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Photocopiable Investigations

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Welcome to hours of mathematical enjoyment!

(Ages 4-7): Make it fair (£0.20)

Raid the games cupboard for hoops and bean bags and you are all set for this engaging talking activity. Children are determined to make it fair and in so doing explore the concepts of odd and even, grouping and sharing.

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(Ages 5-8): How many each and altogether? (£0.40)

How many frogs in each pond? How many ponds? How many frogs altogether?

WORK BIG to get to grips with the key language you need to understand problems with words in them. Extend into the ideas of multiplication and division and how they link together.

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(Ages 5-8): How many fingers? (£0.60)

I wonder how many fingers we have here?
Just 10?
But you have ten, Jamie has ten, Sophie has ten...

A lively and engaging talking investigation exploring counting in 10s and 20s beyond 100.

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(Ages 6-9): The Egyptian Triangle (£0.60)

Discover the special triangle that the Egyptians used in their buildings, while learning about how simple decimals work, the importance of accurate measuring and how to work systematically to solve a problem.

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(Ages 6-9): Number Chains and Digit Wheels (£0.60)

Make beautiful patterns with this wide-ranging investigation into the digit patterns that you get when you repeatedly add or subtract a single digit to or from a larger number.

Links well both to activities for consolidating adding or subtracting a single digit to or from a 2-digit number, and to activities to support learning the 'stations' of the multiplication tables.

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(Ages 7-10): How big is the room? (£0.70)

How do you introduce decimals to young children? This practical investigation works a treat, and also gives you the opportunity to discuss accuracy in measuring, averages and perimeter!

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(Ages 7-10): Half and Quarter Hours (£0.70)

Explore the relationship between hours and minutes. Build patterns in half hours and quarter hours to consolidate understanding and then challenge yourself or a partner to convert times from hours to minutes.

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(Ages 7-10): How many minutes in a day? (£0.70)

Discover a pattern in the number of minutes in different numbers of hours and then extend the pattern to find out how many minutes there are in a day. Discover the link between the 60x table and the 6x table.

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(Ages 7-10): How Many Hula Hoops? (£1.00)

How many hula hoops (the small, crunchy variety!) would it take to stretch from the school to Big Ben in London?

Investigate metres, converting to km, using conversion tables and working with BIG numbers!

Highly motivating!

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(Ages 8-11): Numbers between numbers (£0.60)

Explore where simple fractions and decimals sit on the number line and how they relate to each other.

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(Ages 8-11): Chopping up a Metre Stick (£1.90)

Well, not ACTUALLY cutting it up - but imagine...

Suppose you wanted to make 4 pieces or 5 pieces. Where would you chop? How about 3 pieces?

Get totally immersed in how division, fractions and decimals work...

This was particularly challenging and the children enjoyed the open ended investigations.
Year 5 Co-ordinator, Woodnewton School

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(Ages 8-11): Maps and Scales (£0.90)

Find real life distances from measured distances on a map. Learn practical measurement skills for straight or curved distances. Practise estimating, finding averages and using conversion tables to work out real distances from the map scale. Easily adaptable to suit pupils of different ages and differing levels of ability.

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(Ages 8-11): Shadow Clocks (£0.80)

Investigate how the length and direction of a shadow change during the course of a day. Learn about compass directions, symmetry, practical measurement using a metre stick, time (am/pm) and use of a table to display results.

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(Ages 8-11): How many different kinds of triangle are there? (£1.00)

How many different kinds of triangle are there? Can you have a triangle with two obtuse angles?

These and other questions are all explored in this practical investigation using geostrips (or something similar).

By the end of the investigation you should be able to identify right-angled, acute-angled and obtuse-angled triangles and know what it means for a triangle to be equilateral, isoceles or scalene.

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(Ages 8-11): How far is it round the world? (£1.00)

Create a table relating distances on a globe to distances in real life and then use this to calculate distances between places around the world. Covers concepts in measurement, averaging to minimise errors and the use of conversion tables.

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(Ages 8-11): Populations (£1.90)

Investigate the populations of towns or countries and learn how to work out how many more people live in one town than another and how many times bigger one town is compared with another. Consolidates skills in reading, rounding, subtracting and dividing large numbers and choosing an appropriate scale for a bar chart.

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(Ages 8-11): Multiplication Rectangles and Factor Rainbows (£1.90)

An engaging investigation into multiplication and the concept of factors.

Investigate which numbers have few factors and which have lots. Explore square numbers and look at the ‘specialness’ of the numbers used for measuring time and angle – 12, 24, 60 and 360.

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(Ages 8-11): Angles in Triangles and Quadrilaterals (£1.90)

Investigate the angles in different triangles and quadrilaterals and discover the facts about their totals.

