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- New Mathematics Curriculum (2014)
- Year 2 programme of study
- Year 2: Number and Place Value
- Count in steps of 2, 3, and 5 from 0, and count in tens from any number, forward or backward
- Recognise the place value of each digit in a two-digit number (tens, ones)
- Identify, represent and estimate numbers using different representations, including the number line
- Compare and order numbers from 0 up to 100; use <, > and = signs
- Read and write numbers to at least 100 in numerals and in words
- Use place value and number facts to solve problems
- Year 2: Addition and Subtraction
- Solve simple one-step problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods
- Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- Add and 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;adding three one-digit numbers
- Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
- Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems
- Year 2: Multiplication and Division
- Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
- Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
- Recognise and use the inverse relationship between multiplication and division in calculations
- Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
- solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.
- Year 2: Fractions
- Year 2: Measures
- Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
- Compare and order lengths, mass, volume/capacity and record the results using >, < and =
- Read relevant scales to the nearest numbered unit
- Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
- Solve simple problems in a practical context involving addition and subtraction of money
- find different combinations of coins that equal the same amounts of money
- Compare and sequence intervals of time
- Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times
- Year 2: Geometry: Properties of Shapes
- Identify and describe the properties of 2-D shapes, including the number of sides and symmetry in a vertical line
- Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
- Identify 2-D shapes on the surface of 3-D shapes, for example a circle on a cylinder and a triangle on a pyramid
- Compare and sort common 2-D and 3-D shapes and everyday objects
- Year 2: Geometry: Position, Direction, Motion
- Year 2: Statistics
- Year 2: Number and Place Value
- Year 3 programme of study
- Year 3: Number and Place Value
- Count from 0 in multiples of 4, 8, 50 and 100; finding 10 or 100 more or less than a given number
- Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
- Compare and order numbers up to 1000
- Identify, represent and estimate numbers using different representations
- Read and write numbers to at least 1000 in numerals and in words
- Solve number problems and practical problems involving these ideas
- Year 3: Addition and Subtraction
- Add and subtract numbers mentally, including: a three-digit number and ones; a three-digit number and tens; a three-digit number and hundreds
- Add and subtract numbers with up to three digits, using the efficient written methods of columnar addition and subtraction
- Estimate the answer to a calculation and use inverse operations to check answers
- Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
- Year 3: Multiplication and Division
- Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
- Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to efficient written methods
- Solve problems, including missing number problems, involving multiplication and division, including integer scaling problems and correspondence problems in which n objects are connected to m objects
- Year 3: Fractions
- 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
- Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
- Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
- Recognise and show, using diagrams, equivalent fractions with small denominators
- Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
- Compare and order unit fractions with the same denominator
- Solve problems that involve all of the above
- Year 3: Measures
- Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
- Measure the perimeter of simple 2-D shapes
- Add and subtract amounts of money to give change, using both £ and p in practical contexts
- Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24- hour clocks
- Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight
- Know the number of seconds in a minute and the number of days in each month, year and leap year
- Compare durations of events, for example to calculate the time taken by particular events or tasks
- Year 3: Geometry: Properties of Shapes
- Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations; and describe them with increasing accuracy
- Recognise angles as a property of shape and associate angles with turning
- Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
- Identify horizontal, vertical, perpendicular and parallel lines in relation to other lines
- Year 3: Data
- Year 3: Number and Place Value
- Year 4 programme of study
- Year 4: Number, place value and rounding
- Count in multiples of 6, 7, 9, 25 and 1000
- Count backwards through zero to include negative numbers
- Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- Order and compare numbers beyond 1000
- Identify, represent and estimate numbers using different representations
- Round any number to the nearest 10, 100 or 1000
- Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value
- Solve number and practical problems that involve all of the above and with increasingly large positive numbers
- Year 4: Addition and subtraction
- Add and subtract numbers with up to 4 digits using the efficient written methods of columnar addition and subtraction where appropriate
- Estimate and use inverse operations to check answers to a calculation
- Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
- Year 4: Multiplication and division
- Recall multiplication and division facts for multiplication tables up to 12 × 12
- Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
- Solve problems involving multiplying and adding, including using the distributive law and harder multiplication problems such as which n objects are connected to m objects.
