problem solving ks3 maths tes

Problem solving with standard form

I can use my knowledge of standard form to solve problems.

Lesson details

Key learning points.

• Standard form is used frequently in Science.
• The exponent can tell you how large the number will be.
• The exponent can tell you how small the number will be.

Common misconception

Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.

Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.

Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).

Associative law - The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 questions.

Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton, tes top 10 resources: problem solving and rich tasks.

The following collection of resources have been assembled by the TES Maths Panel . They can be downloaded for free by registering on the TES website.

Here, I have compiled my top 10 problem solving and rich tasks. Enjoy there are some crackers in here.

Carpet your bedroom – functional maths

Age Range:  11-16  Format:  PPT

An activity for students to design a tessellation of carpet tiles for their bedroom. From the design, they need to work out costs from screenshots of carpet tile prices, calculate the cost of the glue. There are three levels to this task, from a basic bronze version to the gold version which includes an algebra extension related to cost of getting a carpet fitted. Very real world focus and some good discussion if you let the students use their own bedroom.

Rich maths tasks to engage KS3

Age Range:  11-16  Format :  Webpage

This website includes many helpful resources relating to the pedagogy associated with Rich Tasks as well as many sources for further tasks. Each Rich Task has been trialled in the classroom and most are accompanied by a detailed task plan which contains an overview and lesson plan.

Maths investigations

Age Range:  11-16  Format:  PDF

Based on science tasks produced in East Sussex, these investigation starter sheets give an introduction to a topic for investigation and progression guide to allow self- and peer-assessment. Targeted at year 7, these may be suitable for several year groups in KS2/3. Please note that the levelling guide is a first draft and may change.

Maths mystery activity: Thinking skills

This is an ideal thinking skills activity for higher KS3 and KS4 students. This is a mystery activity, where learners are presented with a set of cards containing clues to answer a central focus question, in this case: ‘Does Amelie make it to the catwalk?’. Learners will need to work together (in pairs or threes) and use various strands of mathematics to be able to make sense of the clues and come to a conclusion.

My bedroom: Lesson plans and activities 

This is a complete pack of activities, interactive whiteboards and lesson plans for KS3. This activity can be done in pairs or individually. It has lots of differentiation opportunities from the various materials I have created to provide help in groups, individuals or to the whole class, depending on ability. In addition to this, there are also two good extension activities.

Functional maths skills and enterprise task

Age Range:  11-16  Format:  Excel

This is a business game where players compete to make as much money as possible from an initial investment of £200. All pupils need to do is decide how much to spend on making their product, what the sale price should be and the amount to spend on advertising. When every group has entered their decisions into the spreadsheet the figures are compared and sales are decided. Pupils can then predict their available capital for the next round to earn a cash bonus. It was used across the department with all ages and abilities.

Mathematical Rich Tasks

I created this website with a BECTA grant. There are resources (written, interactive, audio and video) to support teachers and students accessing six rich mathematical tasks, that are ripe for creative exploration!

Holiday planning maths investigation

Age Range:  11-16  Format:  Doc & PDF

A structured problem-solving activity based on booking a holiday for a family of four. Includes a resource booklet containing flight, accommodation, car hire and passport prices, and a task sheet setting students task. Suitable for able KS2 pupils. Also includes differentiation by increasing level of difficulty in the tasks set.

Nrich  differentiated mathematical problem solving

Age Range:  11-18  Format:  WEB

Focussed mathematical problem solving on all the required topics of any mathematical syllabus. A good resource to include in the gifted and talented policy and something that allows the children to access mathematics with real-life problem solving, taking them away from the more difficult abstract questions.

Functional mathematics lessons – projects

Age Range:  11-16  Format:  WEB

Maths functional skills classroom projects to use in lessons. Projects designed for one at the end of each half term for years 7, 8 and 9.

Damian Watson,  Maths Secondary Panel

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Rich tasks and maths investigations for KS3

Here you'll find a collection of tried and trusted rich maths tasks and investigations to develop your KS3 students' numeracy skills and understanding. The best investigations are those that encourage curiosity and engage students’ problem-solving skills. Choose from activities that include maths problems in a real-life context, word problems and practical maths tasks to add some fun and creativity to your maths lessons on different shapes, fractions, decimals, and more.

Many of the teaching resources in this collection include lesson plans, PowerPoints or student worksheets. There are a number of resources in this collection that are suitable for learners at both key stages 3 and 4, so can also be used for GCSE practice.

