksheets StudyIsland Smart Board/Chalkboard Observation Worksheets StudyIsland Smart Board/Chalkboard Counters/Pencil/paper Observation Counters/Pencil/paper Observation Observation Materials: Math Resources Computer/StudyIsland Worksheets StudyIsland/Smart Board Chalkboard Observation Materials: Math Resources Assessment StudyIsland
DISCRETE MATHEMATICAL STRUCTURE & GRAPH THEORY, CODE- 211505 L-T-P: 3-1-0 Credit : 4 SNo. Chapter Topics Lectures 1 Mathematical Logic and Set Theory Statement and Notation, Negation, Conjunction, Disjunction, Tautologies, Truth tables, Basic concepts of set theory, Inclusion and equality of sets, power set, ordered pairs and n-tuples. 8 2 Relations and Functions Relation and ordering, Properties of Binary Relations in a set Relation Matrix and the Graphs a Relation, Partition and Covering of a set. Equivalence relation, Partial ordering, Partially ordered set, Functions (definition and introduction), Composition of functions, Inverse functions, Characteristics function of a set. 8 3 Group Theory Semigroups and Monoids(defininitions and examples), Homomorphism of semigroups and monomoids, Subsemi groups and submonoids, Groups(definitions and examples) Subgroups and Homomorphisms, Cosets and Lanranges theorem, Normal subgroups, Codes and group codes. 8 4 Rings(Definition and Examples) Integral domains, ring, homomorphisms, Ideas of Ring polynomial. 4 5 Graph Theory Basic concepts of Graph Theory, Basic definitions, Paths and circuits. Rechability and connectedness, Matrix representation of graphs, Trees and their representation and operations, Rooted trees, Path lengths in rooted trees, Multi graphs and weighted graphs, Shortest paths in weighted graphs. 12 Text Books : Discrete Mathematics Structures with application to Computer Science by J. P.Tremblay & R. Manohar. Discrete Maths for Computer Scientists & Mathematicians. (Chapter 2, 5, by J. L. Mott, A. Kandel, T. P. Baker References : Elements of Discrete Mathematics by C. L. Liu. Discrete Mathematics by Lipschutz Discrete Mathematics by R.Johnsonbaugh.
(a) 314% (b) 219% (c) 48.57% (d) 103.57% 69. This road is only 50 km long We covered c distance of 20 km. What percentage of distance have we covered? (a) 40% (b) 69% (c) 48% (d) 53% 70. The price of a glass set increases Rs.600 to Rs.710. what is the percentage increases? (a) 18.33% (b) 17.33 (c) 10% (d) 14% 71. The original price of a gift pack is A discount of 15% is allowed in shop. What is the sale price, (a) Rs.65 (b) Rs.68 (c) Rs.61 (d) Rs.50 72. 8 men can do a work in 60 days. How long will it take 6 men to do the work? (a) 50days (b) 90 days (c> 120 days (d) 19 days 73. Which number will come next? 1.2.4.8.16. (a) 20 ‘(b) 24 (c) 28 (d) 32 74. Which number wilj come next? 6.3.12.6.24. (a) 12 (b) 18 (c) 30 (d) 48 76 Which number will come next? 64,32,16,8.______
__________________________________________ [2] Put (< ,> or =):- 5 × 2 3 ×4 4 × 2 4 + 4 7 × 4 8 × 3 15 + 10 5 × 5 _______________________________________________ [3] Choose:- 4 × 9 = ………. [36 , 27 , 54] (2 + 3) × 6 = ……….. [25 , 30 , 35] (8 – 2 ) × 4 = ……….. [20 , 24 , 30] 4 × ……… = 28 [6 , 5 , 7 ] Sheet (5) [1] Complete in the same pattern:- 4, 8 , 16, ……., ……. , …….. , …….. 60, 55, 50, ……. , …….., …….
[5] Put (> , = , <):- 1 Sheet (12) [1] A) Arrange in an ascending order:- , , , , …… , …….. , …….. , …….. , …….. B) Arrange in an ascending order:- , , , , …….. , …….. , …….. , …….. , ……..
Arrange the following fraction in an ascending order:- , , , , ……. , …… , …….. , …….. , …….. ____________________________________________________ [5] A) A father devise equally 25 pounds among his five sons. How much money does each son take? What each son takes = …………..……….. = ………. Pounds. B) From the graph Complete the following table:- Month Jan. Feb. March April Amount 30 25 20 15 10 5 0 Jan. Feb. March April
An hour = …………… minutes [60 , 30 , 120] 3 × 8 = 8 × ………….. [3 , 0 , 1 , 2] The last month of year is ……… [May , January , December] 20 ÷ 4 = ……………… [5 , 6 , 4] 6 × 1 = 1 × ………… [6 , 8 , 9] 125 minutes = 2 hours + …… minutes [5, 10 , 15] ___________________________________________________ [4] a) Draw the hands:- It is quarter to nine It's half past 3 b) Colour according to given fraction:- [5] a) Adham bought 3 books for 7 pounds each and a notebook for 3 pounds. What is the total amount he paid? The price of the books = ………………………… The total amount = ………………………….
10 ÷ 5= ……….. [2 , 3 , 4] 1 kg. = kg. + ……….. kg. [ , , ] The month that comes between Rajab and Ramadan is ……… [Safar , Shaban , Shaual] ____________________________________________________ [2] Complete the following :- …………… × 9 = 36 80 minutes = ………….. hour and …………. minutes. There are ……….. third in a whole one. The fifth month in the A.D calendar is ………….. The fraction which represents the shaded part is ……… 18 ÷ ………… = 3 [3] A) Adel bought 6 books for L.E 5 each. How much money did he pay? He paid = ………………………… = L.E ……………. B) Arrange in as ascending order:- , , and The order is : …… , …… , ….... and ……..
