Problem-solving Maths Investigations for Year 5

Nick Barwick

Hamilton provide an extensive suite of problem-solving maths investigations for Year 5 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 5 .

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 5:

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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Reasoning/Problem Solving Maths Worksheets for Year 5 (age 9-10)

Real life problem solving.

A collection of problem solving activities based on real life situations.

Preview of worksheet  Solve single step 'real life' problems

Some of the questions are quite long, but they can be answered with a single step operation.

Preview of worksheet Multi step problems using bar models

Using bar models to help understand what to do to solve multi-step problems.

Preview of worksheet  Solve multi step word problems

Much trickier questions as they all need more than one step to reach the right answer.

Preview of worksheet Multi-step problems: shopping

Multi-step problems with shopping.

Preview of worksheet Multi-step problems: hobbies

Tricky multi-step problems on thew theme of hobbies.

Preview of worksheet Multi-step problems: using cards

Multi-step problems: using cards.

Preview of worksheet Multi-step problems: using place value charts

Multi-step problems: using place value charts.

Preview of worksheet  Solve problems involving money

Money, money, money! Lots of money questions which will need a lot of working out!

Preview of worksheet Work out the price of the plants

Straightforward addition of money which can be done mentally, maybe using jottings to help.

Preview of worksheet Cost of houseplants

Work out the cost of the plants from the information given.

Preview of worksheet Buying three houseplants

Addition of money to really stretch the brain!

Preview of worksheet Days out (1)

Solving problems involving '3 for 2' voucher offer.

Preview of worksheet Days out (2)

Solving money problems with 3 for 2 offers and percentages.

Preview of worksheet Days out (3)

More percentage problems.

Preview of worksheet Solving multi step problems

Tricky word problems needing more than one step to solve.

Preview of worksheet  Solve problems involving measurement

Questions all on the theme of measurement, including length, capacity and weight.

Preview of worksheet  Solve problems involving time

Hours, minutes seconds are all found in these questions on time.

Preview of worksheet 5-digit numbers: problem solving

Find the number from the clues given.

Preview of worksheet Problem solving: inverse operations

Solve multi-step problems and check by carrying out inverse operations.

Preview of worksheet Digit cards: largest and smallest numbers

Find the largest and smallest numbers and the difference between them.

Preview of worksheet  Choose the correct strategy

Not so much the correct answer needed; more choosing the method and an explanation of how to solve the problem.

Fractions, decimals and divisibility

Problem solving involving fractions, decimals and tests of divisibility.

Preview of worksheet Facts about decimal fractions (inc. bar modelling) 1

Finding facts about decimal fractions, including bar modelling.

Preview of worksheet Facts about decimal fractions (2)

Finding facts about decimal fractions, including using bar modelling to help.

Preview of worksheet Order decimals

Order decimals.

Preview of worksheet Find half way between two decimals

Find half way between two decimals.

Preview of worksheet Word problems with decimals

Word problems with decimals.

Preview of worksheet Ordering fractions

Ordering fractions.

Preview of worksheet  Tests of divisibility

Some tests of divisibility are easy, such as divisible by 2, 5 or 10. Others, such as divisible by 6 or 8 are much harder.

Challenges and investigations

Further challenges, investigations and games requiring sound mathematical thinking and working in a systematic way.

Preview of worksheet  Use binary trees to solve problems

Binary trees are often used in science, but here we use them to sort numbers.

Preview of worksheet  More on odd and even numbers

More on odd and even numbers, plus a little bit on multiples.

Preview of worksheet  More problem solving

Some great ideas for children to use as starting points to investigate further.

Preview of worksheet  Make and investigate general statements

Find examples to back up general statements about numbers, shape etc.

Preview of worksheet 12 to 15 square

Place the digits in the rows and columns to make the total shown in the middle.

Preview of worksheet Challenges and Investigations in Year 5

A look at some of the maths concepts involved with investigations in year 5.

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Reasoning problems Year 5/6 with answers

Reasoning problems Year 5/6 with answers

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

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Last updated

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This resource has been created based on KS2 SATs reasoning tests. These can be used to practise a range of skills or identify gaps in learning. Answers are at the bottom of the worksheet.

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Problem Solving Skills Assessment Test

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Problem Solving Skills Assessment

Assessment details, assessment summary, skills tested in this assessment, what to test with this assessment, about the problem solving skills assessment.

