December Challenge - Year 1 & 2

Melody bought 4 boxes of Christmas tree baubles.  Each box held 6 baubles. Unfortunately, there was one broken bauble in each box.  How many baubles could Melody hang on her Christmas tree?

Hint:  Draw a picture of the boxes of baubles.

Solutions are to be completed by Friday 16th December.  Please post them into the Maths Challenge Box in the picture book library.

December Challenge - Year 3 & 4

On the first day of Christmas, my true love gave to me a partridge in a pear tree. (1 present)

On the second day of Christmas, my true love gave to me 2 turtle doves and a partridge in a pear tree. (3 presents)

On the third day of Christmas, my true love gave to me 3 French hens, 2 turtle doves and a partridge in a pear tree.  (6 presents)

So by day 3, I have been given 1 + 3 + 6 = 10 presents.

How many presents will I have by the end of the 12^th day of Christmas?

Hint – To keep organized, calculate how many presents you receive on each of the 12 days, and then find the total.

Solutions are to be completed by Friday 16th December.  Please post them into the Maths Challenge Box in the picture book library.

December Challenge - Years 5 & 6

Who spent the most?

The following characters have just been Christmas shopping.  Who has spent the most money?

Elf – I bought 4 presents.  The cheapest was £15.50 then they increased by £4.50 each up to the most expensive.

Reindeer – I bought gifts for the 8 other reindeer.  The shop was offering “Buy 3 – Get 1 free.”  The usual price per item was £12.50.

Angel – My most expensive gift cost the same as the elf’s cheapest gift.  The other 6 got progressively cheaper by £1.10.

Snowman – I spent an average of £8.10 per present and I bought gifts for my wife, 5 nieces and 4 nephews.  

Solutions are to be completed by Friday 16th December.  Please post them into the Maths Challenge Box in the picture book library.

November Challenge - Years 1 & 2

Jasper’s Beanstalk

Jasper’s bean grew 1 cm on a Friday.  After that, the beanstalk grew 2 cm taller each day.  When did the beanstalk reach 13 cm tall?

 

Possible strategy:

Use blocks to build the beanstalk.  You could even change 2 cm to 2 blocks to make the question more tangible for your child.  Build the height for each day and label it with the days of the week.

Solution: Thursday

November Challenge - Years 3 & 4

Cupcake Conundrum

Dinah goes into the cake shop every week and would like to try a different cupcake on each visit.  By looking at the menu below, can you help her find out how many different combinations she can have?

Cake size	Small	Medium	Large
Icing flavour	Chocolate	Vanilla	Lemon
Topping	Cherries	Sprinkles	Sweets

She must choose the size, icing flavour and topping for each of her choices.  Think about how you could organize your solution so you don’t miss any combinations.

Solution:  There are 27 different combinations.

November Challenge - Years 5 & 6

A square triangle?

It may seem very peculiar to you but I’ve drawn a triangle where all the angles are square.  No, I don’t mean right angles (90^o) – that’s impossible!

What I do mean is that each angle, measured in degrees, is a square number.

Can you tell me how many degrees each angle has?

Reminders:

The total of all three angles in a triangle is 180^o.

Can you remember what square numbers are?  Try 1x1, 2x2, etc.

Solution: 100^o + 64^o + 16^o

October Challenge - Years 1 & 2

The Queen of Hearts made 20 tarts.  

She arranged the tarts on some plates.  Some of the plates had five tarts on and some of the plates had two tarts on.  

How many plates did she use?

Hint:  Find twenty objects to represent the tarts (or even make some playdoh tarts) and have a small pile of plates.  Have your child try different combinations until he/she is able to find the solution.  

For older children, you might be able to talk about odd and even numbers.

Solution:
7 plates are needed - 5 plates with 2 tarts and 2 plates with 5 tarts.

Solutions

Solutions for each challenge will be shown on an updated blog entry of the monthly challenge.  For example, if you would like to see the solutions for the September challenges then visit the September challenge entry.

Remember it is the process that is important.  Even if you don't get to the end solution some learning will have taken place and you will be in a better position to tackle other challenges.

Enjoy!

October Challenge - Years 3 & 4

Tea Time

Mrs Jones loves drinking tea!

At 6 am she drinks two cups of tea.

Then every two hours she drinks three more cups until 10 pm when she drinks two cups before bed.

Altogether, how many cups of tea does she drink in one day?

Solution:
25 cups of tea

October Challenge - Years 5 & 6

Food for thought

Max was lazing on the beach when he was feeling peckish. He went to the café and bought 2 iced buns and 1 lolly. It cost him 80 pence. Dave came along just as Max was finishing the iced bun.

