Hamilton Secondary Numeracy Project
Shining
Term 3
Homework
Name ___________________________
Week 1 Whole number and decimals
 Play the Rounding memory challenge at
http://www.numbernut.com/advanced/activities/estimate_mem20_ro
und1000.shtml. Your aim is to match numbers with their nearest 1000.
Click on pairs of cards to turn them over.

Shuffle a set of playing cards having removed the Jacks, Queens, Kings
and Jokers. Take three. Use them to make at least three different
numbers with two decimal places. Round each to the nearest whole
and to the nearest tenth. Repeat three more times.

Play Ice, ice, maybe at
www.mangahigh.com/en_gb/games/iceicemaybe?localeset=en_gb.
Choose ‘Medium’ and try to make a safe path for the Adelie penguins
across the deadly Estim Ocean to the next piece of ice. Use rounding to
help you to estimate each answer, move the cursor and an iceberg will
appear. If your estimation is good the penguins will bounce on this to
safety! Have several goes and see if you can improve your score. Write
down your best score. If you do well, try the ‘Hard’ level!
HSNP © Hamilton 2013
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Shining Term 2
Week 2 Addition
 Add five consecutive numbers, e.g. 3 + 4 + 5 + 6 + 7. Try another five
consecutive numbers. What do you notice? Try others to see if your
rule is still the case. Try and explain why your rule works.
What do you think will happen if you add seven consecutive numbers?
Nine consecutive numbers?
Can you explain why?

Write the numbers to 10 in order, and the 10 to 1 underneath:
1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1
What do you notice about the sum of numbers in each column? How
could you use this to find the total of all 20 numbers? And of the first
row of 10 numbers?
Use your rule to find the total of numbers 1 to 50.
Now use your rule to find the total of numbers 1 to 100!
You might even be able to generalise how to do this for numbers 1 to
n!

Find the digital roots of the first 14 square numbers: 1, 4, 9, 16...
What pattern can you find in the sequence of digital roots? Can you
predict the digital root of the next square number? Work out the next
square number, and find its digital root to see if you are right!
HSNP © Hamilton 2013
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Shining Term 2
Week 3 Subtraction

Think of a three-digit number with three different digits, e.g. 358.
Reverse it and subtract the smaller from the larger, e.g. 853 – 358.
Repeat with other numbers. What do the answers have in common?
What do you notice about the first and third digits?
Repeat with four-digit numbers. What do you notice about all of the
answers? Do they have anything in common?

Play BondBusta at http://www.hamiltonplay.org.uk/bond-busta.html.
Choose a balloon, find the difference between the two numbers. Click
on the arrow with the difference, then on a balloon to fire the arrow.
You need to be quick! See if you can get bronze, then try again and see
if you can do even better and get silver or gold with more practice!
HSNP © Hamilton 2013
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Shining Term 2
Week 4 Multiplication

In this grid, each group of three numbers in a row are multiplied
together to give the number at the end of the row. Each group of three
numbers in a column are also multiplied together to give the number
at the bottom of the column. The digits 1 to 9 are used once and only
once in this grid. Try and work out where they belong!
?
?
?
12
?
?
?
315
?
?
?
96
72
30 168
Now create your own grid!

Play the video clip under ‘Multiplying with Lines’ at
http://nrich.maths.org/5612. Click on ‘hidden text’ to do this. Watch
how this method is used to multiply 23 by 21. Watch it a few times,
then see if you can use this method to work out 32 × 12. Check that
the answer is correct!
Try and explain how and why this method works..
HSNP © Hamilton 2013
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Shining Term 2
Week 5 Division

Play Factor lines at: http://nrich.maths.org/1138/index. Drag the four
number cards (1, 2, 3 and 21) onto the grid above to make a diagonal,
vertical or horizontal line. You can put a number card on a square with
the same number, a multiple of that number or a factor of that
number.
How many different lines did you make? (The computer will keep a
record.)

Play the Remainders game at http://nrich.maths.org/6402. The
computer will think of a number between 1 and 100 and you must try
and guess what it is by choosing numbers for it to divide by. It will tell
you if there is a remainder, and if so what it is. Try to guess at least
three numbers. What was your score?
HSNP © Hamilton 2013
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Week 6 Decimals

32
16
8
4
2
1
1
0
1
0
0
1
Above is the number 41 written using binary notation. Copy the
headings and underneath write the 4 times table. Can you see any
patterns? Can you predict how the next multiple will be written?
Now write the 5 times table!

