Download Hamilton Secondary Numeracy Project Shining Term 2 Homework

Hamilton Secondary Numeracy Project
Shining
Term 2
Homework
Name ___________________________
Decimals and Fractions 1
1. Use a calculator to divide the numerator by the denominator to find the
decimal equivalents of 1/9, 1/99, 1/999… Can you predict the next decimal?
1÷9=
0.1111111
1/9
1/99
1/999
1/9999
1/99999
2. Use a 0-9 dice or 1-9 cards (or remove the 10s, Jacks,
Queens, Kings and Jokers from a set of cards and use Aces as
1s, or write 1-9 on pieces of paper). Roll dice twice (if you roll
0 roll again) or choose two cards to make a fraction less than 1. Multiply it by
2
/3. For example, if you roll a 5 and a 2, multiply 2/5 by 2/3.
How many can you do in two minutes?
2 × 2 = 4
5
3
15
HSNP © Hamilton 2013
Shining Term 2
Page 1
Decimals and Fractions 1
If you have internet access, try this
Play Fractone at bit.ly/13xZBVl.
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, for example, 4/8
and 1/2.
My time was
__________
just right
How did you find these problems?
too hard
too easy
Page 2
Addition 1
Remove the 10s, Jacks, Queens, Kings and Jokers
from a set of cards and use Aces as 1s (or use 1-9
cards or write 1-9 on pieces of paper).
Take two cards to make a fraction. Take two more to make another fraction.
Find the total of the two fractions using ‘smile and kiss’.
Only record the additions with a total of between 1 and 2. How many can you
do in five minutes with totals of between 1 and 2?
8+ 7
8
9
X
9 x 8 = 72
64/72 +
63/72 =
127/72
or 1 55/72
HSNP © Hamilton 2013
Shining Term 2
Page 3
Addition 1
If you have internet access, try this
Play Fruit Shoot Fraction Addition at bit.ly/11fmvhA.
Choose ‘Level 3’ and ‘Relaxed mode’.
Add the pair of fractions shown and click on the fruit with the answer.
Record the additions you complete below. What was your score out of 10?
Level 3a
Score =
just right
Level 3b
__
10
Score =
__
10
How did you find these problems?
too hard
too easy
Page 4
Subtraction 1
1. Roll a dice twice to make a fraction less than one.
Use ‘smile and kiss’ to subtract this fraction from 8/9.
Do three of these.
8
4
−
9X 6
9 x 6 = 54
- 36/54
= 12/54
or 6/27
48/54
2. Solve the following by thinking about how many of each fraction are in
each number. For example, how many halves are in 20?
20 ÷ 1/2
6 ÷ 1/4
There are 2 halves in 1, so
there must be 20 times that
many in 20. 2 x 20 = 40.
10 ÷ 1/4 = 10 x 4/1 = 40
3 ÷ 1/8
7 ÷ 1/6
30 ÷ 1/5
9 ÷ 1/10
HSNP © Hamilton 2013
Shining Term 2
Page 5
Subtraction 1
If you have internet access, try this
Play Adding and Subtracting Fractions Challenge at
bit.ly/13zR7P1.
Click to roll the dice. Draw a card. Add or subtract the
fractions. Carry on until you reach the finish.
My score was
__________
Play Fruit Shoot Fraction Subtractions at
bit.ly/14rZPwq. Choose ‘Level 3’ and ‘Relaxed mode’. Subtract the pair of
given fractions and click on the fruit with the answer. Record the subtractions
and answers below. What was your score?
Level 3a
2/3
Level 3b
+ 2/6 = 1
__
10
just right
__
10
How did you find these problems?
too hard
too easy
Page 6
Multiplication 1
1. Find the squares of the numbers below. Then find the digital root of each
answer. For example, for 342 = 1156. Adding 1 + 1 + 5 + 6 gives 13. To get to a
single digit, add 1 and 3 to get the digital root of 4.
What do you notice about the digital roots of these numbers?
12
23
34
34 x 34
= 1156
1+1+5
+6 = 13
1+3=
4
4
45
56
67
78
I notice that________________________________________________.
Does the pattern work with 89?_________
Does it matter whether the larger digit is first or second?____________
HSNP © Hamilton 2013
Shining Term 2
Page 7
Multiplication 1
If you have internet access, try this
Play the video about Alex’s Number Plumber at
bit.ly/12F8PnE.
Click on the picture under the video 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?
I noticed that…
Choose your own number to enter and see what happens. Keep re-entering
the output as the next input. Look at the results table.
Can you predict the pattern for a new number?
I predict the pattern to be…
just right
How did you find these problems?
too hard
too easy
Page 8
Division 1
1. Work to find the biggest four-digit number 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 you can do better than that!
1236
1236 ÷ 1 = 1236
1236 ÷ 2 = 618
1236 ÷ 3 = 412
1236 ÷ 6 = 206
HSNP © Hamilton 2013
Shining Term 2
Page 9
Division 1
2. Roll two dice (or choose numbers using 1-6 cards) to make
a fraction less than 1. Divide it by 1/4. For example, if you roll
a 5 and a 2, divide 2/5 by 1/4.
How many can you do in two minutes?
2 ÷ 1 = 8
5
4
5
3. 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?
