key stage 1 problem solving activities

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Learn all about the topics covered in KS1 maths, explore our free resources and have a go at some practice questions!

• What do children learn in the KS1 maths curriculum?

• Topic guides and practice questions

• KS1 maths resources and activities

•   KS1 maths SATs: guides and resources

Select a topic

Explore the topics covered in KS1 maths and have a go at some fun, interactive practice questions!

Number and place value

Learn how to count, read and write numbers up to 100

Find out more

Addition and subtraction

Explore strategies for mental and written problem solving

Multiplication and division

Discover key multiplication and division facts

Find out about data and how to read bar charts and graphs

Measurement

Explore time, volume and length and quantities

Learn how to identify 2D and 3D shapes

Position and direction

Discover how to arrange objects into patterns

Fractions, decimals and percentages

Learn what a fraction is and how to order them

Choose a year group

Select a year group.

Take a look at the skills children learn in each year group and have a go at some questions

What do children learn in KS1 maths?

In Key Stage 1 (KS1), kids explore a wide breath of content to help develop their knowledge of core concepts and gain an understanding of how maths is used in everyday life. From fractions to shapes, they learn lots of key skills that’ll place them in great stead for KS2!  The main topics they learn about are…    

1. Number and place value: In the KS1 maths curriculum, children learn to count, read, write and represent numbers up to 100. They also learn how to compare numbers and use the place value system.  

2. Addition and subtraction: Children learn various strategies for mental and written addition and subtraction. They also explore number bonds, counting techniques and inverse operations.  

3. Multiplication and division: Kids develop their understanding of multiplication and division and learn how to solve problems using multiplication and division facts, arrays and pictorial representations.  

4. Fractions : Learners discover how to recognise, name, find and write fractions in relation to length, shapes and quantity.

  5. Measurement: In KS1 maths, children learn how to use appropriate units, estimate measurements and read scales, including length, capacity and time.  

6. Properties of shapes: Learners explore the fundamentals of shapes, including how to recognise and name different types of 2D and 3D shapes.  

7. Position and direction: Children  learn how to describe position, direction and movement, as well as how to organise objects into patterns and sequences. 

8. Statistics: In the KS1 curriculum, kids explore how to collect and organise data. They also learn how to create graphs and interpret data using a variety of graphs.

Meet Doodle, the personalised maths app that explores the whole KS1 curriculum!

Created by our team of teachers, DoodleMaths is an award-winning maths app that’s filled with interactive questions and games covering the whole KS1 curriculum.    

Designed to be used for just 10 minutes a day, it creates every child a unique learning experience tailored to their needs, boosting their confidence and ability in maths.  And best of all, you can  try it for free !  

Frequently asked questions about KS1 maths

DoodleMaths is an award-winning app that’s filled with fantastic maths games for KS1!

From working in a messy bakery to helping a monkey collect coconuts, all of its games are specifically designed to develop instant recall and mental maths skills, transforming learning into a fun adventure.

Best of all, all of its questions feel like a game, with every exercise using interactive activities and explanations to help bring the subject to life!

Create an account today to enjoy a free 7-day trial .

There are lots of ways that you can help your child or pupils to learn KS1 maths:

• Rather than explaining concepts, use visual representations to explore them, such as number lines and grids.
• Nothing beats doodling! Encourage your child or pupils to draw pictures to help them understand concepts or have a go at working out the answer to a question. 
• Use real-life items to explore number, such as Smarties or pebbles. Encourage your child to sort the items into different amounts; doing this will help them understand concepts such as addition and fractions!
• Boosting their instant recall skills will help them with their mental maths and speed answering questions. Learning times tables in a specific order and using fun activities is a great way to help with this!

An array is an arrangement of items (such as pictures or numbers) in columns or rows.

They let children visualise what happens when they multiply or divide numbers together, helping them master times tables and division!

Reasoning is basically detective work: it’s when learners use what they already know to work out the answer to a question.

For example, if a child knows what 12 – 5 is, they can use this knowledge to work out what 12 – 6 is.

“I know that 12 – 5 is 7. As 6 is 1 higher than 5, the answer must be 1 higher than 7.”

KS1 maths resources and activities

Looking for even more ways to support your child or pupils’ learning? We’ve got you covered!

How to improve at mental maths

Discover our top tips to help any child master mental maths! 

Outdoor learning activities for KS1

When the sun is shining, there’s nothing better than taking your learning outside!

How to support your child's home learning

Practising maths ‘little and often’ is the perfect way to help kids develop their skills

Discover our top tips to help any child master mental maths!

When the sun is shining, there’s nothing better than taking your learning outside!

Practising maths ‘little and often’ is the perfect way to help kids develop their skills

KS1 maths SATs: guides and resources

In Year 2, children complete maths and English SATs papers. Explore what’s covered in the exams and how you can help your child or pupils prepare for them!

KS1 SATs papers 2024: what's included?

See what’s covered in KS1 SATs and how you can help your child prepare for them

How Doodle can help kids prepare for SATs

Our apps cover the whole KS1 curriculum, making them perfect study buddies

How to help your child prepare for SATs

SATs may seem worrying, but these tips will help calm your child (and you!)

KS1 SATs papers: what's included?

See what’s covered in KS1 SATs and how you can help your child prepare for them

Our apps cover the whole KS1 curriculum, making them the ultimate study buddies

Try our KS1 maths app for free!

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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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TES Resource Team

We are pleased to let you know that your resource Reasoning and Problem Solving Questions Collection - KS1 and KS2, has been hand-picked by the Tes resources content team to be featured in https://www.tes.com/teaching-resources/blog/fluency-reasoning-and-problem-solving-primary-maths in April 2024 on https://www.tes.com/teaching-resources/blog. Congratulations on your resource being chosen and thank you for your ongoing contributions to the Tes Resources marketplace.

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

thank you for sharing, this is really good

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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 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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Free Team Building Activity – Alphabet Hunt

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• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

Patterns and Sequences KS1

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Poly Plug Pattern

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

Chairs and Tables

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Next Domino

Which comes next in each pattern of dominoes?

A City of Towers

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Domino Patterns

What patterns can you make with a set of dominoes?

Repeating Patterns

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Cube Bricks and Daisy Chains

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

Three Ball Line Up

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Caterpillars

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Missing Middles

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?

Triple Cubes

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Street Sequences

Investigate what happens when you add house numbers along a street in different ways.

Circles, Circles

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Break it Up!

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Counting Stick Conjectures

How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?

Hundred Square

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

School Fair Necklaces

How many possible symmetrical necklaces can you find? How do you know you've found them all?