75 minutes = …………… minutes + …………. Hour ___________________________________________________ [2] Put (> , = or <):- 5 × 8 9 × 5 An hour and a half 90 minutes 6 + 6 + 6 6 × 3 12 ÷ 2 2 × 3 kg. + kg. 1 kg. A) Find the perimeter of this figure:- The perimeter = ……………… units B)Hanan bought 5 book each one for L.E 6 Find the price of all book.
from one class to the next and also to help avoid confusion for children having difficulties with Mathematics. Our agreed strategies/language are as follows. JUNIOR INFANTS: No signs used Addition: Language: and, makes, add, is the same as, altogether makes SENIOR INFANTS: Introduction of signs: +, = Vocabulary to match this: plus, equals (and, makes initially used as in junior infants) 2 + 1 3 Top down: 2 plus 1 equals 3 2 + 1 equals 3 2+1 =3 reads 2 plus 1 equals 3 or 2 and 1 makes 3 FIRST CLASS Subtraction: - is introduced as a symbol in First class Language: take away, less than, left 16 - 4 Vertical: start from the top using the words ‘take away’ 16 take away four equals 5 – 1= Horizontal: Read from left to right using the words ‘take away’ 5 take away 1 equals PLACE VALUE: THE WORD ‘UNITS’ WILL BE USED RATHER THAN ‘ONES’ RENAMING/GROUPING WILL BE THE METHOD USED THROUGHOUT THE SCHOOL SECOND CLASS Addition: 7+3+8= 18 7 plus 3 plus 8 equals 18 (7plus 3 equals 10 plus 8 equals 18) 6 3 +6 6 plus 3 plus 6 encourage 6 + 6 + 3 Subtraction Language: subtraction, decrease, subtract, take away, from, less than, minus difference than 27 -18 7 take away 8 I cannot do so I change a ‘ten’ to ten units, 7+10= 17. 17 take 8 equals 9. 1 take away 1 leaves O.
Skills The following skills will be acquired by the children through the study of the various strands in the Curriculum: Applying and Problem Solving Communicating and Expressing Integrating and Connecting Reasoning Implementing Understanding and Recalling Estimation Every strand studied must provide opportunities for acquiring skills. Opportunities should also be provided for the transfer of these skills to other areas e.g. Science, Geography and Music. Problem Solving Children are encouraged to use their own ideas as a context for problem solving. With regard to problem-solving children will be taught to apply the following strategies: Understanding the problem Read the problem Read it again Say, in your own words, what you are trying to find out Find the important information Look for key phrases Write what you know The Plan – Do – Review model (Hohmann et al 1979) is a useful strategy. Pupil: I want to make a bed for Teddy Teacher: Have you thought what you could use to make a bed? The child is encouraged to think about the solution. Start the project. Difficulties arise – bed too short etc. Solving the problem Look for a pattern Guess and check Write an equation Break the problem down and solve each part Additional Help Draw a picture Make an organised list or table Use objects to act out the problem Use easier numbers Work backwards
Sacred Heart Primary School Calculation Policy 2017 Calculation Policy Guidance EYFS/Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Addition Combining two parts to make a whole: part whole model. Starting at the bigger number and counting on- using cubes. Regrouping to make 10 using ten frame. Adding three single digits. Use of base 10 to combine two numbers. Column method- regrouping. Using place value counters (up to 3 digits). Column method- regrouping. (up to 4 digits) Column method- regrouping. Use of place value counters for adding decimals. Column method- regrouping. Abstract methods. Place value counters to be used for adding decimal numbers. Subtraction Taking away ones Counting back Find the difference Part whole model Make 10 using the ten frame Counting back Find the difference Part whole model Make 10 Use of base 10 Column method with regrouping. (up to 3 digits using place value counters) Column method with regrouping. (up to 4 digits) Column method with regrouping. Abstract for whole numbers. Start with place value counters for decimals- with the same amount of decimal places. Column method with regrouping. Abstract methods. Place value counters for decimals- with different amounts of decimal places
Multiplication Recognising and making equal groups. Doubling Counting in multiples Use cubes, Numicon and other objects in the classroom Arrays- showing commutative multiplication Arrays 2d × 1d using base 10 Column multiplication- introduced with place value counters. (2 and 3 digit multiplied by 1 digit) Column multiplication Abstract only but might need a repeat of year 4 first(up to 4 digit numbers multiplied by 1 or 2 digits) Column multiplication Abstract methods (multi-digit up to 4 digits by a 2 digit number) Division Sharing objects into groups Division as grouping e.g. I have 12 sweets and put them in groups of 3, how many groups? Use cubes and draw round 3 cubes at a time. Division as grouping Division within arrays- linking to multiplication Repeated subtraction Division with a remainder-using lollipop sticks, times tables facts and repeated subtraction. 2d divided by 1d using base 10 or place value counters Division with a remainder Short division (up to 3 digits by 1 digit- concrete and pictorial) Short division (up to 4 digits by a 1 digit number including remainders) Short division Long division with place value counters (up to 4 digits by a 2 digit number) Children should exchange into the tenths and hundredths column too