- Year 4: Fractions
- Count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten
- Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
- identify, name and write equivalent fractions of a given fraction, including tenths and hundredths
- Add and subtract fractions with the same denominator
- Year 4: Decimals and fractions
- Recognise and write decimal equivalents of any number of tenths or hundredths
- Recognise and write decimal equivalents to 1/4; 1/2; 3/4
- Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths
- Round decimals with one decimal place to the nearest whole number
- Compare numbers with the same number of decimal places up to two decimal places
- Solve simple measure and money problems involving fractions and decimals to two decimal places
- Year 4: Measures
- Convert between different units of measure (e.g. kilometre to metre; hour to minute)
- Find the area of rectilinear shapes by counting
- Estimate, compare and calculate different measures, including money in pounds and pence
- Read, write and convert time between analogue and digital 12 and 24-hour clocks
- Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.
- Year 4: Geometry: properties of shapes
- Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
- Identify acute and obtuse angles and compare and order angles up to two right angles by size
- Identify lines of symmetry in 2-D shapes presented in different orientations
- Complete a simple symmetric figure with respect to a specific line of symmetry
- Year 4: Geometry: position, direction, motion
- Year 4: Data
- Year 4: Number, place value and rounding
- Year 5 programme of study
- Year 5: Number and place value
- Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
- Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
- Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers through zero
- Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
- Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
- Year 5: Addition and subtraction
- Add and subtract whole numbers with more than 4 digits, including using efficient written methods (columnar addition and subtraction)
- Add and subtract numbers mentally with increasingly large numbers
- Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
- Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
- Year 5: Multiplication and Division
- Identify multiples and factors, including finding all factor pairs
- Solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors
- Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
- Establish whether a number up to 100 is prime and recall prime numbers up to 19
- Multiply numbers up to 4 digits by a one- or two-digit number using an efficient written method, including long multiplication for two-digit numbers
- Multiply and divide numbers mentally drawing upon known facts
- Divide numbers up to 4 digits by a one-digit number using the efficient written method of short division and interpret remainders appropriately for the context
- Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
- Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)
- Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
- Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
- Year 5: Fractions
- Compare and order fractions whose denominators are all multiples of the same number
- Recognise mixed numbers and improper fractions and convert from one form to the other
- Add and subtract fractions with the same denominator and related fractions; write mathematical statements >1 as a mixed number (e.g. 2/5 + 4/5 = 6/5 = 11/5)
- Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.
- Year 5: Decimals and fractions
- Read and write decimal numbers as fractions (e.g. 0.71 = 71/100)
- Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
- Round decimals with two decimal places to the nearest whole number and to one decimal place
- Read, write, order and compare numbers with up to three decimal places
- Solve problems involving number up to three decimal places.
- Year 5: Percentages, decimals and fractions
- Recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred”, and write percentages as a fraction with denominator hundred, and as a decimal fraction
- Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25.
- Year 5: Measures
- Convert between different units of measure (e.g. kilometre and metre; metre and centimetre; centimetre and millimetre; kilogram and gram; litre and millilitre)
- Understand and use basic equivalences between metric and common imperial units and express them in approximate terms
- Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
- Calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes
- Recognise and estimate volume (e.g. using 1 cm3 blocks to build cubes and cuboids) and capacity (e.g. using water)
- Solve problems involving converting between units of time
- Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.
