Using halves.
Stg 5
props & rats
Name: _________________________
Halves, for some reason, are the easiest fraction for folks to get their heads around. If someone asks you to
chop a muffin in half to share with your sister/brother – and they choose – you can bet your halving will be
microscopically accurate. On that note, have a look at these shapes – Use a ruler to see if you can draw a
line through that chops them exactly in half. – Both sides must be equal. (You might find there
is more than one way to chop it up – just choose one)
Let’s have a closer look at what a half is as a number. It’s kind of special in that it has its own name for a start –
there’s no such thing as ‘twoths’! (Although there should be, it sounds awesome).
The top number (the numerator) tells you it’s one part.
The bottom bit (the denominator) tells you it’s been chopped into
2 parts.
1
2
N.B. Halves can be shown as a decimal or a percentage as well:
1
2
= ÷2
= 0.5 = 50%
Here’s a question though – can you have halves of numbers or sets? Well, of course you can!
Any even number can easily be halved – try halving some of these cheeky little fellas here:
1/2 of 6 = __
1/2 of 8 = __
1/2 of 12 = __
1/2 of 16 = __
OK, this time without pictures: (You can use counters if you get stuck)
1. 1/2 of 18 = ___
2. 1/2 of 20 = ___
3. 1/2 of 26 = ___
4. 1/2 of 28 = ___
5. 1/2 of 14 = ___
6. 1/2 of 48 = ___
7. 1/2 of 4 = ___
8. 1/2 of 46 = ___
9. 1/2 of 42 = ___
‘One half’ in Te Reo Māori is ‘kotahi haurua’.
Dave Moran V2 2016
Using halves. Stg E6
props & rats
Name: _________________________
The many names of half – when we were chopping numbers in half, a thought may have occurred to you – if I
can say 4 is half of 8 (for example) can I also say that 4/8ths is the same as ½? How very insightful, you clever
thing! Yes, you can say that. These are called ‘equivalent fractions’. See if you can figure out whether these
fractions are equivalent to ½ or not: (Tip: odd numbers are tricky to halve)
= 1
2
True
False
4 eighths
True
= 1
2
False
1
2
True
=
False
True
1
2
7 = 1
2
14
True
9 = 1
2
18
True
False
False
=
False
1 third
5 elevenths
1
2
True
1
2
True
False
2 quarters
6 tenths
=
=
False
6 twelfths
3 = 1
2
7
True
50 = 1
2
100
True
False
False
12 = 1
2
24
True
9 = 1
2
19
True
False
False
Here’s a thought. Can you have a fraction that is more than one whole? You sure can, but naturally, you need
another whole. We know 2 halves (2/2) is the whole thing. So what would 3/2 look like? The circles are still
chopped into halves, but now there is a whole circle plus another piece.
Shade
Shade
3
2
5
2
Shade
4
2
Shade
7
2
I could also figure out how many halves would be in a mixed fraction.
Say I had 1 and 1/2 pies. How many halves is that? I can see 1/2, and I know there are 2 halves in the whole pie.
So 2 + 1 = 3. There are 3 halves, or 3/2
a.
b.
c.
d.
e.
2 1/2 =
3 1/2 =
5 1/2 =
7 1/2 =
4 2/2 =
(4/2 + 1/2) = ____ (Tip: when adding fractions, leave the denominator, just add the tops)
(6/2 + 1/2) = ____ (Show your answers as an improper fraction)
(10/2 + 1/2) = ____
Slightly useless fact: In the old days to ‘halve’ something
(14/2 + 1/2) = ____
simply meant to divide it up. Now we use it to talk about
splitting something into precisely 2 equal parts
(8/2 + 2/2) = ____
Dave Moran V2 2016
Using halves. Stg E7
props & rats
Name: _________________________
How to halve any number. Any number at all, even funny looking ones. As we know ½ has many names, like
0.5, 50 %, any equivalent fraction, or ÷ 2. In fact knowing that halving is the same as dividing by 2 is very
useful for the strategy we’re learning today.
