Overcoming Barriers
Support, advice and identified learning targets across the mathematical strands to help children progress to level 2 in mathematics by the end of Year 2.
Overcoming Barriers topics
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Overcoming barriers in mathematics: Helping children move from level 1 to 2
These materials are designed to help you ensure that as many children as possible progress to level 2 in mathematics by the end of Year 2.
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Calculating
This is the first strand of Overcoming barriers - helping children move from level 1 to level 2.
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Add to a two-digit number to make multiples of ten
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Add and subtract a multiple of ten
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Add or subtract a one-digit number to or from a two-digit number
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Describe an array and write number sentences
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Find a difference between a pair of numbers
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Record number sentences and explain the signs and numbers
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Solve problems with multiplication as repeated addition
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Use grouping to solve division
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Work out and record the information I need to solve a puzzle or problem
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Write addition and subtraction sentences using the same three numbers
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Counting and understanding numbers
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including counting, ordering and partitioning two-digit numbers, and rounding two-digit numbers to the nearest 10. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 1 to 2’.
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Count in equal steps and explain patterns
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Describe how to order two-digit numbers
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Partition a two-digit number into tens and ones to create addition and subtraction sentences
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Partition one and two-digit numbers
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Round a two-digit number to the nearest ten
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Show a whole number on a 0 to 100 number line
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Knowing and using number facts
This is the fourth strand of Overcoming barriers – helping children move from level 1 to level 2.
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Understanding shape
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including naming and describing 2-D and 3-D shapes, and sorting shapes by similarities and differences. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 1 to 2’.
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Measuring
This is the fifth strand of Overcoming barriers - helping children move from level 1 to level 2.
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Overcoming barriers in mathematics: Helping children move from level 3 to 4
These materials are designed to help you ensure that as many children as possible progress to level 4 in mathematics by the end of Year 6. The materials address key areas of mathematics that commonly present barriers to learning for children working towards level 4. They provide support and advice on teaching approaches designed to help children overcome these barriers.
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Calculating
These lesson activities, questions and key vocabulary lists can be used to help children understand concepts that they find difficult, including multiplication, division and fractions. There are suggestions for teaching and consolidating learning. This information is part of 'Overcoming barriers in mathematics: Helping children move from level 3 to 4'.
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Add and subtract two numbers in my head quickly
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Calculate a fraction of a number or quantity
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Calculate simple percentages of whole numbers or quantities
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Interpret numbers on a calculator display
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Multiply and divide by 10 and 100 and 1000
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Use a calculator to solve problems with more than one step
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Use a written method to multiply
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Use a written method to subtract
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Use my tables to multiply and divide
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Counting and understanding number
These lesson activities, questions and key vocabulary lists can be used to help children understand concepts that they find difficult, including counting on when counting backwards, equivalent fractions and decimal numbers. This information is part of 'Overcoming barriers in mathematics: Helping children move from level 3 to 4'.
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Count on in whole-number steps beyond zero when counting backwards
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Express tenths and hundredths as percentages
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Find simple equivalent fractions
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Position positive and negative numbers on a number line and find the difference
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Read, write, partition and order decimal numbers
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Relate simple fractions to their decimal equivalents
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Handling data
These lesson activities, questions and key vocabulary lists can be used to help children understand concepts that they find difficult, including understanding graphs, charts and diagrams, and the vocabulary relating to probability. This information is part of 'Overcoming barriers in mathematics: Helping children move from level 3 to 4'.
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Draw a conclusion from a graph or chart
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Explain what information a graph or chart is showing
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Interpret the sectors in a pie chart
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Sort and interpret data in Venn and Carroll diagrams
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Understand the meaning of points between labelled divisions on graphs
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Use the vocabulary of probability to predict outcomes and discuss and explain events
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Work out the mode and range of a set of data and use this to answer questions
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Knowing and using number facts
These lesson activities, questions and key vocabulary lists can be used to help children understand concepts that they find difficult, including using tables to multiply and divide, and to work with decimals. This information is part of 'Overcoming barriers in mathematics: Helping children move from level 3 to 4'.
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Understanding shape
This is the sixth strand of Overcoming barriers - helping children move from level 3 to level 4.
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Measuring
This is the fifth strand of Overcoming barriers - helping children move from level 3 to level 4.
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Overcoming barriers in mathematics: Helping children move from level 2 to 3
These materials are designed to help you ensure that as many children as possible progress to level 3 in mathematics by the end of Year 4. The materials address key areas of mathematics that commonly present barriers to learning for children working towards level 3. They provide support and advice on teaching approaches designed to help children overcome these barriers.
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Calculating
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including subtraction as the inverse of addition, multiplication by 10 and 100 and recording mathematical methods. This is part of 'Overcoming barriers in mathematics: Helping children move from level 2 to 3'.
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Subtract mentally combinations of one-digit and two-digit numbers
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Subtraction fact that is the inverse of an addition fact and vice versa
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Multiply one-digit and two-digit numbers by 10 and 100
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Multiply a two-digit number by a one-digit number
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Find a unit fraction of a shape, number or quantity by splitting it into the correct number of equal parts
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Identify the calculation needed to solve a word problem
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Identify the stages involved in a two-step problem
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Divide a two-digit number by a one-digit number and explain any remainders
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Explain and record my methods and solutions
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Handling data
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including creating and interpreting bar charts, pictograms and making and using lists and tables of data. These activities are part of ‘Overcoming barriers in mathematics: Helping children move from level 2 to 3’.