“You can do Maths with Aboriginal dancing.” “Staff, students, teacher, supervisors were relaxed and easy to get along with.” “I was surprised and interested in the cultural and maths stuff we did.” Students from St Peter Claver College were interviewed some sixteen months after the camp as a follow up and stated: “It actually showed me that maths had something to do with real life. I was in year 9 then and doing algebra which I couldn’t see how this had anything to do with real life. But some things that we did on the camp helped – showed how maths can go with a story.” Another student commented that as a result of the camp, their maths results had improved: “I used to get Cs in maths and now I get B+s.” camp or excursion is a great way to get students and teachers motivated learning about Maths and Culture. Some teachers expressed that the activities on the day were a start for further exploring the mathematical concepts that were touched on. With this in mind the students who were involved and their teachers could model the activities with the rest of the staff and their class. This would be an ideal time to invite local Aboriginal community members and into the school. Consultation for events like this is essential. Throughout the planning process, , Community representatives, Academics, teachers and staff from the various schools all had input into the planning of activities. Schools must also ensure they know each of their Indigenous students, their families and backgrounds. It has been identified by both clusters that any connection to and learning based around Culture is always embraced. Conclusion Both clusters recognised students’ engagement through active participation in the camp and excursion. The diversity of activities provided both a different perspective of mathematics and a context for learning that promoted mathematics and Aboriginal culture. References Matthews, C. & Morris, C.2011 Numeracy, and Indigenous : Not the same old thing. In Indigenous Education: Pathways to Success, Research Conference. Sullivan, P.2011 Teaching : Using research-informed strategies, ACER Press, Camberwell, Victoria. Stanton, R. 1994 Location: A cross cultural mathematics theme in Aboriginal teacher education, paper presented to Australian Bridging Mathematics Network Conference, University of Sydney, July. Matthews, C. (2008). Stories and symbols: Maths as storytelling. Retrieved August, 2009, from http://www.aeuvic.asn.au/professional/files/PV_Mathews_6_3.pdf
04 TRIANGLES Similarity of Triangles *** Theo:6.1 Example:1,2,3 Ex:6.2 Q:2,4,6,9,10 Criteria for Similarity of Triangles ** Example:6,7 Ex:6.3 Q:4,5,6,10,13,16 Area of Similar Triangles *** Example:9 The:6.6 Ex:6.4 Q:3,5,6,7 Pythagoras Theorem *** Theo:6.8 & 6.9 Example:10,12,14, Ex:6.5 Q:4,5,6,7,13,14,15,16 05 Introduction to Trigonometry Trigonometric Ratios * Ex:8.1 Q:1,2,3,6,8,10 Trigonometric ratios of some specific angles ** Example:10,11 Ex:8.2 Q:1,3 Trigonometric ratios of complementary angles ** Example:14,15 Ex:8.3 Q:2,3,4,6 Trigonometric Identities *** Ex:8.4 Q:5 (iii,v,viii) 06 STATISTICS CONCEPT 1Mean of grouped data Direct Method *** Example:2 Ex:14.1 Q:1&3 Assumed Mean Method * Ex:14.1 Q:6 Step Deviation Method * Ex:14.1 Q:9 CONCEPT 2 Mode of grouped data *** Example:5 Ex:14.2 Q:1,5 CONCEPT 3 Median of grouped data *** Example:7,8 Ex:14.3 Q1,3,5 CONCEPT 4 Graphical representation of c.f.(ogive) ** Example:9 Ex:14.4 Q:1,2,3
(in cm) -p xi a= 147.5,h=5 135-140 140-145 145-150 150-155 155-160 160-165 4 7 18 11 6 5 137.5 142.5 147.5 152.5 157.5 162.5 -2 -1 0 1 2 3 -8 -7 0 11 12 13 Mean=a+h x =147.5+5 x 23/51 =147.5+115/51 =(147.5+2.255)cm=149.755cm Let us find median of the data:- Class of height (in cm) Frequency number of girls Cumulative frequency 135-140 140-145 145-150 150-155 155-160 160-165 4 7 18=f 11 6 5 4 11=cf 29 40 46 51 Total n median=1+ x h=145 + x5 =145+14.5 x5 18 =145+4.028 =149.028cm Let us find mode of the data:- Class of heights (in cm) FREQUENCY (No of Girls) 135-140 140-145 145-150 150-155 155-160 160-165 4 7=f1 18=fm 11=f2 6 5 Total 51 (Modal class) Modal class is 145-150 Thus 12=45,h=5,fm=18,f1=7,f2=11 Mode=H xh=145 + x 5 =145+55/18 =145+3.055 =148.055 cm CONCLUSION:- Mean=149.755, median=149.028 and mode=148.055 3x median=3x149.028=447.084 Mode+xmean=148.055+2x149.755
Miles Coverdale School Overview of Curriculum – Maths 2018/19 Autumn Spring Summer Nursery Baseline Assessment-staggered intake EYFS outcomes. Number. Shape /Space/Measure. EYFS outcomes. Number. Shape/Space/Measure. EYFS outcomes. Number. Shape/Space/Measure Reception Baseline Assessment-staggered intake EYFS outcomes. Number. Shape/Space/Measure. EYFS outcomes. Number. Shape/Space/Measure Class E Number: Place Value Number: Addition and Subtraction Geometry: Shape Measures :Time Number : Place Value Number: Addition and Subtraction Measures: Length and Height Number: Multiplication and Division Number: Fractions Number: Place Value Number: Addition and Subtraction Measurement: Money Measurement: Weight and Volume Class 1 Number: Place Value Number: Addition and Subtraction Geometry: Shape Measures:Time Number: Place Value Number: Addition and Subtraction Measures: Length and Height Number: Multiplication and Division Number: Fractions Number: Place Value Number: Addition and Subtraction Measurement: Money Measurement: Weight and Volume Yr 2 Number: Place Value Number: Addition and Subtraction Measurement: Length and Mass Graphs Measurement: Money Geometry: Properties of Shape Number: Fractions Measurement: Time Measurement, Capacity, Volume and Temperature. Class P Number: Place Value Number: Addition and Subtraction Measurement: Length and Mass Graphs Measurement: Money Geometry: Properties of Shape Number: Fractions Measurement: Time Measurement, Capacity, Volume and Temperature. Yr 3 Number: Place Value Number: Addition and Subtraction Number: Multiplication and Division Measurement : Perimeter and Area Number: Multiplication and Division Measurement : Money Number: Fractions Measures: Perimeter and Length Geometry: Angles Geometry: Shape and Symmetry Statistics Measurement: Area and Perimeter Yr 4 Number: Place Value Number: Addition and Subtraction Number : Fractions Measurement : Time Number : Decimals Measures: Perimeter and Length Geometry: Angles Geometry: Shape and Symmetry