Play the Binary game at
http://forums.cisco.com/CertCom/game/binary_game_page.htm. You
click on the 0 and 1 cards to change 0 to 1 or 1 to 0 to make them
equal the decimal number on the right. Or if the box on the right is
blank, click on the box and use the key pad which pops up to enter the
decimal number shown by the cards on the left. You have to solve
each number problem before the screen fills up with problems, then
it's game over! Can you get to level 2?
HSNP © Hamilton 2013
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Shining Term 2
Week 7 Addition
This week’s home work is all about PRIMES!

Add pairs and trios of prime numbers. Write some rules about whether
the answers are odd or even numbers.

Think of a two-digit prime number. Reverse the digits and add to the
first number. Is the answer prime?
E.g. 17 + 71 = 88.
What do you notice about your answers?
Do you think you will ever get a prime answer? Why/why not?

4 is a square number which can be made by adding two primes 2 + 2.
The next square number is 9 which can be made by adding 7 and 2,
two primes. Investigate whether this is the case for all square
numbers. Go to at least 122. What did you find out?
HSNP © Hamilton 2013
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Shining Term 2
Week 8 Subtraction

Work out the answer to each of these subtractions:
22 – 2
32 – 3
42 – 4
52 – 5…
What do you notice about the answers? Carry on the sequence of
subtractions to see if the pattern of answers continues.

Work out the answers to these subtractions:
42 – 22
52 – 32
62 – 42 …
What do you notice?
Now try:
52 – 22
62 – 32
72 – 42 …
What happens this time?

Find the difference between squares of two even numbers, e.g. 82 – 22.
Try different pairs of even numbers. Are the answers always odd,
always even, or either?
Find the difference between squares of odd numbers. What happens
this time?
Now try pairs of odd and even numbers, e.g. 92 – 42
HSNP © Hamilton 2013
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Shining Term 2
Week 9 Multiplication




Play Alien Powers at
http://www.ezschool.com/Games/Exponents.html. First choose
‘squares’. Click on the correct answers before the spaceships land.
How many aliens landed?
Now try squares and cubes. You may not have time to work out all the
answers, but use clues (such as the last digit for example) to make an
educated guess, as time is not on your side!
Work out :
12 + 22 + 2 2
22 + 32 + 6 2
32 + 42 +122
42 + 52 + 202
What do you notice about the answers?
Can you work out the rule that makes this pattern?
HSNP © Hamilton 2013
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Shining Term 2
Week 10 Division

Triangular numbers can be made like this:
Add next door pairs of triangular numbers. What do you notice about
the answers? Imagine rotating the third picture through 180° and
placing to the right of the third picture. It would look like this:
Imagine the same happening to the next pair of triangular numbers.
Draw the next few results. Does this help to explain what you found?

Play the Square root game at http://www.math-play.com/square-rootgame.html Try and match numbers with their square roots.
HSNP © Hamilton 2013
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Shining Term 2
Shining Term 3 websites
Rounding memory challenge
http://www.numbernut.com/advanced/activities/estimate_mem20_round10
00.shtml
Ice, ice, maybe
www.mangahigh.com/en_gb/games/iceicemaybe?localeset=en_gb
BondBusta http://www.hamiltonplay.org.uk/bond-busta.html
Multiplying with Lines http://nrich.maths.org/5612
Factor lines http://nrich.maths.org/1138/index
Remainders game http://nrich.maths.org/6402
Binary game
http://forums.cisco.com/CertCom/game/binary_game_page.htm
Alien Powers http://www.ezschool.com/Games/Exponents.html
Square root game http://www.math-play.com/square-root-game.html
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specified on this list (hereafter collectively referred to as the ‘Links’) have been checked by
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time of publication. Notwithstanding the foregoing or any other terms and conditions on the
Hamilton Trust website, you acknowledge that Hamilton Trust has no control over such Links
and indeed, the owners of such Links may have removed such Links, changed such Links
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HSNP © Hamilton 2013
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Shining Term 2