Can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.

Read and write numbers from 1 to 20 in numerals and words.

Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.

Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens.

Given a number, identify one more and one less.

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.

Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and 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.

Count from 0 in multiples of 4, 8, 50 and 100; find 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 up to 1000 in numerals and in words.

Solve number problems and practical problems involving these ideas.

Order and compare numbers beyond 1000.

Use the four operations with whole numbers to solve problems.

Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line.

Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.

Compare, describe and solve practical problems for lengths and heights [for example, long/short, longer/shorter, tall/short, double/half].

Compare, describe and solve practical problems for mass/weight [for example, heavy/light, heavier than, lighter than].

Compare, describe and solve practical problems for capacity and volume [for example, full/empty, more than, less than, half, half full, quarter].

Measure and begin to record the lengths.

Measure and begin to record mass/weight.

Measure and begin to record capacity and volume.

Measure and begin to record time (hours, minutes, seconds).

Recognise and know the value of different denominations of coins and notes.

Recognise and use language relating to dates, including days of the week, weeks, months and years.

Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

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.

Know the number of minutes in an hour and the number of hours in a day.

Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml).

Read, write and convert time between analogue and digital 12- and 24-hour clocks.

Read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs.

Represent and use number bonds and related subtraction facts within 20.

Add and subtract one-digit and two-digit numbers to 20, including zero.

Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

Solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures.

Solve problems with addition and subtraction 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 solve missing number problems.

add and subtract numbers mentally, including a three-digit number and ones, a three-digit number and tens, a three-digit number and hundreds.

Recognise, find and name a half as one of two equal parts of an object, shape or quantity.

Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables.

Interpret and construct simple pictograms, tally charts, block diagrams and simple tables.

Represent and solve problems involving addition and subtraction.

Understand and apply properties of operations and the relationship between addition and subtraction.

Apply properties of operations as strategies to add and subtract.

Understand subtraction as an unknown-addend problem.

Add and subtract within 20.

Relate counting to addition and subtraction.

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

Work with addition and subtraction equations.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

Understand that the two digits of a two-digit number represent amounts of tens and ones.

Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences).

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10.

Measure lengths indirectly and by iterating length units.

Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Tell and write time.

Reason with shapes and their attributes.

Compose two-dimensional shapes or three-dimensional shapes.

Understand place value.

Extend the counting sequence.

Use place value understanding and properties of operations to add and subtract.

Represent and interpret data.

Tell and write time in hours and half-hours using analog and digital clocks.

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end.

Organize, represent, and interpret data with up to three categories.

Partition circles and rectangles into two and four equal shares, describe the shares using the words like halves, fourths, and quarters.

Understand place value

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.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Work with equal groups of objects to gain foundations for multiplication.

Count within 1000; skip-count by 5s, 10s, and 100s.

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and <.(Skill)

Use addition and subtraction within 100 to solve one- and two-step word problems.

Measure and estimate lengths in standard units.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure the length of an object twice, using length units of different lengths for the two measurements.

Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

Work with time and money

Add and subtract within 1000, using concrete models or drawings and strategies based on place value and properties of operations.

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Fluently add and subtract within 100 using strategies based on place value and properties of operations.

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories.

Tell and write time from analog and digital clocks to the nearest ve minutes, using a.m. and p.m.

Generate measurement data by measuring lengths of several objects to the nearest whole unit.

Relate addition and subtraction to length.

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

Estimate lengths using units of inches, feet, centimeters, and meters.

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Partition a rectangle into rows and columns of same-size squares and count to nd the total number of them.

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ...

Recognize and draw shapes having speci ed attributes, such as a given number of angles or a given number of equal faces.

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc.

Represent and solve problems involving multiplication and division.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

Develop understanding of fractions as numbers.

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects

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.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).

Understand division as an unknown-factor problem.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Multiply and divide within 100.

Relate area to the operations of multiplication and addition.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.

Understand properties of multiplication and the relationship between multiplication and division.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Use place value understanding to round whole numbers to the nearest 10 or 100.

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.

Fluently add and subtract within 1000 using strategies and algorithms based on place value and properties of operations.

Recognize area as an attribute of plane figures and understand concepts of area measurement.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Understand that shapes in different categories may share attributes, and that the shared attributes can de ne a larger category.

Interpret whole-number quotients of whole numbers.

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Multiply or divide to solve word problems involving multiplicative comparison.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Recognise and name common 2-D and 3-D shapes, including 2-D shapes [for example, rectangles (including squares), circles and triangles] and 3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

Geometric measurement: understand concepts of angle and measure angles.

Recognize right triangles as a category, and identify right triangles.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

Recognize and generate equivalent fractions.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

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.

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