key stage 1 maths problem solving

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Problem-solving maths investigations for year 1.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 1 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 1 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 1:

• Individually, they are incorporated into every unit in our Year 1 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 1 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Key stage 1 tests: 2022 mathematics test materials

Mathematics test materials administered to eligible pupils at the end of key stage 1 in May 2022.

2022 key stage 1 mathematics paper 1- arithmetic

PDF , 540 KB , 20 pages

This file may not be suitable for users of assistive technology.

2022 key stage 1 mathematics administering paper 1- arithmetic

PDF , 241 KB , 4 pages

2022 key stage 1 mathematics paper 2- reasoning

PDF , 4.07 MB , 32 pages

2022 key stage 1 mathematics administering paper 2- reasoning

PDF , 331 KB , 12 pages

2022 key stage 1 mathematics test mark schemes

PDF , 3.99 MB , 24 pages

2022 copyright ownership key stage 1 national curriculum tests

PDF , 188 KB , 3 pages

Key stage 1 mathematics tests were administered in schools in May 2022. Test administration instructions and mark schemes are also provided.

Please refer to the copyright ownership report for details of how schools, educational establishments and third parties can use these materials.

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Reasoning and Problem Solving Questions Collection - KS1 and KS2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

10 March 2023

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These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the back of the booklet and for some problems supplementary questions and variation has been provided.

As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team

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A very good and engaging way to teach mastery of maths. Thank you for sharing

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Problem Solving

Problem Solving and the New Curriculum   Age 5 to 11

Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics   Age 5 to 11

Developing Excellence in Problem Solving with Young Learners   Age 5 to 11

Using NRICH Tasks to Develop Key Problem-solving Skills   Age 5 to 11

Trial and Improvement at KS1   Age 5 to 7

Trial and Improvement at KS2   Age 7 to 11

Working Systematically at KS1 - Primary Teachers   Age 5 to 7

Working Systematically at KS2 - Primary Teachers   Age 7 to 11

Number Patterns   Age 5 to 11

Working Backwards at KS1   Age 5 to 7

Working Backwards at KS2   Age 7 to 11

Reasoning   Age 5 to 11

Visualising at KS1 - Primary Teachers   Age 5 to 7

Visualising at KS2 - Primary Teachers   Age 7 to 11

Conjecturing and Generalising at KS1 - Primary Teachers   Age 5 to 7

Conjecturing and Generalising at KS2 - Primary Teachers   Age 7 to 11

• Mathematical Problem Solving in the Early Years
• Low Threshold High Ceiling - an Introduction
• What's All the Talking About?
• Group-worthy Tasks and Their Potential to Support Children to Develop Independent Problem-solving Skills
• Developing the Classroom Culture: Using the Dotty Six Activity as a Springboard for Investigation

I See Reasoning - KS1

The ebook i see reasoning - ks1 gives 281 thought-provoking images and questions linked to all areas of the ks1 maths curriculum. tasks help to build children's conceptual understanding, promoting non-counting calculation and providing opportunities for reasoning and talk. there are rich tasks for deepening learning every day.

I See Reasoning - KS1 Addition  is a free sample section from the resource. Visual prompts help children to see likely mistakes, notice similarities between questions and develop new strategies for calculating. Techniques such as  Read the Pictures, Explain the Mistakes  and  Which Answer?  draw attention to key learning points and help to generate focused talk. For order enquiries, please read the Frequently Asked Questions .

There are prompts that open up mathematical investigations, for example the  Different Ways  tasks.  True or False? questions draw children's attention to key differences between correct and incorrect responses. There are also different question types that are specific to particular areas of the curriculum, like the  Missing Hand questions in the time section. There are answers too!

I See Reasoning - KS1 Addition  gives a free copy of one of the sections from the resource. Please use and share it!

The 281 tasks of  I See Reasoning - KS1  cover all areas of the Year 1&2 mathematics curriculum. There are many other question types that display maths concepts visually, including the use of bar models. All of the tasks encourage meaningful mathematical talk and challenge children to apply their understanding flexibly. This helps pupils to develop mastery in KS1 mathematics.

I See Reasoning - KS1  corresponds to US grade levels K and grade 1, and Australian school years 1&2. The sale price is  £15  When ordered, the PDF file is emailed direct to your inbox for your use. To purchase, click on the link below:

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Problem Solving

Problem-solving lessons offer the perfect opportunity for your class to use and apply their knowledge and understanding of different mathematical concepts. Logic or skills-based lessons help your children become fluent, reason mathematically and become able to solve problems creatively. 

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The handout is clear with the words easily visible as a quick reference but also my son is able to learn the words by heart.

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As usual a thorough piece of work, with a good balance of planning, input and worksheets. Properly differentiated. it will become the core of my planning for my schools Y1/2 geography topic 'Cities, Towns and Villages'.

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What your child learns in Key Stage 1 maths

Children in KS1 will be learning about maths in a practical hands-on way, using everyday objects to solve problems and do simple calculations.

They will be working individually, as a whole class and in groups, and will be learning to think about the methods they use for solving problems.

They will be talking about their methods and using pictures, lists and tables to present their results.

What your child will be learning in KS1 maths

• Reading and writing numbers 0 to 20 and beyond

• Counting up to 100 objects and beyond

• Learning which pairs of numbers add up to 10 and to 20 ( number bonds )

Unique Year 1 Learning Programme!

• Weekly maths & English worksheets direct to your inbox
• Follows the National Curriculum
• Keeps your child's learning on track

• Recognising number patterns

• Odd and even numbers

• Using a number line

• The 2, 5 and 10 times tables , plus division facts

• Adding and subtracting one-digit and two-digit numbers

• Doubling and halving

• Finding a quarter, a third and a half of a shape or quantity

• Simple mental maths

• Recognising, naming and describing 2D and 3D shapes

• Using shapes to make models and pictures

• Finding lines of symmetry

• Measuring and weighing

• Addition and subtraction of small amounts of money

• Knowing that a quarter turn is a right angle

• Recognising and using mathematical symbols

• Drawing and interpreting graphs and pictograms

• Telling the time on an analogue clock to the nearest five minutes

• Naming and describing 2D and 3D shapes

Give your child a headstart

• FREE articles & expert information
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