School_type_primary - state (including Church schools) or private. School_type_secondary - state (including Church schools) or private. School_type_A-levels - state (including Church schools) or private. Primary_teacher_patience - 1 = very patient, 7 = very impatient Primary_teacher_kindness - 1 = very kind, 7 = very unkind Primary_teacher_explanatory - this refers to the teacher's perceived ability to explain maths concepts. 1 = very poor, 7 = very good Primary_teacher_knowledge - this refers to the teacher's perceived knowledge of maths. 1 = poor, 7 = very good. Secondary_teacher_patience - 1 = very patient, 7 = very impatient Secondary_teacher_kindness - 1 = very kind, 7 = very unkind Secondary_teacher_explanatory: this refers to the teacher's perceived ability to explain maths concepts. 1 = very poor, 7 = very good Secondary_teacher_knowledge: this refers to the teacher's perceived knowledge of maths. 1 = poor, 7 = very good. Lifetime_rating: respondent's ratings of their lifetime experiences of learning maths. 1 = very good, 7 = very poor. Maths_confidence: 1 = very low confidence, 7 = very high confidence. Arithmetic_ability: 1 = very poor , 7 = very high. Course_confidence: confidence about coping with the course . 1 = very high, and 7 = very low. Statistics_anxiety: anxiety about learning statistics: 1 = not all anxious, 7 = very highly anxious. Essay_ability: rating of ability to write essays. 1 = very poor, and 7 = very high. Essay_anxiety: anxiety about writing Psychology essays. 1 = not at all anxious, and 7 = very anxious. StatsAnxietycategorical: the data in statistics anxiety were turned into a categorical variable by dichotomising them. and a "high anxiety" group. People who gave ratings of 1, 2 or 3 were classified as belonging to the "low anxiety" group, and people who gave ratings of 5, 6
Exercise 2C 1 a b c 2 a b c d 3 i a b A(1, 4), B(4, 1), C(1, 1) c A’(−4, 1), B’(−1, 4), C’(−1, 1) ii a b A(−2, 4), B(−2, 1), C(−4, 1) c A’(4, 2), B’(1, 2), C’(1, 4) iii a b A(−1, −1), B(−1, −3), C(−5, −3) c A’(1, 1), B’(1, 3), C’(5, 3) iv a
Exercise 2D 1 a 6 units right b 3 units right and 3 units down c 6 units down d 7 units right and 5 units down e 6 units left and 6 units down f 4 units right and 2 units down g 7 units right and 1 unit up h 7 units left and 5 units up 2 a A(1, 4), B(4, 2), C(1, 2) b and d c (–5, 2), (–2, 0), (–5, 0) e (0, –2), (3, –4), (0, –4) f 1 unit right and 6 units up 3 a b A’ (5, 3), B’ (0, 3), C’ (0, 1), D’ (3, 1) c Only the position has changed. The size and orientation of the trapezium have stayed the same. 4 a A (3, −1), B (2, −3), C (3, −5), D (4, −3) b and d c A’ (1, 5), B’ (0, 3), C’ (1, 1), D’ (2, 3)
Maths Frameworking Pupil Book 2.3 Answers Exercise 1A 1 a 1 b -11 c 8 d -1 e -7 f -12 g -12 h -5 i -21 j -3 2 a −12 b −20 c −18 d 28 e −36 f −30 g 20 h 14 i −9 j −3 k 4 l −17 m 12 n −4 o 9 p 10 3a b 4 for example −2 × 12, −12 × 2, 4 × −6, −4 × 6, −3 × 8 5 a −5 b −7 c −8 d 21 e 5 f 9 g 9 h 7 i −4.5 j −1.5 k −7.5 l −4.5 m 7.5 n −10 o 10.5 p 10 6 a −63 b 6 c −13 d 60 e 63 f 11 g −2 h 4 i −36 j 4 k −1 l −48 m −4 n −15 o −3.2 7 a i 1 ii 25 iii 49 iv 81 b Because same sign multiplied gives positive, but a negative always comes from different signs, hence no square root of a negative number 8 a 48 b 75 c −3 d −4 e −20 f −9 g −12 h −12 9 a 3 × (−6 + 2) b (−3 + −4) × 2 c 8 – (4 − 1) 10 a −2 × −2 × −2 b −3 × −3 × −3 c −5 × −5 × −5 Challenge: Multiplication square × 3 5 −6 −8 2 6 10 −12 −16 −4 −12 −20 24 32 7 21 35 −42 −56 9 27 45 −54 −72
17 a 190 000 000 cm³ b 6.57 m 18 No, you can only see a distance of 39.5 km Exercise 2A 1 a a = 70° b b = 75°, c = 85° c d = 90°, e = 42° d f = 65°, g = 115°, h = 65°, i = 115° e j = 98°, k = 33°, l = 147°, m = 98° f n = 35°, o = 83°, p = 118°, q = 118° 2 a 80° b 20° c 15° d 45° e 10° 3 a 128° b 30° c 20° d 15° e 25° 4 a = 82° (corresponding angles) b = 52° split angle f into angles c and d c = 23° (alternate angles) d = 54° (alternate angles) so f = 77°
3 a b A' (2, –1), B' (4, –1), C' (5, –4), D' (1, –4) c Only the position has changed. The size and orientation of the trapezium have stayed the same. 4 a A (−3, 4), B (−1, 4), C (−2, 1), D (−4, 1) b and d c A' (2, 3), B' (4, 3), C' (3, 0), D' (1, 0) e A'' (−3, −1), B'' (−1, −1), C'' (−2, −4), D'' (−4, −4) f Translation 5 units up 5 a and b
Problem solving: Constructing triangles Exercise 5C 1 PS is common RS = PQ (given) RSP = QPS (alternate angles) So ∆PRS ≡ ∆PQS (SAS) 2 BD is common AB = BC (given) BAD = BCD = 90° So ∆ABD ≡ ∆BCD (RHS) 3 Consider ∆XYP and ∆XZP. XP is common to both triangles XY= XZ (given) PY = PZ (given) So ∆XYP ≡ ∆XZP (SSS) Hence XYP = XZP 4 Consider ∆ABD and ∆BCD. BD is common to both triangles AB = BC (given) AD = CD (given) So ∆ABD ≡ ∆BCD (SSS) Hence A = C 5 AB = CD (given)