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Problem Solving is all about using logic, imagination, and creativity, to understand a situation and then come up with an intelligent solution to the problem. The best problem solvers can actively anticipate potential future problems and act quickly to prevent them from ever happening or to mitigate the effects.

This Problem Solving test assesses whether job candidates have the ability to learn, solve problems, and understand instructions while allowing you to see how adaptable they are to coaching and training.

Candidates who perform well on this Problem Solving assessment will have all the technical skills to successfully understand and articulate a problem and plan for it. They will also have the necessary soft skills to critically think about solutions to problems and effectively communicate this back to stakeholders.

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Many jobs require problem solving as part of their skill set, but some are more obviously oriented toward this type of work than others. For instance, jobs in the field of engineering often require employees to find solutions to complex technical problems. Similarly, positions in sales or customer service frequently entail finding creative ways to resolve customer issues. Even jobs that are not traditionally seen as requiring problem solving skills can benefit from employees who are able to think on their feet and come up with solutions to challenges as they arise. In today’s ever-changing business landscape, the ability to solve problems is an essential skill for success in any career.

Problem solving tests are designed to assess a range of skills that are essential for success in the workplace. The ability to creative think is perhaps the most important skill that is tested, as it allows candidates to generate multiple solutions to a problem. This is important as it allows different perspectives to be considered and the best solution to be chosen. Other skills that are assessed include the ability to think logically and rationally, as well as the ability to communicate effectively. These skills are all highly relevant to job performance, making problem solving tests an excellent way to identify the best candidates for a role.

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Year 5 Maths Worksheets UK Hub Page

Welcome to our Year 5 Maths Worksheets area.

Here you will find a wide range of free printable Maths Worksheets for pupils in Year 5, and Math activities for your child to enjoy.

Take a look at our decimal place value sheets, our mental math sheets, or maybe some of our equivalent fraction worksheets. Perhaps you would prefer our statistics worksheets, or how to measure angles?

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This page contains links to other Math webpages where you will find a range of activities and resources.

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Year 5 Maths Learning

Here are some of the key learning objectives for the end of Year 5:

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 5 is generally equivalent to 4th Grade in the US.

On this page you will find link to our range of math worksheets for Year 5.

Quicklinks to Year 5 ...

Word Problems Zone

Geometry Zone

Data analysis zone.

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

Place Value & Number Sense Zone

Year 5 place value worksheets.

Using these Year 5 maths worksheets will help your child to:

Year 5 Number Worksheets

Using these Year 5 Maths worksheets will help your child to:

Year 5 Counting Worksheets

Using these sheets will support you child to:

Year 5 Mental Maths Zone

Here you will find a range of printable Year 5 mental maths sheets for your child to enjoy.

Each quiz tests the children on a range of maths topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math test or math quiz!

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Year 5 Addition Worksheets

Year 5 Subtraction Worksheets

Year 5 Multiplication Worksheets

Using these 4th grade math worksheets will help your child to:

Year 5 Division Worksheets

Using these Year 5 maths worksheets will help your child learn to:

These sheets involve solving a range of division problems.

Year 5 Math Problems

Using the problems in this section will help your child develop their problem solving and reasoning skills.

These sheets involve solving one or two more challenging longer problems.

These sheets involve solving many 'real-life' problems involving data.

These sheets involve solving a range of multiplciation problems.

Fractions & Percentage Zone

Quicklinks to ...

Year 5 Percentage Worksheets

Year 5 fraction worksheets.

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

Year 5 Geometry Worksheets

Using these sheets will help you to:

Measurement Zone, including Time & Money

Year 5 measurement worksheets.

Using these sheets will help your child understand how to:

Area and Perimeter Worksheets

Year 5 Time Worksheets (4th Grade)

Using the sheets in this section will help your child to:

On this webpage there is a selection of printable 24 hour (military time) conversion worksheets which will help you learn to convert from 24 hour clock to standard 12 hour time, and from standard time to 24 hour time.

Time Interval Worksheets

These sheets will help you learn to add and subtract hours and minutes from times as well as working out a range of time intervals.

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

Using these 4th grade math worksheets will help you to:

Fun Zone: Puzzles, Games and Riddles

Year 5 maths games.

