Download Hamilton Secondary Numeracy Project Shining Term 2 Homework

Hamilton Secondary Numeracy Project
Shining
Term 2
Homework
Name ___________________________
Week 1 Fractions
 Play Math matching at
http://www.harcourtschool.com/activity/con_math/con_math.html.
Click on matching fractions and decimals to reveal the pictures in the
least number of moves that you can.

Use a calculator to divide the numerator by the denominator to find
the decimal equivalents of 1/9, 1/99, 1/999… What do you notice? Can
you predict the next in the pattern?

Solve the following by thinking of how many halves are in 20 for
example:
20 ÷ 1/2

6 ÷ 1/4
3 ÷ 1/8
7 ÷ 1/6
30 ÷ 1/5
Roll a 0-9 dice twice to create a fraction (if you roll 0, roll again).
Multiply the fraction by 2/3.
□ × 2
□
3
How many can you do in two minutes?
Repeat, this time dividing each fraction by 1/4.
HSNP © Hamilton 2012
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Week 2 Addition of fractions
 Play Fractone at http://www.coolmath-games.com/0fractone/index.html. Choose ‘pretty good’ or ‘I’m going for it’! Click on
pairs of fractions with a total of 1 as quickly as you can. Sometimes you
will need to click on pairs with different denominators, e.g. 4/8 and 1/2.
What was your time?

Take the Jacks, Queens, Kings and Jokers out of a deck of playing cards.
Shuffle what’s left. Take two and make a fraction less than one. Repeat
to make another fraction. Find the total using ‘smile and kiss’. Repeat
until you have eight additions with a total of between 1 and 2.

Play Fruit shoot fractions additions at
http://www.sheppardsoftware.com/mathgames/fractions/FruitShootF
ractionsAddition.htm. Choose level 3 and relaxed mode. Add the pair
of given fractions and click on the fruit with the answer. Record the
addition and answer in your homework book. What was your score?
HSNP © Hamilton 2012
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Week 3 Subtraction of fractions

Play Fruit shoot fractions subtractions at
http://www.sheppardsoftware.com/mathgames/fractions/FruitShootF
ractionsSubtraction.htm. Choose level 3 and relaxed mode. Subtract
the pair of given fractions and click on the fruit with the answer.
Record the subtraction and answer in your homework book. What was
your score?

Roll two dice (or roll one twice) to generate a fraction less than one.
Use ‘smile and kiss’ to subtract this fraction from 8/9. How many can
you do in five minutes?
8 − 4
9
6
 Play Adding and subtracting fractions challenge at http://www.mathplay.com/adding-and-subtracting-fractions-game.html. Click to roll the
dice, then draw a card. Add or subtract the fractions. You win or lose
points for each right or wrong answer. Carry on until you reach the
finish. What was your score?
HSNP © Hamilton 2012
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Week 4 Multiplication

Play the video about Alex’s number plumber at
http://nrich.maths.org/8387. Click on the picture below and enter the
same number as on the video. Keep pressing ‘drop’ so that the last
output becomes the next input. Click on ‘results table’ on the far right.
What do you notice about the final digits of each number?
Choose your own number to enter and see what happens. Keep reentering the output as the next input and look at the results table. Can
you predict the pattern for a new number? Record what you find.

Find the squares of the following numbers: 12, 23, 34, 45 and 56. Find
the digital root of each answer, e.g. for 1156 add 1, 1, 5 and 6 to give
13, then add 1 and 3 to give the single-digit number 4. What do you
notice about the digital roots of these numbers?
Try other two-digit numbers with consecutive digits. Does it matter
whether the larger digit is first or second?
Try three-digit numbers with consecutive digits, e.g. 234.
HSNP © Hamilton 2012
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Week 5 Division

Work to find the biggest four-digit number that you can that is divisible
by each of its digits. Each digit must be different.
E.g. 1236 is divisible by 1, 2, 3 and 6, but I’m sure you can do better
than that!

Two people are thinking of the same number less than 100. One
divides it by 3 and gets a remainder of 1; the other divides it by 20 and
gets a remainder of 3. What is the number?
Make up a similar puzzle to try on someone else, try and make sure
that there is only one answer.
HSNP © Hamilton 2012
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Shining Term 2
Week 6 Decimals

Play Fruit shoot at
http://www.sheppardsoftware.com/mathgames/fractions/FractionsTo
Decimals.htm. Start with level 4. Click on fruits with decimal
equivalents to the given fractions. Record your score.
Now have a go at level 5!

