Challenges

How many different ways could you split a square cake between 4 people so that everyone eats the same amount of cake?

Are there more inches in a mile or seconds in a day?

Source: https://playwithyourmath.com/

If you start at 27 and count by 5s, then start at 32 and count by 2s, what are some numbers that will appear in both patterns.

What do you notice about these numbers?

Create as many multiplication sentences as you can that have a product between 400 and 500.

Do you notice any patterns in your number sentences?

Source: https://playwithyourmath.com/

We can represent a group of friends by drawing a graph.

Each node represents a person. ~ An edge joins two nodes if and only if those two people are friends.

Here is a graph showing a group of friends.

Can you work out who's who using the clues below?

Alan has 3 friends, Barney, Charlie, and Daniel.
Barney and Ed are both friends with Charlie.
Ed is Frank's only friend.

Here is a second network of friends.

Again, use the clues below to figure out who's who.

Bella and Ciara are friends
Emily and Ciara are not friends
Bella is Fiona's only friend
Anna has more friends than anyone else
Daphne has three friends
Gill and Daphne are not friends
Emily has two friends

Once you've solved the two puzzles, here are some questions to consider:

Did each problem have a unique solution?
Were there any clues you didn't need to use?

If you label each node with the number of friends the person has, and add together all the numbers, what can you say about the answer? Can you explain why?

Can you design a puzzle with five friends, where some people have more than two friends, with a unique solution?

Source: https://wild.maths.org/

6 Beads

If you put three beads onto a tens/units abacus you could make the numbers 3, 30, 12, or 21.

What numbers could you make if you had six beads?

Explore other ideas. What if you had a different number of beads? What if you had a hundreds peg on your abacus?

Source: https://nrich.maths.org/

Finding Fifteen

Tim had nine cards, each with a different number from 1 to 9 on it.

He put the cards into three piles so that the total in each pile was 15.

How could he have done this?

Can you find all the different ways Tim could have done this?

Source: https://nrich.maths.org/

Find the value of each image.

Source: https://mashupmath.com/

Find the value of each image in the multiplication table.

Source: https://mashupmath.com/

Sam created a number using 9 base ten blocks. What different numbers could Sam have made?

Source: Howard County Public School System

Source: https://playwithyourmath.com/

The Tall Tower

You have been imprisoned at the top of the Tall Tower by the Wicked Magician!

You can get out by climbing down the ladders. As you come down you collect useful spells.

You can go down the ladders and through the doorways into an adjoining room, but you cannot go into the same room twice, nor climb up the ladders.

The numbers in the rooms show how many spells there are in each one.

Which way should you go to collect the most spells?

And which way to collect as few as possible?

Can you find a route that collects exactly 35 spells?

Source: https://nrich.maths.org/

A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from the ten statements below?

Here is a clock-face with letters to mark the position of the numbers so that the statements are easier to read and to follow.

No even number is between two odd numbers.
No consecutive numbers are next to each other.
The numbers on the vertical axis (a) and (g) add to 13.
The numbers on the horizontal axis (d) and (j) also add to 13.
The first set of 6 numbers [(a) - (f)] add to the same total as the second set of 6 numbers [(g) - (l)] .
The number at position (f) is in the correct position on the clock-face.
The number at position (d) is double the number at position (h).
There is a difference of 6 between the number at position (g) and the number preceding it (f).
The number at position (l) is twice the top number (a), one third of the number at position (d) and half of the number at position (e).
The number at position (d) is 4 times one of the numbers adjacent (next) to it.

Source: https://nrich.maths.org/

Domino Window

Directions: Use four of these dominoes to form a square with the same number of dots on each side.

Source: https://www.openmiddle.com/domino-window/

Subtraction with Regrouping 2

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the difference equal to 39.

Source: https://www.openmiddle.com/subtraction-with-regrouping-2/

How much room do you need at a table?

Polygon's Restaurant has square tables that seat one person on each side. To seat larger parties, two or more tables are pushed together. What is the least number of tables needed to seat a party of 19 people who want to sit together?

Further Questions:

What is the maximum number of people who can be seated at seven tables put together?
If every seat is filled, what is the least number of people that can be seated in an arrangement of nine tables?

Think About It:

If you were waiter, would it be easier to seat a large group at one big table or two smaller tables? How about serving them?
Why do some restaurants use round tables?

Source: https://figurethis.nctm.org/challenges/c44/challenge.htm

How can you use old stamps?

Suppose you found old rolls of 15 cent and 33 cent stamps. Can you use a combination of $0.33 and $0.15 stamps to mail a package for exactly $1.77.

Further Questions:

Using only $0.33 and $0.15 stamps, can you make postage equal to $2.77? $4.77? $17.76?
Can every whole number greater than 1 be made by adding some combination of twos and threes?
What is a postage amount you cannot make?