Year 5 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Math Salamanders Year 5 Maths Games Ebook

Our Year 5 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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Problem-Solving Aptitude Test Questions 2023 - Placement Mock Exam Papers with Answers

Practice free online solved Problem-Solving Aptitude Mock Test 2023: Download previous year's solved Problem-Solving placement exam question papers with answers.

What is Problem-Solving Aptitude Test?

Problem-Solving placement aptitude test is a popular pre-employment cognitive ability assessment. To make better hiring decisions, companies conducts a Problem-Solving test to predict candidates' competency level and likelihood of success in a job role. A company uses Problem-Solving tests during the recruitment process to compare applicants.

Placement aptitude test is designed to assess the Problem-Solving skills of the candidates. Problem-Solving placement aptitude test contains multiple-choice questions.

How to Pass Problem-Solving Aptitude Test?

If you are going to appear in the upcoming Problem-Solving aptitude test 2023, follow these top 5 tips to easily pass the test:

[1] Practice Realistic Problem-Solving Online Tests

If you want to pass the Problem-Solving aptitude test, then you need to practice a lot. You should take online tests under simulated exam conditions and start practicing tricky questions for the Problem-Solving aptitude test.

[2] Know the Latest Exam Format of the Problem-Solving Placement Test

Researching the format of the Problem-Solving aptitude test beforehand will prevent any surprises during the real exam conducted by Problem-Solving.

[3] Focus on your Weakest Areas

While practicing time-bound Problem-Solving mock tests, try to find some difficult topics from the Problem-Solving aptitude test syllabus and create strategies to improve exam results.

[4] Manage your Time Carefully During the Problem-Solving Mock Test Papers

Time-bound Problem-Solving mock tests are conducted under strict time restrictions. Keep an eye on the clock during the Problem-Solving aptitude test and work steadily.

[5] What if I Fail Problem-Solving Aptitude Exam on my First Attempt?

Problem-Solving is not that difficult but some candidates are not able to score high in the Problem-Solving aptitude test on their first attempt. Such applicants are advised to practice the previous year's Problem-Solving aptitude questions. It will help candidates understand the Problem-Solving aptitude test format. This way, test givers will be able to score well in the Problem-Solving section of the placement examination next time.

Is Problem-Solving Aptitude Test Difficult?

The overall difficulty level of the Problem-Solving placement aptitude exam is moderate. Problem-Solving aptitude question papers are one of the important study materials for preparing effectively for the Problem-Solving placement exam. Candidates should analyse Problem-Solving aptitude test papers thoroughly to find the most important and scoring topics of the latest Problem-Solving aptitude exam pattern and syllabus.

Best Tips to Prepare for Problem-Solving Aptitude Test for the Latest Campus Placements 2023

Watch this video if you are searching:

Practice 100+ Free Online Problem-Solving Aptitude Tests with Solved Questions and Answers

When you are preparing for the Problem-Solving aptitude test, do not forget to practice with old Problem-Solving question papers. There are many good sources online, where you can download PDF exam papers or practice free Problem-Solving aptitude mock tests:

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Maths problems with answers for grade 5.

Grade 5 maths problems with answers are presented. Also Solutions and explanations are included.

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Worksheets and Daily Practice, Home Learning

Rapid reasoning year 5 weeks 1 to 6.

Six weeks of daily reasoning and problem solving questions (approximately three per day) mapped to a progression document for Year 5; use in conjunction with daily arithmetic practice from Fluent in Five.

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Grade 5 Multiplication & Division Worksheets

Multiply & divide with grade 5 worksheets.

These grade 5 worksheets provide more challenging practice on multiplication and division concepts learned in earlier grades.

year 5 problem solving test

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More division worksheets

Explore all of our division worksheets , from simple division facts to long division of large numbers.

More multiplication worksheets

Find all of our multiplication worksheets , from basic multiplication facts to multiplying multi-digit whole numbers in columns.

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"TSA contains a Critical Thinking component – which is essential for university study, and not something students may necessarily focus on at school. The test helps us to identify those who will thrive at UCL as it allows students to demonstrate their potential to develop this skill."

Tessa Robinson, Administrative Manager, European and Social Political Studies

University College London, UK

TSA is an assessment of critical thinking and problem-solving skills, skills that are widely identified as the most important skills for study and employment.

The test is designed to help you select students with the potential to succeed in higher education. This includes degree courses, such as Engineering, Economics, Politics, and Psychology.

Developed in collaboration with world-leading universities, TSA has been enhancing selection processes since 2001.

