Pupils need to be able to read, write and order numbers to at least 20 Subitise small groups of objects (i.e. can say how many there are without needing to count each individual object.) Calculation, Calculate Odd, Even Multiply, Multiplication, Times, Product Repeated addition Array Divide, Division Groups Grouping Sharing This is the first pupils explore multiplication and division. Through grouping and sharing, pupils make connections between arrays, number patterns, and counting in twos, fives and tens. Pupils need to work with small quantities and experience: doubling and halving numbers and quantities; and finding simple fractions of objects, numbers and quantities. Note: Calculating mathematical statements for multiplication and division within the multiplication tables and writing them using the multiplication (×), division (÷) and equals (=) signs is in Stage 2 Showing that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot is explored in Stage 2 KM: and NCETM: NCETM: , , NCETM: Common approaches A variety of concrete apparatus – Numicon, Cuisenaire, 10 Frame, Counters -, are used to help pupils visualise odd /even numbers, doubling/halving and solve multiplication and division problems. Teachers say equally’ and not just ‘share’ when solving problems involving division. Reasoning opportunities and probing questions Suggested activities Possible misconceptions
Show me a number that you can half. And another. And another. Convince me double 6 is 12. Convince me 3 multiplied by 4 is 12 (using concrete apparatus such as Numicon, Cuisenaire, etc). Convince me if 12 sweets are shared equally between 3 friend, each friend will receive 4 sweets (using concrete apparatus such as Numicon, Cuisenaire, etc). Benny thinks you can double any number but only halve even numbers. Do you agree with Benny? Explain your answer. KM: NRICH: NRICH: NCETM: Learning review NCETM: Some pupils may interpret ‘3 multiplied by 4’ as ‘4 groups/lots of 3’ rather than ‘3 groups/lots of 4’ Some pupils may try to give whole number answers for the half of an odd number – eg Half of 9 is 4 (or 5) Some pupils may not share equally when solving division problems – eg Divide 10 by 2: Answer 6 and 4 Numbers and the number system: deeper 12 hours Key concepts (National Curriculum statements) The Big Picture: read and write numbers from 1 to 20 in numerals and words. identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least read and write numbers to 100 in numerals; count in multiples of twos, fives and tens Themes Possible key learning points Explore the value of numbers Explore numbers live in our number system Solve problems comparing the value of numbers Investigate number patterns Solve problems involving: reading and writing numbers from 1 to 20 in numerals and words. identifying and representing numbers objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least counting, reading and writing numbers to 100 in numerals; count in multiples of twos, fives and tens Prerequisites Mathematical language Pedagogical notes
Themes Possible key learning points Explore ways of writing mathematical statements Solve addition and subtraction problems problems involving: - reading , writing and interpreting mathematical statements involving addition (+), subtraction (–) and equals (=) signs - adding and subtracting and two-digit numbers to 20, including zero - one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9 Prerequisites Mathematical language Pedagogical notes Know the symbols ‘+’, ‘–‘ and ‘=’ Know the language of addition Know the language of subtraction Read statements involving the symbols ‘+’, ‘–‘ and ‘=’ involving numbers up to 20 Interpret statements involving the symbols ‘+’, ‘–‘ and ‘=’ involving numbers up to 20 Write statements involving the symbols ‘+’, ‘–‘ and ‘=’ involving numbers up to 20 Solve calculations involving numbers up to 20 given statements using the symbols ‘+’, ‘–‘ and ‘=’ missing number problems involving numbers to 20 given statements using the symbols ‘+’, ‘–‘ and ‘=’ Add and subtract one- and two-digit numbers to 20, including zero Add, subtract Count on, count back More, less Plus, minus, total, sum Difference between equal to Notation The symbols ‘+’, ‘–‘ and ‘=’ Note: Curriculum time has been prioritised to ensure all pupils secure a deep understanding of the age related expectations for the Number strands of the Year 1 Programme of The key concepts for this unit are the same as the other Stage 1 ‘Calculating: addition and subtraction lI’ unit but this unit should be taught with an increased emphasis on developing pupils’ reasoning skills, solving more complex problems and using explicit misconceptions and mistakes to deepen and challenge pupils’ understanding. Further guidance on teaching for mastery can be found in the ‘Introduction’ of the NCETM: resources. Reasoning opportunities and probing questions Suggested activities Possible misconceptions
Describe position using language such as ‘behind’, ‘next to’, ‘on top of’ and ‘between’ Describe position, direction and movement, including whole, half, quarter and three-quarter turns Connect moving clockwise with movement on a clock face Forwards, Backwards Left, Angle Right angle Turn Quarter, Half, Three quarters Rotation Position Direction Straight Line Clockwise, anticlockwise Pupils experience following instructions, devising and stating instructions for other pupils to follow and programming a robot with instructions. This unit is an ideal opportunity to introduce the four points of the compass. Understanding degrees as a way of measuring angles is not introduced Stage 5. It is thought that the origin of the name angle’ is the Latin word for ‘upright’; as in perpendicular to the horizontal base in architectural contexts. NCETM: Common approaches All pupils experience the ‘feel’ of a angle by turning through quarter turns Reasoning opportunities and probing questions Suggested activities Possible misconceptions
