This article for primary teachers suggests ways in which to help children become better at working systematically.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Number problems at primary level that require careful consideration.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
What two-digit numbers can you make with these two dice? What can't you make?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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?
Follow the clues to find the mystery number.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you substitute numbers for the letters in these sums?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you work out some different ways to balance this equation?
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Have a go at balancing this equation. Can you find different ways of doing it?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you find the chosen number from the grid using the clues?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
What happens when you round these numbers to the nearest whole number?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
This activity focuses on rounding to the nearest 10.
What happens when you round these three-digit numbers to the nearest 100?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you find all the different ways of lining up these Cuisenaire
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?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
How many different triangles can you make on a circular pegboard that has nine pegs?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An investigation that gives you the opportunity to make and justify
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.