"Hey, where's mine?" he shouted.

"All gone!" muttered Max, feeling rather guilty.

"Well, I'll just get my own then," said Dave. "I'll show you!" Showing off, Dave bought 3 iced buns and 2 lollies. It cost him £1.30. He took them back and sat down next to Max and then ate all the buns in one go.

Five minutes later: "Err, I don't feel very well," groaned Dave, "Would you like to buy the lollies off me?"

"OK," said Max, "How much did they cost?"

Good question: How much did each lolly cost?

Solution:
Each lolly cost 20p.

It might have taken some trial and improvement to solve this question. You could make a reasonable guess for the cost of a lolly and then work out what an iced bun would cost using Max's total. Does it work for Dave's total as well? Adjust the amount until you find numbers that work.

Welcome back!

Hello!

I hope everyone has had a wonderful summer holiday.  As the new school year starts, I have another selection of monthly Maths problems to challenge and excite you.  At the start of each month I will post three Maths Challenges - one for Years 1&2, one for Years 3&4 and one for Years 5&6.  The purpose of the problems is to provide an opportunity for you to engage with your children in some mathematical problem solving.  The solution is not as important as the effort that you put in and the discussion you have along the way.  Children who attempt the problems or even find an end solution are encouraged to hand in their work to the Maths Challenge Box in the picture book library by the end of the month.  The problems for this September are listed below this blog entry.

Have fun,
Mrs. Hopkins

September Challenge - Years 1 & 2

Here are two dice.
 

If you add up the dots on the top you will get 8.
 

Find two dice to roll yourself. 

Add the numbers that are on the top.

What other totals could you get if you roll the dice again?

Notes for adults:
You will need two dice to play this game. 

The children can count the total number of spots on the dice or add them together using number facts they already know.
Record the results and explore the different totals that you can get.
Help them to find all the possible combinations (although not all combinations are necessary for your solution).

Some guiding questions:

Can you make a bigger/smaller total?

What is the highest total you could make?
What is the lowest total you could make?
If one dice shows 6, what could the other dice be showing?

How will you know when you've found all the totals?  

Solutions: 

Possible totals include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

September Challenge - Years 3 & 4

Number Detective

You need to be a detective to uncover the value of my secret number.  Follow the clues below.  You must use the clues in the order given.

a) What is my number?

b) What is the least number of clues you need to use to be absolutely certain of the value of my number?

The clues:

1. I am a three digit number.

2. I am an odd number.

3. I am divisible by 5.

4. Each of my digits is different.

5. My digits add up to 8.

6. The tens digit is smaller than the hundreds digit.

7. I am less than 300.

8. I have only one even digit.  

Solution:

Work through each clue one by one.
1. _ _ _
2. Must have 1, 3, 5, 7 or 9 in the units place.
3. Must end in 5 or 0, so _ _ 5.
4. The hundreds and tens place cannot be 5.
5. 5 + ? = 8 so the hundreds and tens digit must add to 3, so the number could be 215,125 or 305.
6. It could be 215 or 305.
7. It can only be 215.

Seven clues are needed.

September Challenge - Years 5 & 6

The Largest Number

Using the numbers 2, 4, 6 and 8, the multiplication sign, the addition sign and the equals sign, what is the largest number you can make? You may only use each digit and sign once, but you don't have to use all of the signs.

Hint:  The question has referred to the 2, 4 6 and 8 as digits (not numbers) so it is possible to put digits together to make a larger number.  For example, the digits 2 and 4 can be used to make the number 24 (twenty-four) or 42 (forty-two).

Solution:  The biggest number you can make is simply by rearranging the digits to make a four-digit number - 8642.  You don't need to use a calculation.

Well done if you found 64 x 82 = 5248.

July Challenge - Years 5 & 6

Using each of the numbers 1, 2, 4, 6, 8 and 12 once, fill in the circles so that the product of the three numbers on each side is 48. 

Hints:

Remember what product means.

There are three sides to the triangle.

Write each number on a bit of paper and move them around until you get the solution.  

Solutions are to be completed by Thursday 14th July.  Please post them into the Maths Challenge Box in the picture book library.

July Challenge - Years 1 & 2

When Jack was one year old his mother bought a packet of 24 candles for his birthday cake.  That year she put 1 candle on Jack's cake. When he was two he had 2 candles and when he was three he had 3 candles, and so on.

On which birthday did Jack’s mother need to buy more candles?  

Hint:  Draw cakes with candles or make cakes from playdoh and use straws or cocktail sticks for candles.

Solutions are to be completed by Thursday 14th July.  Please post them into the Maths Challenge Box in the picture book library. 

July Challenge - Years 3 & 4

Some Product!

