Numbers to 10,000: Reasoning and Problem Solving

Numbers to 10,000: Reasoning and Problem Solving

National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

  • National Curriculum Tool

Year 6 - Number and Place Value

New curriculum.

read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
round any whole number to a required degree of accuracy
use negative numbers in context, and calculate intervals across zero
  • solve number problems and practical problems that involve all of the above.

Non-Statutory Guidance

Pupils use the whole number system, including saying, reading and writing numbers accurately.

Links and Resources

  • Making connections
  • Exemplification
Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

– Mathematics programmes of study: key stages 1 and 2. National curriculum in England, September 2013, p3

Connections within Mathematics

Making connections to other topics within this year group.

Number – Fractions

  • identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
  • solve problems which require answers to be rounded to specified degrees of accuracy

Making connections to this topic in adjacent year groups

  • read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
  • interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
  • round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
  • solve number problems and practical problems that involve all of the above

Key Stage 3

  • understand and use place value for decimals, measures and integers of any size
  • order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
  • interpret and compare numbers in standard form A x 10 n 1≤A<10, where n is a positive or negative integer or zero
  • round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
  • use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b

Cross-curricular and real life connections

There are lots of opportunities to consider the size and scale of numbers in real life, many of which fit well with other areas of the curriculum.

Ordering and understanding population size of different towns, cities, countries and continents gives a useful context for looking at larger numbers.

National newspapers and news programmes often provide statistics comparing values of money or other measures.

Temperature is often the easiest context through which to teach a good understanding of negative numbers.

The ‘In Order’ activity from Nrich requires children to consider and order the temperature, speed, volume and length of time taken for various different ‘real life’ activities.

  • Maths 4 life Number (pdf)

This booklet provides a useful guide to understanding the relationships between numbers and the structure of our number system. It is aimed at teachers working with adult learners but many of the activities are adaptable for children.

Activity A(i)

Activities related to space will provide opportunities for children to work with large numbers, ordering and rounding. Try these:

  • model of the solar system
  • alternative way to model the solar system

Activity A(ii)

Activities in the context of space and the solar system also provide excellent opportunities for working with positive and negative integers. There are a number of interactive and relevant activities.

Activity B - Tug Harder

This two player game from Nrich requires the children to use their knowledge of both positive and negative numbers, and the effect they have on each other. Some useful question prompts are included too – to really get them thinking!

It is important that children become familiar with both ordinal and cardinal aspects of number so although moving along a number line is the most common way to teach negative numbers, it is also important for them to see negative numbers as the absence of something – teachers often dig (concretely or pictorially) holes to represent a negative value. You could have a lot of fun with moles and holes that will help children develop a robust concept of negative numbers.

The videos ‘Negative Numbers 1’ and ‘Negative Numbers 2’ show Josie Clark helping her class develop their understanding of the concept of negative numbers and how to do calculations with negative numbers. She takes particular care to get the children to use precise mathematical language.

The interactive spreadsheet ‘Positive and Negative Numbers - Brick Walls’ is a resource that can be used with children to discuss calculations involving negative numbers.

Activity C - Sometimes we lose things

This intriguing activity introduced children to working in base 9, with a real focus on understanding our number system more deeply.

Useful Resources

Number lines, thermometer

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

Children should be able to determine the steps used in different scales, and so complete activities such as;

Children should be able to circle the best estimate of the answer to questions such as;

72.34 ÷ 8.91

6 7 8 9 10 11 as possible answers

Children should estimate the position of numbers on a number line. They should suggest which number lies about two-fifths of the way along a line from 0 to 1000, or a line from 0 to 1. They should be able to justify their decisions.

Children should be able to work with negative numbers in a similar way, determining values on a scale and estimating.

solve number and practical problems that involve all of the above

Children should be able to use rounding and inverse operations to estimate and check calculations such as;

The temperature inside an aeroplane is 20°C The temperatures outside the aeroplane is -30°C. What is the difference between these temperatures?

Children developing understanding of fluency with number

This suite of videos demonstrates children developing understanding and fluency with number. Children from across the primary school can be seen developing confidence in understanding and applying key concepts, such as inverse relationships and place value.

