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|FIRST HALF SPRING TERM PLANNING – Year 3 and 4 2016 |
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|Fractions: Recognising tenths. Recognise fractions of a discrete set. Unit and non-unit fractions with small denominators. Simple equivalent fractions. |
|Number: Counting in hundredths. Round decimals with 1decimal place to a whole number. Counting in tenths |
|Calculation: Recognise hundredths arise by dividing by 100 equal parts. Solve simple measure and money problems involving fractions. Recognise tenths arise |
|by dividing by 10 equal parts. |
| |Year 3 objectives |Year 4 objectives. |
|Number-|count up and down in tenths; recognise that tenths arise from dividing |Count up and down in hundredths; recognize that hundredths arise when |
|Fractio|an object into 10 equal parts and in dividing one-digit numbers or |dividing an object by 100 and dividing tenths by ten |
|ns |quantities by 10 |Activity B – tenths and hundreths |
| |Activity A – visualizing along a line | |
| | |find the effect of dividing a one- or two-digit number by 10 and 100, |
| |recognise, find and write fractions of a discrete set of objects: unit |identifying the value of the digits in the answer as ones, tenths and |
| |fractions and non-unit fractions with small denominators |hundredths |
| |Problem solving A: Fraction match |Activity F – dividing by 10 and 100 |
| | |round decimals with one decimal place to the nearest whole number |
| |recognise and use fractions as numbers: unit fractions and non-unit |Activity G – rounding and comparing decimals |
| |fractions with small denominators |Problem solving C: Round the dice decimals |
| |Activity C - Trains | |
| | |compare numbers with the same number of decimal places up to two decimal |
| |recognise and show, using diagrams, equivalent fractions with small |places |
| |denominators |Activity G – rounding and comparing decimals |
| |Activity D – equivalent fractions | |
| |Problem solving B: Matching Fractions |solve simple measure and money problems involving fractions and decimals to |
| | |two decimal places. |
| |add and subtract fractions with the same denominator within one whole. | |
| |Activity E – adding fractions |recognise and show, using diagrams, families of common equivalent fractions |
| | |Activity A – interactive programs |
| |compare and order unit fractions, and fractions with the same |Problem Solving D: Fractional Triangle |
| |denominators |Problem solving D: Bryony’s triangle |
| |Activity F |Problem solving D: Fair Feast |
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| |solve problems that involve all of the above. |solve problems involving increasingly harder fractions to calculate |
| |Activity G – solving problems |quantities, and fractions to divide quantities, including non-unit fractions|
| | |where the answer is a whole number |
| | |Activity C – fractions to calculate quantities |
| | |Problem solving E: Fractions in a box |
| | |Problem solving E: Chocolate |
| | |add and subtract fractions with the same denominator |
| | |Activity D –adding and subtracting fractions |
| | |recognise and write decimal equivalents of any number of tenths or |
| | |hundredths |
| | |Activity A and E – decimals equivalents |
| | | |
| | |recognise and write decimal equivalents to |
| | | |
|Activities and possible problem solving /reasoning |
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|(From NCETM website Year 3 Fractions) |
|Activity A – visualising fractions along a line |
|(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) |
|Use counting sticks and bead strings to help children visualise fractions. |
|If the bead string represents one whole, then each set of ten coloured beads could represent one tenth and each individual bead could represent one |
|hundredth. |
|[pic] |
|[pic] |
|Label the two ends of the bead string as 0 and 1. Give students tags to place each tenth on the bead string. You could use a 1-10 bead string instead of a |
|1-100 bead string. |
|Join several bead strings together to create fraction lines that extend over one. For example, five bead strings allow fractional numbers from 0 to 5. Label |
|simultaneously in mixed numbers (2 ½) and improper fractions (5/2). |
|Ask the pupils to represent each tenth with a variety of manipulatives, for example, Numicon, Dienes (Big Base) and coins. |
|Extend pupils’ understanding to include the equivalence of fractions, decimals and percentages. For example, ½ = 0.5 = 50% or 2 2/10 = 2.2 = 220% |
|Activity C - Trains |
|(Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators) |
|An activity from New Zealand that involves using number rods to develop children’s understanding that fractions can extend beyond 1. |
|Children can make number lines for display around the classroom that demonstrate counting in different fractional steps. For example counting in steps of ½ |
|an apple, 1/4s of pizza, 1/10 of a £1 (steps of 10p) |
|Daily practice of counting forwards and backwards in 1/2s, 1/4s, 1/10s and 1/3s, including extending to below zero |
|Activity D – equivalent fractions |
|Use equivalence circles, for example pizza or cake slices in a variety of activities for pupils to explore equivalence. |
|[pic] |
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|Activity E – adding fractions |
|(Add and subtract fractions with the same denominator within one whole.) |
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|Addition, subtraction and equivalent fractions |
|A series of activities based on deepening students’ understanding of adding and subtracting fractions with the same denominator. |
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|Use a variety of representations, for example, number rods, paper strips and equivalence circles to model what happens when you add or subtract fractions |
|with the same denominator. This will help children understand why the denominator doesn’t change. |
|[pic] |
|Activity F |
|(Compare and order unit fractions, and fractions with the same denominators) |
|Fractions interactive teaching programme |
|NB This resource was produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resource has the potential to |
|complement teaching in line with the new 2014 mathematics curriculum) |
|This ITP allows you to divide a green strip into a number of equal parts and colour the individual parts in yellow, clearly showing any comparison. |
|Smartie Fractions |
|Use mini packets of smarties for children to find the fraction of each colour in a packet. This is useful for comparing fractions with the same denominator |
|and for adding and subtracting fractions |
|More wonderful ‘Maths and Smarties’ ideas. |
|Activity G – solving problems |
|(Solve problems that involve all of the above) |
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|Use the Bar Model to solve problems |
|Use the ‘Thinking blocks on the maths playground’ website to model word problems involving fractions and to model adding and subtracting unit fractions. |
|There are video demonstrations, guided problems and the ability to use the blocks to solve your own problems. |
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|Problem Solving A: Fractional Triangles (nrich) |
|(Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators) |
|This practical activity develops an understanding of the part and the whole. |
