problem solving challenges year 3

Reasoning/Problem Solving Maths Worksheets for Year 3 (age 7-8)

Money problems and challenges.

A variety of problem solving activities involving money.

50p to spend, but can you make sure you get the correct change?

Watch out when writing pence as pounds and remember to always have two digits after the decimal point.

The hardest part of these money problems is to read the question and work out what to do.

Put three items in your basket that you would like to buy and then use the money cards to work out the sum.

Solve money problems using the information provided.

Solve money problems at the skating rink.

Plenty of monkey business here!

It's a trip to the zoo to find the very best value.

Some tricky money problems to solve.

More tricky money problems to solve.

Finding different amounts from a given set of coins.

Number and calculating problems

Solve number problems and calculating using addition, subtraction, multiplication and division.

Find the 2-digit numbers that can be made using these digit cards.

Make 2-digit numbers and find the smallest and largest numbers.

More on finding 2-digit numbers from three digit cards.

Tricky little problems involving monsters' legs.

Use logic, addition and subtraction to find out how many strawberries are eaten.

Bar Model: addition and subtraction facts.

Use bar models to add and subtract.

Encourage children to make addition and subtraction come to life by writing short number stories.

What numbers can you make with digit cards?

What are the largest and smallest numbers that can be made with 3 cards?

More number stories to write: this time all about multiplication and division.

All the numbers are here, but the signs are missing! Can you work out what the signs should be?

Investigating odd and even numbers and what happens when you add them together.

Use knowledge of place value to find all possible answers.

Finding the numbers and missing digits to make number sentences correct.

Investigate statements involving odd and even numbers.

Investigate statements about multiplication and times tables.

I?m good at thinking of numbers, but can you work out what number I am thinking about ? I do give a clue!

Work out the missing value using division and addition.

Use reasoning to find the missing values.

More on finding the missing values - an early introduction to algebra.

Use division and addition to find the missing values.

Find the missing values from the information given.

More on finding the value using reasoning.

Real life and word problems

A selection of real life problems and word problems.

Tricky word problems.

More tricky word problems.

Tricky questions, but you only have to carry out one maths step to answer them.

Even trickier questions, and you have to carry out at least two steps to work them out!

More word problems, from the library to shopping and on to flying around the world.

Here we have four pages of questions all on time, including a trip to Alicante!

Solving tricky fraction problems.

More challenges and activities

A great selection of activities requiring logical thinking.

Investigation looking at possibilities when adding the digits from 1 to 5.

This time you can decide the total for the sides of the triangle.

Can you put the numbers 1 to 9 in the diagram so that the difference between each pair of joined numbers is odd?

This challenge is to find as many ways as possible of making 12 using three number cards and the add, subtract and multiply signs.

A development of the 'Caterpillar investigation' but using multiples of 10. Great for practising addition.

3 dinosaurs laid some eggs. They laid 19 altogether. How many did they each lay?

How many ways can three runners cover a distance of 19 miles? They all have to run an odd number of miles.

A book challenge here. How accurately can you guess the number of pages in books?

2D card shapes and a 3 x 3 pinboard are useful for these shape activities.

A calculator is needed to find how many different answers can be made from the numbers given. Good for working in an organised, logical way.

A brief summary of some of the most important maths concepts to be taught in Year 3 by way of challenges and investigations.

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Year 3 Money Challenges Solving Money Problems

Welcome to our Year 3 Money Challenges page. Here you will find our selection of printable money problem worksheets to help your child learn to use their money skills to solve a range of problems.

These challenges are a great resource as an extension for more able pupils, or to consolidate and extend learning.

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Year 3 Money Learning

Knowing how to handle and calculate with money is a very important life-skill.

During Year 3, children build on their knowledge and skills they have achieved during Year 2.

By the time children reach the end of Year 3, they should be able to:-

• use decimal notation for amounts of money, e.g. £3.27
• change amounts in £ to amounts in pence and back;
• count money up to £10;
• calculate change for amounts of money up to £1 mentally;
• solve simple problems involving money;
• use informal methods to add and subtract money amounts in £ and pence.

Our worksheets will support your child with these objectives.

