Resources tagged with Generalising similar to What Do You Need?:
Other tags that relate to What Do You Need?
Odd and even numbers. Addition & subtraction. Place value. Generalising. Factors and multiples. Mathematical reasoning & proof. Properties of numbers. Multiplication & division. Working systematically. Divisibility.There are 141 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising
Crossings
Age 7 to 11 Challenge Level:
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
Always, Sometimes or Never? Number
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Surprising Split
Age 7 to 11 Challenge Level:
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Number Tracks
Age 7 to 11 Challenge Level:
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Three Dice
Age 7 to 11 Challenge Level:
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Neighbourly Addition
Age 7 to 14 Challenge Level:
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Got it for Two
Age 7 to 14 Challenge Level:
Got It game for an adult and child. How can you play so that you know you will always win?
Calendar Calculations
Age 7 to 11 Challenge Level:
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Digit Addition
Age 5 to 11 Challenge Level:
Try out this number trick. What happens with different starting numbers? What do you notice?
Repeaters
Age 11 to 14 Challenge Level:
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Oddly
Age 7 to 11 Challenge Level:
Find the sum of all three-digit numbers each of whose digits is odd.
Have You Got It?
Age 11 to 14 Challenge Level:
Can you explain the strategy for winning this game with any target?
Three Times Seven
Age 11 to 14 Challenge Level:
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Always, Sometimes or Never?
Age 5 to 11 Challenge Level:
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Adding in Rows
Age 11 to 14 Challenge Level:
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Round and Round the Circle
Age 7 to 11 Challenge Level:
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.
Spirals, Spirals
Age 7 to 11 Challenge Level:
Here are two kinds of spirals for you to explore. What do you notice?
Magic Vs
Age 7 to 11 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Broken Toaster
Age 7 to 11 Short Challenge Level:
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Elevenses
Age 11 to 14 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Centred Squares
Age 7 to 11 Challenge Level:
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Special Sums and Products
Age 11 to 14 Challenge Level:
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Up and Down Staircases
Age 7 to 11 Challenge Level:
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Sitting Round the Party Tables
Age 5 to 11 Challenge Level:
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Journeys in Numberland
Age 7 to 11 Challenge Level:
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Button-up Some More
Age 7 to 11 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Doplication
Age 7 to 11 Challenge Level:
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?
Break it Up!
Age 5 to 11 Challenge Level:
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Snake Coils
Age 7 to 11 Challenge Level:
This challenge asks you to imagine a snake coiling on itself.
Magic Letters
Age 11 to 14 Challenge Level:
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
What Numbers Can We Make Now?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Sums and Differences 1
Age 7 to 11 Challenge Level:
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Bundles of Cubes
Age 7 to 11 Challenge Level:
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Truth or Lie
Age 7 to 11 Challenge Level:
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Magic Constants
Age 7 to 11 Challenge Level:
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?
Build it Up
Age 7 to 11 Challenge Level:
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Build it up More
Age 7 to 11 Challenge Level:
This task follows on from Build it Up and takes the ideas into three dimensions!
Walking the Squares
Age 7 to 11 Challenge Level:
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Cut it Out
Age 7 to 11 Challenge Level:
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Roll over the Dice
Age 7 to 11 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?
Division Rules
Age 7 to 11 Challenge Level:
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Sums and Differences 2
Age 7 to 11 Challenge Level:
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Number Differences
Age 7 to 11 Challenge Level:
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Round the Four Dice
Age 7 to 11 Challenge Level:
This activity involves rounding four-digit numbers to the nearest thousand.
Window Frames
Age 5 to 14 Challenge Level:
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Dotty Circle
Age 7 to 11 Challenge Level:
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Magic Circles
Age 7 to 11 Challenge Level:
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Round the Three Dice
Age 7 to 11 Challenge Level:
What happens when you round these three-digit numbers to the nearest 100?
Counting Counters
Age 7 to 11 Challenge Level:
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Christmas Chocolates
Age 11 to 14 Challenge Level:
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
NRICH is part of the family of activities in the Millennium Mathematics Project.