External certification and level All students have the opportunity to study Entry level mathematics. We currently use Edexcel Entry level Mathematics. This covers entry levels 1-3. Most students will also study and take an external entry level exam in Edexcel Functional Mathematics. Entry levels 1-3.. Some students will have the opportunity to study GCSE mathematics. We currently use AQA 9-1mathematics. Year 10 Programme of study Key stage 4 Number systems including fractions, decimals and percentages Data and statistics Problems and puzzles Time Assessment tests Shape and construction Calculating Finance Measures Fill in the gaps Number systems including fractions, decimals and percentages Data and statistics Problems and puzzles Time Entry level tests for year 11 Shape and construction Calculating Finance Fill in the gaps Number systems including fractions, decimals and percentages Data and statistics Problems and puzzles Time Assessment tests Shape and construction Calculating Finance Measures Fill in the gaps
up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 add and subtract fractions with the same denominator within one [for example, 5/7 + 1/7 = 6/7] Themes Possible key learning points Develop knowledge of place value Explore decimals Calculate with fractions Bring on the Maths+: Lower Key Stage 2 Fractions & decimals: Counting in tenths Recognise that tenths arise from dividing a number or object into ten equal parts Write tenths as a fraction and as a decimal up in tenths Count down in tenths Add fractions with the same denominator within one whole Subtract fractions with the same denominator within one whole Prerequisites Mathematical language Pedagogical Understand place value in numbers up to 1000 Connect the ten times table to place value Recognise and write unit and non-unit fractions Understand unit and non-unit fractions as numbers on a number line Place value Tenth Decimal Divide Fraction Unit fraction Non-unit fraction Numerator Denominator Add Subtract Notation Decimal point t notation for tenths Horizontal bar for fractions Diagonal bar for fractions Pupils will need to know the value headings of tenths. Some countries use a comma for a decimal point. It is important to start at different numbers when counting up and down in tenths. Counting should be practised as part of everyday practice: choral counting should not be restricted to this unit. Pictorial representations of calculations involving the addition and subtraction are essential for pupils to understand why only the numerators are added or subtracted, not the denominators (e.g. ‘1 of 5 equal parts’ add ‘ 2 of 5 equal parts’ equals ‘3 of 5 equal parts’) NCETM: NCETM: Common approaches Pupils are expected to use horizontal bar notation for fractions Teachers and pupils adopt the mantra: ‘We say one fifth we think one of five equal parts; we say two fifths, we think two of five equal parts, etc’
Reasoning opportunities and probing questions Suggested activities Possible misconceptions Show me a decimal and fraction equivalent pair. And another. And another. Jenny is counting in tenths ‘…. 2.7, 2.8, 2.9, 2.10, 2.11 …’. Do you agree with Jenny? Explain your answer. Convince me that 6 ÷ 10 = 0.6 Show me two fractions that add together to make a And another pair. And another pair. Kenny thinks that . Do you agree with Kenny? Explain your answer. Convince me how to subtract fractions. NCETM: NCETM: NCETM: Learning review KM: NCETM: Some pupils may think that the first place value heading after the decimal point is ‘one-ths’ or ‘unit-ths’ Some pupils may think that you simply add the numerators and add the denominators when adding fractions. Some pupils may that you simply subtract the numerators and subtract the denominators when subtracting fractions. Some pupils may move from 2.9 to 2.10 when counting in tenths Some pupils may read the number 2.10 as ‘two point ten’ Exploring 8 Key concepts (National Curriculum statements) The Big Picture: add and subtract amounts of to give change, using both £ and p in practical contexts Themes Possible key learning points Explore money Solve problems involving money Recognise the value of coins Add amounts of money when the units are the same Add amounts of money when the units are different Subtract amounts of money when the units are the same Subtract amounts of money when the units are different Record a practical money problem using £ and/or p notation Solve practical problems that involve calculating change in manageable amounts Prerequisites Mathematical language Pedagogical notes
Prerequisites Mathematical language Pedagogical notes Reflect a in a vertical line of symmetry Use a ruler to construct a straight line joining two points Know the of special quadrilaterals Symmetry Line of symmetry, Mirror line Reflect, Reflection Congruent Perpendicular, Parallel Vertex (Vertices) Side, Edge Quadrilateral Square, Rectangle, Parallelogram, (Isosceles) Trapezium, Kite, Rhombus Triangle Scalene, Isosceles, Equilateral Polygon, Hexagon, Pentagon, Octagon, Decagon Circle Notation Dash notation to represent lengths in shapes and geometric diagrams Right angle notation to indicate perpendicular lines Pupils should be able to identify a mirror line at 45°, but not to use one to carry out a reflection. Isosceles ‘equal legs’ Encourage pupils to draw irregular polygons, especially hexagons, pentagons, octagons and decagons NCETM: Useful resources: Sets of 2D and 3D shapes, polydron, mirrors, pegboards, pinboards, rulers, dot isometric 2-D shape dice, string Common approaches classroom has a set of and on the wall Every classroom displays shapes in different orientations. Every classroom displays regular and irregular hexagons, pentagons, octagons and decagons Reasoning opportunities and probing questions Suggested activities Possible misconceptions