OK, you’ve done this before! Easily the most efficient way to divide big numbers by 2 is to use the fast long
division standard form shown below. Once you have practiced and mastered this method you are set, and the
whole world (of halving) is open to you! Try halving 59.2
2 9. 6
2 519.12
1. Look at numbers that can be divided by 2, starting on the left. The ‘5’ in the 10s column
can fit 2 2s with 1 left over Put the ‘2’ above on the answer line, and the leftover 1 beside
the 9 to make 19
2. 19 ÷ 2 = 9 r1 Put the ‘9’ above on the answer line
3. Put the r1 in the 10ths column on the left of the 2, to make ‘12’
4. 12 ÷ 2 = 6. Put the ‘6’ in the 10ths place on the answer line – all done! Answer: 29.6
Feeling some deja vu? Yes, it’s very much like the other types of division you know and love – you can use the
same idea with any fractions actually. So, let’s have a go at chopping some interesting numbers in half. Keep
your place value!
a. 2 7 8.4 8
e. 2 5 2 2 8 4
b. 2 1 0.3 7
f. 2 3 9 6 6 3
h. 2 3 1.6 8
i. 2 1 5. 17
l. 2 2 3 4 5 6
m. 2 9 8 7 6 5
o. 2 9 9.3 8
p. 2 1 9.1 7
s. 2 8 3 2 8 1
v. 2 7 1.4 4
z. 2 0.0 5 2 7
c. 2 4 5 6.7
g. 2 4 8 2 5 7 0 2
j. 2 6 5.3 7
k. 2 1.0 0 6
n. 2 1 3 5 7 9 0 2
q. 2 3 7 2.7
t. 2 5 4 4 6 3
w. 2 1 1.7 7
d. 2 2.9 1 6
r. 2 2.0 7 0
u. 2 5 9 3 6 8 9 3
x. 2 6 7 8.9
y. 2 4.1 3 8
aa. 2 0.3 0 0 7
Dave Moran V2 2016
Using halves. Stg E7
props & rats
Name: _________________________
Halving inquiry: What’s the use of all this halving stuff then? Like most maths, there is actually a purpose for it
somewhere. Also like many real-life situations, it’s realty about problem solving. For example, no-one ever
comes up to you desperately needing to know what 6 x 1.37 is. But you might come across a situation where
you want to buy a half dozen cans of fizz, they are on sale for $1.37 each. How much will it cost me? So, this
leads us to today’s inquiry – the first thing to do is figure out what kind of maths you need (operations). Then,
how do they work together to solve the whole problem? Try this one.
Problem one: Iesha and Leah were doing some fund-raising for a school camp together. At the end they
needed to split the money raised equally. During their weeks fundraising they kept a record of the money they took in. Use what you
know about adding up to get the total. Then use another skill to
Bake Sale $23.50
divide that total into 2 equal parts. – Watch your place value!
Christmas cards $46.20
Sausage sizzle $107.70
Yard work $55.00
Cupcakes $19.50
Dog walking $68.40
Working out space
Problem two: Nick and Yash decided to build a Lego robot together, and agreed to pay half each for the parts
they needed. Here’s a list of the pieces and the prices – how much do they need to pay each?
Robot brain (evil version): $199.00
Android app $2.99
‘Eye’ remote camera $39.99
Tank track wheels: $45.70
Servo controlled arms (both) $93.20
Remote I.R. receiver $29.90
Clamp ‘hands’ x 2, (each) $18.50
360 degree rotating torso $118.60
Problem three: Holly and Tate earned a whole lot of house points over the term doing jobs around the class,
They belong to different houses, so needed to split them up evenly. How many points each can they record?
Putting up chairs: 3300 pts, Dusting shelves: 2400 pts, Shelving books: 3140 pts, Being polite: 450pts, Helping
on Ag day: 9500 pts, Looking after a new girl: 500 pts, washing Edmond the mini: 12000 pts, feeding Tui the cat:
8320 pts, Handing out notices 520 pts, Cleaning up after Tui the cat had an ‘accident’ 90 000 pts.
Dave Moran V2 2016