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|Problem Solving B: Fractional Walls (nrich) |
|(Recognise and show, using diagrams, equivalent fractions with small denominators) |
|An activity based on Cuisenaire / number rods. |
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|Problem Solving B: Matching Fractions (nrich) |
|(Recognise and show, using diagrams, equivalent fractions with small denominators) |
|A ‘pelmanism’ style matching activity based on fractions. |
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|(From NCETM website Year 4 Fractions) |
|Activity A – interactive programmes |
|(Recognise and show, using diagrams, families of common equivalent fractions) |
|(Recognise and write decimal equivalents of any number of tenths or hundredths) |
|Game matching pictures and equivalent fractions |
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|Activity B – Tenths and Hundredths |
|(Count up and down in hundredths; recognize that hundredths arise when dividing an object by 100 and dividing tenths by ten) |
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|A resource pack of materials including an interactive place value grid to teach tenths and hundredths, activities on key vocabulary and terms, reference |
|material and animations and three differentiated worksheets on tenths and hundredths |
|A series of activities to introduce and use hundredths |
|Make a hundred square of pennies in the classroom and talk about one hundredth of a pound and a tenth of a pound. Consider how, for example, 23p is written |
|as a decimal. How would we write four pound and eighty-two pence? What would it look like in our coins? |
|Interactive matching of decimal notation to a shaded 10x10 grid representation |
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|Activity C – fractions to calculate quantities |
|(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) |
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|Game for one or two players required to match the answer to the unit fraction of amount requested |
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|Activity D – adding and subtracting fractions |
|(Add and subtract fractions with the same denominator) |
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|Game practising adding two or more fractions with the same denominator |
|Online adding and subtracting fractions activities written as word problems. Some useful ideas. |
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|Activity E – decimal equivalents |
|(Recognise and write decimal equivalents of any number of tenths or hundredths) |
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|Excellent ‘splat’ game accessible at several different levels, requiring children to match the fraction (in tenths or hundredths) to the decimal |
|representation |
|‘The Decifractor’. A flexible resource demonstrating equivalences between fractions and decimals. |
|Pelmanism-style game , matching fractions to decimals. |
|Arcade type game, where ‘Fraction Man’ has to defeat the decimals (by matching them). |
|Note – this does get challenging! 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 |
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|Activity F – dividing by 10 and 100 |
|(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 ones, tenths and hundredths) |
|Interactive Teaching Program – ‘Moving Digits’. A good modelling program to show how digits move when multiplied or divided by 10 or 100. |
|Interactive game where children are required to find the calculation that matches the answer given… to help them cross the river. |
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|Activity G – rounding and comparing decimals |
|(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) |
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|Rounding decimals activity – uses one and two decimal places. |
|Practise rounding numbers to one decimal place. |
|Spreadsheets ‘Rounding’ and ‘Rounding Decimals’ |
|Arrange the decimals in order from lowest to highest. |
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|Problem solving C: Round the dice decimals (nrich) |
|(Round decimals with one decimal place to the nearest whole number ) |
|Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number? |
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|Problem Solving D: |
|Fractional Triangle (nrich) |
|Use the lines on this figure to show how the pattern of triangles can be used to divide the square into two halves, three thirds, six sixths and nine ninths |
|Bryony’s triangle (nrich) |
|Fair Feast (nrich) |
|Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have |
|(Recognise and show, using diagrams, families of common equivalent fractions |
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|Problem solving E: Fractions in a box (nrich) |
|Problem solving E: Chocolate (nrich) |
|(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) |
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|Other Resources |
|Fractions and decimals |
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|Website with more fraction problems using pattern blocks. |
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|Link to a nice sequence of lesson on fractions including equivalents and calculating with fractions using pattern blocks. |
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|Fractions using pattern blocks |
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|A great website with lesson plans suggesting how to use pattern blocks to teach fraction. Lesson on equivalent fractions and comparing fractions. |
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|Red balloons, blue Balloon |
|This task involves adding fractions together to solve the problem of the size of the balloon. |
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|Smartie Fractions: |
|Use mini packets of smarties for children to find the fraction of each colour in a packet. This is useful for comparing fractions with the same denominator |
|and for adding and subtracting fractions |
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|Pizzas: |
|This pizza themed fraction resource from the TES can be used in many different ways, and includes several suggestions from the author. |
|Assessment and independent application. |
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|Exemplar materials from NCETM website |
|Past SAT questions |
|Mental maths tests |
|Resources and manipulatives. |
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|Cuissenaire, Fraction wall ITP, Pattern Blocks |
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|Mental Images for Fractions, Decimals, Percentages, Ratio and Proportion (FDPRP) |
|A list of models and images to support the development of children’s understanding of fractions. Includes ideas on how to use them in the classroom. |
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|Overcoming Barriers in Fractions |
|All the Overcoming Barriers materials from level 1 to level 5 linked to fractions, decimals and percentages contain useful assessment questions and a range |
|of models and images. |
|Pedagogies. |
|What’s the same? What’s different? |
|What do you notice? |
|Can you explain? |
|Would it work with? |
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