Counting in steps of one and ten

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Round Within 100,000 Year 5 Place Value Resource Pack

Round Within 100,000 Year 5 Resources

Step 6: Round Within 100,000 Year 5 Resources

Round Within 100,000 Year 5 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Autumn Block 1.

numbers to 10 000 reasoning and problem solving

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What's included in the pack?

This pack includes:

  • Round Within 100,000 Year 5 Teaching PowerPoint.
  • Round Within 100,000 Year 5 Varied Fluency with answers.
  • Round Within 100,000 Year 5 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 5: (5N2) Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

Mathematics Year 5: (5N4)  Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

Mathematics Year 5: (5N6) Solve number problems and practical problems that involve (5N1) (5N2) (5N4) (5N5)

Differentiation:

Varied Fluency Developing Questions to support rounding numbers within 100,000 to the nearest 1,000 or 10,000. Numerals only. Expected Questions to support rounding numbers within 100,000 to the nearest 10, 100, 1,000 or 10,000. Numbers represented as numerals and words. Greater Depth Questions to support rounding numbers within100,000 to the nearest 10, 100, 1,000 or 10,000. Numbers represented as numerals, words and Roman numerals.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Use four digit cards to create numbers which round to a given number (rounding to 1,000). Using numerals only. Expected Use five digit cards to create numbers which round to a given number (rounding to 10,000). Using numerals and words. Greater Depth Use six digit cards to create numbers which round to a given number (rounding to 100). Using numerals, Roman numerals and words.

Questions 2, 5 and 8 (Reasoning) Developing Compare two statements and explain any errors in rounding a 5-digit number to the nearest 10,000. Using numerals only. Expected Compare three statements and explain any errors in rounding a 5-digit number to the nearest 10. Using numerals and words. Greater Depth Compare three statements and explain any errors in rounding a 6-digit number to the nearest 10. Using numerals, Roman numerals and words.

Questions 3, 6 and 9 (Reasoning) Developing Find the odd one out from three 5-digit numbers by rounding to the nearest 1,000 or 10,000. Using numerals only. Expected Find the odd one out from four 5-digit numbers by rounding to the nearest 10, 100, 1,000 or 10,000. Using numerals and words. Greater Depth Find the odd one out from five 6-digit numbers by rounding to the nearest 10, 100, 1,000 or 10,000. Using numerals, Roman numerals and words.

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numbers to 10 000 reasoning and problem solving

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ORIGINAL RESEARCH article

Anecdata: children's and adults' evaluation of anecdotal and statistical evidence.

  • 1 Boston University, United States
  • 2 The University of Texas at Austin, United States

The final, formatted version of the article will be published soon.

Pseudoscientific beliefs, including vaccine-related and other types of conspiracy theories, are often formed through reliance on personal anecdotes shared by people with similar belief sets. In the present study, we explore one aspect of pseudoscientific versus scientific reasoning by studying the development of the use of anecdotal versus statistical evidence. To do so, we asked 7-and 10-yearolds and adults to help an agent solve a problem by choosing one of two potential solutions, one supported by an anecdote and one by a graph. Results revealed significant age differences, with older participants more likely to value the graphical over the anecdotal evidence. Participants who chose the anecdotal solution frequently justified their choices by referring either to an inferred causal relationship between the chosen solution and the outcome or to characteristics of the person who provided the anecdote. Participants who chose the graphical solution frequently referred to quantity. Our findings suggest that both a greater valuation of statistical information and an increased ability to reflect critically about causal relationships may be critical in resisting the persuasive power of anecdotes, and hence, making valid evidence-based decisions.

Keywords: Anecdotes, reasoning, cognitive development, narratives, Pseudoscience

Received: 20 Oct 2023; Accepted: 13 Feb 2024.