Use a calculator to find the decimal equivalents for 1/13, 2/13, 3/13…
11/13.
Is there a pattern of recurring digits?
Which fractions have the same pattern?
What do you notice about the sum of the digits? Can you find any
other interesting digit sums?
Explore any other patterns you find! Write up what you discovered,
your teacher will be interested to read what you found!
HSNP © Hamilton 2012
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Week 7 Addition patterns

Carry on Pascal's triangle so that you have at least 12 rows.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
Look at the second number in each row. Does this go into each
number in the row apart from 1? Look to see if there is pattern for this
rule.

Use the internet to research Fibonacci sequences and spirals in nature.
Write about one fact which you found interesting.

This sequence is a twist on Fibonacci sequence. The fourth number is
the sum of the first three numbers, the fifth number is the sum of the
previous three numbers and so on. Continue the sequence so that you
write at least 15 numbers.
0, 1, 1, 2, 4, 7, 13, 24…
What patterns can you find? Is there a pattern of odd and even
numbers?
HSNP © Hamilton 2012
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Week 8 Positive and negative integers

Josh says if you subtract a positive number from a positive number,
you will always get a positive answer. What do you think? Explain your
thinking with some examples.

Roll a 0 to 9 dice and flip a coin to determine whether the number is
positive (heads) or negative (tails). Repeat, then find the difference
between the two numbers. Draw a number line jotting if it helps.
Record five subtractions.
7
-7
5
0
5
5 – (-7) = 12

Play Walk the plank at http://www.math-play.com/integersgame.html. Choose attributes for the person you want to walk the
plank. You will be asked a question, click on each pirate to view their
answers and choose the one you think is right. If correct, you’ll be
asked to click on the dice to move the person forward on the plank.
Click for the next question. Carry on until the game is complete. Were
you successful in getting the person to walk the plank?!
HSNP © Hamilton 2012
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Week 9 Multiplication



Work out 1! 2! 3!...10! and record the answers.
1! 1
2! 2 × 1 =
3! 3 × 2 × 1 =
4! 4 × 3 × 2 × 1 =
…
Remember to use your previous answer to help work out the next one.
Are the answers odd or even? Why? Are you convinced that all further
factorials will be even?
Look at the digital roots, e.g. for 9! 3 + 6 + 2 + 8 + 8 + 0 = 27, 2 + 7 = 9,
so the digital root is 9. What do you notice about the digital roots?
What do you think will happen for further factorials? Why? What do
you notice about the digital roots of multiples of 9? Does this help?
Use a written method, e.g. the grid method, to work out the following
multiplications:
12 × 21
23 × 32
34 × 43
45 × 54
56 × 65
67 × 76
78 × 87
89 × 98
Work out the digital root for each. Can you spot any patterns?
HSNP © Hamilton 2012
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Week 10 Division

The factors of 48 are:
1 and 48
2 and 24
3 and 16
4 and 12
6 and 8
If we add all the factors less than 48, we get 76:
1+2+3+4+6+8+12+16+24=76
48 is called an abundant number because it is less than the sum of its
factors (without itself).
32 has factors 1, 2, 4, 8 and 16 (apart from 32) and the sum of these
factors is 31, so 32 is not an abundant number 
See if you can find some more abundant numbers!

Use a factor tree to find the prime factors of five two-digit numbers.
Try and make the biggest tree that you can!
24
6
3
HSNP © Hamilton 2012
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Shining Term 2 websites
Math matching
http://www.harcourtschool.com/activity/con_math/con_math.html
Fractone http://www.coolmath-games.com/0-fractone/index.html.
Fruit shoot fractions additions
http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractio
nsAddition.htm
Adding and subtracting fractions challenge http://www.mathplay.com/adding-and-subtracting-fractions-game.html
Fruit shoot fractions subtractions
http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractio
nsSubtraction.htm
Adding and subtracting fractions challenge http://www.mathplay.com/adding-and-subtracting-fractions-game.html
Alex’s number plumber http://nrich.maths.org/8387
Fruit shoot
http://www.sheppardsoftware.com/mathgames/fractions/FractionsToDecim
als.htm
Walk the plank http://www.math-play.com/integers-game.html.
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specified on this list (hereafter collectively referred to as the ‘Links’) have been checked by
Hamilton Trust and to the best of Hamilton Trust’s knowledge, are correct and accurate at the
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
and/or contents associated with such Links. Therefore, it is your sole responsibility to verify
any of the Links which you wish you use. Hamilton Trust excludes all responsibility and liability
for any loss or damage arising from the use of any Links.
HSNP © Hamilton 2012
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