- Year 5: Geometry: properties of shapes
- Identify 3-D shapes, including cubes and cuboids, from 2-D representations
- Know angles are measured in degrees; estimate and measure them and draw a given angle, writing its size in degrees (°)
- Identify: multiples of 90°, angles at a point on a straight line and ½ a turn (total 180°); angles at a point and one whole turn (total 360°); reflex angles; and compare different angles
- Draw shapes using given dimensions and angles
- State and use the properties of a rectangle (including squares) to deduce related facts
- Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
- Year 5: Geometry: position, direction, motion
- Year 5: Data
- Year 5: Number and place value
- Year 6 programme of study
- Year 6: Number and place value
- Year 6: Addition, subtraction, multiplication and division
- Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the efficient written method of long multiplication
- Divide numbers up to 4 digits by a two-digit whole number using the efficient written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
- Perform mental calculations, including with mixed operations and large numbers
- Identify common factors, common multiples and prime numbers
- Use their knowledge of the order of operations to carry out calculations involving the four operations
- Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
- Solve problems involving addition, subtraction, multiplication and division
- Use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy.
- Year 6: Fractions
- Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
- Compare and order fractions, including fractions >1
- Associate a fraction with division to calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8)
- Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
- Multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1/4 × 1/2 = 1/8)
- Divide proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/6 ).
- Year 6: Decimals and fractions
- Identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places
- Multiply one-digit numbers with up to two decimal places 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
- Year 6: Percentages, decimals and fractions
- Year 6: Ratio and proportion
- Solve problems involving the relative sizes of two quantities, including similarity
- Solve problems involving unequal sharing and grouping.
- 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
- Year 6: Algebra
- Year 6: Measures
- Year 6: Geometry: properties of shapes
- Recognise, describe and build simple 3-D shapes, including making nets
- Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
- Find unknown angles where they meet at a point, are on a straight line, and are vertically opposite
- Describe positions on the full coordinate grid (all four quadrants)
- Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.
- Draw 2-D shapes using given dimensions and angles
- Year 6: Statistics
- Year 2 programme of study
- Addition and Subtraction
- Multiplication and Division
- Ordering, Comparing and Reading Numbers
- Word Problems
- Using a Calculator
- Fractions Decimals and Percentages
- Measuring and Time
- Shape and Space
- Data Handling
- Money
- Sorting and Classifying
- Partitioning and Place Value
- Common Core Standards
- Grade 1
- Grade 2
- Grade 2 Operations & Algebraic Thinking
- 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations w
- 2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers
- 2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends
- 2.OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
- Grade 2 Number and Operations in Base Ten
- 2.NBT.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
- 2.NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s.
- 2.NBT.3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- 2.NBT.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons
- 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in a
- Grade 2 Measurement and Data
- 2.MD.1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
- 2.MD.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
- 2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and c symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
- 2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph
- Grade 2 Geometry
- 2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
- 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
- Grade 2 Operations & Algebraic Thinking
- Grade 3
- Grade 3 Operations & Algebraic Thinking
- 3.OA.1.Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
- 3.OA.2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ├À 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of
- 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem
- 3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48..
- 3.OA.5. Apply properties of operations as strategies to multiply and divide. Examples: If 6 ├ù 4 = 24 is known, then 4 ├ù 6 = 24 is also known. (Commutative property of multiplication.) 3 ├ù 5 ├ù 2 can be found by 3 ├ù 5 = 15, then 15 ├ù 2 = 30, or by 5 ├
- 3.OA.6. Understand division as an unknown-factor problem. For example, find 32 ├À 8 by finding the number that makes 32 when multiplied by 8
- 3.OA.7.Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 ├ù 5 = 40, one knows 40 ├À 5 = 8) or properties of operations. By the end of Grade 3, know from memory all
- 3.OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rou
- 3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be de
- Grade 3 Number & Operations in Base Ten
- Grade 3 Number & OperationsÔÇöFractions
- 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b
- 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- Grade 3 Measurement and Data
- 3.MD.1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
- 3.MD.2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same
- 3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ÔÇ£how many moreÔÇØ and ÔÇ£how many lessÔÇØ problems using information presented in scaled bar graphs. For example, draw a
- 3.MD.5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
- Grade 3 Geometry
- Grade 3 Operations & Algebraic Thinking
- Grade 4
- Grade 4 Operations & Algebraic Thinking
- 4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations
- 4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison
- 4.OA.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the u
- 4.OA.4. Find all factor pairs for a whole number in the range 1ÔÇô100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1ÔÇô100 is a multiple of a given one-digit number. Determine whe
- 4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule ÔÇ£Add 3ÔÇØ and the starting number 1, generate terms in the resulting s
- Grade 4 Number & Operations in Base Ten
- 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ├À 70 = 10 by applying concepts of place value and division.