Copyright: © 2024 Nissel and Woolley. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Jacqueline D. Woolley, The University of Texas at Austin, Austin, 78705, Texas, United States

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COMMENTS

  1. PDF Year 5 Numbers to 10,000 Reasoning and Problem Solving

    Reasoning and Problem Solving Step 1: Numbers to 10,000 National Curriculum Objectives: Mathematics Year 5: (5N2) Read, write, order and compare numbers to at least 1 000 000 Mathematics Year 5: (5N3a) Determine the value of each digit in numbers up to 1 000 000 Differentiation:

  2. PDF Year 5 Numbers to 100,000 Reasoning and Problem Solving

    2019 Reasoning and Problem Solving - Numbers to 100,000 - Year 5 Greater Depth Reasoning and Problem Solving Numbers to 100,000 Developing 1a. 25,914 2a. B is the odd one out as it represents 34,200. A and C represent 34,002. 3a. 24,250; 15,250; 14,350; 14,260; 14,251 Expected 4a. 34,497 5a. B is the odd one out as it represents 21,125.

  3. Y5 Diving into Mastery: Step 2 Numbers to 10 000 Pack

    This is a fantastic Diving into Mastery teaching pack that has been written to complement the White Rose Maths scheme of learning for year 5 autumn term block 1 small step 2 'Numbers to 10 000'. In the pack is an easy-to-follow PowerPoint that contains fluency, reasoning and problem-solving activities for your children to work through together.

  4. PDF Year 4 Number Line to 10,000 Reasoning and Problem Solving

    Reasoning and Problem Solving Number Line to 10,000 Developing 1a. 9,000 (intervals of 500) 2a. Huw is correct. If you find the midpoint of 7,100, you can see that the number is above 7,100.

  5. PDF Year 5 Numbers to a Million Reasoning and Problem Solving

    Questions 2, 5 and 8 (Problem Solving) Developing Complete a part whole model to represent a number up to 1,000,000 in digits, using conventional partitioning using multiples of 10, 100 or 1,000. Expected Complete a part whole model to represent a number up to 1,000,000 in words, using conventional partitioning, where two parts are missing.

  6. PDF Year 5 Compare and Order to a Million Reasoning and Problem Solving

    Greater Depth Use understanding of comparing and ordering numbers up to and beyond1,000,000 to determine whether or not a statement is true or false and explain why. Questions 2, 5 and 8 (Problem Solving) Developing Use understanding of comparing and ordering numbers up to 100,000 to identify which child has which number from given statements.

  7. PDF Year 6 Numbers to Ten Million Reasoning and Problem Solving

    Reasoning and Problem Solving Step 1: Numbers to Ten Million National Curriculum Objectives: Mathematics Year 6: (6N2) Read, write, order and compare numbers up to 10,000,000 Mathematics Year 6: (6N3) Determine the value of each digit in numbers up to 10,000,000 Differentiation:

  8. Free Year 5 Numbers to 10,000 Lesson

    This worksheet recaps number lines to 10,000, comparing 4-digit numbers and ordering numbers ready for numbers to 10,000. Download Worksheet Free Video Tutorial Aaron shows pupils how to show a number in its numeral form and in words by drawing Base 10 in this Represent Numbers to 1,000 Video Tutorial. Watch Video on CS Kids

  9. Numbers to 10,000: Reasoning and Problem Solving

    Numbers to 10,000: Reasoning and Problem Solving, Maths, Year 5, Number, Number and Place Value, Numbers, Sign Up to Download

  10. PDF Discussion Problems Step 4: Numbers to 100,000

    Discussion Problems Step 4: Numbers to 100,000 National Curriculum Objectives: Mathematics Year 5: (5N2) Read, write, order and compare numbers to at least 1,000,000 ... provides pupils with more opportunities to enhance their reasoning and problem solving skills through more challenging problems. Pupils can work in pairs or small groups to

  11. PDF Year 5 Round Within 100,000 Reasoning and Problem Solving

    1a. 8,693; 8,639; 8,963; 8,936; 9,386; 9,368 2a. Theresa is correct. David has rounded the 6 thousands down, but 6 rounds up. 3a. The odd one out is 1,700.

  12. Year 4 Number Line to 10,000 Lesson

    This Year 4 Number Line to 10,000 lesson covers the prior learning of comparing objects and using a number line up to 1,000, before moving onto the main skill of identifying and estimating numbers on a number line up to 10,000. ... This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main ...

