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Resources tagged with Making and proving conjectures similar to Division Rules:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Making and proving conjectures

Division Rules

Stage: 2 Challenge Level:

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

Tiling

Stage: 2 Challenge Level:

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

Three Dice

Stage: 2 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Open Squares

Stage: 2 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Magic Vs

Stage: 2 Challenge Level:

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

Six Ten Total

Stage: 2 Challenge Level:

This challenge combines addition, multiplication, perseverance and even proof.

Path to the Stars

Stage: 2 Challenge Level:

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Take Three Numbers

Stage: 2 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Three Neighbours

Stage: 2 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Becky's Number Plumber

Stage: 2 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Become Maths Detectives

Stage: 2 Challenge Level:

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.

Sheep Talk

Stage: 2 Challenge Level:

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Square Subtraction

Stage: 2 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Always, Sometimes or Never? Number

Stage: 2 Challenge Level:

Are these statements always true, sometimes true or never true?

Spirals, Spirals

Stage: 2 Challenge Level:

Here are two kinds of spirals for you to explore. What do you notice?

Always, Sometimes or Never?

Stage: 1 and 2 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Roll over the Dice

Stage: 2 Challenge Level:

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Helen's Conjecture

Stage: 3 Challenge Level:

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Tables Without Tens

Stage: 2 Challenge Level:

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Move Those Halves

Stage: 2 Challenge Level:

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Dining Ducks

Stage: 2 Challenge Level:

Use the information about the ducks on a particular farm to find out which of the statements about them must be true.

Exploring Simple Mappings

Stage: 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

Consecutive Negative Numbers

Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Dice, Routes and Pathways

Stage: 1, 2 and 3

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

Problem Solving, Using and Applying and Functional Mathematics

Stage: 1, 2, 3, 4 and 5 Challenge Level:

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

Rotating Triangle

Stage: 3 and 4 Challenge Level:

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

Happy Numbers

Stage: 3 Challenge Level:

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Always a Multiple?

Stage: 3 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Take One Example

Stage: 1 and 2

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

Always, Sometimes or Never? Shape

Stage: 2 Challenge Level:

Are these statements always true, sometimes true or never true?

Center Path

Stage: 3 and 4 Challenge Level:

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of. . . .

Charlie's Mapping

Stage: 3 Challenge Level:

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

On the Importance of Pedantry

Stage: 3, 4 and 5

A introduction to how patterns can be deceiving, and what is and is not a proof.