63 ÷ 20 = 3 r3
63 ÷ 3 = 21
just right
X
How did you find these problems?
too hard
too easy
Page 10
Decimals and Fractions 2
1. Use a calculator to find the decimal equivalents for 1/13, 2/13, 3/13 and so
on up to 12/13.
1/13 = 1 ÷ 13
0.076923
7/13 = 7 ÷ 13
2/13 = 2 ÷ 13
8/13 = 8 ÷ 13
3/13 = 3 ÷ 13
9/13 = 9 ÷ 13
4/13 = 4 ÷ 13
10/13 = 10 ÷ 13
5/13 = 5 ÷ 13
11/13 = 11 ÷ 13
6/13 = 6 ÷ 13
12/13 = 12 ÷ 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?
HSNP © Hamilton 2013
Shining Term 2
Page 11
Decimals and Fractions 2
If you have internet access, try this
Play Fruit Shoot at bit.ly/12S4dHe.
Start with ‘Level 4’. Click on fruits with decimal equivalents to the given
fractions. Record your score.
Now have a go at ‘Level 5’!
Level 4 score
Level 5 score
__________
__________
just right
How did you find these problems?
too hard
too easy
Page 12
Addition 2
1. 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
1 7 21 35 35 21 7 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.
I noticed that…
HSNP © Hamilton 2013
Shining Term 2
Page 13
Addition 2
2. Use the internet to research Fibonacci sequences and spirals in nature.
Write about one fact which you found interesting.
I found out…
3.
0
1
1
2
4
7
13
24
44
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 17
numbers.
What patterns can you find? Is there a pattern of odd and even numbers?
I noticed…
just right
How did you find these problems?
too hard
too easy
Page 14
Subtraction 2
1. 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.
15 – 8 = 7
J
2. Roll a 0 to 9 dice (roll again if you roll a 0)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.
4 4 – (-7) = 11
7
-7
0
HSNP © Hamilton 2013
4
Shining Term 2
Page 15
Subtraction 2
If you have internet access, try this
Play Walk the Plank at bit.ly/16d1IQY.
Choose hair and skin colours for the person you
want to walk the plank.
You will be asked a question. Roll the mouse over the pirates to see their
answers. Click 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.
Did you make the person
walk the plank? ________
Score __________
just right
How did you find these problems?
too hard
too easy
Page 16
Multiplication 2
Work out 1! 2! 3! up to 10! and record the answers below. Remember to use
your previous answer to help work out the next one.
Are all the answers odd or
even?
1! 1
2! 2 × 1 = 2
3! 3 × 2 × 1 =
4! 4 × 3 × 2 × 1 =
5! 5 x 4 x 3 x 2 x 1 =
6! 6 x 5 x 4 x 3 x 2 x 1 =
7! 7 x 6 x 5 x 4 x 3 x 2 x 1 =
8! 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =
9! 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =
10! 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
=
Why?
Will all further factorials be the
same?
2. Now look at the digital roots.
For example, 9! 3 + 6 + 2 + 8 + 8 + 0 = 27. Add 2 + 7 to get 9, so the digital
root is 9.
What do the digital roots have in common?
What do you think will happen to further factorials?
Why?
What do you notice about the digital roots of multiples of 9?
HSNP © Hamilton 2013
Shining Term 2
Page 17
Multiplication 2
3. Use a written method, to work out the following multiplications. Work out
the digital root for each.
Can you spot any patterns? ________________________________________________
12 x 21
Digital root
x
10
2
20
200
40
1
10
2
34 x 43
252 = 2 + 5
+2=9
Digital root
45 x 54
Digital root
67 x 76
Digital root
89 x 98
Digital root
x
Digital root
x
23 x 32
x
56 x 65
Digital root
x
x
78 x 87
x
Digital root
x
just right
How did you find these problems?
too hard
too easy
Page 18
Division 2
The factors of 48 are:
1. If we add all the factors of
1 and 48
48 less than 48, we get 76.
2 and 24
1+2+3+4+6+8+12+16+24=76
3 and 16
48 is called an abundant
4 and 12
number because it is less than
6 and 8
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!
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 X
1 + 2 + 3 + 4 + 6 + 8 + 12 = 36
36 > 24, so 24 is an abundant number.
HSNP © Hamilton 2013
Shining Term 2
Page 19
Division 2
2. Use factor trees to find the prime factors of
five two-digit numbers. Try and make the
biggest tree that you can!
just right
How did you find these problems?
too hard
too easy
Page 20
Shining websites
Fractone
bit.ly/13xZBVl or
www.coolmath-games.com/0-fractone/index.html
Fruit Shoot Fraction Additions
bit.ly/11fmvhA or
www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsAddition.htm
Adding and Subtracting Fractions Challenge
bit.ly/13zR7P1 or
www.math-play.com/adding-and-subtracting-fractions-game.html
Fruit Shoot Fraction Subtractions
bit.ly/14rZPwq or
www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsSubtraction.
htm
Alex’s Number Plumber
bit.ly/12F8PnE or
nrich.maths.org/8387
Fruit Shoot
bit.ly/12S4dHe or
sheppardsoftware.com/mathgames/fractions/FractionsToDecimals.htm
Walk the Plank
bit.ly/16d1IQY or
www.math-play.com/integers-game.html
The links to the websites and the contents of the web pages associated with such links 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.
Well done!
You’ve finished
Shining
Term 2