Contact us about using TSA at your university.

Why use TSA?

Discover students with the right skills TSA focuses on academic thinking skills such as problem-solving and critical thinking, which are crucial for university study but are not the focus of school qualifications.

Predict success TSA helps you identify applicants who will thrive on your course. Validity studies show a positive relationship between test scores and on-course performance.

Support widening access TSA is designed to be accessible to all applicants. It is a test of skills, not prior knowledge and therefore provides students with another opportunity to show what they can do.

Gain international reach TSA can be taken either through our global network of test centres or online as a secure remote-proctored test. You can reach applicants from across the world.

Make a fair comparison TSA gives a common benchmark of an applicant’s core thinking skills, providing you with a fair way to compare candidates from different educational or cultural backgrounds.

Who uses TSA?

We are a trusted partner to universities around the world. Here’s a selection of institutions using TSA:

Test format

Read the TSA question guide  for an overview of the test format and content. 

View a TSA sample paper

Costs and administration

TSA can be administered:

We keep test fees to affordable levels to ensure they do not present a barrier to students entering university.

The test fee depends on how and where the test is administered. The fee can be either charged to the institution direct, or passed on to test-takers.

Preparing for TSA

TSA measures problem-solving and critical thinking skills and is designed to be taken with minimal preparation. There is no need for students to take a preparation course or undertake additional preparation, beyond familiarising themselves with the test format and question style.

We support test-takers with a range of free materials and resources to help them prepare for the test, including specimen papers and the TSA question guide.

You can see samples of TSA preparation materials here .

TSA research

TSA is produced using research and processes conforming to international quality standards. We conduct extensive research to ensure validity and fairness of our admissions tests.

Key TSA research points:

The Stockholm School of Economics uses TSA in the admission process of one quota of students to our BSc program in Business and Economics. The students selected based on their TSA scores and interviews have performed very well in the program. We are also very happy with the ease of the TSA administration process and the helpfulness of our company contacts. Anna Nyberg , Program Director, BSc Business & Economics, Stockholm School of Economics

Maths problem solving questions year 5

Best of all, Maths problem solving questions year 5 is free to use, so there's no sense not to give it a try!

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Daily Math Word Problems

Here you will find our selection of 5th Grade Math Problems which will help you practice and apply your math skills to solve a range of longer

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  5. Year 5 Problem-Solving Investigations: Addition and Subtraction

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  1. FREE Year 5 Maths Worksheets, Tests and Homework (PDF)

    This Year 5 maths worksheet focuses on finding fractions of amounts, and includes an arithmetic warm up involving adding and subtracting fractions, before moving onto reasoning questions that test how well children have learned how to calculate fractions of amounts. Example sheets from our Independent Recap activities.

  2. 5th grade word problem worksheets

    The four operations Mixed 4 operations Estimating and rounding word problems Grade 5 fractions and decimal word problems Addition and subtraction of fractions Addition and subtraction of mixed numbers Division of numbers with fractional answers Dividing by unit fractions Multiplying fractions word problems Mixed operations with fractions

  3. Problem-solving Maths Investigations for Year 5

    Explore all our in-depth problem solving investigations for Year 5. Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

  4. Reasoning/Problem Solving Maths Worksheets for Year 5 (age 9-10)

    Year 5 (age 9-10) Reasoning/Problem Solving Maths Worksheets for Year 5 (age 9-10) Expectations are high for the end of Year 5! All four number operations of addition, subtraction, multiplication and division are used to solve one-step and two-step problems involving money, measurement and time.

  5. Reasoning problems Year 5/6 with answers

    Reasoning problems Year 5/6 with answers Subject: Mathematics Age range: 7-11 Resource type: Worksheet/Activity 2 reviews File previews docx, 14.96 KB Creative Commons "Sharealike" to let us know if it violates our terms and conditions. Last updated 8 May 2019 Not quite what you were looking for? Search by keyword to find the right resource:

  6. Year 5 problem solving

    Year 5 problem solving Short problem solving activity using place value of numbers ID: 2863604 Language: English School subject: Math Grade/level: Year 5 Age: 8-10 Main content: Problem solving Other contents: Add to my workbooks (2) Add to Google Classroom Add to Microsoft Teams

  7. PDF Abacus Year 5 Problem Solving and Reasoning Test Sample

    Abacus Year 5 Problem Solving and Reasoning Test Sample

  8. Problem Solving Skills Assessment Test

    Problem solving tests are designed to assess a range of skills that are essential for success in the workplace. The ability to creative think is perhaps the most important skill that is tested, as it allows candidates to generate multiple solutions to a problem.

