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Prime Numbers Reasoning and Problem Solving

This Year 5 Prime Numbers Reasoning and Problem Solving resource will allow children to apply their prime numbers and prime factors skills to. We've created two problem solving questions and one reasoning style question and have given two of each question type for children. This resource has been differentiated to three levels of challenge to support all learners in your class.

Use this worksheet alongside our accompanying modelling PowerPoint and our varied fluency resources for this lesson. An ideal independent task or you could use this in a small group or in pairs to encourage mathematical discussion and problem solving skills. A fully explained and modelled answer sheet is provided to aid marking.

Curriculum Objectives

• Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
• Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

Multiplication and Division

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White Rose Maths - Year 5 - Block 4 - Prime Numbers (Problem Solving and Reasoning)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

13 November 2018

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A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included.

This set of worksheets is for Year 5, Autumn Block 4 (Multiplication and Division), focusing on the fourth small step of prime numbers. Details of how it has been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to identify prime numbers up to 20 and find prime factors of numbers up to 30. • 2 Star sheet (Expected Level): Be able to identify prime numbers up to 100 and find prime factors of numbers up to 30. • 3 Star sheet (Working at greater depth): Be able to identify prime numbers up to 200 and find prime factors of numbers above 100.

Each worksheet contains a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

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White Rose Maths - Year 5 - Block 4 - Multiplication and Division (Problem Solving and Reasoning Practice)

A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. These sets of worksheets are for Year 5, Autumn Block 4 (Multiplication and Division), focusing on the first to eighth small steps. Details of how they have been differentiated can be found below: Multiples: • 1 Star sheet (Working Towards Expected Level): Be able to find and identify multiples of 2, 5 and 10. • 2 Star sheet (Expected Level): Be able to find and identify multiples of whole numbers up to x12 of each number. • 3 Star sheet (Working at greater depth): Be able to identify multiples of whole numbers up to and beyond x12 of each number. Common multiples are also covered more in depth. Factors: • 1 Star sheet (Working Towards Expected Level): Be able to find factors of numbers up to 30. • 2 Star sheet (Expected Level): Be able to find factors of numbers up to 100. • 3 Star sheet (Working at greater depth): Be able to find factors of numbers from 50-100 and beyond. Prime Numbers: • 1 Star sheet (Working Towards Expected Level): Be able to identify prime numbers up to 20 and find prime factors of numbers up to 30. • 2 Star sheet (Expected Level): Be able to identify prime numbers up to 100 and find prime factors of numbers up to 30. • 3 Star sheet (Working at greater depth): Be able to identify prime numbers up to 200 and find prime factors of numbers above 100. Square and Cube Numbers: • 1 Star sheet (Working Towards Expected Level): Be able to calculate square and cube numbers up to 10x10 and 5x5x5 • 2 Star sheet (Expected Level): Be able to calculate square and cube numbers up to 12x12 and 12x12x12 • 3 Star sheet (Working at greater depth): Be able to calculate square and cube numbers up to and beyond 12x12 and 12x12x12 Multiplying and Dividing by 10, 100 and 1000: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide whole numbers by 10 and 100. • 2 Star sheet (Expected Level): Be able to multiply and divide whole and decimal numbers by 10, 100 and 1000. • 3 Star sheet (Working at greater depth): Be able to multiply and divide whole and decimal numbers by 10, 100, 1000 and 10,000. Each worksheet contains a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

White Rose Maths - Year 5 - Block 4 - Multiplication and Division (Varied Fluency and Problem Solving and Reasoning Practice)

A block set of varied fluency and a block set of problem solving and reasoning worksheets to use alongside the White Rose Maths scheme. Both sets of questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. These sets of worksheets are for Year 5, Autumn Block 4 (Multiplication and Division), focusing on the first to eighth small steps. Details of how they have been differentiated can be found below: Multiples: • 1 Star sheet (Working Towards Expected Level): Be able to find and identify multiples of 2, 5 and 10. • 2 Star sheet (Expected Level): Be able to find and identify multiples of whole numbers up to x12 of each number. • 3 Star sheet (Working at greater depth): Be able to identify multiples of whole numbers up to and beyond x12 of each number. Common multiples are also covered more in depth. Factors: • 1 Star sheet (Working Towards Expected Level): Be able to find factors of numbers up to 30. • 2 Star sheet (Expected Level): Be able to find factors of numbers up to 100. • 3 Star sheet (Working at greater depth): Be able to find factors of numbers from 50-100 and beyond. Prime Numbers: • 1 Star sheet (Working Towards Expected Level): Be able to identify prime numbers up to 20 and find prime factors of numbers up to 30. • 2 Star sheet (Expected Level): Be able to identify prime numbers up to 100 and find prime factors of numbers up to 30. • 3 Star sheet (Working at greater depth): Be able to identify prime numbers up to 200 and find prime factors of numbers above 100. Square and Cube Numbers: • 1 Star sheet (Working Towards Expected Level): Be able to calculate square and cube numbers up to 10x10 and 5x5x5 • 2 Star sheet (Expected Level): Be able to calculate square and cube numbers up to 12x12 and 12x12x12 • 3 Star sheet (Working at greater depth): Be able to calculate square and cube numbers up to and beyond 12x12 and 12x12x12 Multiplying and Dividing by 10, 100 and 1000 (Separated into a set of multiplying and a set of dividing for the Varied Fluency): • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide whole numbers by 10 and 100. • 2 Star sheet (Expected Level): Be able to multiply and divide whole and decimal numbers by 10, 100 and 1000. • 3 Star sheet (Working at greater depth): Be able to multiply and divide whole and decimal numbers by 10, 100, 1000 and 10,000. The varied fluency worksheets contain a total of 8 questions, some broken down into parts (a, b, c etc.) with 2 examples of each question type. This provides children with the varied fluency that White Rose aim for. These questions can be used as a quick starter and cut up so that only the first 4 questions are used, or given as more of a main activity with all 8 questions. They could also be used for partner work, depending on the ability of the children. The problem solving and reasoning worksheets contain a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

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Year 5 - Number

Standard 5.NS.1.3 - Practice identifying prime and composite numbers.

Included Skills:

Number - multiplication and division • Pupils should be taught to: - identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers - know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers - establish whether a number up to 100 is prime and recall prime numbers up to 19 - multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers - multiply and divide numbers mentally drawing upon known facts - divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context - multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 - recognise and use square numbers and cube numbers, and the notation for squared (�) and cubed (�) - solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes - solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign - solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

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