Download Divide by 3. Stg 5 x - Ngahinapouri School

Divide by 3.
Stg 5 x/÷
Name: __________________________
Let’s try chopping things up into 3 equal groups. That’s all division is really – the opposite of multiplying. Say
you had 9 rhubarb pies to share out with you and two other buddies. If you start by giving everybody one,
then another and so on, how many do they get each? Try putting little circles in each oval to show the pies:
Dave
So, what does the maths look like for this?
Tim
Leonie
9 ÷ 3 = ___
OK, good. Let’s try another. Mrs C. Atladi had 3 cats, but she was starting to run low on kitty treats. There
were only 21 left in the bag. How did she share them out so they all had the same fair amount?
So, what does the maths look like for this?
21 ÷ 3 = ___
By now though you might be able to see that we can find the same answers
in a quicker way. What if we took a large number and just counted the sets of 3
we find. Have a look at the 18 marbles in a line below. How many sets of 3 can you make?
18 ÷ 3 = ____
24 ÷ 3 = ____
15 ÷ 3 = ____
27 ÷ 3 = ____
What about if we used a ruler instead of all these random things? We nearly always have a ruler handy, and
all the numbers are printed on it already. Remember to count the spaces, not the marks! How many sets of 3
do you need to get to 30?
30 ÷ 3 = ____
How about 12?
12÷ 3 = ____
Have another go at 21, see if it comes out the same:
21÷ 3 = ____
•
Use the ruler above to see how many 3s fit in 6, 18 and 27
Dave Moran v2 2016
Divide by 3.
Stg E6 x/÷
Name: __________________________
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
3 x 4 = ___
3 x 7 = ___
3 x 5 = ___
3 x 9 = ___
3 x 11 = ___
3 x 2 = ___
3 x 8 = ___
3 x 12 = ___
3 x 6 = ___
3 x 10 = ___
So __ ÷ 3 = 4
So __ ÷ 3 = 7
So __ ÷ 3 = 5
So __ ÷ 3 = 9
So __ ÷ 3 = 11
So __ ÷ 3 = 2
So __ ÷ 3 = 8
So __ ÷ 3 = 12
So __ ÷ 3 = 6
So __ ÷ 3 = 10
and
and
and
and
and
and
and
and
and
and
___ ÷ 4 = 3
___ ÷ 7 = 3
___ ÷ 5 = 3
___ ÷ 9 = 3
___ ÷ 11 = 3
___ ÷ 2 = 3
___ ÷ 8 = 3
___ ÷ 12 = 3
___ ÷ 6 = 3
___ ÷ 10 = 3
Son: "My teacher is crazy".
Mother: "Why?"
Son: "Yesterday she told us that five is 4+1; today
she is telling us that five is 3 + 2."
Sadly, there is no super easy trick for dividing by 3… Or is there? If you know your 3 times tables
you might be alright! Using the family of facts will help you to divide multiples of 3 by 3.
E.g. What is 9 ÷ 3? We know that 3 x 3 = 9, so using the ‘family’ we know 9 ÷ 3 = 3
Try these ones to build up your division basic facts:
Ok, but what if the number I’m dividing doesn’t fit? Like if it’s not a multiple of 3? Now it starts to get
interesting, because we start to learn about ‘remainders’ – the leftover bits.
E.g 20 ÷ 3 = ?? Oh no, it doesn’t fit! We know that 18 ÷ 3 = 6, and that 21 ÷ 3 = 7. Hmm. We just choose the
one that fits inside 20 (18), then take away 18 from 20 (20 – 18 = 2) So 20 ÷ 3 = 6 r2 That’s 6 with a
‘remainder’ of 2. Well that makes sense! Let’s try:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
8 ÷ 3 = __ r __
5÷3= 1 r2
13 ÷ 3 = __ r __
29 ÷ 3 = __ r __
26 ÷ 3 = __ r __
34 ÷ 3 = __ r __
23 ÷ 3 = __ r __
10 ÷ 3 = __ r __
43 ÷ 3 = __ r __
50 ÷ 3 = __ r __
61 ÷ 3 = __ r __
122 ÷ 3 = __ r __
31 ÷ 3 = __ r __
20 ÷ 3 = __ r __
3x2 =6
3 x ___ = 3
3 x ___ = 12
3 x ___ = 27
3 x ___ = 24
3 x ___ = 33
3 x ___ = 21
3 x ___ = 9
3 x ___ = 42
3 x ___ = 48
3 x ___ = 60
3 x ___ = 120
3 x ___ = 30
3 x ___ = 18
8 - 6 = 2 (remainder)
5 - 3 = ___ (r) Tip: to check if a
13 - 12 = ___ (r) number is divisible
29 - 27 = ___ (r) by 3, add up its
If they add up
26 - 24 = ___ (r) digits.