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• 42 Maths Teasers For Ks3 4 A Puzzle A Day For The Summer Holidays

Maths puzzles – 42 summer holiday teasers for KS3/4

42! It's the answer to 'how many days are there in six weeks?' as well as 'Life, the Universe and everything'…

We’ve picked out 42 maths puzzles, one for each day of the six-week holiday (even though it’s very unlikely students will have exactly six weeks off).

Give students this link before they leave for the year, or email each question out a day at a time if you have the patience.

Day 1 | 12 to 15

Can you put the numbers 1 to 8 in each of the squares so that each side adds up to middle number?

Try more of these puzzles at MathSphere and take a look at the answers too.

Day 2 | Puzzling Taxi Fares

Two salespeople (A and B) hired a car to take them from their office to their customers. 

A’s customer lived 10km away from the office. 

B’s customer lived 20km away from the office. 

The road to B’s customer went directly past A’s customer. 

The trip cost £20 in total. 

What part of the bill was it fair for each salesperson to pay? 

Get worksheet and Powerpoint versions of this puzzle and check out the answers .

Day 3 | 24 from 8, 8, 3, 3

How can you get the answer 24 by only using these numbers: 

8, 8, 3, 3  

You can use add, subtract, multiply, divide and parentheses. 

Bonus rules: you can also use logarithms, factorials and roots 

Day 4 | Weighty problem maths puzzles

I have ten boxes with a total weight of 75kg 

I want to pack the boxes into three crates. Each create can carry a maximum of 25kg. 

How can I pack the boxes into the crates? 

(There may be more than one way).

Check out this puzzle on Math is Fun and look at the answer too. 

Day 5 | Absolutely Christmas crackers

A make-your-own Christmas cracker kit contains: 

• Three colours of hat: red, yellow, blue 
• Four prizes: toy car, spinning top, magnifying glass, mini hairbrush 
• Four different jokes 

All the other parts are the same.  

The kit contains enough bits for 50 crackers. Can you make all the crackers different to one another? 

This is another one from Math is Fun . View the answers here .

Day 6 | Roll the dice

Player A's score is determined by taking the highest of 3 dice. Player B's is determined by taking second-highest of 8. Who wins more games? — Ben Orlin (@benorlin) June 16, 2016

Read people’s answers to this one under the original tweet from Ben Orlin .

Day 7 | Game on

Sergio is playing two different games on the computer: game 1 and game 2. 

The two events are independent. 

The tree diagram shows some of the information below. 

Given that the probability of Sergio losing both games is 12/25, find the values of a, b, c, d and e.

View this problem and more GCSE ‘wordy’ problems at m4ths.com , as well as the answer.

Day 8 | Compound rectangular shapes

Sami worked out the area of the orange shape as 10 x 4 + 8 x 7 = 96cm 2 .

Razina worked out the area as 12 x 7 + 3 x 4 = 96cm 2 .

Lukas worked out the area as 10 x 10 – 2 x 2 = 96cm 2 .

Are you convinced by Sami, Razina or Lukas’ reasoning? Explain your answer.

View this puzzle on Don Steward’s blog .

Day 9 | The stupid gardener

A gardener planted a row of 100 strawberry plants in his garden, setting them exactly 1m apart.

Each plant produced just one strawberry.

When picking time came, the stupid gardened placed a basked 1m from the end of the row. He then proceeded to pick and carry each strawberry to the basket, one by one.

Starting and ending at the basket, how far had the gardener walked when he finished picking all 100 strawberries?

Download this puzzle as Worksheet and PowerPoint versions, and view the answer.

Day 10 | 1996 puzzle

Use the numbers 1, 9, 9 and 6 , exactly in that order, to make the following numbers:

You can use the mathematical symbols +, −, ×, /, √, ^ (exponent symbol) and brackets.

Example: 1 × 9 + 9 × 6 = 63

View this puzzle on Math is Fun , where you’ll also find the answer .

Day 11 | Dizzy digits maths puzzles

This puzzle is in three parts. You need to answer all three parts.

Part 1: Use four 4s to make 44

Part 2: Use five 5s to make 55

Part 3: Use six 6s to make 66

You can use any of the +, −, x , ÷ and = keys.

These maths puzzles are from MathSphere. View it and the answer here .

