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Mathematical Division Mastery: Concrete to Abstract Problem Solving

Enhance division skills from concrete objects to abstract symbols. Solve real-life problems, relate division to fractions, develop efficient methods using mental math. Advance to dividing up to 4 digits by 2 digits through long division, interpreting remainders in various forms.

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Mathematical Division Mastery: Concrete to Abstract Problem Solving

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  1. Division Progression YR to Y6

  2. YR Objectives • Solve problems in real life contexts using concrete objects and pictorial representation, including halving and sharing. Concrete Use real life contexts Grouping Mum had 6 socks. She grouped them into pairs. How many pairs did she make? Halving Pictorial Sharing I have 10 sweets. I want to share them with my friend. How many will we have each?

  3. Y1 Objectives • Calculate the answer using concrete objects, pictorial representations and arrays, showing repeated addition. • Halving • Non-statutory: • Grouping and sharing small quantities. Grouping Concrete and pictorial representations. Real life contexts Sharing coins between two purses. Sharing Halving by sharing on ten frames using real life objects Half of 10 is the same as 5.

  4. Y2 Objectives • Sharing and grouping • Abstract symbols used • Grouping using a numberline • Missing number problems • Non-statutory: • Begin to relate division to fractions and measures Concrete and pictorial representations Link division to fractions

  5. Y3 Objectives • Sharing and grouping • Abstract symbols used • More efficient using a numberline • Missing number problems • 2 dn ÷ 1 dn • Remainders • Non-statutory: • Develop efficient mental methods using related • multiplication and division facts. Concrete and pictorial representations Use correct terminology. Related multiplication and division facts. Use bar model. Divide by partitioning the dividend. Divide by regrouping the dividend.

  6. Y4 Objectives • Division facts up to 12x • Divide by 1. • Divide up to 3 dn by 1 dn • Factor pairs • Solving problems – scaling and correspondence. • Non-statutory: • Derive related facts (If 24 ÷ 6 = 4, 2400 ÷ 6 = 400) • Fluency in short division method Use the terms dividend, divisor and quotient Continue to use CPA approach Use place value counters to divide using the bus stop method alongside 42 ÷ 3= Start with the biggest place value, we are sharing 40 into three groups. We can put 1 ten in each group and we have 1 ten left over. Use table facts with which the children are fluent Divide 3 dn by 1 dn – no remainder We exchange this ten for ten ones and then share the ones equally among the groups. Divide 3 dn by 1 dn – with remainder We look how much in 1 group so the answer is 14. Bar Model Division and fractions

  7. Y5 Objectives • Divide mentally using known facts • 4 dn ÷ 1 dn – short division • Divide whole and decimal numbers by 10, 100 and 1000 • Solve problems, including scaling by fractions • Non-statutory: • Express non-integer results in different ways eg. remainders, fractions, decimals or by rounding • (98 ÷ 4 = = 24 r 2 = 24 = 24.5 ≈ 25) • Use multiplication and division as inverses to support the introduction of ratio in year 6 Use the terms dividend, divisor and quotient Solve problems Write remainder as fraction 4 dn ÷ 1 dn Bar Model Use chunking to explain what is happening in short division and then move swiftly onto short division method. Use dividends just over 10x the divisor when the divisor is a teen number eg. 173 ÷ 15

  8. Use the terms dividend, divisor and quotient • Y6 Objectives • Divide numbers up to 4 dn by a 2dn using long division • Interpret remainders as whole number remainders, fractions, or by rounding • Common factors • Order of operations • Solve problems • Estimation • Non-statutory: • Practise short and long division • Explore order of operations using brackets. • Relate common factors to finding equivalent fractions Decimals ÷ 2 dn Long division Decimals ÷ 1 dn Decimals ÷ 2 dn Short division Use chunking to explain what is happening in short division and then move swiftly onto short division method.

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