to a multiple of 3,
34 - 33 = ___ (r) you can ÷ 3! Check:
23 - 21 = ___ (r) 36: 3 + 6 = 9
2+7=9
10 - 9 = ___ (r) 27:
24: 2 + 4 = 6
43 - 42 = ___ (r) 105: 1 + 0 + 5 = 6
50 - 48 = ___ (r)
61 - 60 = ___ (r)
122 - 120 = ___ (r)
31 - 30 = ___ (r)
20 - 18 = ___ (r)
You’ll notice that the remainders are either 1 or 2. It can’t be 3 or more or else it becomes another multiple.
Why do we need to know about remainders? They help us with the next level of chopping up, called ‘fast long
division’. Long division can help us to divide any number by 3 (or whatever). All we need is our basic facts and
to know what remainders are!
Maths inquiry: They say that 2520 is the smallest number that can be neatly divided
by all of the numbers 1 to 10 (Write out a table in your maths book)
Dave Moran v2 2016
Stg 6/E7 x/÷
Divide by 3.
Name: _________________________
Learning how to do fast long-division is something you’ve always wanted, I can tell. It’s the sort of request
that Santa gets all the time. Well maybe not, but it is a handy skill. Here’s the thing, interesting numbers
hardly ever divide neatly into sets. So how do we solve a nasty like 234 ÷ 3? The answer (as it often is) is to
split it into smaller easier bits! In this case it’s actually kind of fun too!
1. Look at numbers that can be divided by 3, starting on the left. The ‘2’ in the 100s
column is too small, so go to ‘23’. (it’s actually 23 tens BTW)
2. 23 ÷ 3 = 7 r2 (23-21=2) Put the ‘7’ above on the answer line
3. Put the r2 in the 1s column on the left of the 4. to make ‘24’
78
3 2 324
4. 24 ÷3 = 8. Put the ‘8’ in the 1s place on the answer line – all done! Answer: 78
To see a video of this technique in action, scan the QR code here
with your tablet.
Why did the student do division strategy problems on the floor?
The teacher told her not to use tables!... Oh dear, I’m so sorry.
The time has come, my little minions of maths, to have a try for your selves:
a. 3 5 4 6
b. 3 2 7 0
c. 3 9 8 4
d. 3 4 3 5
e. 3 7 8 4 2
f. 3 9 0 4 5
g. 3 3 7 0 2
h. 3 9 5 7
Next, don’t forget to stick in the remainder at the end! How would you turn the remainder into a decimal?
Hint: 1 ÷ 3 = 0.33(recurring) – so a remainder of 2, would be 2 x 0.33 = 0.66 (It’s OK to stop at 2 decimal places
for what we’re doing here, they’d go on forever if you didn’t stop them. Yadda yadda.
r
r
r
r
i. 3 8 6 5 3
j. 3 2 3 4 8
k. 3 1 0 9 6
l. 3 2 0 0 9
m. 3 4 3 2 9
n. 3 2 8 5 6
o. 3 9 8 6 5
p. 3 8 7 2
Lovely! Ready for some ‘harder’ ones? Really, not too tricky once you’re in the swing of it though!
.
q. 3 7 8.4 5
u. 3 5 2 2 8 4
.
.
r. 3 1 0. 3
s. 3 4 5 6 .7
v. 3 3 9 6 6 3
A number is divisible by 3 when the sum of its digits can be divided by 3.
Eg 3702. 3 + 7 + 0 + 2 = 12, 12 ÷ 3 = 4 (3702 ÷ 3 = 1234)
.
t. 3 2.9 1 6
x. 3 4 8 2 5 7 0 2
Dave Moran v2 2016