Show me a three-digit number with a tens unit of ‘6’. And another. And another … Benny writes the number three hundred and six as ‘3006’. Do you agree with Benny? Using a number line, show me the number 243, 567, 909, etc. NCETM: NRICH: Learning review KM: NCETM: Some pupils may write three-digit numbers literally, for example, four hundred and six as ‘4006’ Some pupils may ignore place value and simply write the digits mentioned in a number, for example, four hundred and six as ‘46’ Counting and comparing 12 hours Key concepts (National Curriculum statements) The Big Picture: compare and order numbers up to 1000 count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number solve number problems and practical problems involving these ideas Themes Possible key learning points Work with numbers up to 1000 Explore ways of counting problems involving counting and comparing on the Maths+: Lower Key Stage 2 Number and Value: Ordering numbers, Counting I, Counting II Order numbers up to 1000 Compare numbers up to 1000 Count (from 0) in multiples of 4 Count (from 0) in multiples of 8 Count (from 0) in multiples of 50 Count (from 0) in multiples of 100 Find 10 more than a given number Find 10 less than a given number Find 100 more than a given number Find 100 less than a given number Prerequisites Mathematical language Pedagogical
Measure length m, cm Measure mass kg, g Measure volume / capacity using l, ml Length, distance Mass Volume Capacity centimetre, millimetre Kilogram, gram Litre, millilitre Perimeter 2-D Notation Abbreviations of units in the metric system: m, cm, mm, kg, g, l, ml In this unit pupils should only measure perimeter; e.g. with string. Calculating perimeter is in 4. Weight and mass are distinct though they are confused in everyday language. Weight is the force due to gravity, and is calculated as mass multiplied by the acceleration due to gravity. Therefore weight varies due to location while mass is a constant measurement. The prefix means one hundredth, and the prefix ‘milli-‘ means one thousandth. These words are of Latin origin. The prefix ‘kilo-‘ means one thousand. This is Greek in origin. NCETM: Common approaches Every classroom has a sack of sand (25 kg), a bag of sugar (1 kg), a cheque book (1 cheque is 1 gram), a bottle of water (1 litre, and also 1 kg of water) and a teaspoon (5 ml) Teachers ensure that pupils correctly position the ‘0’ on the ruler when measuring the line. Reasoning opportunities and probing questions Suggested activities Possible misconceptions Show me something in the classroom that is between 20 cm and 40 cm. And another. And another. measures two lines; 1 m and 35 cm. He says the difference is 650 mm. Do you agree with Kenny? Explain your answer. Convince me how to find the perimeter of a shape. Create a shape with a perimeter greater than 30 cm. NRICH: NRICH: NCETM: Learning review KM: , NCETM: Some pupils may think that you put the end of the ruler (rather than the ‘0’) at the start of a line to measure it. Some pupils may think that the conversion factor between all measures is multiply or divide by 10. Some pupils may think that milli- refers to ‘million’
Show me a right angle in this classroom. And another. And another. Show me an angle in this classroom less (greater) than a right angle. And another. And another. Is this a right angle? Explain your answer. Convince me why this is not called a ‘left’ NCETM: NRICH: NCETM: NCETM: Learning review NCETM: Some pupils may think that right angles have to look like this: Some pupils may think that right angles have to be created from a horizontal and vertical line Some pupils may that all turns have to be in a clockwise direction Calculating fractions and decimals 8 hours Key concepts (National Curriculum statements) The Big Picture: count 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 tenths as a fraction and as a decimal Count 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 notes
Measuring space 8 hours Key concepts (National Curriculum statements) The Big Picture: convert between different units of measure [for example, kilometre to metre; hour to minute] solve simple measure and money problems involving fractions and decimals to two decimal places Themes Possible key learning points Convert between measures Solve problems involving measurement problems involving money on the Maths+: Lower Key Stage 2 Measures: Measures Convert between kilometres and metres Convert between centimetres and millimetres Convert between kilograms and grams Convert between litres and millilitres Solve measurement problems involving fractions Solve money problems involving fractions Solve measurement problems involving decimals to two decimal places Solve money problems involving decimals to two decimal places Prerequisites Mathematical language Pedagogical notes Use a ruler to measure lengths to the nearest millimetre Use digital and mechanical scales to measure mass Use measuring vessels to measure a volume of liquid Choose appropriate to state the result of a measurement Compare the length (mass, volume, capacity) of two or more objects measurement problems involving addition or subtraction Length, distance Mass Volume Capacity centimetre, millimetre Kilogram, gram millilitre Hour, minute, second Decimal Notation Abbreviations of units in the metric system: m, cm, mm, kg, g, l, ml Weight and mass are distinct though they are confused in everyday language. Weight is the force due to gravity, and is calculated as mass multiplied by the acceleration due to gravity. Therefore weight varies due to location while mass is a constant measurement. The prefix ‘centi-‘ means one hundredth, and the prefix ‘milli-‘ means one thousandth. These words are of Latin origin. The prefix ‘kilo-‘ means one thousand. This is Greek in origin. Common approaches classroom has a sack of sand (25 kg), a bag of sugar (1 kg), a cheque book (1 cheque is 1 gram), a bottle of water (1 litre, and also 1 kg of water) and a teaspoon (5 ml) Reasoning opportunities and probing questions Suggested activities Possible misconceptions