Check pupils’ posters. Chapter 6: Answers to Review questions 1 a 2 b 4 2 C is the odd one out. A, B and D are all enlargements/similar. 3 a b 4 5 6 a A(2, 4), B(4, 4), C(4, 2), D(2, 2 b Check pupils’ drawings. c Aʹ(4, 8), Bʹ(8, 8), Cʹ(8, 4), Dʹ(4, 4) d Aʹʹ(6, 12), Bʹʹ(12, 12), Cʹʹ(12, 6), Dʹʹ(6, 6) Chapter 6: Answers to Problem solving – Photographs 1 £191.25 2 a 13 square inches b 11 square inches c 22 square inches 3 12ʹʹ × 8ʹʹ and 6ʹʹ × 4ʹʹ, with a scale factor of 2 4 a 6ʹʹ × 4ʹʹ and 7ʹʹ × 5ʹʹ b Fast Print, £4.50 5 a 6ʹʹ × 4ʹʹ 6 : 4 6 ÷ 4 = 1.5 1.5 : 1 7ʹʹ × 5ʹʹ 7 : 5 7 ÷ 5 = 1.4 1.4 : 1 8ʹʹ × 6ʹʹ 8 : 6 8 ÷ 6 = 1.33 1.33 : 1 12ʹʹ × 8ʹʹ 12 : 8 12 ÷ 8 = 1.5 1.5 : 1 13ʹʹ × 8ʹʹ 13 : 8 13 ÷ 8 = 1.625 1.625 : 1 b the 13ʹʹ × 8ʹʹ print
b i €24 ii €60 iii €156 c i £33 ii £67 iii £133 Challenge: Strolling sisters A 10:40 am B 6.6 km Exercise 11C 1 a Check pupils’ graphs. b 1.25 c 0.7 and −2.7 d y = −1 e 0.4 and −2.4 2 a Check pupils’ graphs. b −1.25 c 0.8 and −3.8 d y = −2.25 e 0.3 and −3.3 3 a Check pupils’ graphs. b 3.75 c 1.6 and −0.6 d y = −0.25 e 2.8 and −1.8 4 a Check pupils’ graphs. b −0.75 c 2.7 and −0.7 d y = −1 e 3.6 and −1.6 5 a Check pupils’ graphs. b −1.25 c 3.6 and −0.6 d y = −2.25 e 3.8 and −0.8 Investigation: You can’t solve them all A B a 1.6 and −2.6 b 0.6 and −1.6 C The graph does not cut the x-axis. D pupils’ own work Exercise 11D 1 a b 13.5 m c 1.5 seconds d 3.5 seconds 2 a
Chapter 14: Answers to Revision Exercise 14G 1 a 25 b 10 c 12 d 12 e 12 f 37 2 a 30 b 3 c 9 d 12 e 4 f 12 3 a 8 b 49 c 11 d 3 e 3 f 32 g 13 h 23 i 4 j 50 k 48 l 20 4 a 4 × (3 + 7) = 40 b 10 ÷ (2 + 3) = 2 c 18 ÷ (3 + 3) = 3 d (5 – 2) × 4 = 12 e (20 – 5) × 2 = 30 f 5 × (12 – 8) = 20 g (10 – 22) × 2 = 12 h 10 – (22 × 2) = 2 i (20 – 42) × 5 = 20 5 a 30 b 22 c 21 d 12 e 7 f 81 Exercise 14H 1 Transaction Amount paid in Amount paid out Balance £64.37 Standing order £53.20 £11.17 Cheque £32.00 £43.17 Direct debit £65.50 –£22.33 Cash £20.00 –£2.33 Wages £124.80 £122.47 Loan £169.38 –£46.91 2 a 20 °C b 82 °C c 128 °C d 72 °C e 108 °C f 62 °C g 56 °C h 46 °C 3 a 8 b –5 c –13 d 8 e 7 f –5 g –6 h –2 i 12 j –2 k –9 l –1 m –10 n 17 o 12 p –16 4 a b c d 5 a –2 b 4 c –3 d –2 e –9 f 3 g –15 h 4 i 7 Exercise 14I 1 a 4, 8, 12, 16, 20 b 9, 18, 27, 36, 45 c 12, 24, 36, 48, 60 d 25, 50, 75, 100, 125 2 a 3, 15, 18, 24, 36, 39, 45, 48, 69, 90, 120 b 15, 45, 90, 120 c 8, 24, 36, 48, 64, 120 d 24, 36, 48, 120 3 a 48 b 48 c 45 d 45 4 a 2, 3, 5, 7, 11, 13, 17, 19 b prime numbers 5 a 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 b 1, 2, 4, 13, 26, 52
curved line vertical line perpendicular lines parallel lines Angles Any two lines meet at an angle. Angles are measured in degrees (º). There are different kinds of angles. a right angle equals 90º an acute angle is less than 90º an obtuse angle is more than 90º. a reflex angle is more than 180º
and 12 edges A cone has a circle as its base, a curved face and a point on the top A prism is a solid shape with matching ends. It has the same cross-section all across its length A cylinder has circular faces at each end and a curved face A net is what a 3D shape would look like if it were opened out flat Symmetry A line of symmetry is the line which divides the shape into two equal parts. Different shapes can have 0, 1, 2, 3, etc. lines of symmetry 0 lines 1 line 4 lines Rotational symmetry is when a shape can be rotated without changing its form Order 1 (none) Order 2 Order 3 Order 4 Order 5
Decimal point 75.25–5.45 = 75.25 -3.21 78.46 Rounding to one decimal place less than 5 (1,2,3,4) round down 7.35 = 7.4 5 or above (5,6,7,8,9) round up Percentage Percentage means ‘out of 100’ Fraction Decimal Percentage 2 2÷20 0.1 0.1 x 100 10% 20 Diagram Fraction Decimal Percentage 1/4 0.25 25% 1/2 0.50 50% 0f means x 15% of £50 is 15x50 = £7.50 100 3/4 0.75 75% 4/4 = 1 1 100% Measurements Length 10mm = 1cm 100cm = 1m Weight 1000mg = 1g 1000g = 1kg* Time 60s = 1 min 24h = 1 day Comparison more than / greater than less than heavier than lighter than higher than lower than
KENDRIYA VIDYALAYA SANGATHAN (For Summer Station Kendriya Vidyalayas) SPLIT-UP SYLLABUS SESSION 2018-19 NCERT TEXT BOOK: Math-Magic – Book-4CLASS:_IV_SUBJECT:Mathematics S.NO Name of the Examination CHAPTER TENTATIVE NO.OF PERIODS REQUIRED MONTH 1 PART – I Periodic Test 1 Building with bricks 14 April 2 Long and Short 12 3 A trip to Bhopal 10 May/June 4 A trip to Bhopal Tick – Tick - Tick 10 17 July 5 PART – II Half Yearly Examination (Cumulative) The way the world looks 10 August 6 The Junk seller 15 7 Jugs and Mugs 12 September 8 PART – III Periodic Test 2 Carts and Wheels 10 October 9 Halves and Quarters 16 November 10 Play with patterns 7 11 Tables and Shares 19 December
KENDRIYA VIDYALAYA SANGATHAN (For Summer Station Kendriya Vidyalayas) SPLIT-UP SYLLABUS SESSION 2018-19 NCER T TEXT BOOK OF MATHEMATICS CLASS : IX SUBJECT : MATHEMATICS S.NO Name of the Examination CHAPTER Tentative No of periods required Tentative No.of working days available MONTH 1 PART – I Periodic Test 1 NUMBER SYSTEMS 18 23 APRIL 2 POLYNOMIALS 10 POLYNOMIALS (CONTD) 13 10 MAY/JUNE 3 CO-ORDINATE GEOMETRY 6 25 JULY 4 LINEAR EQUATIONS IN TWO VARIABLES 14 5 INTRODUATION TO EUCLID’S GEOMETRY 6 6 PART – II Half Yearly Examination (Cumulative) LINES AND ANGLES 13 24 AUGUST 7 TRIANGLES 10 TRIANGLES CONTD. 12 23 SEPTEMBER 8 QUADRILATERALS 10 9 PART – III Periodic Test 2 AREAS OF PARALLELOGRAMS AND TRIANGLES 10 18 OCTOBER 10 CIRCLES 8 CIRCLES (CONTD) 8 22 NOVEMBER 11 CONSTRUCTIONS 11 12 HERONS FORMUA 6 13 SURFACE AREAS AND VOLUMES 10 18 DECEMBER PART – IV Session Ending Examination (Cumulative) SURFACE AREAS AND VOLUMES CONTD. 10 23 JANUARY 14 STATISTICS 10 STATISTICS CONTD. 4 23 FEBRUARY 15 PROBABILITY 9 SESSION ENDING EXAM MARCH