Year 3 Money Challenges Information

The following worksheets involve solving challenges involving money amounts. They are a great way to consolidate and extend money learning once children are confident with counting money amounts.

The challenges start off at a fairly easy level with problems that involve lower value coins and smaller money amounts. The challenges later on involve more complex problems with larger values to calculate.

If you are teaching a class or group of children, then these sheets should give you some great differentiated learning activities with a money theme.

An answer sheet is available for each challenge provided.

The money challenges in each section are carefully graded, allowing you to introduce concepts at an easier level before introducing harder work, or differentiate within your class.

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

• count money in coins up to £1;
• develop their reasoning and thinking skills;
• solve problems involving money.

All the money worksheets in this section will help your child to become more confident with money, and develop better problem solving skills.

Year 3 Money Challenges Worksheets

There are 3 challenges - Tyger's Money Square Challenge, Row of Coins Challenge and How Much Money Challenge.

Each main challenge has several versions which start with the easiest level and progress onto harder levels of challenge.

Row of Coins Challenges

• Row of Coins Challenge 1
• PDF version
• Row of Coins Challenge 2
• Row of Coins Challenge 3
• Row of Coins Challenge 4

Tyger's Money Square Challenges

• Tyger's Money Square Challenge 1
• Tyger's Money Square Challenge 2
• Tyger's Money Square Challenge 3
• Tyger's Money Square Challenge 4

How Much Money Challenges

• How Much Money Challenge 1
• How Much Money Challenge 2
• How Much Money Challenge 3

Extension Activity Ideas

If you are looking for a way to extend learning with the How Much Money challenge, why not...

Try playing 'How Much Money' in pairs.

One person chooses 2 or 3 coins and the other person has to ask questions which involve 'yes' or 'no' answers.

To make the game more interesting, have a maximum of 5 questions before you make a guess!

Looking for some more UK money worksheets?

We also have some counting money worksheets with amounts up to £1 or £5.

The sheets are at a more basic level than those on this page.

• Free UK Money Worksheets Coins up to £1
• Year 3 Money Worksheets Coins up to £5
• Year 4 Money Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Money Riddles

These puzzles are a great money starter activity to get children thinking and puzzling out which the correct answer is out of a set number of choices. They are great for partner work too.

UK Money Riddles

If you are looking for some fun learning puzzles involving money, then look no further.

The puzzle sheets in this section are designed primarily for children in Years 3 and 4 who need to develop their problem solving skills and mathematical language.

Using these challenges will help your child to:

• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.
• Money Riddles for Kids (UK coins)

Money Column Addition Worksheets

Here you will find a selection of Column Addition Money sheets designed to help your child add different amounts of money.

Using these sheets will help your child to:

• add up a range of money amounts involving decimals.

The worksheets in this section are aimed at children in Years 4 and 5.

• Column Addition Money Worksheets (UK)

Money Column Subtraction Worksheets

Here you will find a selection of Column Subtraction Money sheets designed to help your child subtract different amounts of money.

• subtract a range of money amounts involving decimals.
• Column Subtraction Money Worksheets (UK)
• Counting Money Games

Here is our collection of counting money games for kids.

All of these games are suitable for kids aged from 1st grade and upwards.

Playing games is a great way to practice math skills in a fun way. Games also help to develop reasoning, thinking and memory.

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Resources tagged with: NC Yr 3

There are 67 NRICH Mathematical resources connected to NC Yr 3 , you may find related items under NC .

Class 5's Names

Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?

Fifteen Cards

Can you use the information to find out which cards I have used?

The Time Is ...

Can you put these mixed-up times in order? You could arrange them in a circle.

Journeys in Numberland

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

The Car That Passes

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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.

Follow the Numbers

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Stick Images

This task requires learners to explain and help others, asking and answering questions.

Arranging Cubes

A task which depends on members of the group working collaboratively to reach a single goal.

Planning a School Trip

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

Fraction Match

A task which depends on members of the group noticing the needs of others and responding.

Number Match

How Do You Do It?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Strike it Out

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Coded Hundred Square

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

How Much Did it Cost?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Overlapping Again

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

What's in the Box?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Music to My Ears

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Real Statistics

Have a look at this table of how children travel to school. How does it compare with children in your class?

