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NRICH Perimeter, Area and Volume Key Stage 3
This list supports teaching of perimeter, area and volume in secondary mathematics. It provides investigations, problems and games from NRICH as well as classroom activities on the STEM Learning website that compliment them.
Here are some of the favourite activities selected by the NRICH team.
- Cuboids Find a cuboid (with edges of whole number lengths) that has a surface area of exactly 100 square units. Is there more than one and if so can you find them all?
- Warmsnug Double Glazing A variety of windows and frames are presented on a grid, together with prices. The challenge is to find out which window has been priced incorrectly.
- Cuboid Challenge A square sheet of paper 20cm by 20cm has a square cut from each corner and is then folded to make an open box. The challenge is to find the maximum possible volume.
- Perimeter Possibilities The investigation starts with finding possible perimeters for a rectangle with an area of 24cm 2 . The investigation is broadened to consider a rectangle with fractional perimeter but a whole number area.
These are just a few of the activities on Perimeter, area and volume that you can find on the NRICH curriculum pages .
The activities below, taken from the STEM Learning website, complement the NRICH activities above.
Surface Area and Volume
Quality Assured Category: Mathematics Publisher: SMILE
This SMILE resource contains two packs of games, investigations, worksheets and practical activities supporting the teaching and learning of surface area and volume, from counting the number of cubes in a solid to find the volume to finding maximum volumes of a solid.
The materials are useful in preparing students for tackling the NRICH problems on surface area and volume.
Boxes and Bottles
Quality Assured Category: Mathematics Publisher: cre8ate maths
These Cre8ate maths activities explore some of the mathematics behind packaging decisions taken by manufacturers.
'Stock cubes' asks students to design a box to hold stock cubes and poses the question as to which cuboid would they choose. This is a useful activity to use with students to prepare them for the NRICH 'Cuboid Challenge' activity.
'Folding cubes' is particularly helpful in preparing students for the NRICH task 'Cuboids'.
'How much does it hold' is an interesting exercise in estimating capacity.
Quality Assured Category: Mathematics Publisher: Department for Education
This Study Plus unit from the National Strategies develops an understanding of volume and surface area of 3D objects through exploring nets. The materials are particularly helpful to use in preparation for the NRICH activities 'Cuboids' and 'Cuboid Challenge'.
Simultaneous Equations
Quality Assured Category: Mathematics Publisher: Nuffield Foundation
One way of tackling the NRICH activity 'Warmsnug double glazing' is to form simultaneous equations.
This Nuffield Foundation resource introduces students to simultaneous equations and demonstrates a rather unusual way of approaching the topic. This would is a useful resource to use prior to students tackling the NRICH activity.
Factors, Multiples and Primes
Quality Assured Category: Mathematics Publisher: William Emeny
The NRICH activity 'Perimeter Possibilities' can be tackled by using factors of 24.
This video resource from 'Great Maths Teaching Ideas' provides an introduction to factors and is helpful to use in advance of tackling the NRICH activity. The video begins by defining a factor and then finds the factors of 12 with the aid of a factor bug.
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Area and Perimeter
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- Calculations and Numerical Methods
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- Properties of Numbers
- Patterns, Sequences and Structure
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Geometry and measure
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- Transformations and constructions
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- Vectors and Matrices
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- Probability
Working mathematically
- Thinking mathematically
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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
Resources tagged with: Perimeter
There are 14 results.
Perimeter Challenge
Can you deduce the perimeters of the shapes from the information given?
Perimeter Possibilities
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Changing Areas, Changing Perimeters
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
Perimeter Expressions
Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
Can They Be Equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Warmsnug Double Glazing
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
On the Edge
If you move the tiles around, can you make squares with different coloured edges?
Pick's Theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Is There a Theorem?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Smaller and Smaller
Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
Coins on a Plate
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
Coke Machine
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
NRICH: Perimeter Possibilities
An inspiring resource for learning numeracy
Use this NRICH resource to explore the possibilities of perimeter
Numeracy Focus: Understanding, estimating and using measurement
Many tasks about area and perimeter focus on the two separately.
This problem combines both by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed.
Stage: Level 3 to 8
This resource supports:
Proficiency
- Problem-solving
- Explicit teaching
Cross-curricular
- Technologies: Digital Technologies
Teaching and Learning Cycle:
Sourced from:
Reflective Prompt
How might you use digital technologies such as BeeBots (for younger students), Ollie or Sphero (for older students) to teach perimeter and area?