Solve linear equations with unknowns on both sides Plot and interpret graphs of linear functions Apply the formulae for circumference and area of a circle Calculate theoretical probabilities for single events Know that area of a circle = πr² Know that volume of prism = area of cross-section × length Know to use the midpoints of groups to estimate the mean of a set of grouped data Know that probability is measured on a 0-1 scale Know that the sum of all probabilities for a single event is 1 Solving equations and inequalities Calculating space Algebraic proficiency: visualising Understanding risk II Presentation of data Measuring data Mathematics overview: Stage 7 Unit Mastery indicators Essential knowledge Numbers and the number system Use positive integer powers and associated real roots Apply the four operations with decimal numbers Write a quantity as a fraction or percentage of another Use multiplicative reasoning to interpret percentage change Add, subtract, multiply and divide with fractions and mixed numbers Check calculations using approximation, estimation or inverse operations Simplify and manipulate expressions by collecting like terms Simplify and manipulate expressions by multiplying a single term over a bracket Substitute numbers into formulae Solve linear equations in one unknown Understand and use lines parallel to the axes, y = x and y = -x Calculate surface area of cubes and cuboids Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines Know the first 6 cube numbers Know the first 12 triangular numbers Know the symbols =, ≠, <, >, ≤, ≥ Know the order of operations including brackets Know basic algebraic notation Know that area of a rectangle = l × w Know that area of a triangle = b × h ÷ 2 Know that area of a parallelogram = b × h Know that area of a trapezium = ((a + b) ÷ 2) × h Know that volume of a cuboid = l × w × h Know the meaning of faces, edges and vertices Know the names of special triangles and quadrilaterals Know how to work out measures of central tendency Know how to calculate the range Counting and comparing Calculating Visualising and constructing Investigating properties of shapes Algebraic proficiency: tinkering Exploring fractions, decimals and percentages Proportional reasoning Pattern sniffing Measuring space Investigating angles Calculating fractions, decimals and percentages Solving equations and inequalities Calculating space Checking, approximating and estimating Mathematical movement Presentation of data Measuring data Mathematics overview: Stage 6
hundred Convert between adjacent metric units of measure for length, capacity and mass Measure and draw angles Calculate the area of rectangles Distinguish between regular and irregular polygons Calculating fractions, decimals and percentages Calculating space Checking, approximating and estimating Mathematical movement Presentation of data
GRADE 12 MATHEMATICS PAPER 2 DATE: July 2008 TIME: 3 HOURS TOPIC: MID YEAR EXAM TOTAL MARK: 150 EXAMINER: Mrs. M Klein MODERATOR: Mrs. P Copeland Name: ________________________ Teacher: _______________________ Learning Outcomes Assessment Standards Question Mark 3 Space, Shape & Measurement 11.3.1Surface Area & Volume: Pyramids, Cones & Spheres Coordinate Geometry: 11.3.3 Distance, Gradient, Mid-point, Equation of line, Inclination. 12.3.3 Equation of a Circle & Tangent to a Circle Transformation Geometry: 11.3.4 Translations, Reflections, Rotations, Enlargements. 12.3.4 Rotation about the origin through any angle. Rigid Transformations & Enlargements Trigonometry: 11.3.5 Special Angles, Identities, Reduction Formulae, Equations, Solving Triangles. 12.3.5 Compound Angle Formulae 11.3.6 Solving 2-D problems 12.3.6 Solving 2–D & 3-D Problems A: 1; 2 B: 1; 7 A: 3 B: 5 A: 5 B: 2; 3; 6 A: 27 B: 28 A: 14 B: 9 A: 24 B: 25 4 Data Handling & Probability Descriptive Statistics: 11.4.1 Univariate Data, Central Tendency ( Mean, Median, Mode) & Dispersion (Range, Quartiles, Variance); Bivariate Data Scatter Plots & graphs of best fit. A:4 B: 4 A: 15 B: 12 Total 150 COMMENT SECTION A: KNOWLEDGE & ROUTINE PROCEDURES 80 MARKS
b) A container is lifted off a boat at point D by crane AG. The arm of the crane AB is rotated through an angle of to AC. The container is then lowered onto the quay from E to F. The angle of elevation of D from F is. The length of AB is r metres. 1) Prove that (3) 2) Determine the distance the container was lowered onto the quay. (The length of EF.) (2) QUESTION 7 13 Marks A dartboard consists of three concentric circles with diameters dividing it into 12 equal sectors as shown. The radii of the circles are 10cm, 8cm, and 6cm respectively. The diameter AB is parallel to the x-axis. Diagonals CD and EF have equations and respectively. a) Determine the co-ordinates of the centre P of the dartboard. (Leave your answer in surd form if necessary). (5) b) Hence find the equation of the second circle (2) c) Write down the equation of the diameter AB (1) d) Scores for a particular sector are shown on the outer ring of the dartboard. If a dart lands on the inner ring of that sector, the score remains unchanged. If a dart lands between the first and second rings of that sector, the score is doubled, and if a dart lands in the outer ring of that sector, the score is halved. For example, the dart shown in the
