2. L.O.1
To be able to read and write whole
numbers and know what each digit
represents.
3. 347 256
In your book write the value of
each digit as it is pointed to.
4. 347 256Use the last answer you made to start each calculation and
write the new answer in your book each time.
1. Add 40 000 to 347 256.
2. Add 300
3. Subtract 100 000
4. Add 6000
5. Subtract 4
6. Subtract 50 000
7. Add 700
8. Add 20
5. L.O.2
To be able to solve a problem by
representing and interpreting data in tally
charts and bar charts.
6. Q. Which number is most likely to turn up
when a normal 1 – 6 die is rolled?
I will roll this die until I reach 20 or more and
you will need to keep a record in your books
of the running total.
Before I begin you will need to predict and
we will record how many times you think I
will need to roll the die to reach my total.
7. Now we’ll try again.
First we will record your predictions.
And again!
8. Q. Is it possible to predict the number of rolls
needed to get a total of 20 or more?
Q. Suppose I put a number 3 on each face,
could we predict how many rolls we would
need to get a total of 20 or more?
Q. How accurate would our prediction be?
Why?
9. This time the target is 24 or more and there will
be a normal 1 – 6 die.
Q. What could be the greatest number of rolls
needed to score 24 or more? What could
the fewest number of rolls be?
Work with a partner and conduct this experiment
10 times. Each time record the number of rolls
you needed to reach 24 or more.
10. Q. Did anyone get a 24 in exactly 24 rolls or in
exactly 4 rolls?
I want to collect the class results and
put them on a chart.
Q. How can we collect and display the class’
results?
Would a tally chart or a bar chart be useful?
11. Work with the people on your table to
collect all your experiment results
using tallies and counting the
different numbers of
rolls taken.
12. In order to collect the class’ results we are
going to write the results from each group
in the middle column of OHT 8.1.then
work
out the totals.
14. REMEMBER…
The total in the final column is called the
Frequency
of the number of rolls taken.
15. Q. Which number of rolls was the most
frequent? Which was the least?
Answer these:
1. Which frequencies occurred more than ¼ the time?
2. Which occurred less than 1/3 the time?
3. Which occurred exactly half the time?
4. Which occurred twice as much as any others?
16. OHT 8.1 can be turned round so the totals
can be shown as a
BAR CHART
with the horizontal axis showing the
NUMBER OF ROLLS
and the vertical axis showing the
FREQUENCIES
.
18. Q. If we are to draw this bar chart what scale
do we need on the vertical axis?
When the scale has been decided you may
each draw the bar chart on your squared paper.
19. By the end of the lesson the children
should be able to:
Test a hypothesis from a simple
experiment;
Discuss a bar chart showing the
frequency of the event;
Discuss questions such as “Which
number was rolled most often?”
21. L.O.1
To be able to order a set of positive and
negative integers
22. Place the numbers in their correct position on
the number line. – Volunteers!
-10 18 - 4 - 16
4 - 11 17 - 9
9 -14 2 15
-20 200
23. Write the numbers in order in your book
starting with the lowest.
- 10 18 - 4 - 16
4 - 11 17 - 9
9 - 14 2 15
24. Now try these - starting with the lowest.
- 16 11 - 6 - 17
14 - 8 17 - 10
7 - 19 1 -15
25. Prisms and spheres only.
Order these starting with the highest:
23 -19 18 -7
-5 -22 -11 29 -4
-13 6 25 -28 34
-17 -30 16 27 -1
26. L.O.2
To be able to solve a problem by representing
and interpreting data in bar line charts where
intermediate points have no meaning, including
those generated by a computer.
27. Yesterday we rolled dice to make 24 or more.
Rolling 24 1’s to make 24 was
VERY UNLIKELY.
Which numbers of rolls of the dice appear to be
MOST LIKELY …. LEAST LIKELY ?
28. We are going to do some more
experiments using dice.
What is happening in this sequence of
numbers?
2, 3, 5 (3)
What is happening now?
2, 3, 5, 1 (4)
29. Q. What is happening in these sequences?
3, 3, 5, 6, 2 (5)
1, 2, 4, 2, (4)
3, 4, 5, 6, 3 (5)
1, 5, 1 (3)
Q. What is the rule here?
30. The rule is to continue rolling until the
number decreases, then stop.
Write down 3 sequences we might get when
rolling a die and abiding by the rule.
Q. What is the shortest sequence we could
have?
Q. What is the longest?
31. The shortest sequence we could have has
only 2 terms e.g.
6, 1 (2)
4, 2 (2)
The longest sequence of terms would have
repeats e.g.
1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 1 (11)
1, 3, 3, 3, 3, 4, 4, 6, 5 (9)
32. I have read this in a book:
“more than half the time the sequences
will have 4 or less terms.” (copy onto board)
Q. Do you think this is true?
?
Using your dice each of you is to generate 20 sequences
using the stopping rule “when it decreases stop.”
List your sequences and the number of terms in each.
33. In groups of 5 pool your results using
tallies for the number of terms.