  9. PISA Test

    Questions from the OECD PISA test in 2018, 2015 and 2012. Also includes information on test criteria. Toggle navigation. Follow us. English Follow us. English Home; About; PISA Test ... Science and Collaborative Problem Solving Items (Field Trial) pdf. Science and Collaborative Problem Solving Items - interactive Items PISA 2012. Mathematics ...

  10. McKinsey Problem Solving Test Practice Test A

    A. Hours grew by 24% across all ten countries over the last 12 years B. Slovenia had the greatest growth in Productivity over the last 12 years C. Spain had the least growth in Productivity over the last 12 years D. Germany had the least growth in Hours over the last 12 years 7. To the nearest tenth of a percentage point, what is the difference

  11. PDF Year 5 Autumn 1 Problem solving and reasoning Commentary chart

    Year ssessment oolkit earson ucation t 21 General information Questions in the Arithmetic test are usually worth 1 mark. In Key Stage 2, two marks may be available for the use of an appropriate written method. Questions in the Problem solving and reasoning test can be worth 1, 2 or 3 marks.

  12. Year 5 Maths Worksheets

    Here you will find a range of printable Year 5 mental maths sheets for your child to enjoy. Each quiz tests the children on a range of maths topics from number facts and mental arithmetic to geometry, fraction and measures questions. A great way to revise topics, or use as a weekly math test or math quiz! Year 5 Mental Maths Worksheet Top of Page

  13. Year 5 Maths Reasoning Test Set 1 Assessment Pack & Analysis Grid

    Year 5 Maths Reasoning Test Set 1 Assessment Pack and Analysis Grid Free Account Includes: Thousands of FREE teaching resources to download Pick your own FREE resource every week with our newsletter Suggest a Resource! You want it? We'll make it 24/7 customer support (with real people!)

  14. Year 5 Australia School Math Problem solving

    Problem solving problems, practice, tests, worksheets, questions, quizzes, teacher assignments | Year 5 | Australia School Math

  15. Grade 5 Mixed Word Problems Worksheets

    Mixed Grade 5 Mixed Word Problems Mixed word problem worksheets Below are mixed word problems including the 4 basic operations, fractions, decimals, LCM / GCF and variables. Mixing different types of word problems encourages students to read and think about the questions, rather than simply recognizing a pattern to the solutions.

  16. Problem-Solving Aptitude Test Questions 2023

    26 Good Examples of Problem-Solving (Interview Answers) 8 Common Problem-Solving Interview Questions and Answers. Problem-Solving Questions and Answers for Interviews. 250+ TOP MCQs on Problem-Solving and Answers. Free Problem-Solving Online Practice Tests - WizIQ. Problem-solving test: Telomere replication - PubMed.

  17. Maths Problems with Answers for Grade 5

    Grade 5 maths problems with answers are presented. Also Solutions and explanations are included. A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? It takes John 25 minutes to walk to the car park and 45 to drive to work.

  18. Rapid Reasoning Year 5 Weeks 1 to 6

    Rapid Reasoning Year 5 Weeks 1 to 6. Six weeks of daily reasoning and problem solving questions (approximately three per day) mapped to a progression document for Year 5; use in conjunction with daily arithmetic practice from Fluent in Five. Year 5. Problem Solving.

  19. Grade 5 Multiplication & Division Worksheets

    Grade 5 Multiplication & Division Worksheets Multiply & divide with grade 5 worksheets These grade 5 worksheets provide more challenging practice on multiplication and division concepts learned in earlier grades. Sample Grade 5 Division Worksheet More division worksheets

  20. Thinking Skills Assessment (TSA)

    TSA is an assessment of critical thinking and problem-solving skills, skills that are widely identified as the most important skills for study and employment. The test is designed to help you select students with the potential to succeed in higher education. This includes degree courses, such as Engineering, Economics, Politics, and Psychology.

  21. Maths problem solving questions year 5

    Maths problem solving questions year 5 - Best of all, Maths problem solving questions year 5 is free to use, so there's no sense not to give it a try! ... Algebra 1 polynomials test ch 8 ...