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Counting and understanding numbers
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including rounding up, decimal notation, reading and writing fractions, and ordering numbers on a number line. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 2 to 3’.
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Knowing and using number facts
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including recalling and using addition, subtraction, multiplication and division facts for numbers and times-tables. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 2 to 3’.
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Understanding shape
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including making, naming and describing 2-D and 3-D shapes, and sorting shapes using their own criteria. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 2 to 3’.
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Measuring
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including the relationship between weights, scale on a number line and digital and analogue time. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 2 to 3’.
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Explain the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres
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Explain what each division means on a number line to read a scale to the nearest division
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Read the time to the nearest five minutes on an analogue clock, using the correct vocabulary
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Show on a digital clock a time given to me on an analogue clock, and the other way round
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Work out how long it is between two times
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Overcoming barriers in mathematics: Helping children move from level 4 to 5
These materials are designed to help you extend as many children as possible towards achieving level 5 in mathematics by the end of Key Stage 2. The materials address key areas of mathematics that commonly present barriers to learning for children working towards level 5. They provide support and advice on teaching approaches designed to help children overcome these barriers.
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Calculating
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including solving multi-step problems of multiplication and division with and without a calculator. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 4 to 5’.
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Use my understanding of place value to explain how to mentally multiply or divide a decimal number by an integer
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Use a non-calculator method for dividing a three-digit integer by a two-digit integer
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Extend my written methods for multiplying whole numbers to multiplying decimals by whole numbers
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Solve multi-step problems involving percentages and/or fractions
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Solve multi-step problems that involve using inverse operations and explain my methods
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Make and justify decisions about when and how to use a calculator effectively to solve problems
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Explain and record my method when I use a calculator to solve a problem
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Handling data
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including using the 0 to 1 probability scale and interpreting data in line graphs and pie charts. This is part of ‘Overcoming barriers in mathematics: Helping children move from level 4 to 5’.
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List all the outcomes that may result from repeating an experiment
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Use the 0–1 probability scale to measure the probabilities of outcomes
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Interpret and explain data presented in line graphs
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Interpret sets of data with different sample sizes represented in pie charts
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Explain what different diagrams and graphs represent, and draw conclusions
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Explain range, mode, median and mean and use them to describe data
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Counting and understanding numbers
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including using ratio and proportion, creating simple algebraic expressions and explaining why numbers belong in sequences. This is part of ‘Overcoming barriers in mathematics: Helping children move from level 4 to 5’.
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Work out the whole, having been given the fraction
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Understand and explain the relationships between two or more parts of a whole and describe them using the language and notation of ratio
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Solve simple problems involving ratio and proportion
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Create an algebraic expression that describes a simple relationship
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Make generalisations and explain why numbers belong in sequences
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Knowing and using number facts
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including using knowledge of factors and multiples, and using approximations to estimate an answer. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 4 to 5’.
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Measuring
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including solving problems requiring the conversion of units and reading a variety of partially labelled scales. This information is part of ‘Overcoming barriers in mathematics: Helping children move from level 4 to 5’.
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Understanding shape
These lesson activities, questions and vocabulary lists can help children to understand mathematical concepts they find difficult, including matching nets to 3-D shapes, working out missing angles and using the terms ‘perpendicular’ and ‘parallel’. This is part of ‘Overcoming barriers in mathematics: Helping children move from level 4 to 5’.
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Planning the teaching and learning of mathematics using Overcoming barriers in mathematics – helping children move from level 1 to level 2
Planning the teaching and learning of mathematics using Overcoming barriers in mathematics – helping children move from level 1 to level 21. Introduction to the materials2. The structure of the materials3. Getting started – targeting children 4. Planning from and using the materialsa. Using the materials – Year 2 teacher and teaching assistantb. Using the materials – teaching assistant and an individual child
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Planning the teaching and learning of mathematics using Overcoming barriers in mathematics – helping children move from level 1 to level 2
Planning the teaching and learning of mathematics using Overcoming barriers in mathematics – helping children move from level 1 to level 21. Introduction to the materials2. The structure of the materials3. Getting started – targeting children 4. Planning from and using the materialsa. Using the materials – Year 2 teacher and teaching assistantb. Using the materials – teaching assistant and an individual child
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Introduction to materials
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The structure of materials
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Getting started—targeting children
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Planning from and using the materials
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Research—Year 2 children who get 'stuck' at level 2C in mathematics (summary of findings)
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Research—Year 2 children who get 'stuck' at level 2C in mathematics (place value and mental calculation)
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Research—year 2 children who get 'stuck' at level 2C in mathematics (problem solving, recording, using mathematical vocabulary)
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Place value and ordering three-digit numbers
Ideas for planning and teaching guided activities to enable children to interpret the value of a digit in a three-digit number and to order numbers 0 to 1000 in relation to landmark multiples.
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Addition and subtraction facts
Ideas for planning and teaching guided activities to enable children to know addition and subtraction facts for each number to 20 and quickly derive all pairs of multiples of 5 that total 100.
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Understanding division and multiplication
Ideas for planning and teaching guided activities to enable children to understand division as grouping.
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Subtraction by counting on from the smaller number
Ideas for planning and teaching guided activities to enable children to find a small difference by counting on from the smaller to the larger number, and apply this to compare lengths of objects.
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Recognising and using unit fractions to find fractions of numbers
Ideas for planning and teaching guided activities to enable children to recognise unit fractions such as ½, ¼ and 1/10 and use them to find fractions of numbers.