● If two towers have a difference of 3 cubes, how tall might they be? 26 − ■ =16; ■ − 40 = 28; ■ − ▲ = 40 ● You have 70p and spend 30p, what do you have left? What number sentence would you write? Subtraction – Stage 3 Subtract numbers using concrete objects, pictorial representations, and mentally, including: A two digit number and ones A two digit number and tens Two two-digit numbers NB Ensure that children are confident with the methods outlined in the previous stage’s guidance before moving on. Counting back using an empty number line within 100, in ones… 34 - 6 = 28 …and in tens 58 – 30 = 28 Use in conjunction with a 100 square to show jumps of tens. Subtraction, using partitioning, on an empty number line: 76 – 45 = 31 -1 -1 -1 -1 -1 -10 -10 -10 -10 - 31 32 33 34 35 36 46 56 66 76 Use in conjunction with a 100 square to show jumps of tens and ones. If children are confident, use more efficient jumps… -5 -40 31 36 76 Progression in subtraction autumn spring summer ● You have 57p in your pocket and spend 49p, how much do you have left? ● There were 24 people on a bus. There are now only ● What is 35 take away 8? Take 7 from 42.Subtract 40 from 95. ● What must I take ● There are 20 pegs on a coat hanger. 14 are showing. How many are hidden? What number sentences could we write? ● I think of a number. I add 45.The
• Understand and use lines parallel to the axes, y = x and y = -x • Calculate surface area of cubes and cuboids • Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines Knowledge • Know the first 6 cube numbers • Know the first 12 triangular numbers • Know the symbols =, ≠, , ≤, ≥ • Know the order of operations including brackets • Know basic algebraic notation • Know that area of a rectangle = l × w • Know that area of a triangle = b × h ÷ 2 • Know that area of a parallelogram = b × h • Know that area of a trapezium = ((a + b) ÷ 2) × h • Know that volume of a cuboid = l × w × h • Know the meaning of faces, edges and vertices • Know the names of special triangles and quadrilaterals • Know how to work out measures of central tendency • Know how to calculate the range • Know the characteristic shape of a graph of a quadratic function • Know how to measure and write bearings • Know how to identify alternate • Know how to identify corresponding angles • Know how to find the angle sum of any polygon • Know that circumference = 2πr = πd • Know that area of a circle = πr² • Know that volume of prism = area of cross-section × length • Know to use the midpoints of groups to estimate the mean of a set of grouped data • Know that probability is measured on a 0-1 scale • Know that the sum of all probabilities for a single event is 1 Use geometrical reasoning to construct simple proofs Use tree diagrams to list outcomes Knowledge Know how to interpret the display on a scientific calculator when working with standard form Know the difference between direct and inverse proportion Know how to represent an inequality on a number line Know that the point of intersection of two lines represents the solution to the corresponding simultaneous equations Know how to find the nth term of a quadratic sequence Know the characteristic shape of the graph of a cubic function Know the characteristic shape of the graph of a reciprocal function Know the definition of speed Know the definition of density Know the definition of pressure Know Pythagoras’ Theorem Know the definitions of arc, sector, tangent and segment Know the conditions for congruent triangles
KENDRIYA VIDYALAYA SANGATHAN (For Summer Station Kendriya Vidyalayas) SPLIT-UP SYLLABUS SESSION 2018-19 NCERT TEXT BOOK: Text book for Class VII SUB: MATHEMATICS S.NO. Name of the Examination CHAPTER TENTATIVE NO.OF PERIODS REQUIRED MONTH Tentative No of working days available 1. PART – I Periodic Test 1 Integers 10 April 23 2. Fractions and Decimals 10 Fractions and Decimals Continues 7 May/June 10 3. Data Handling 10 July 25 4. Simple Equations 10 5. PART – II Half Yearly Examination (Cumulative) Lines and Angles 07 August 24 6. The Triangle and its Properties 10 7. Congruence of Triangles 08 September 23 8. Comparing quantities 10 9. PART – III Periodic Test 2 Rational Numbers 08 October 18 10. Practical Geometry 08 November 22 11 Perimeter and Area 14 12 Algebraic Expressions 12 December 18 13 PART – IV Session Ending Examination (Cumulative) Exponents and Powers 12 January 22 14. Symmetry 08 15. Visualizing solid shapes 10 February 23 Session Ending Examination-2018-19
GCSE Monday Tuesday Wednesday Thursday Friday 8.00-8.30 Mr Cooper C11 Target 4-6 Miss Lloyd C15 Target 4-6 Mrs Kalicharan C14 Target 3-5 1.20 – 1.50 Mrs Beddoe A25 Level 7-9 3-3.45 Miss Clewes C11 Up to grade 4 Mrs Lam C18 Level 4-7 Miss Paris C12 Target 7-9 Miss Sheldon C1 Target 5-8 *Miss Ashton /Miss Reid C2 ALL LEVELS *Thursday revision with Miss Ashton has already started. A ‘level Monday Tuesday Wednesday Thursday Friday 8.00-8.30 1.20 – 1.50 3-3.45 Yr 13 revision C1, C2, S1 Mr Rose A24 Yr 13 Core 3 and C4 Mr Griffiths C16
(2) (Total 6 marks) 7. (a) Rationalise ..................................... (2) (b) (i) Expand and simplify (3 + 15)2 Give your answer in the form n + m5, where n and m are integers. ..................................... (ii) All measurements on the triangle are in centimetres. ABC is a right-angled triangle. k is a positive integer. Find the value of k.