- 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- 4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place.
- 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm
- 4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, recta
- 4.NBT.6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and ex
- Grade 4 Number and Operations - Fractions
- 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle
- 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2
- 4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
- 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
- 4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions,
- Grade 4 Measurement and Data
- 4.MD.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit
- 4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given
- 4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
- 4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 4.MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
- Grade 4 Operations & Algebraic Thinking
- Browse by Primary Framework Objectives
- Year 2 Primary Framework
- Year 2 Block A
- Read and write two-digit and three-digit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers
- Count up to 100 objects by grouping them and counting in tens, fives or twos; explain what each digit in a two-digit number represents, including numbers where 0 is a place holder; partition two-digit numbers in different ways, including into multiples of
- Order two-digit numbers and position them on a number line; use the greater than (>) and less than (<) signs
- Estimate a number of objects; round two-digit numbers to the nearest 10
- Add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers
- Understand that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentences
- Year 2 Block B
- Describe patterns and relationships involving numbers or shapes, make predictions and test these with examples
- Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence
- Understand Derive and recall all addition and subtraction facts for each number to at least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 100
- Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10
- Read and write two-digit and three-digit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers
- Visualise common 2-D shapes and 3-D solids; identify shapes from pictures of them in different positions and orientations; sort, make and describe shapes, referring to their properties
- Identify reflective symmetry in patterns and 2-D shapes and draw lines of symmetry in shapes
- Year 2 Block C
- Follow a line of enquiry; answer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagrams
- Use lists, tables and diagrams to sort objects; explain choices using appropriate language
- Estimate, compare and measure lengths, weights and capacities, choosing and using standard units (m, cm, kg, litre) and suitable measuring instruments
- Read the numbered divisions on a scale, and interpret the divisions between them (e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions 0, 5, 10, 15 and 20 numbered); use a ruler to draw and measure lines to the nearest centimetre
- Year 2 Block D
- Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence
- Add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers
- Estimate, compare and measure lengths, weights and capacities, choosing and using standard units (m, cm, kg, litre) and suitable measuring instruments
- Read the numbered divisions on a scale, and interpret the divisions between them (e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions 0, 5, 10, 15 and 20 numbered); use a ruler to draw and measure lines to the nearest centimetre
- Use units of time (seconds, minutes, hours, days) and know the relationships between them; read the time to the quarter hour; identify time intervals, including those that cross the hour
- Year 2 Block E
- Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence
- Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division
- Use the symbols +, -, x, ÷ and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence
- Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves
- Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10
- Year 2 Block A
- Year 3 Primary Framework
- Year 3 Block A
- Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations
- Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to zero in single-digit steps or multiples of 10.