How might this positively impact student engagement and learning?
Proficiency Reflective Prompt
How would you use this resource in your context to foster children and young people’s problem solving?
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KS2/KS3 Area/Perimeter Problems - Year 5, 6, 7, 8
Subject: Mathematics
Age range: 7-11
Resource type: Other
Last updated
25 February 2021
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Having looked online at various area and perimeter questions, i felt they were all too similar, with very little problem solving/investigation skills being used. So, I decided to create these. They are different from other activities i found, and i feel fit brilliantly with the new curriculum.
I created these resources myself, and have used them in a class where i have got children from every year in ks2. They love problem solving and it was a hit in my class.
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PrimaryEducator1989
A nice alternative to White Rose and similar resources! We used the problems as a discussion point in class and children really enjoyed the challenge. Thanks.
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Thanks for sharing. Very useful.
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Area and Perimeter. Age 7 to 11. Challenge Level. What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
This is part of our collection of Short Problems. You may also be interested in our longer problems on Perimeter, Area and Volume Age 11-14 and Age 14-16. Printable worksheets containing selections of these problems are available here: Stage 3 ★. Sheet 1.
Pick's Theorem Live. Age 14 to 16. Challenge Level. Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
This printable worksheet may be useful: Perimeter Expressions.pdf. The worksheet is also available in French: Expressions de périmètres. We are grateful to Clara Huizink for translating the original. Hand out sheets of paper (A4 is ideal) and introduce the problem, giving students time to cut out their five rectangles.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
NRICH Short Problems Perimeter, Area and Volume 2. Triangle in a hexagon Call the length of one side of the hexagon 2 and the height of the hexagonℎ. So ×the area of the shaded triangle is "! 2 ...
F'arc'tion. Age 14 to 16. Short Challenge Level. At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
Daniel from Staplehurst Primary School sent us a very clear solution to this problem: Alison's shape with a perimeter of 8a + 6b combined the largest and smallest rectangles, with the smaller rectangle's side of length a against one of the larger rectangle's sides. I have made the largest possible perimeter, 12a + 12b, using all the pieces ...
We have found 14 NRICH Mathematical resources connected to Perimeter, you may find related items under Measuring and calculating with units Resources tagged with: Perimeter ... Problem Primary curriculum Secondary curriculum. Perimeter Challenge.
The NRICH activity 'Perimeter Possibilities' can be tackled by using factors of 24. This video resource from 'Great Maths Teaching Ideas' provides an introduction to factors and is helpful to use in advance of tackling the NRICH activity. The video begins by defining a factor and then finds the factors of 12 with the aid of a factor bug.
90mm 30mm 3cm. Reasoning and Problem Solving Calculate Perimeter Reasoning and Problem Solving Calculate Perimeter. Developing 1a. Regular pentagon. Each side 4cm long. 2a. True because the triangle has 3 equal sides which are all 2cm long. 3a. Various answers, for example: (Same) A and B are both regular shapes,
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Interactive tasks and games. These primary activities and games all have interactive content, making them ideal for use on tablets, laptops or in a computer room. World of Tan 9 - Animals. World of Tan 22 - An Appealing Stroll. World of Tan 3 - Mah Ling. World of Tan 16 - Time Flies. World of Tan 29 - The Telephone. World of Tan 10 - Butterflies.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
We have found 14 NRICH Mathematical resources connected to Perimeter, you may find related items under Measuring and calculating with units Resources tagged with: Perimeter ... Problem Primary curriculum Secondary curriculum. Perimeter Challenge.
Reasoning and Problem Solving Measure Perimeter Reasoning and Problem Solving Measure Perimeter Developing 1a. C because the other shapes have a 10cm perimeter. 2a. 4cm 3a. Ann drew A and Tom drew B. Ann's measurements give a 12cm perimeter and Tom's give an 8cm perimeter. A has a longer perimeter than B. Expected 4a. D because the other ...
This first blog provides an introduction to problem solving with NRICH, and explores how important it is to choose appropriate tasks. The second will explore how you can structure the problem-solving process, and embed problem solving into every school day. Becoming a confident and competent problem solver is a complex process that requires a ...
This problem combines both by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed. Stage: Level 3 to 8 This resource supports:
Having looked online at various area and perimeter questions, i felt they were all too similar, with very little problem solving/investigation skills being used. So, I decided to create these. They are different from other activities i found, and i feel fit brilliantly with the new curriculum.