Curriculum Development Deborah Harper, South Farnham School

Collaborative project with the White Rose Maths Hub Based in Halifax, Yorkshire Trinity Teaching School alliance Published free scheme of work for KS1 and KS2 Mastery Curriculum Model Fluency, reasoning and problem solving questions Assessments http://www.trinitytsa.co.uk/maths-hub/

White Rose – Year 5 overview

What might the 5 week spring unit on fractions look like? How can teachers turn these into 25 lessons?

Fluency, reasoning and problem solving example questions:

Turning the 5 week block into lessons: NC Learning Objective Lesson Lesson learning objective Identify and name equivalent fractions of a given fraction, represented visually including tenths and hundredths. 1 Recognising equivalent fractions using a fraction wall. 2 Calculating equivalent fractions. 3 Reasoning about equivalent fractions. Compare and order fractions whose denominators are multiplies of the same number. 4 Ordering fractions with similar denominators. 5 Finding common multiples and the lowest common multiple. 6 Ordering fractions whose denominators are multiples of the same number. 7 Problem solving to apply understanding of ordering fractions. Add and subtract fractions with the same denominator and denominators that are multiplies of the same number. 8 Add fractions with the same denominator expressing answers as improper fractions. 9 Subtract fractions with the same denominator expressing answers as improper fractions. 10 Add fractions with denominators which are multiples of the same number expressing answers as improper fractions. 11 Subtract fractions with denominators which are multiplies of the same number expressing answers as improper fractions. 12 Reasoning about adding and subtracting fractions. 13 Problem solving using addition and subtraction of fractions. Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number. 14 Recognise using diagrams how improper fractions can be expressed as a mixed number. 15 Convert improper fractions to mixed numbers. 16 Convert mixed numbers to improper fractions.

Lesson learning objective NC Learning Objective Lesson Lesson learning objective Multiply proper fractions and mixed numbers by whole numbers supported by materials and diagrams. 17 Multiply unit fractions by one digit numbers using diagrams and recognising multiplication as repeated addition. 18 Multiply non unit fractions by one digit numbers using diagrams and recognising multiplication as repeated addition. 19 Multiply mixed numbers by whole numbers. 20 Reasoning and problem solving about multiplying fractions and mixed numbers by whole numbers. Read and write decimal numbers as fractions. 21 Understand the relationship between tenths, hundredths and thousandths and their decimal equivalent. Solve problems involving multiplication and division including scaling by simple fractions and problems involving simple rates. 22 Solve division problems where the remainder is expressed as a fraction. 23 Solve problems involving scaling by simple fractions. Review 24 Review unit. Assess 25 Assess children's understanding. Map onto text books. Add PowerPoint lesson resources.

Text book mapping: Text book mapping NC Learning Objective PPT Lesson Lesson learning objective Busy Ants Inspire Maths Maths No Problem Add and subtract fractions with the same denominator and denominators that are multiplies of the same number. Yes 8 Add fractions with the same denominator expressing answers as improper fractions. 5B p40   9 Subtract fractions with the same denominator expressing answers as improper fractions. 5B p42 10 Add fractions with denominators which are multiples of the same number expressing answers as improper fractions. 5A TB p71 11 Subtract fractions with denominators which are multiplies of the same number expressing answers as improper fractions. 5A TB p74 12 Reasoning about adding and subtracting fractions. 5B p40, 5B p42 5A TB p73 13 Problem solving using addition and subtraction of fractions. 5A TB p99

Fluency To add and subtract fractions with the same denominator, and denominators that are multiples of the same number. Find the answer to these calculations. 3 7 + 2 7 = 3 7 + 2 14 = 4 5 - 9 15 = Find the missing fractions. 11 7 + = 18 7 18 5 − = 9 10 + 4 6 = 1 6

What would you say to him and why? Reasoning To add and subtract fractions with the same denominator, and denominators that are multiples of the same number. Write down two fractions which have a difference of 1 2 . ? ? - ? ? = 1 2 Sam thinks 2 3 + 3 5 = 5 8 What would you say to him and why? ? ? + ? ? = 1 8 The answer is 1 8 , what is the question?

Problem solving To add and subtract fractions with the same denominator, and denominators that are multiples of the same number. A gardener bought 2 3 kg of compost on Monday and another 1 6 kg on Tuesday. She filled flower pots with 1 4 kg of compost. How much compost did she have left? There were some people at a concert. 1 5 of them were men and 1 7 of them were women. The rest were children. What fraction of the people were children?

Assessment materials: 2 tests per term for years 1 – 6

In summary…. Mastery Schemes of Learning for KS1 and KS2 Lesson by lesson learning objectives Mapping to popular text books Bank of questions for each learning objective PowerPoint resources with fluency, reasoning and problem solving questions Termly assessments FREE!!