- Partition three-digit numbers into multiples of 100, 10 and 1 in different ways
- Round two-digit or three-digit numbers to the nearest 10 or 100 and give estimates for their sums and differences
- Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100
- Add or subtract mentally combinations of one-digit and two-digit numbers
- Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers
- Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000
- Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect
- Use practical and informal written methods to multiply and divide two-digit numbers; round remainders up or down, depending on the context
- Year 3 Block B
- Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations
- Identify patterns and relationships involving numbers or shapes, and use these to solve problems
- Read and write proper fractions, interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents
- Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100
- Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000
- Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check calculations
- Relate 2-D shapes and 3-D solids to drawings of them; describe, visualise, classify, draw and make the shapes
- Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side
- Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles
- Year 3 Block C
- Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres; choose and use appropriate units to estimate, measure and record measurements
- Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy
- Read the time on a 12-hour digital clock and to the nearest 5 minutes on an analogue clock; calculate time intervals and find start or end times for a given time interval
- Answer a question by collecting, organising and interpreting data; use tally charts, frequency tables, pictograms and bar charts to represent results and illustrate observations; use ICT to create a simple bar chart
- Use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion
- Year 3 Block D
- Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations
- Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check calculations
- Add or subtract mentally combinations of one-digit and two-digit numbers
- Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers
- Use practical and informal written methods to multiply and divide two-digit numbers
- Understand that division is the inverse of multiplication and vice versa; use this to derive and record related multiplication and division number sentences
- Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side
- Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles
- Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres; choose and use appropriate units to estimate, measure and record measurements
- Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy
- Read the time on a 12-hour digital clock and to the nearest 5 minutes on an analogue clock; calculate time intervals and find start or end times for a given time interval
- Year 3 Block E
- Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations
- Identify patterns and relationships involving numbers or shapes, and use these to solve problems
- Partition three-digit numbers into multiples of 100, 10 and 1 in different ways
- Read and write proper fractions interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents
- Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100
- Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000
- Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers
- Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect
- Use practical and informal written methods to multiply and divide two-digit numbers
- Understand that division is the inverse of multiplication and vice versa; use this to derive and record related multiplication and division number sentences
- Year 3 Block A
- Year 4 Primary Framework
- Year 4 Block A
- Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate
- Partition, round and order four-digit whole numbers; use positive and negative numbers in context and position them on a number line; state inequalities using the symbols < and >
- Recognise and continue number sequences formed by counting on or back in steps of constant size
- Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one-place and two-place decimals on a number line
- Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000
- Add or subtract mentally pairs of two-digit whole numbers
- Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and £ & p
- Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple
- Multiply and divide numbers to 1000 by 10 and then 100 (whole-number answers), understanding the effect; relate to scaling up or down
- Identify the doubles of two-digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves
- Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders
- Use knowledge of rounding, number operations and inverses to estimate and check calculations
- Year 4 Block B
- Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples
- Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate
- Use knowledge of rounding, number operations and inverses to estimate and check calculations
- Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000
- Identify the doubles of two-digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves
- Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple
- Draw polygons and classify them by identifying their properties, including their line symmetry
- Year 4 Block C
- Answer a question by identifying what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate
- Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measureme
- Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit
- Compare the impact of representations where scales have intervals of differing step size
- Year 4 Block D
- Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate
- Add or subtract mentally pairs of two-digit whole numbers
- Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and £ and p
- Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple
- Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders
- Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one-place and two-place decimals on a number line
- Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measureme
- Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit
- Read time to the nearest minute; use am, pm and 12-hour clock notation; choose units of time to measure time intervals; calculate time intervals from clocks and timetables
- Draw rectangles and measure and calculate their perimeters; find the area of rectilinear shapes drawn on a square grid by counting squares
- Know that angles are measured in degrees and that one whole turn is 360°; compare and order angles less than 180°
- Year 4 Block E
- Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple
- Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders
- Recognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths
- Use diagrams to identify equivalent fractions; interpret mixed numbers and position them on a number line (e.g. 31/2)
- Find fractions of numbers, quantities or shapes
- Year 4 Block A
