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Resources tagged with Working systematically similar to Factors and Multiple Challenges:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

Factors and Multiple Challenges

Stage: 3 Challenge Level:

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Ones Only

Stage: 3 Challenge Level:

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

A First Product Sudoku

Stage: 3 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

How Old Are the Children?

Stage: 3 Challenge Level:

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Stage: 3 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Football Sum

Stage: 3 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Masterclass Ideas: Working Systematically

Stage: 2 and 3 Challenge Level:

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. . . .

Medal Muddle

Stage: 3 Challenge Level:

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

Cayley

Stage: 3 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Stage: 3 Challenge Level:

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Stage: 3 Challenge Level:

A few extra challenges set by some young NRICH members.

Counting on Letters

Stage: 3 Challenge Level:

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Twinkle Twinkle

Stage: 2 and 3 Challenge Level:

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Stage: 3 Challenge Level:

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

More on Mazes

Stage: 2 and 3

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.

Ben's Game

Stage: 3 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Crossing the Town Square

Stage: 2 and 3 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Inky Cube

Stage: 2 and 3 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Colour Islands Sudoku

Stage: 3 Challenge Level:

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Pair Sums

Stage: 3 Challenge Level:

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Tea Cups

Stage: 2 and 3 Challenge Level:

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Magic Potting Sheds

Stage: 3 Challenge Level:

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Creating Cubes

Stage: 2 and 3 Challenge Level:

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Oranges and Lemons, Say the Bells of St Clement's

Stage: 3 Challenge Level:

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Crossing the Bridge

Stage: 3 Challenge Level:

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Coins

Stage: 3 Challenge Level:

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

9 Weights

Stage: 3 Challenge Level:

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Pole Star Sudoku 2

Stage: 3 and 4 Challenge Level:

This Sudoku, based on differences. Using the one clue number can you find the solution?

Product Doubles Sudoku

Stage: 3 and 4 Challenge Level:

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

Given the products of diagonally opposite cells - can you complete this Sudoku?

Cuboids

Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Building with Longer Rods

Stage: 2 and 3 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

Special Numbers

Stage: 3 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Consecutive Numbers

Stage: 2 and 3 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Integrated Product Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Consecutive Negative Numbers

Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

American Billions

Stage: 3 Challenge Level:

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

A pair of Sudoku puzzles that together lead to a complete solution.

More Children and Plants

Stage: 2 and 3 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

Weights

Stage: 3 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Sticky Numbers

Stage: 3 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

More Plant Spaces

Stage: 2 and 3 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Stage: 3 and 4 Challenge Level:

Four small numbers give the clue to the contents of the four surrounding cells.

Summing Consecutive Numbers

Stage: 3 Challenge Level:

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

More Magic Potting Sheds

Stage: 3 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Maths Trails

Stage: 2 and 3

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

The Naked Pair in Sudoku

Stage: 2, 3 and 4

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

Two and Two

Stage: 2 and 3 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.