These clocks have only one hand, but can you work out what time they are showing from the information?

Board Block Challenge

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Number Differences

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Finding Fifteen

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Building Blocks

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

5 on the Clock

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

These clocks have been reflected in a mirror. What times do they say?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Sealed Solution

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

The Third Dimension

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Square Corners

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

A Puzzling Cube

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Super Shapes

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Amy's Dominoes

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Wonky Watches

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

How Many Times?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Which Scripts?

There are six numbers written in five different scripts. Can you sort out which is which?

Buying a Balloon

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Use these four dominoes to make a square that has the same number of dots on each side.

Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Problem-solving maths investigations for year 3.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 3 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 3 .

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 3:

• Individually, they are incorporated into every unit in our Year 3 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 3 .

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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50 years later, international experts discuss importance of 'Lucy' discovery at ASU symposium

Illustration of "Lucy" species by Michael Hagelberg

“Lucy” is one of the most famous human ancestor fossils of all time.

Discovered by ASU Institute of Human Origins  Founding Director  Donald Johanson in 1974, in the deserts of Hadar, Ethiopia, the unearthing of this 3.2-million-year-old species had a major impact on the science of human origins and evolution and on the public’s understanding of our origins. Now, 50 years later, those in the field are asking how that impact has evolved.

During a three-day event celebrating the 50th anniversary of this discovery, the institute gathered a group of international experts from across every field of human origins study for a one-day symposium to address this question.

Organized by  Curtis Marean , ASU Foundation Professor in the School of Human Evolution and Social Change and IHO research scientist, and  Yohannes Haile-Selassie , Virginia M. Ullman Professor in the School of Human Evolution and Social Change and IHO director, the event's goal was to specifically discuss the discovery’s impact through time, starting with what we knew about human origins before the 1974 discovery, its lasting impact on science, and the state of the art in that research area today.

The symposium coincided with the April 5 cover feature article, “Lucy at 50,” in the journal Science written by Ann Gibbons, who also participated in the symposium and discussed Lucy’s impact on understanding human origins science and its appeal to the public .

The article delves into the history of such discoveries — Lucy’s and those of other human ancestor species (hominins) — by a variety of human origins scientists over the past 50 years, including by the institute’s current director Haile-Selassie, who has found early hominin specimens dating back to six million years ago.

In addition to significant field sites where Lucy’s species, Australopithecus afarensis, and other earlier and later hominins were found, the article highlights the three significant Ethiopian field sites currently being investigated by institute researchers — Hadar (where Lucy was found), Woranso-Mille (Haile-Selassie’s research site where three hominin species, including the ancestor of Lucy’s species, have been found) and Ledi-Geraru (where the earliest evidence of our own genus Homo was discovered by a research team led by ASU research scientist Kaye Reed ).

In the article, Gibbons highlights the significance of comparing these three sites.

“Lucy’s species was the only known hominin at Hadar — yet only 30 kilometers away at Woranso-Mille, it shared the steeper, more wooded terrain with its potential ancestor, Australopithecus anamensis, and A. deyiremeda, as well as the owner of the 3.4-million-year-old Burtele foot," she wrote. "Reed and Haile-Selassie aim to figure out why one site has so many hominins and only one at Hadar. Haile-Selassie thinks the greater diversity of habitat at Woranso-Mille may have allowed different hominins to coexist in different niches.”

The 1970s was a particularly significant time — the golden decade of paleoanthropology. Donald Johanson Virginia M. Ullman Chair of Human Origins in ASU's School of Human Evolution and Social Change and founding director of the ASU Institute of Human Origins

Before Lucy

During the thee-day event, Johanson led a discussion  on the history of what was known and discovered about our human origins before those early field seasons at Hadar beginning in 1970.

Ian Tattersall,  curator emeritus of the American Museum of Natural History, followed with describing what the scientific community thought about Lucy’s discovery, noting that it was a “tipping point” in paleoanthropology.

Bernard Wood, a medically trained paleoanthropologist and professor at George Washington University, reflected on comparing what researchers knew about other species in her genus and members of another related genus, Paranthropus, with Lucy — who, Wood emphasized, was and continues to be the most complete specimen of an early human ancestor ever discovered.