- Year 5 Primary Framework
- Year 5 Block A
- Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use
- Count from any given number in whole-number and decimal steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line
- Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers
- Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences and doubles and halves of decimals
- Use efficient written methods to add and subtract whole numbers and decimals with up to two places
- Recall quickly multiplication facts up to 10 x 10 and use them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division facts
- Identify pairs of factors of two-digit whole numbers and find common multiples
- Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000
- Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations
- Year 5 Block B
- Explore patterns, properties and relationships and propose a general statement involving numbers or shapes; identify examples for which the statement is true or false
- Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences and doubles and halves of decimals
- Recall quickly multiplication facts up to 10 x 10 and use them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division facts
- Identify pairs of factors of two-digit whole numbers and find common multiples
- Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations
- Use efficient written methods to add and subtract whole numbers and decimals with up to two places
- Identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge of properties to draw 2-D shapes and identify and draw nets of 3-D shapes
- Complete patterns with up to two lines of symmetry; draw the position of a shape after a reflection or translation
- Year 5 Block C
- Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6kg to 2600g)
- Interpret a reading that lies between two unnumbered divisions on a scale
- Year 5 Block D
- Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use
- Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations
- Use efficient written methods to add and subtract whole numbers and decimals with up to two places
- Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000
- Refine and use efficient written methods to multiply and divide HTU x U, TU x TU, U.t x U and HTU ÷ U
- Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides
- Complete patterns with up to two lines of symmetry; draw the position of a shape after a reflection or translation
- Estimate, draw and measure acute and obtuse angles using an angle measurer or protractor to a suitable degree of accuracy; calculate angles in a straight line
- Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place
- Interpret a reading that lies between two unnumbered divisions on a scale
- Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangles area
- Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals
- Year 5 Block E
- Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use
- Express a smaller whole number as a fraction of a larger one (e.g. recognise that 5 out of 8 is 5/8); find equivalent fractions (e.g. 7/10 = 14/20, or 19/10 = 19/10); relate fractions to their decimal representations
- Recall quickly multiplication facts up to 10 x 10 and use them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division facts
- Identify pairs of factors of two-digit whole numbers and find common multiples
- Extend mental methods for whole-number calculations, for example to multiply a two-digit number by a one-digit number (e.g. 12 x 9), to multiply by 25 (e.g. 16 x 25), to subtract one near-multiple of 1000 from another
- Refine and use efficient written methods to multiply and divide HTU x U, TU x TU, U.t x U and HTU ÷ U
- Find fractions using division (e.g. 1/100 of 5 kg), and percentages of numbers and quantities (e.g. 10%, 5% and 15% of 80)
- Year 5 Block A
- Year 6 Primary Framework
- Year 6 Block A
- Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use
- Find the difference between a positive and a negative integer, or two negative integers, in context
- Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line
- Use knowledge of place value and multiplication facts to 10 x 10 to derive related multiplication and division facts involving decimals
- Calculate mentally with integers and decimals
- Use approximations, inverse operations and tests of divisibility to estimate and check results
- Year 6 Block B
- Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols
- Use knowledge of multiplication facts to derive quickly squares of numbers to 12 x 12 and the corresponding squares of multiples of 10
- Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit numbers
- Use approximations, inverse operations and tests of divisibility to estimate and check results
- Describe, identify and visualise parallel and perpendicular edges or faces; use these properties to classify 2-D shapes and 3-D solids
- Make and draw shapes with increasing accuracy and apply knowledge of their properties
- Year 6 Block C
- Select and use standard metric units of measure and convert between units using decimals to two places
- Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs; interpret pie charts
- Read and interpret scales on a range of measuring instruments, recognising that the measurement made is approximate and recording results to a required degree of accuracy; compare readings on different scales, for example when using different instruments
- Use a calculator to solve problems involving multi-step calculations
- Year 6 Block D
- Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use
- Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U
- Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer
- Use a calculator to solve problems involving multi-step calculations
- Use approximations, inverse operations and tests of divisibility to estimate and check results
- Select and use standard metric units of measure and convert between units using decimals to two places (e.g. change 2.75 litres to 2750ml, or vice versa)
- Read and interpret scales on a range of measuring instruments, recognising that the measurement made is approximate and recording results to a required degree of accuracy; compare readings on different scales, for example when using different instruments
- Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares
- Estimate angles, and use a protractor to measure and draw them, on their own and in shapes; calculate angles in a triangle or around a point
- Use coordinates in the first quadrant to draw, locate and complete shapes that meet given properties
- Year 6 Block E
- Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use
- Use knowledge of place value and multiplication facts to 10 x 10 to derive related multiplication and division facts involving decimals
- Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer
- Use a calculator to solve problems involving multi-step calculations
- Express one quantity as a percentage of another find equivalent percentages, decimals and fractions
- Relate fractions to multiplication and division
- Year 6 Block A
- Year 2 Primary Framework
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