Resources tagged with Sequences similar to Reasoned Rounding:
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Estimating and approximating. Sequences. Mathematical reasoning & proof. Limits of Sequences. Rounding. Calculating with fractions. Creating expressions/formulae. Percentages. Powers & roots. Algorithms.There are 65 results
Broad Topics > Sequences, Functions and Graphs > Sequences
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.
Sissa's Reward
Stage: 3 Challenge Level:
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Lower Bound
Stage: 3 Challenge Level:
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Converging Means
Stage: 3 Challenge Level:
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
Adding Triangles
Stage: 3 Challenge Level:
What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .
1 Step 2 Step
Stage: 3 Challenge Level:
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Light Blue - Dark Blue
Stage: 2 Challenge Level:
Investigate the successive areas of light blue in these diagrams.
Seven Squares
Stage: 3 Challenge Level:
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Power Mad!
Stage: 3 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Seven Squares - Group-worthy Task
Stage: 3 Challenge Level:
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Sums of Powers - A Festive Story
Stage: 3 and 4
A story for students about adding powers of integers - with a festive twist.
Differs
Stage: 3 Challenge Level:
Choose any 4 whole numbers and take the difference between consecutive numbers, ending with the difference between the first and the last numbers. What happens when you repeat this process over and. . . .
Farey Sequences
Stage: 3 Challenge Level:
There are lots of ideas to explore in these sequences of ordered fractions.
Intersecting Circles
Stage: 3 Challenge Level:
Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?
LOGO Challenge - Sequences and Pentagrams
Stage: 3, 4 and 5 Challenge Level:
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Regular Hexagon Loops
Stage: 3 Challenge Level:
Make some loops out of regular hexagons. What rules can you discover?
Big Powers
Stage: 3 and 4 Challenge Level:
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
What an Odd Fact(or)
Stage: 3 Challenge Level:
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
Two Much
Stage: 3 Challenge Level:
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Clock Squares
Stage: 3 Challenge Level:
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
Odds, Evens and More Evens
Stage: 3 Challenge Level:
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
Maxagon
Stage: 3 Challenge Level:
What's the greatest number of sides a polygon on a dotty grid could have?
Remainder
Stage: 3 Challenge Level:
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Generating Number Patterns: an Email Conversation
Stage: 2, 3 and 4
This article for teachers describes the exchanges on an email talk list about ideas for an investigation which has the sum of the squares as its solution.
Carrying Cards
Stage: 2 Challenge Level:
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Play a Merry Tune
Stage: 2 Challenge Level:
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Calendar Patterns
Stage: 2 Challenge Level:
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?
Mobile Numbers
Stage: 1 and 2 Challenge Level:
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
First Forward Into Logo 12: Puzzling Sums
Stage: 3, 4 and 5 Challenge Level:
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Function Machines
Stage: 2 Challenge Level:
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Pebbles
Stage: 2 and 3 Challenge Level:
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Polygonals
Stage: 2 Challenge Level:
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Lawn Border
Stage: 1 and 2 Challenge Level:
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
Designing Table Mats
Stage: 3 and 4 Challenge Level:
Formulate and investigate a simple mathematical model for the design of a table mat.
Charlie's Delightful Machine
Stage: 3 and 4 Challenge Level:
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Number Tracks
Stage: 2 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?
Holes
Stage: 1 and 2 Challenge Level:
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
Times Tables Shifts
Stage: 2 Challenge Level:
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
The Numbers Give the Design
Stage: 2 Challenge Level:
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Cuisenaire Environment
Stage: 1 and 2 Challenge Level:
An environment which simulates working with Cuisenaire rods.
Paving Paths
Stage: 3 Challenge Level:
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
A Shapely Network
Stage: 2 Challenge Level:
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
The Mathemagician's Seven Spells
Stage: 2 Challenge Level:
"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?
Sets of Numbers
Stage: 2 Challenge Level:
How many different sets of numbers with at least four members can you find in the numbers in this box?
Magazines
Stage: 2 Challenge Level:
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
A Calendar Question
Stage: 2 Challenge Level:
July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?
NRICH is part of the family of activities in the Millennium Mathematics Project.