Day 12 | Medal muddle

Thirteen nations competed in a sports tournament. Unfortunately, we do not have the final medal table, but we have the following pieces of information:

1. Turkey and Mexico both finished above Italy and New Zealand.

2. Portugal finished above Venezuela, Mexico, Spain and Romania.

3. Romania finished below Algeria, Greece, Spain and Serbia.

4. Serbia finished above Turkey and Portugal, both of whom finished below Algeria and Russia.

5. Russia finished above France and Algeria.

6. Algeria finished below France but above Serbia and Spain.

7. Italy finished below Greece and Venezuela, but above New Zealand.

8. Venezuela finished above New Zealand but below Greece.

9. Greece finished below Turkey, who came below France.

10. Portugal finished below Greece and France.

11. France finished above Serbia, who came above Mexico.

12. Venezuela finished below Mexico, and New Zealand came above Spain.

Can you recreate the medal table from this information?

Can you describe an efficient strategy for solving problems like this?

This puzzle is from the NRICH website . Look here for approaches, key questions, extensions and support.

Day 13 | Tea cups maths puzzles

Aunt Jane has bought a whole lot of cups and saucers. There are four sets:

In each set there are four cups and four saucers (16 cups and 16 saucers altogether).

You decide to mix them around so that there are 16 different-looking cup/saucer combinations laid out on the table in a very long line.

So, for example:

a) there is a red cup on a green saucer but not another the same, although there is a green cup on a red saucer b) there is a red cup on a red saucer but that’s the only one like it

There are these 16 different cup/saucer combinations on the table. and you think about arranging them in a big square. Because there are sixteen, you realise that there are going to be four rows with four in each row (or if you like, four rows and four columns).

Here is the challenge: place these 16 different combinations of cup/saucer in a four by four arrangement with the following rules:

• In any row there must only be one cup of each colour
• In any row there must only be one saucer of each colour
• In any column there must only be one cup of each colour
• In any column there must be only one saucer of each colour

View the full puzzle on the NRICH website .

Day 14 | Insert 1-15

DAY 163 | https://t.co/gPLkNjN0jc Insert the numbers 1-15, once each, into the gaps below: ◯+◯=◯ ◯+◯=◯ ◯+◯=◯ ◯+◯=◯ ◯+◯=◯ #MATHELONA pic.twitter.com/lMVsmsFlzK — Croeso i Paul Godding (@7puzzle) June 11, 2017

Day 15 | Place the 12 numbers

day/dydd 57 at https://t.co/gPLkNjN0jc Can you place the 12 numbers: 1 1 2 2 3 3 4 4 5 6 7 8 into the 12 gaps below so that all three lines work out arithmetically? ◯ + ◯ =  5 = ◯ – ◯ ◯ + ◯ = 9 = ◯ × ◯ ◯ + ◯ = 8 = ◯ ÷ ◯ #Mathelona https://t.co/DlR8te8Zeb — Croeso i Paul Godding (@7puzzle) February 26, 2022

Day 16 | Bavarian

One glass has 10cl of tonic water and another 10cl of fernet.

Pour 3cl of tonic into the glass with fernet. After mixing thoroughly, pour 3cl of the mixture back into the glass with tonic water.

Is there more tonic in the glass of fernet or more fernet in the glass of tonic? (Ignore the chemical composition!)

View this puzzle and more on BrainDen , as well as the answer.

Day 17 | The puzzled farmer maths puzzles

A farmer set out to market with a turkey, a fox and a basket of wheat.

When he came to the river, he found there only an empty rowing boat, so small that he could only carry one thing with him at a time.

If the fox was left with the turkey, he would eat it. If the turkey was left with the wheat, she would eat it.

How did the farmer get them all across safely? What is the minimum number of crossings necessary?

Download worksheet and Powerpoint versions of this classic puzzle, and look at the answer .

Day 18 | Algebra cow

Solve the following (each letter is a digit):

COW x COW = DEDCOW

Day 19 | Five card trick

I am thinking of one of these five cards:

You have to try to find out which one I am thinking of. Here are some clues:

• The value of my card is a prime number
• The values of my two neighbours add up to a multiple of 3
• My card is next to a card which is next to the 2 of hearts

See this problem and the solution at Math is Fun .

Day 20 | Tricky twenty triangle

Put the numbers 1-9 in the boxes below so that each side of the triangle adds up to 20.

View this puzzle and the solution at Maths Sphere .

Day 21 | Working with ratios

In a factory the ratio of men to woman is 2:3.

The ratio of right handed men to left handed men is 7:3.

