Transcript Y5T2U2D1_5 - Primary Resources

L.O.1
To be able to identify factor pairs of
small 2-digit numbers
36
A factor is a number that goes into
another exactly.
One factor of 36 is 9, what is its pair?
Write the other factor pairs of 36.
Factor pairs of 36 are:
9 x 4
= 36
3 x 12
= 36
18 x 2
= 36
1 x 36
= 36
6 x 6
= 36
The number 36 is special as one factor pair has
two identical numbers - 6 x 6.
Q. What do we call numbers like 36?
36 is a
square number.
In your book write the factor pairs for :
40
24
64
Two minutes
L.O.2
To be able to use factors as a strategy
for mental multiplication.
LOOOOOK!
4X3X5
Q. How would you work this out in your
head?
The operation of multiplication is commutative…..
a sum can be done in different ways.
4x3x5
e.g.
4 x 3 = 12 x 5 = 60
4 x 5 = 20 x 3 = 60
3 x 5 = 15 x 4 = 60
The answer is the same whichever way you do it.
Try doing these in different ways in your
books.
1.
15 x 3 x 2
1. 2 x 3 x 4 x 5
Four minutes
LOOOOOOK!
17 x 12
This may look hard but isn’t once we find the
factors.
Q. What factors can we find for 17 and 12
17 x 12 = 17 x 3 x 2 x 2
Q. How does this make the calculation
easier?
We can multiply 17 by 3 then double and
double.
e.g. 17 x
12
17 x
6 x 2
17 x 3 x 2 x 2
=
51 x 2 x 2 = 102 x 2 = 204
Work in pairs and use this method to find
answers to :
23 x 6
17 x 4
19 x 8
Not long
26 x 6
To help us do this sum we will find factor pairs for
each number.
26 x 6 = ( 2 x 13 ) x ( 2 x 3 )
= 3 x 13 x 2 x 2
= 39 x 2 x 2
= 78 x 2
= 156
Let’s try : 34 x 6
Calculations for you to do in the same way :
Prisms : 14 x 8 ; 23 x 6 ; 24 x 9 ; 18 x 22
16 x 9 ; 27 x 12
Spheres: 15 x 9 ; 11 x 12 ; 14 x 6 ; 16 x 8
Tetrahedrons: 14 x 8 ; 16 x 6 ; 13 x 15
Here’s one to do as a class…..
22 x 18
By the end of the lesson children
should be able to:
Use factors to carry out
multiplication mentally.
L.O.1
To be able to order a set of positive
and negative integers
Copy this number line into your books:
-20
0
+20
We need 6 numbers which will fit somewhere on
your line.
The numbers are :
Put the numbers in the correct place on your
line.
If we change the sign for each number so that
positive numbers become negative and
negative numbers become positive we get :
Q. How will the numbers change on the number
line?
A. …….
Draw a new number line and insert the new
numbers.
The new numbers become a reflection about 0.
Loooooook!
Mirror
-6
6
-20
20
0
Draw another number line and put in these
numbers:
-14 ; 8 ; -9 ; 10 ; 3 ; -17 .
Now change the signs and insert the new
numbers – use a different colour.
Check your partner’s!
4 minutes
L.O.2
To be able to solve simple word
problems.
To begin to use brackets.
Fish £2 Chips £1
Q. I have just spent £9. What could I have
bought?
Q. How many fish could I have bought?
A good way to sort all the possibilities is like this:
Fish
Chips
0
9
You can see there are
1
7
2
5
3
3
4
1
5 possible combinations.
Try this:
Cola 50p. Pizza £1:50
Q. If I spend £8 what could I buy?
Record your working in the same way as
the problem we have just done.
Q. How many possible combinations are
there?
Create a similar problem for the other
pairs on your table to answer.
5 minutes
Let’s go back to our first problem
Fish £2 : Chips £1
A child goes to the chip shop and asks for
“Two fish and chips”. The owner asks for
£6. but the child expects to be charged
only £5.
Q. Can you explain why?
“ two ( fish and chips)” : “ ( two fish ) and chips”
Q. What is the difference between the two
statements?
Using brackets can help us solve the problem.
2 x ( £2 + £1)
:
( 2 x £2 ) + £1
The brackets help remove confusion.
REMEMBER
THE STEP IN BRACKETS
IS
ALWAYS DONE
FIRST !
compare
6+3–2
6–3 + 2
Q. How would you work out this calculation?
Consider these:
(6 + 3) – 2 = 7
9 -2=7
compare:
6 –3 +4 = ?