(b) Calculate the value of y. Give your answer correct to 1 decimal place. y = ...........................cm (3) 22. Diagram NOT accurately drawn The diagram represents a vertical pole ACD. AB is horizontal ground. BC is a wire of length 8.5 metres. The height of the pole AD is 9 metres. For the pole to be correctly installed, the length DC has to be at least 1 metre. Show that the pole has been correctly installed. ..................................... (Total 4 marks)
(3) (b) Solve the equation x2 – 15x – 199.75 = 0 ………………………… (3) (Total 6 marks) 31. (a) Factorise 2x2 – 35x + 98 ................................... (a) Solve the equation 2x2 – 35x + 98 = 0 32. AT is a tangent at T to a circle, centre O. OT = x cm, AT = (x + 5) cm, OA = (x + 8) cm. (a) Show that x2 – 6x – 39 = 0
x = ..................................... y = ..................................... (Total 4 marks) 46. Solve the simultaneous equations. 2x + 3y = 0 x – 3y = 9 x=........................... , y = ............................ (Total 3 marks) 47. Solve the simultaneous equations x2 + y2 = 5 y = 3x + 1
4c 4b 4a Shape Properties *I can name and draw polygons from 3 to 12 sides and can describe their properties * I can draw the nets of the 3D shapes listed in Level 3b *I can recognise quadrilaterals – square, rectangle, trapezium, parallelogram, rhombus, kite and describe their properties *I can recognise right angled, isosceles, equilateral and scalene triangles and describe their properties *I know vertical, horizontal and congruent *I can draw an oblique line of symmetry in a shape Position and movement *I can draw polygons in different orientations on a grid * I can reflect a shape in a diagonal mirror line where the line does not touch the shape *I can complete a shape (eg rectangle) which has two sides drawn at an oblique angle on a grid * I can translate a shape horizontally and vertically *I am beginning to rotate a shape about its centre or vertex Measures *I know and can use the units of measure in length, mass, capacity. I can use decimal notation (eg 3.06m =3m 6cm) *I can use timetables and calendars *I can find the perimeter of simple shapes (eg squares/rectangles) * I can use the 24 hour clock *I can draw and measure acute angles *I can calculate angles along a straight line *I can measure accurately in mm * I can draw and measure acute/obtuse angles *I can find the area of a shape that can be divided into small squares (eg centimetre squares) by counting the squares/ part squares. Data Specifying the problem. Planning and collecting data *I can plan an investigation and know what data to collect *I can collect discrete data (eg record how many scores of 6 in fifty throws of the dice) and record in a frequency table * I can group data into equal class intervals Processing/ representing * I can calculate the median of a set of data * I can use Venn/Carroll diagrams using two criteria such as ‘multiples of 8’ and ‘multiples of 6’ * I can draw a line graph Interpreting *I understand ‘certain’, ‘impossible’, ’more likely’, ’equally likely’, fair’, ’unfair’ in probability. * I can interpret data in frequency tables * I can interpret data in line graphs with various scales
Term by Term Objectives Y6 Mathematics Spring term coverage Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 Week 12 Number: Decimals Identify the value of each digit in numbers given to three decimal places and multiply numbers by 10, 100 and 1000 giving answers up to 3dp. Multiply one digit numbers with up to 2dp by whole numbers. Use written division methods in cases where the answer has up to two decimal places. Solve problems which require answers to be rounded to specified degrees of accuracy. Number: Percentages Solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison . Recall and use equivalence s between simple FDP including in different contexts. Measurement Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate. Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3dp. Convert between miles and kilometres. Recognise that shapes with the same areas can have different perimeters and vice versa. Recognise when it is possible to use formulae for area and volume of shapes. Calculate the area of parallelograms and triangles. Calculate, estimate and compare volume of cubes and cuboids using standard units, including cm3, m3 and extending to other units (mm3, km3) Number: Algebra Use simple formulae Generate and describe linear number sequences. Express missing number problems algebraically. Find pairs of numbers that satisfy an equation with two unknowns. Enumerate possibilities of combinations of two variables. Number: ratio Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts. Solve problems involving similar shapes where the scale factor is known or can be found. Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples. Geometry and Statistics Illustrate and name parts of circles, including radius, diameter and circumferenc e and know that the diameter is twice the radius. Interpret and construct pie charts and line graphs and use these to solve problems. Calculate the mean as an average. Time at the beginning or end of the term for consolidatio n ,gap filling, seasonal activities, assessments , etc.