Other tags that relate to En-counters for Two
Video. Team-building. Investigations. Questioning. Working systematically. Visualising. Practical Activity. Addition & subtraction. Dominoes. Making and proving conjectures.There are 317 results
Broad Topics > Thinking Mathematically > Working systematically
Counting Cards
Age 7 to 11 Challenge Level:
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Counters in the Middle
Age 7 to 11 Challenge Level:
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
More and More Buckets
Age 7 to 11 Challenge Level:
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Folded Number Line
Age 7 to 11 Challenge Level:
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
Polydron
Age 7 to 11 Challenge Level:
This activity investigates how you might make squares and pentominoes from Polydron.
Calcunos
Age 7 to 11 Challenge Level:
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
A City of Towers
Age 5 to 7 Challenge Level:
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Buying a Balloon
Age 7 to 11 Challenge Level:
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Is a Square a Rectangle?
Age 7 to 11 Challenge Level:
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
Seven Flipped
Age 7 to 11 Challenge Level:
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Routes 1 and 5
Age 5 to 7 Challenge Level:
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Sticks and Triangles
Age 7 to 11 Challenge Level:
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Triangle Animals
Age 5 to 7 Challenge Level:
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Multilink Cubes
Age 7 to 11 Challenge Level:
If you had 36 cubes, what different cuboids could you make?
Roll These Dice
Age 7 to 11 Challenge Level:
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
Egyptian Rope
Age 7 to 11 Challenge Level:
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
Whose Sandwich?
Age 5 to 7 Challenge Level:
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Briefcase Lock
Age 5 to 7 Challenge Level:
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Seven Pots of Plants
Age 7 to 11 Challenge Level:
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Brush Loads
Age 7 to 11 Challenge Level:
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Ancient Runes
Age 7 to 11 Challenge Level:
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Jumping Cricket
Age 5 to 7 Challenge Level:
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Mixed-up Socks
Age 5 to 7 Challenge Level:
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
Whose Face?
Age 5 to 11 Challenge Level:
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Room Doubling
Age 7 to 11 Challenge Level:
Investigate the different ways you could split up these rooms so that you have double the number.
Square Corners
Age 7 to 11 Challenge Level:
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
The Third Dimension
Age 5 to 11 Challenge Level:
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Stairs
Age 5 to 11 Challenge Level:
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Quadrilaterals
Age 7 to 11 Challenge Level:
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Making Squares
Age 7 to 11
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
2,4,6,8
Age 5 to 7 Challenge Level:
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Fencing Lambs
Age 7 to 11 Challenge Level:
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Eight Queens
Age 7 to 11 Challenge Level:
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Two on Five
Age 5 to 11 Challenge Level:
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
It Figures
Age 7 to 11 Challenge Level:
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
6 Beads
Age 5 to 7 Challenge Level:
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Dienes' Logiblocs
Age 5 to 7 Challenge Level:
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Ice Cream
Age 7 to 11 Challenge Level:
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Pasta Timing
Age 7 to 11 Challenge Level:
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Bean Bags for Bernard's Bag
Age 7 to 11 Challenge Level:
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Fake Gold
Age 7 to 11 Challenge Level:
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Sweets in a Box
Age 7 to 11 Challenge Level:
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Numerically Equal
Age 7 to 11 Challenge Level:
Can you draw a square in which the perimeter is numerically equal to the area?
Making Boxes
Age 7 to 11 Challenge Level:
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Making Cuboids
Age 7 to 11 Challenge Level:
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Symmetry Challenge
Age 7 to 11 Challenge Level:
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
Family Tree
Age 7 to 11 Challenge Level:
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Two by One
Age 7 to 11 Challenge Level:
An activity making various patterns with 2 x 1 rectangular tiles.
NRICH is part of the family of activities in the Millennium Mathematics Project.