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(Ages 9-12): How much snow would fill the classroom? (£1.00)

Estimate distances, work with volume of cuboids, convert metric volumes - cm3 - litre - m3, measure with metre sticks, minimise sources of error, average using the median, draw diagrams, round numbers and find out about significant figures. Wow!

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(Ages 9-12): Properties of Quadrilaterals (£1.00)

Find out why a square is a special kind of rectangle but a rectangle is not a special kind of square!

Explore the differences rhombuses and parallelograms, kites and trapeziums.

Investigate questions like 'Is there a quadrilateral with three acute angles?'

A practical approach using construction material such as geostrips.

First impressions - detail excellent especially to support those teachers who are not so confident.
Year 5 teacher, Kent

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(Ages 9-12): Constructing Shapes (£1.00)

Constructing shapes with compasses is always great fun because you get pretty patterns. But this investigation goes well beyond regular activities with pupils being given an open-ended challenge to create as many different types of shape as possible using a pair of compasses and a straight edge.

You first learn how to construct an equilateral triangle, how to bisect a line to make a right angle and how to bisect an angle. Armed with these three simple techniques see what other shapes you can create. Square, rectangle, kite, rhombus, trapezium, parallelogram, hexagon and octagon are all possible!

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(Ages 9-12): Angles in Polygons (£1.40)

Investigate the total interior and exterior angles of polygons (triangle, quadrilateral, pentagon, hexagon etc.) Explore patterns in the numbers and establish rules and experiment with formulas.

The investigations were very challenging and it made the children think independently and look for patterns, developing their enquiring minds. I would not have thought of presenting such an investigation and in such an open ended way. (Pattern of total of interior angles in 2D shapes V number of sides). The children really enjoyed the level of difficulty and had obviously never looked at such an investigation before.
Year 5 co-ordinator, Woodnewton School

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(Ages 9-12): Perimeter and Area of Triangles & Quadrilaterals (£0.80)

You may be able to calculate the perimeters and areas of a rectangle and a triangle, but can you explain why the formulas work?

Build on this to explore other quadrilaterals: rhombus, kite, trapezium and parallelogram.

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(Ages 9-12): The Great 2D Shape Investigation (£0.90)

An umbrella investigation stimulating a wide variety of explorations into 2-D shapes. Depending on the lines of enquiry that develop, you can then use material from related investigations such as Properties of quadrilaterals, Constructing polygons, Angles in Polygons etc.

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(Ages 9-12): Pythagoras Puzzle (£0.40)

Have fun making this simple puzzle which very beautifully illustrates Pythagoras' Theorem that the sum of the squares on two sides of a right-angled triangle = the square on the third side.

Make and solve the puzzle and then through measuring areas discover Pythagoras' Theorem.

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(Ages 9-12): How tall is that building? (£0.80)

An outdoor team challenge to estimate the height of a building, either by counting bricks, using shadows or using similar triangles. Covers skills in estimating, measuring, minimising errors and ratio.

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(Ages 10-13): Train Journey (£1.80)

Investigate how to use train timetables, calculate journey times, interpret maps, measure distances, use averages and work with scale.

Create an information booklet about a forthcoming train journey.

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(Ages 10-13): Equations through pictures (£1.80)

Straight line graphs are often not taught until somewhere in the middle secondary years. But they can actually be an excellent way of helping younger children to explore how equations work if you introduce them in the right way. This investigation shows you how.

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(Ages 10-13): The Algebra of Throwing (£1.80)

Children often ask what algebra is FOR. This investigation allows capable pupils at the top end of primary school to use simple algebraic skills to investigate an area of Maths that is normally reserved for upper secondary pupils.

Children love throwing things in the air. By the end of this investigation they will have equations, tables and graphs that will allow them to work out how high they can throw something, and what speed they can throw it at. Beware. It is good fun!

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(Ages 10-13): Election Results (£1.20)

Compare the results of a recent election with a previous one and present findings using a hand drawn pie chart. Covers the skills of expressing quantities as percentages and calculating pie chart angles as well as basic skills in interpreting tables.

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(Ages 10-13): Flights (£1.20)

An investigation into flight times for an aeroplane between different places. Covers map scales, averages, conversion tables and speeds.

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(Ages 10-13): Handshakes, Cards, Roses and Triangles (£1.20)

An investigation into four related problems which all generate number patterns linked to the triangular numbers: 1, 3, 6, 10 etc. Consolidates pupils' use of problem-solving strategies such as drawing diagrams and using tables and shows how to investigate a problem thoroughly by building a pattern from simpler cases to more challenging ones.

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(Ages 10-13): Formulas for Sequences (£1.20)

Investigate he connection between number sequences and the rules that generate them. Begin by exploring two simple matchstick patterns and develop into investigating line graphs for formulas.

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This Month's FREE Resources


Maths Investigations - Challenging Children to Think about Maths