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Resources tagged with Investigations similar to Using Questioning to Stimulate Mathematical Thinking: Addendum:

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Pedagogy. Generalising. Team-building. Moving averages. Shape, space & measures - generally. Mathematical Thinking. Questioning. Mean.

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Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations

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Stacks of Maths!

Stage: 1, 2 and 3

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.

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Polo Square

Stage: 2 Challenge Level: Challenge Level:1

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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Move a Match

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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Sorting the Numbers

Stage: 1 and 2 Challenge Level: Challenge Level:1

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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Times

Stage: 2 Challenge Level: Challenge Level:1

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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It's a Fence!

Stage: 1 and 2 Challenge Level: Challenge Level:1

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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Sometimes We Lose Things

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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Opening Out

Stage: 1 and 2

Bernard Bagnall describes how to get more out of some favourite NRICH investigations.

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Polygonals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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Experiencing Problem Solving

Stage: 1 and 2

Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.

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Let's Investigate Triangles

Stage: 1 Challenge Level: Challenge Level:1

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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More Pebbles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Have a go at this 3D extension to the Pebbles problem.

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Become Maths Detectives

Stage: 2 Challenge Level: Challenge Level:1

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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It Was 2010!

Stage: 1 and 2 Challenge Level: Challenge Level:1

If the answer's 2010, what could the question be?

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Triangle Pin-down

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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The Pied Piper of Hamelin

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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Street Sequences

Stage: 1 and 2 Challenge Level: Challenge Level:1

Investigate what happens when you add house numbers along a street in different ways.

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Sticky Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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Caterpillars

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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Abundant Numbers

Stage: 2 Challenge Level: Challenge Level:1

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Investigating Pascal's Triangle

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

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Magic Constants

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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Round and Round the Circle

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Calendar Patterns

Stage: 2 Challenge Level: Challenge Level:1

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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Follow the Numbers

Stage: 2 Challenge Level: Challenge Level:1

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.

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Homes

Stage: 1 Challenge Level: Challenge Level:1

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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Olympic Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is intended to get children to look really hard at something they will see many times in the next few months.

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Teddy Town

Stage: 1, 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Lost Books

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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Exploring Number Patterns You Make

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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Month Mania

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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The Great Tiling Count

Stage: 2 Challenge Level: Challenge Level:1

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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Number Squares

Stage: 1 and 2 Challenge Level: Challenge Level:1

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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Steps to the Podium

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

It starts quite simple but great opportunities for number discoveries and patterns!

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Sending and Receiving Cards

Stage: 2 Challenge Level: Challenge Level:1

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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Balance of Halves

Stage: 2 Challenge Level: Challenge Level:1

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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Eye View

Stage: 2 Challenge Level: Challenge Level:1

Why does the tower look a different size in each of these pictures?

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Consecutive Numbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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Division Rules

Stage: 2 Challenge Level: Challenge Level:1

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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Doplication

Stage: 2 Challenge Level: Challenge Level:1

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A follow-up activity to Tiles in the Garden.

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Problem Solving: Opening up Problems

Stage: 1, 2, 3 and 4

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

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Troublesome Triangles

Stage: 2 and 3 Challenge Level: Challenge Level:1

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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Tessellating Transformations

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

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Baked Bean Cans

Stage: 1 Challenge Level: Challenge Level:1

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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Hexpentas

Stage: 1 and 2 Challenge Level: Challenge Level:1

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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All Wrapped Up

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the largest cuboid you can wrap in an A3 sheet of paper?

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2 Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

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Cutting it Out

Stage: 1 and 2 Challenge Level: Challenge Level:1

I cut this square into two different shapes. What can you say about the relationship between them?