The ratio of right handed women to left handed women is 11:1.

What proportion of the people working in the factory are right handed?

View this problem and the answer .

Day 22 | Give me a hand

A professor and their spouse are at a party. At the party there are four more couples (five couples overall).

During the party, couples shake hands with the following rules:

• One does not shake hands with oneself
• One does not shake his/her spouse’s hand

At the end of the party the professor asked all the other guests at the part (including their spouse) how many different people they shook hands with. Each person tells him a different answer (meaning, if one person said “five”, no one else said “five”).

With how many people did the professor shake hands?

Day 23 | Bridge over troubled students

There are four men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side.

It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either one or two people, must have the flashlight with them.

The flashlight must be walked back and forth, it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the rate of the slower man.

Man 1: 1 minute to cross Man 2: 2 minutes to cross Man 3: 5 minutes to cross Man 4: 10 minutes to cross

For example, if Man 1 and Man 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge.

If Man 4 returns with the flashlight, a total of 20 minutes have passed, and you have failed the mission.

This puzzle is from Steve Miller’s Math Riddles .

Day 24 | Three spinners maths puzzles

The 3 spinners below are each spun once and the number written down.

Find the probability that when the three spinners are spun, the numbers are either all prime numbers or all cube numbers.

View this problem and the answer at M4ths.com .

Day 25 | Pipes and pathways

These three houses are putting in gas, to be piped from the containers shown.

House A must be connected with container F, house B with D, and house C with E.

A clause in the title deed forbids laying one pipe across another, and owners of land around this plot refuse to allow the pipes onto their land. How will the gas company lay the pipes?

View this puzzle and the solution .

Day 26 | Monk steps

A monk has a very specific ritual for climbing up the steps to the temple.

First he climbs up to the middle step and meditates for 1 minute.

Then he climbs up 8 steps and faces east until he hears a bird singing.

Then he walks down 12 steps and picks up a pebble.

He takes one step up and tosses the pebble over his left shoulder.

Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps are there?

View the solution at Braingle .

Day 27 | Circles maths puzzles

Write the numbers 1-9 in the black circles so that the sum of the numbers around each blue circle (and including the centre circle) and along both horizontal and vertical lines is the same.

View the solution at the Guardian .

Day 28 | Head over tails

Put four coins on table, in a row, all tails up.

Turn any three coins over: this counts as one move. You must turn three different coins to complete one move.

How many moves will it take to get all the coins on heads?

View the answer at Math Sphere .

Day 29 | Two jugs maths puzzles

You have an 8 litre jug full of water and two smaller jugs, one that contains 5 litres and the other 3 litres.

None of the jugs have markings on them, nor do you have any additional measuring device.

You have to divide the 8 litres of water equally between your two best friends, so that each gets 4 litres of water. How can you do this?

View the solution at Future Learn .

Day 30 | Going to St Ives

As I was going to St Ives I met a man with seven wives. Each wife had seven sacks, Each sack had seven cats, Each cat had seven kits; Kits, cats, sacks, wives, How many were going to St Ives?

Look at the solution to this well-known problem.

Day 31 | Alison’s quilt

Alison joins together nine squares with side lengths to form a rectangular quilt: 

There are no gaps and no overlaps. 

Can you find the dimensions of the finished quilt, and show how Alison fitted the squares together?

Take a look at this problem on NRICH .

Day 32 | Secret locker code

A man forgot the secret code to open his locker. But he remembers the following clues:

• Fifth number plus the third number equals fourteen
• First number is one less than twice the second number
• Fourth number is one more than the second number
• Second number plus the third number equals ten
• Sum of all five numbers is 30

Can you find out the secret code to help him out?

View the answer at DoRiddles .

Day 33 | Celebrity murder mystery

Ant and Dec couldn’t believe what they had discovered. The secret they had just learnt about a certain celebrity’s private life was unbelievable.

They confronted the celeb but were warned to keep their mouths shut. But the celebrity decided they couldn’t take any chances. Later that week, Ant and Dec were found poisoned in their dressing room.

When police arrived on the scene, they found 6 celebrities lurking around, but who is the guilty one? Your job is to find out who did it.

Download this KS3 algebra lesson activity and browse more  algebra games .

Day 34 | Pairwise adding

Charlie chose five numbers: 2, 3, 4, 7, 10.

He added together pairs of numbers from his set, and got the following totals: 5, 7, 9, 10, 11, 12.

