NRICH: The Box Game
NRICH (University of Cambridge)

In this game, children will use their addition and subtraction skills to keep track of the number of toys hidden inside a box when toys are added in or taken out.

NRICH: 8 in a Row
NRICH (University of Cambridge)

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

NRICH: Grow up Fast
NRICH (University of Cambridge)

How old will Julie be when her age is equal to the sum of her daughters’ ages?

NRICH: Adding in Pairs
NRICH (University of Cambridge)

These are the results when 3 numbers were added in pairs. What were the numbers?

NRICH: Sum and Differences
NRICH (University of Cambridge)

Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

NRICH: Adding and Multiplying
NRICH (University of Cambridge)

Amy misread a question and got an incorrect answer. What should the answer have be?

NRICH: Perfectly Square
NRICH (University of Cambridge)

The sums of the squares of three related numbers is also a perfect square – can you explain why?

NRICH: Summing Consecutive Numbers
NRICH (University of Cambridge)

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

NRICH: Elevenses
NRICH (University of Cambridge)

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

NRICH: What Numbers Can We Make?
NRICH (University of Cambridge)

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Illuminations: Sum of Consecutive Integers
National Council of Teachers of Mathematics

What is the smallest positive number that can be represented as a sum of consecutive positive integers in six different ways?

Illuminations: Sum of Threes
National Council of Teachers of Mathematics

Can you find n?