(6 – 3) + 4 = 5
6 - ( 3 + 4) = -1
6+(3-2) =7
6 +
1
=7
6 – 3 +2 =?
6–(3 +2)=1
(6 – 3 ) + 2 = 5
We will try to get as close to a target number
as we can using 3 digits, 5 signs and
some brackets.
Target Number = 30
Digits are 6 ; 4 ; and 1.
(6 x 4)+1=25
(6-1)x4=20
(6+1)x4=28
6 x (4+1)=30
With a partner choose a target number between 20
and 50. Use 3 rolls of the die to give you the
digits you need. Get as close to your target
number as you can.
Record your attempts in your book.
Prisms : 4 different target numbers.
Circles : 3 different target numbers.
Tetrahedra : 2 different target numbers.
5 minutes maximum
Try these in your book:
4+2x3
4+2+3
4x 2x3
4 –2x3
You can use brackets anywhere.
Q. Which calculation could give the biggest /
smallest answer? Why?
By the end of the lesson children
should be able to:
Use brackets,
Solve simple word problems by
listing.
L.O.1
To be able to use doubling and
halving starting from known facts.
7
Double this ad infinitum.
Now halve the last number!
24 x 4 = 24 x 2 x 2
Q. How can we work out the answer to
24 x 4 using the above statement?
A.
……
48 X 2
To multiply by 4 we use doubling then
doubling again.
As 2 is a factor of 4 this method is really
using factors.
560 ÷ 4
Q. How can we work this out?
(560 ÷ 2) ÷ 2
Dividing by 2 is the same as halving and
halving again.
Look : 560 ÷ 2 = 280
280 ÷ 2 = 140
L.O.2
To be able to use all four operations to
solve simple word problems.
To begin to use brackets.
1.
3.
5.
7.
48 ÷ 8
617 – 322
23 – 17
( 12 ÷ 2 ) x 2
2.
4.
6.
8.
43 + 27 + 12 +17
(33 – 18) x 2
(3 + 5) x 2
36 ÷ ( 4 + 2 )
Brackets always indicate the first stage of a calculation.
Q. In a class of 33 children, 18 had no pets, the others had
two pets each. How many pets is that?
Which calculation from those shown would you use to
solve this problem?
1. 48 ÷ 8
2.
43 + 27 + 12 +17
3. 617 – 322
4.
(33 – 18) x 2
5. 23 – 17
6.
(3 + 5) x 2
7. ( 12 ÷ 2 ) x 2
8.
36 ÷ ( 4 + 2 )
With a partner work out some word- based
problems for which the other calculations on the
board will be the solutions :
Prisms – do all 7
Spheres – do at least 5
Tetrahedra – do at least 3
10 minutes
A. ….. Read problems aloud.
Q. Which calculation matches the word
problem? How did you decide?
Work out a calculation ON YOUR OWN
using all four operations and develop a
word problem from it.
Make it as interesting as possible.
A. ……
The answer to a problem is “ 37 legs”.
With a partner make up an interesting
word problem which has this answer.
By the end of the lesson children should be
able to :
Solve “story problems about numbers in real
life, choosing the appropriate operation and
method of calculation.
Explain and record using numbers, signs
and symbols how the problem was solved.
L.O.1
To develop calculator skills and use a
calculator effectively.
To begin to use brackets
A class of 37 children were deciding what type of
drink they should have when they go on their
day out. 15 children said they would like cola, 17
said they would like orange and the remainder
said they would like fruit juice.
Cola and orange cost 35p. Fruit juice costs 25p.
Work in pairs to calculate how much the drinks would
cost for the class. Record every calculation you make.
We will check your working to see whose
strategy was the most efficient .
( 37 x 0.35 ) – ( 5 x 0.08 )
Work out the answer to this problem using
your calculators.
This calculation gives the answer to the problem on the last screen.
Q. How does this calculation work?
L.O.2
To be able to check with the inverse
operation when using a calculator.
To be able to use all four operations to
solve simple word problems.
22 children have each received the same
number of merits. Between them they
have 242 merits. How many merits does
each child have?
Q. What calculation would I carry out to solve this
problem.
The calculation will be :
242 ÷ 22 = 11
Q. What calculation would I carry out to
check that the answer is 11?
The calculation will be :
22 x 11 = 242
This checks that the calculation is correct by
“using the inverse operation”.
A reading book is 14mm wide. There are
36 reading books on the classroom shelf.
The shelf is 65 cm wide.