  13. Year 6 DiM: Step 2 Numbers to 10 000 000 Teaching Pack

    Teaching year 6 to represent and identify numbers to 10 000 000? In this teaching pack, you will find a wonderful Powerpoint and some complementary activity sheets, all written to be in line with the new White Rose's small step for Year 6 in Autumn Block 1, Step 2: Numbers to 10 000 000. Show more Related Searches

  14. White Rose Maths Compatible Numbers to 10 Million Year 6

    Use these fantastic Numbers to 10 Million Year 6 mastery worksheets that support the White Rose Maths small step 'Numbers to 10 Million' when you teach your year 6 class about place value. This resource includes fluency, reasoning and problem-solving activities of increasing complexity and also links to the year 6 national curriculum maths objective 'Read, write, order and compare numbers up ...

  15. PDF Year 5 Counting in Powers of 10 Reasoning and Problem Solving

    Mathematics Year 5: (5N1) Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000 Mathematics Year 5: (5N5) Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Mathematics Year 5: (5N6) Solve number problems and practical problems t...

  16. PDF Year 5 Multiplying by 10, 100 and 1,000 Reasoning and Problem Solving

    National Curriculum Objectives: Mathematics Year 5: (5C6b) Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000 Differentiation: Questions 1, 4 and 7 (Problem Solving) Developing To calculate an answer based on 3 and 4 digit numbers multiplied by 10, 100 and 1,000.

  17. National Curriculum Resource Tool

    New Curriculum. read, write, order and compare numbers up to 10 000 000 and determine the value of each digit. round any whole number to a required degree of accuracy. use negative numbers in context, and calculate intervals across zero. solve number problems and practical problems that involve all of the above.

  18. Y4 Diving into Mastery: Step 5 Represent Numbers to 10 000

    In this resource pack is a PowerPoint that takes children through fluency, reasoning and problem-solving activities that help the children tackle this learning and interpret and create a variety of representations for numbers up to 10 000. Show more Related Searches

  19. PDF Year 5 Dividing by 10, 100 and 1,000 Reasoning and Problem Solving

    The calculation should be 32,000 ÷ 10 ÷ 10 ÷ 10 because the answer is 32. 8b. Dan has divided the number by 1,000 rather than 100. The correct answer is £27.40 not £2.74 9b. Various answers, for example: 30,600; 52,200; 41,400. Reasoning and Problem Solving - Dividing by 10, 100 and 1,000 ANSWERS.

  20. PDF Year 5 Multiples of 10, 100 and 1,000 Reasoning and Problem Solving

    Reasoning and Problem Solving Multiples of 10, 100 and 1,000 Reasoning and Problem Solving Multiples of 10, 100 and 1,000 Developing 1a. No. 400 x 2 = 800 and 20 x 4 = 80 2a. 120, 12 and 12. Various answers for other number sentences, for example: 70 x 120 = 8,400, 8,400 ÷ 12 = 700 and 840 ÷ 7 = 120. 3a. Sammy and Laura are both wrong.

  21. Round Within 100,000 Year 5 Place Value Resource Pack

    Greater Depth Questions to support rounding numbers within100,000 to the nearest 10, 100, 1,000 or 10,000. Numbers represented as numerals, words and Roman numerals. Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Use four digit cards to create numbers which round to a given number (rounding to 1,000). Using ...

  22. Rounding 6-digit numbers to the nearest 1000, 10 000 and 100 000

    Rounding 6-digit numbers to the nearest 1000, 10 000 and 100 000 In this lesson, we will be using number lines to round 6-digit numbers to the nearest multiple of 1000, 10 000 and 100 000. This quiz includes images that don't have any alt text - please contact your teacher who should be able to help you with an audio description.

  23. Y6 DiM: Number Line to 10 000 000 Teaching Pack

    Helpful mmm.sa9008 - Verified member since 2021 Reviewed on 14 September 2022 Helpful How can I teach year 6 about number lines to 10 000 000? This year 6 Diving into Mastery teaching pack wonderfully complements the year 6 White Rose Maths small step 5: Number Line to 10 000 000.

  24. Anecdata: Children's and Adults' Evaluation of Anecdotal and

    In the present study, we explore one aspect of pseudoscientific versus scientific reasoning by studying the development of the use of anecdotal versus statistical evidence. To do so, we asked 7-and 10-yearolds and adults to help an agent solve a problem by choosing one of two potential solutions, one supported by an anecdote and one by a graph ...