Can you find the totals that Charlie has missed? 

Look at this problem on wild.maths.org .

Day 35 | Are they parallel?

Are the four vertical lines parallel, or not?

Find out the answer (and the reason behind it) .

Day 36 | From town to town

The table below shows the distances (in miles) between a number of different towns

Bob drives from Town A to Town E via Town D. He spends a total of 45 minutes driving to complete the journey.

Jane travels directly between two of the towns at exactly the same average speed as Bob.

Given that Jane’s journey took seven and a half minutes, find which two towns she drove between.

View the solution at M4ths.com .

Day 37 | Initial numbers maths puzzles

Each number has some initials after it. Work out what the initials mean – the numbers are clues. For example: 7 D in a W is 7 Days in a Week.

• 26 L in the A
• 7 C in the R
• 6 W of H the E
• 7 S on a F P P
• 1000 M in a K
• 64 S on a C B
• 1066 B of H
• 24 H in a D

View more and see the answers at Math Sphere .

Day 38 | Midnight

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?

View the answer at BrainDen .

Day 39 | Aunt’s old jalopy

After visiting my Great Aunt Annie, I travelled home in her old jalopy. The car was old and battered. It had a leak from the petrol tank. I was stuck in second gear.

This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel.

At the start of the journey I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour.

Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.

How far was it from my Great Aunt’s to my home?

See the answer at Braingle .

Day 40 | Gift of gems

Four jewellers had respectively:

• 10 sapphires
• 5 diamonds 

Each gave one gem from their collection to each of the rest.

Afterwards they noticed that they all had collections of gems of precisely equal value.

Can you work out the relative values of each gem?

Can you then work out how much each jeweller gained or lost?

This puzzle comes from NRICH .

Day 41 | The largest number

Using the numbers 2, 4, 6 and 8, the multiply sign, the add sign and the equals sign, what is the largest number you can make?

You may only press each digit and sign once, but you don’t have to press all the signs.

See the solution at Math Sphere .

Day 42 | Cross numbers maths puzzles

3: 6 across plus 3

6: 7 across plus 6

7: 7 down plus 2

1: 11 times 3 across

2: add digits of 5 down

4: 6 across plus 7 across

5: 9 times 7 across

7: two digits

Generate your own maths puzzles like this at Maths is Fun .

Browse more  KS3 maths  games and lesson ideas and GCSE maths games .

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30 Problem Solving Maths Questions, Solutions & Strategies

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Monsters Inc Math Movie Guide Questions | Word Problems | Grades 6 to 8

Subject: Mathematics

Age range: 11 - 13

Resource type: Worksheet/Activity

Last updated

13 September 2024

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This Monsters Inc Math Movie Guide Questions (G6 to 8) resource challenges students to solve real-world math problems like converting temperatures in Monstropolis, calculating the total number of jumps by tentacles, and figuring out the volume of a tunnel dug by Mike. These math activities reinforce key skills through fun scenarios, helping students understand math in a practical and entertaining way.

The following math standards are addressed: 6.EE.A.2: Write and evaluate expressions where letters stand for numbers 6.RP.A.1: Understand and use ratios and rates 6.RP.A.3: Solve real-world problems using unit rates 6.G.A.1: Solve problems involving area and perimeter of polygons 7.RP.A.1: Compute unit rates involving ratios 7.RP.A.3: Solve problems using proportional relationships 7.G.B.5: Solve problems involving angle measures 7.G.B.6: Solve real-world volume problems 8.EE.A.1: Apply properties of exponents to powers of ten

This product includes a zip file consisting of:

• An Answer Key w/ CCSS Alignment (4 Pages)
• A Student Movie Guide (4 Pages)
• A DIFFERENTIATED Student Movie Guide (4 Pages) (Includes hints and formulas necessary to solve the problem)
• 2 PDFs with link to both student Google Slide versions (2 Pages)
• CCSS alignment, Admin Movie Request and Permission Slip (2 Pages)

This resource is meant to supplement the viewing of this movie, see the IMDb listing by searching the movie title.

Check the preview file for high resolution sample questions to see if this math focused movie guide is suitable for your students. This resource consists of 10 math related questions and 2 optional long format questions that will do more than just ask your students to regurgitate information.

Is this movie guide worth it? Download two of my movie guides for free below:

• Trolls World Tour (PG - 2020)
• Onward by Disney (PG - 2020)
• The Lightning Thief
• Kung Fu Panda 3

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