Andra Meneganzin , of the Kaatholieke Universiteit Leuven in Belgium, provided an overview on the many names of Lucy  — not just “Lucy in the sky with diamonds” — and species relationships between fossils and evolutionary genetics.

We are all Lucy’s children — 8 billion people on the planet. Zeresenay Alemseged Donald N. Pritzker Professor of Organismal Biology and Anatomy, University of Chicago

Understanding the 'paleoenvironment'

Not discovered until 2000 by Zeresenay Alemseged, the Dikika child, or “Lucy’s child,” was Australopithecus afarensis species and about 2.4 years old when it died. This fossil uncovered secrets of the developing brains of this species, which were about 20% larger than a chimpanzee’s.

By imaging the interior of the skull, researchers were able to determine that Lucy’s species had a longer period of brain growth — or childhood, which is a hallmark of later humans, including us.

Institute of Human Origins Research Professor Kaye Reed reviewed the effect of the “savanna hypothesis” on scientific theories about how a more open environment may have been the cause of hominin bipedality — like Lucy’s species, who were obligate bipeds.

Building on the importance of understanding the “paleoenvironment” were University of Missouri Professor Carol Ward, who discussed the interconnection of bipedality, diet and the encephalization of the brain, and Yale University Professor Jessica Thompson , who touched on the “paleo diet” of Lucy’s species, which is much different than today’s use and understanding of the term.

Tracy Kivell, of the Max Planck Institute for Evolutionary Anthropology, detailed the evolution of the hand and its ability to grasp and use tools before and after Lucy.

Finally, Smithsonian Institution curator Kay Behrensmeyer focused her discussion on how Lucy became a fossil and the past and current ideas about how she may have died and been so well preserved, which is unusual for a fossil of her geological age.

By the discovery of Lucy, there was a real momentum in primate field studies to understand how these (chimpanzee) species think, behave, and interact with their environment. Melissa Emery Thompson Department of Anthropology, University of New Mexico

Reconstructing early hominin behavior

The deep past serves us as a guide to the present and our global future. The present also provides significant clues to understanding the behavior of our earliest ancestors.

Because behavior of these ancient ancestors does not fossilize, science looks to our living nonhuman primate cousins — chimpanzees — to provide clues to how cooperation and species bonding may have developed.

During the event, Emery Thompson reviewed the past and future of primate research , including that of Jane Goodall, whose Jane Goodall Institute Gombe Research Archive is now housed at ASU .

Another way researchers try to understand how these ancient species may have lived is by considering how traditional modern communities live today.

Kim Hill , an Institute of Human Origins research scientist and professor in the ASU School of Human Evolution and Social Change, has spent over 40 years living with traditional societies in South America and the Philippines and talked about understanding the sequence of steps leading to human uniqueness — how our adaptability, cooperation, and cumulative culture are the foundations of our success as a species.

Lucy’s impact on the development of African paleosciences is as important as the impact that Lucy had on our knowledge on human origins. Yohannes Haile-Selassie Virginia M. Ullman Professor of Natural Sciences and the Environment, ASU School of Human Evolution and Social Change, and ASU Institute of Human Origins director

Teaching and learning after Lucy’s discovery

Another highlight from the symposium came from National Museums of Kenya Head of Paleontology and Paleoanthropology Job Kibii , who reviewed the history of fossil discoveries — both hominins and other animals — on the African continent by researchers from the United States and Europe, and the development of “paleodoms” by these groups of researchers, which restricts cooperation among each other and by African researchers as well.

To follow this up, Haile-Selassie highlighted the success of African countries in developing preservation and heritage guidelines and laboratories and the success of paleoanthropologist scholars in Ethiopia since the discovery of Lucy.

However, educational programs in Africa to train the next generation of paleoscience researchers has lagged behind, and most students have had to leave the country for advanced training.

To address this, Haile-Selassie suggests developing new advanced educational programs between African, U.S. and European universities.

Watch the presentations

Each of the symposium presentations can be found on the IHO YouTube channel . 

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