Use analogue and digital 12-hour clocks Know the number of seconds in a minute, minutes in an hour, hours in a day, and the number of days in each week, month, year and leap year Know the value of all British coins and notes Know the number of pence in a pound Calculate the duration of time for a given event or task Analogue Digital 12-hour 24-hour Second, Minute, Hour Day, Week, Month, Year Pound (£) (p) Length Mass Volume Notation £ and p 12-hour and24-hour notation use a ‘:’, for example 18:40 and 9:30 a.m. Some Jewish clocks rotate anti-clockwise. There is a 24-hour analogue clock at Greenwich observatory. 24 clock notation using four digits. Any time before 10:00 a.m. uses a zero as the second hour digit, for example 9:15 a.m. is written as ‘09:15’. Noon is 12:00 and midnight is 00:00 NCETM: Common approaches Use of a colon to write 12- and 24- hour times Noon is treated as 12:00 and midnight as 00:00 Use either the ‘£’ or ‘p’ symbol but not both symbols at the same time, for example, £4.56p Reasoning opportunities and probing questions Suggested activities Possible misconceptions Compare quantities by estimation Ask students to tell the time of using images of the Greenwich Observatory Clock or 24 Hour watches. How does a 24-hour watch need to operate differently to a 12-hour watch? Convince me that 18:40 is the same as 6:40 pm. Convince me that ‘two pounds and five pence’ is not written as ‘£2.5p’ NCETM: NRICH: NRICH: NRICH: NRICH: NCETM: : Activity A Learning review NCETM: Some pupils do not write 24-hour times as four digits, for example 1:50 rather than 01:50 for 1.50 a.m. Some pupils may write ‘one pound and eight pence’ as ‘£1.8’ Some pupils may use both ‘£’ and ‘p’ symbols, for example ‘£4.56p’ Some pupils may write ‘four pounds and fifty six pence’ as ‘4.56p’ or ‘£456’
Convince me that 15 rounds to 20 to the nearest 10 What is the same and what is different: 595, 649, 534 and 634 Kenny thinks that 4.6 rounds to 4 to the nearest whole number. Do you agree? Explain your answer. KM: KM: NCETM: Learning review KM: Some pupils may truncate instead of round Some pupils may misunderstand the rounding process as one that from the end of the number; for example 347 to the nearest 100 is worked out as 347 350 400. Some pupils may round down at the half way point, rather than round up. Mathematical movement 8 Key concepts (National Curriculum statements) The Big Picture: describe positions on a 2-D grid as coordinates in the quadrant plot specified points and draw to complete a given polygon describe movements between positions as translations of a unit to the left/right and up/down Themes Possible key learning points Understand and use Cartesian coordinates Use transformations to move shapes Bring on the Maths+: Moving on up! Position and direction: v2 Bring on the Maths+: Lower Key Stage 2 Position and direction: Coordinates in the first quadrant Use coordinates to describe the position of a point in the first quadrant Plot points in the first quadrant using co-ordinates Use coordinates to plot a set of points to construct a polygon Solve problems involving coordinates Describe movements between positions as translations of a given unit to the left/right Describe movements between positions as translations of a given unit to the up/down Describe movements between positions as translations of a given unit to the left/right and up/down Prerequisites Mathematical language Pedagogical
Add and subtract numbers mentally, including a three-digit number and ones, tens or hundreds Use column addition and subtraction for numbers up to four digits Estimate the answer to a calculation Bring on the Maths+: Moving on up! Calculating: #1 Addition Subtraction Sum, Total Difference, Minus, Less Column addition Column subtraction Exchange Operation Estimate Pupils understand ‘mentally’ as ‘in your head’ or ‘with jottngs’. Ensure that pupils can deal with column subtractions that include a 0 within the first number; e.g. 48027 – 8437. Later in this stage there is a further opportunity to develop and practice calculation skills with a particular emphasis on checking, approximating or estimating the answer. KM: and NCETM: , NCETM: Common approaches To avoid confusion with language, all teachers use ‘sum’ to refer only to the result of an addition. Teachers say ‘complete these calculations’ instead of ‘complete these sums’ All pupils use books / paper with 7mm squares and ensure that each digit is written in one square When carrying, numbers being carried are placed beneath the answer line During column subtraction the language of ‘exchanging’ is used instead of ‘borrowing’. When exchanging, numbers being altered or moved are written above the calculation Reasoning opportunities and probing questions Suggested activities Possible misconceptions
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 Possible learning intentions Possible success criteria Solve problems involving scaling Explore enlargement Solve problems involving sharing and grouping on the Maths+: Moving on up! and proportion: #1 Y7 Bring on the Maths Problem Solving: #1, #2, #3 Identify when a comparison problem can be solved multiplication Identify when a comparison problem can be solved using division Identify when a comparison problem requires both division and multiplication Find the value of a single item in a comparison problem Use the value of a single item to solve a comparison problem Understand the meaning of enlargement Understand the meaning of factor Recognise when one shape is an enlargement of another Use a factor to complete an enlargement Find the scale factor for a given enlargement Use knowledge of fractions to solve a sharing (or grouping) problem Use knowledge of multiples to solve a sharing (or grouping) problem Prerequisites Mathematical language Pedagogical notes Recall multiplication for multiplication tables up to 12 × 12 Recall division facts for multiplication tables up to 12 × 12 Find fractions of an amount Find multiples of a given number Proportion Quantity Integer Similar (shapes) Enlargement factor Group Share Multiples Any work on enlargement should only include enlargements using a scale factor. The concept of a centre of enlargement is a future development. NCETM: NCETM: Common approaches All pupils are explicitly taught to use the bar model as a way to represent a problem involving proportional reasoning Reasoning opportunities and probing questions Suggested activities Possible misconceptions