Numeracy problems to solve for Key Stage 1, 2 and 3

Try these on your own, with friends or your family.

Task A

Balanced Numbers

Can you divide the box into 4 equal parts? The number in each part
must add up to the same total.

Task B

House Conversions

What is the smallest number of rods you need to move to convert
the first house into each of the others?

(a)	(b)	(c)

Task C

Have fun with Fraction Patterns

These are half patterns.

Half of each grid is patterned.

These are 1/4 patterns.

1/4 of each grid is patterned.

An extra challenge

• Click here for the grid of 9 squares
• Explore patterns where one third (1/3) of the grid is patterned
• Click here for the grid of 25 squares
• Explore patterns where one fifth (1/5) of the grid is patterned.

Task D

Polygon Puzzle

To play the game you must print this out

Use 18 Counters

Can you place them on the polygon mat

The number of counters in each row must be even

The number of counters in each column must also be even

Can you find more ways to solve the puzzle?

Challenge your friends to find more ways than you.

Task A

A few puzzles to get you started

What is triskaidekaphobia? ________________________

Task B

Sort out the symbols!

In this 4 x 4 array each symbol
stands for a different number. The sum of the symbols in three of
the rows and three of the columns is given. What are the two missing totals? What are the values of each symbol? They may not be whole numbers.

Task C

Change the equations

Good! Now remove twelve more letters so that what remains still
gives a correct equation.

Task D

Sailing boat

This sailing boat is made up of 12 coloured triangles.

• Cut them out separately.
• Then fit them all together to make one large triangle

Task E

Formation Flying

The leader of the Red Arrows display team was always looking for
new formations to show off the flying skills of his team at their public displays all over the world. After one brain-storming session he came
up with a way to change from a pattern of two rows of five planes to a pattern in which there were five lines each containing 4 planes. The change of formations was achieved by only 4 planes changing their positions relative to the other 6 planes who held formation. Which
planes changed position relative to the other and what was their new formation?

Task F

Amazing Numbers

Mathematics really is amazing

The number 142857 is amazing.
Do the multiplications below, using a calculator, and you will discover why?

1. 142857 x 2
2. 142857 x 3
3. 142857 x 4
4. 142857 x 5
5. 142857 x 6

Why do you think this number 142857 is called a roundabout
number?

What about the amazing number 7.
Do these multiplications again, using a calculator
What happens?

1. 15873 x 7
2. 31746 x 7
3. 47619 x 7
4. 63492 x 7
5. 79365 x 7
6. 95238 x 7
7. 111 111 x 7
8. 126 984 x 7
9. 142 857 x 7

A mother bird has three fledglings to feed.
Each baby bird will eat 20 grams of food per day.

The difficulty is the mother bird can only carry 5 grams of food on each flight. However towards the end of the day she grows tired and
only manages to carry half as much food for her last 4 trips.

Food is plentiful for the first 3 trips of the day. She manages to find enough food. Her return to nest distance id half a mile for these three journeys. On her 4th flight however a flock of sea gulls have eaten everything and she needs to travel an extra half a mile for this and each subsequent trip to find enough food.

Questions

1. What is the total weight of food the mother birds will need to fetch
her fledgling for the day?

2. How far does she travel on
a. the 5th flight?
b. the 8th flight?

3. How many flights must she make in total during the day?

4. How far will she have travelled during the course of 1 day?

An extra challenge

If the mother bird could carry an extra 2 grams each journey how
many flights would it take to have enough food? Would there be any
food left over? How many miles shorter would her daily journey be? (Because she is carrying more she gets tired after 7 fights.)