Think About It:

Airmail stamps, which cost more than first-class postage, were once very popular for domestic mail. Why do you think this is no longer true today?
Compare the cheapest way of mailing a package or letter using the U.S. Postal Service, Federal Express, or United Parcel Service.

Source: https://figurethis.nctm.org/challenges/c08/challenge.htm

Coded Hundreds Square

Can you rebuild this hundreds grid? It starts with 1 and ends with 100. You can use the paper and cut out the pieces, or use the interactivity at NRICH.

Coded hundred square.pdf

Source: https://nrich.maths.org/6554/note

Open the lock

Adding two digit numbers

Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) sum.

Source: https://www.openmiddle.com/adding-two-digit-numbers-elementary/

Balanced Equation

Use the operation symbols (+, -, x, and ÷) to make the equation true. Operations may be used more than once.

Source: https://www.openmiddle.com/balanced-equation/

School Fair Necklaces

Rob and Jennie were making necklaces to sell at the school fair.

They decided to make them very mathematical.

Each necklace was to have eight beads, four of one color and four of another.

And each had to be symmetrical, like this.

How many different necklaces could they make?

Can you find them all?

How do you know there aren't any others?

What if they had 9 beads, five of one colour and four of another?

What if they had 10 beads, five of each?

What if.....??????

Source: https://nrich.maths.org

A Puzzling Cube

Here are the six faces of a cube - in no particular order.

Here are three views of the cube.

Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Hint: Scissors and tape might be helpful!

Source: https://nrich.maths.org/1140/note

Gummy Pyramid

Source: https://mashupmath.com/freemathpuzzles

Square Totals

Source: https://mashupmath.com/freemathpuzzles

Source: https://mathjokes4mathyfolks.wordpress.com/activities/

Zombie Bridge Riddle

Taking that internship in a remote mountain lab might not have been the best idea. Pulling that lever with the skull symbol just to see what it did probably wasn’t so smart either. But now is not the time for regrets because you need to get away from these mutant zombies...fast. Can you use math to get you and your friends over the bridge before the zombies arrive?

Window Sum

Directions: Using the digits 0-9, no more than once, complete the puzzle so that the sum of each side is equivalent.

Source: https://www.openmiddle.com/window-sum/

Adding 3 Fractions to Get 1

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make a true statement.

Source: https://www.openmiddle.com/adding-3-fractions-to-get-1/

Sticker-bility Sum Puzzle

The addition sum below is a puzzle I've been trying to solve. The idea is that each type of sticker stands for a different number, but that this number is the same wherever that sticker occurs.

So far I've got it to the picture shown in the second diagram. Can you finish it off for me?

Source: https://www.mathsisfun.com/puzzles/sticker-bility.html

Placing Sheets Puzzle

Eight squares of paper, all exactly the same size, have been placed on top of each other so that they overlap as shown.

In what order were the sheets placed?

Source: https://www.mathsisfun.com/puzzles/placing-sheets.html

10 Digit Number Puzzle

Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.

Source: https://www.mathsisfun.com/puzzles/10-digit-number.html

Algebra Puzzle

Solve the following (each letter represents a particular digit 0 to 9):

ABC + DEF = GHIJ

Source: https://www.mathsisfun.com/puzzles/algebra-15.html

Interpreting Data

Make a graph that shows a possible result of 7 students’ favorite color with red being the most popular color.

Source: https://www.openmiddle.com/interpreting-data-2/

Operations with Time

Use the digits 1 to 9, at most one time each, to fill in the boxes to make a time that is 4:37 pm.

Source: http://www.openmiddle.com/operations-with-time/

Calculate your next travel destination!

What do you notice?

What do you wonder?

Can you explain the math behind this image?

Source: https://www.math-salamanders.com/math-puzzles.html

Factors and Multiples Chain

Choose a starting number from a 1-100 square and cross it out.

Then choose a factor or multiple of that number.

Keep crossing out factors or multiples of the last number in the chain. Once you have crossed out a number, you can't use it again.

For example, Charlie started with 60, 30, 6, 96, 16, 32, 8, 56, 7, 21, 42,...

What's the longest chain you can make?

You may wish to download a 1-100 square to work on, or you could use the interactivity at wild.maths.

Source: https://wild.maths.org/factors-and-multiples-chain

X-Box

Can you place 6 X's (or objects) into a 3x3 box so that there are 2 X's in each row and column?

Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs.

The great planetary explorer Nico, who first discovered the planet, saw a crowd of Zios and Zepts. He managed to see that there was more than one of each kind of creature before they saw him. Suddenly they all rolled over onto their backs and put their legs in the air.

He counted 52 legs. How many Zios and how many Zepts were there?

Do you think there are any different answers?

Source: https://nrich.maths.org/1005