How much space is left on the shelf?
Q. What calculation would I carry out to solve this problem?
The calculation is :
650 – ( 36 x 14 )
CANS
BOXES
CHILDREN
MONEY
TIME
WEIGHT
Work with a partner to make up some word
problems. Each word problem must contain at
least two of the above words.
For each problem you make you should record
the calculation needed to solve the problem.
8 minutes
This screen is blank so some of you can record your
problems and the calculations needed to solve them.
We may check some of your calculations by using the
inverse operation.
( 18 x 7 ) + 3
18 x ( 7 + 3 )
Work in pairs to produce a word problem for
each calculation. The 18 must represent
children and the 7 must be pounds.
Q. What could the 3 represent?
Q. Why must the 3 be money if the problem is to make sense?
By the end of the lesson the children should
be able to:
Check an answer by performing the
inverse calculation.
Solve “story” problems about numbers in
real life by choosing the most appropriate
operation and method of calculation.
L.O.1
To be able to add or subtract any pair
of 2-digit numbers, including crossing
100
23
57
Q. What is the sum of these numbers?
Q. What is the difference between these numbers?
Write the answers in your books.
I am going to choose a number that is greater
than 50 and is also a multiple of 5.
Q. What number might I choose?
Before I choose my number you must write in
your book a 2-digit number which, when added
to mine, will also give a multiple of 5.
My number is
65.
Work out the sum of our two numbers and
also the difference between the two.
I am going to choose a number below 50 which
is a multiple of four.
Q. Which number might I choose?
Before I choose my number you must write in
your book a 2-digit number which, when added
to mine, makes 100.
My number is 44.
Work out the sum of our numbers and also
the difference between the two.
I am going to choose a number which is less
than 30 but which is a multiple of 6.
Q. Which number might I choose?
Before I choose my number you must write in
your book a number which, when multiplied by
mine, gets as close to 100 as possible.
My number is 18.
Work out the sum of our two numbers, the
difference between the two and their product.
L.O.2
To be able to solve problems.
To be able to choose appropriate
methods and operations.
What does a large mushroom pizza cost?
With an extra topping of cheese?
NOW DO PART ‘A’
Q. For question 1, did you find the cost of toppings first or
start with the cost of the pizza? Which method is easier?
Q. For question 4, did you work out the cost of each pizza
and then add them together or list the items and add
them?
Q. What calculations did you use for Q.2 and Q.3?
The calculations are :
Question 2 :
(2 x £4.65 ) + £4.50
Question 3 :
£3.80 + £0.60 + £5.80 + £0.40
The only operations used were addition and
multiplication and brackets were not always
needed.
Do part ‘B’. You may use a calculator if
you wish.
Remember to record your calculations.
A sensible approach is to take away the cost of
the toppings which total £ 1.00 so the pizzas
must cost £9 or less.
Was the calculator helpful in solving the problem
in part ‘B’?
3, 4 ,5
You are going to find sets of 3 consecutive
numbers.
For one of the numbers 3 will be a factor, for
another one 4 will be a factor and 5 will be a factor
of the other number.
One group is 8, 9, 10 because
4 is a factor of 8; 3 is a factor of 9; 5 is a factor of 10.
The factors do not have to be in the order 3,4,5.
What answers did you find?
Q. What numbers did you try and why?
Q. As 5 is a factor what can you say about one of
the consecutive numbers?
end in 5 or 0
Q. As 4 is a factor what must one of the other
numbers be?
even
100
Q. What 3 consecutive numbers can we try if 100
is to be one of them?
Remember one number must end in 5 or 0 and
another must be even so they could be
98, 99,100, or
100,101,102
but not 99, 100, 101 as neither 99 nor 101 is even.
Q. Which of the other sets of numbers can be
discarded? Why?
We can discard these:
100,101,102
One number ends in 5 or 0.
One number is even but not a multiple of 4.
Dividing by 4 is the same as halving and halving
again. Half of 102 is 51 so 4 will not divide into
102.
Q. Does 3 divide into 99?
3 does divide into 99
but
we can discard 98, 99, 100
as
although one number ends in 5 or 0
the other even number is not a multiple of 4
since half of 98 is 49 and cannot be halved
again so 4 does not divide into 98.
So neither set of numbers works.
Even though you could have used a
calculator it may be more efficient to solve
a problem by applying what you know
about numbers.
By the end of the lesson children should be
able to:
Solve ‘story’ problems about numbers in
real life choosing the appropriate operation
and method of calculation.
Make and justify decisions.