1) Find two numbers whose sum is 9 and their product is 20.

2) Find two numbers whose sum is 10 and their product is 21.

3) Find two numbers whose sum is 10 and their product is 24.

4) Find two numbers whose sum is 9 and their product is 14.

5) Find two numbers whose sum is 15 and their product is 54.

For an extra challenge try:

a) Find three numbers whose sum is 10 and their product 20.

b) Find three numbers whose sum is 13 and their product 60.

Hints:

A sum is the answer to an addition question.

A product is the answer to a multiplication question.

Solutions are to be completed by Thursday 14th July.  Please post them into the Maths Challenge Box in the picture book library.

June Maths Challenge - Years 1 & 2

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Example:  5 - 2  = 3

It will take some perseverance.  You can try different solutions by cutting out numbers to move around on the circles or you can use the interactive area on http://nrich.maths.org/6227 .

Solutions are to be completed by Thursday 30^th June.  Please post them into the Maths Challenge Box in the picture book library.

June Challenge - Years 3 & 4

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Example:  6 – 5 = 1

It will take some perseverance.  You can try different solutions by cutting out numbers to move around on the circles or you can use the interactive area of http://nrich.maths.org/927.

Solutions are to be completed by Thursday 30^th June.  Please post them into the Maths Challenge Box in the picture book library.

June Challenge - Years 5 & 6

Mystery Matrix

Can you fill in this multiplication square?

The numbers 2 to 12 were used to generate it, with exactly one number used twice.  Fill in the bold boxes with the numbers from 2 to 12.  Of course, you can fill in the numbers in the middle boxes as well.

X
	32			40
					49
			22
		15				27
			24
					42

Solutions are to be completed by Thursday 30^th June.  Please post them into the Maths Challenge Box in the picture book library.

May Challenge - Years 1 & 2

Button-up

My coat has three different buttons.
Sometimes, I do them up starting with the top button.  Sometimes, I start somewhere else.

How many ways can you find to do up my coat?

Think about:

What could you change about the buttoning? 
Do you always have to start in the same place? 
Do you think there are any more ways?  How do you know?

Solutions are to be completed by Thursday 26^th May.  Please post them into the Maths Challenge Box in the picture book library.

May Challenge - Years 3 & 4

Lighthouses

On the coast there are three lighthouses.

The first light shines for 3 seconds, then is off for 3 seconds.

The second light shines for 4 seconds, then is off for 4 seconds.

The third light shines for 5 seconds, then is off for 5 seconds.

All three lights have just come on together.

Questions:

1) When is the first time that all three lights will be off?

2) When is the next time that all three lights will come on at the same moment?

Hints:
Think about drawing three number lines (one for each lighthouse) to show when each light is on and off.  Be sure to match the three lines up so they are easy to compare.
Question 2 will require some careful work and perseverance if you use the number lines.  Alternatively, you may wish to think about the number of seconds between each turning on of  a light.  For example, the first lighthouse turns on every 6 seconds.  Think about how you could use your knowledge of multiples.

Solutions are to be completed by Thursday 26^th May.  Please post them into the Maths Challenge Box in the picture book library.

May Challenge - Years 5 & 6

Letter Land (Updated)

A to H represent the numbers from 0 to 7.

A + C = A   (Please note that I originally incorrectly published this sum as A + B = A)

F x D = F

B – G = G

A + H = E

B / H = G

E – G = F

Find the values of A, B, C, D, E, F, G and H.

Hints – Only read the hints once you have tried on your own first.

1) Solve for C and D first.

2)  Next solve for B and G.  You may need to consider a few possibilities.

April Solutions - Year 3 & 4

There were 11 solutions in total.  You need to work systematically to find them all.

April Solutions - Years 5 & 6

1. I am 48 (or even 104).

2. I am 26 now, and in 38 years I will be 64 (which is both a square number and a cube number).

3. I am 9 years old now.

A couple possible ways to solve question 3:

a) Create a table and test the possibilities one by one.

My age	Mum’s age		My age now	Mum’s age eight years ago	My age in 5 years time doubled
0	27
1	28		1	19	12
2	29		2	21	14
3	30		3	22	16
4	31		4	23	18
5	32		5	24	20
6	33		6	25	22
7	34		7	26	24
8	35		8	27	26
9	36		9	28	28
10	37
11	38
12	39

b) You could also solve an algebraic equation where x represents my age now.

x= my age now, so x + 27 is my mum’s age now.

x + 5 is my age in five years time.

2(x + 5) is my age in five years time doubled.

x + 27 – 8 is my mum’s age eight years ago.

So, 2(x+5) = x + 27 -8.

When you solve for x, you find that x=9.