Q. What was the longest sequence of terms in
your group?
Q. Do the results in your group suggest that the
statement on the board is true?
Q. What table should we use to collect and
display the results to the whole class?
34. Our table needs to cover the numbers
from 2 to the largest number of terms
we have.
The graph will be shown as a bar-line
graph.
Q. Will there be gaps between the lines?
35. Frequency / Number of Terms
N
u
m
b
e
r
o
f
T
e
r
m
s
2 4 6 8 10 12 14 16 18 20 22 24 26 28
Frequency
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
23
36. .
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Number of Terms
F
r
e
q
u
e
n
c
y
37.
38. On your squared paper draw the bar-line
chart using the whole-class data set.
39. Q. Is this graph similar in shape to the bar
chart you drew yesterday?
Q. How many data items are there in the
grand total?
Q. Were there 4 or less terms in our
sequences in more than half our data items?
Q. Is this more than half our data?
Do we think the claim is true or false?
40. With a partner work out some statements
about the behaviour of the sequences.
Be prepared to share your ideas.
41. By the end of the lesson the children
should be able to:
Test a hypothesis about the frequency of an
even number by collecting data quickly;
Discuss a bar chart or bar line chart and
check the prediction.
43. L.O.1
To be able to recognise which simple
fractions are equivalent.
44. ½ ¾ ¼
Q. Which figure is the NUMERATOR?
Q. Which is the DENOMINATOR?
Q. Are the fractions in order of size,
smallest first?
45. The order should be : ¼ ½ ¾
We will list some fractions which are equal to
½. Volunteers!
Q. Can you describe the relationship between the
numerator and the denominator?
46. Here are some fractions equivalent to ½ :
2/4 8/16 3/6 4/8
9/18 5/10 7/14 11/22
50/100 12/24 15/ 42/
Q. If the numerator is 15 what must the
denominator be to go with these equivalent
fractions? What if the numerator is 42?
47. We will list some fractions which are
equivalent to ¼. Volunteers!
Q. What is the relationship between the
numerator and the denominator?
48. : Here the fraction is ¼.
Here are some equivalent fractions:
¼ 2/8 4/16 20/80
5/20 3/12 7/28 6/24
9/36 11/44 14/ 27/
Q. If the numerator is 14 what must the
denominator be to go with these equivalent
fractions? What if the numerator was 27?
49. We will list some fractions which are
equivalent to ¾.
One is 15/20.
How does this work?
Q. What is the relationship between the
numerator and the denominator?
50. : Here the fraction is ¾ .
Here are some equivalent fractions:
3/4 6/8 12/16 60/80
18/24 9/12 21/28 18/24
27/36 33/44 21/ 27/
Q. If the numerator is 21 what must the
denominator be to go with these equivalent
fractions? What if the numerator was 27?
51. L.O.2
To be able to solve a problem by
representing and interpreting data in bar
line charts where intermediate points may
have meaning.
52. This table shows the temperature in °C of a surface
exposed to the sun over a 24 hour period.
Q. When was it hottest / coldest?
Q. If we are going to put the data onto a graph which
numbers should we put on the time axis and which on
the temperature axis?
53. The time axis must be 0 to 24
and the temperature axis must be 0 to 60.
Q. Which way round shall we place the graph paper?
Q. Where should we place the first X on our record.
57. Complete your own graph.
Q. Can you work out at what times of day the different
temperatures were taken?
Q. What time of day were the 7th
, 8th
and 9th
temperatures taken?
What about the 19th
, 20th
and 21st
?
Q. How could we estimate the temperature at 3.5 hours?
Q. Are there values in the spaces between the X ‘s ?
58. Use a ruler to join the points you have
plotted.
If we had more detailed measurements
would the points make a smoother curve?
59. REMEMBER…
Time and temperature are MEASURES
and not COUNTS or FREQUENCIES so
the intermediate points have meaning
and we can join the X ‘s and use them to
answer different questions.
Q. For how long was the temperature greater than 40°C?
Less than 20°C?
Work out some questions about your graph for your
partner to answer.
Prisms – 10; Spheres – 8; Tetrahedra – 5.
60. Here is another set of measurements collected
over the same 24 hours. These show the intensity
of the light and are measured in lux.
Q. Why are there 0’s for hours 8 to 12?
Q. When was the light strongest?
61. There are 0’s for hours 8 to 12 because
there was no light so it must have been
night time.
The light was strongest at hour 21 – this
must have been close to midday.
62. By the end of the lesson the children
should be able to:
Draw and interpret a line graph;
Understand that intermediate points may
or may not have meaning.
82. Where is 3.2
on the
horizontal
axis?
How can we
use the graph
to find:
3.2 x 4?
If the graph
was in cm.
squares we
could use a
ruler to help
us.
83. On your cm paper draw a graph of the
5x table.
The horizontal axis will be 10cm and the
vertical axis will be 25cm with each cm
representing 2 units.
84. .
0 1 2 3 4 5 6 7 8 9 10
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Graph of
the 5x
table
Let’s say it
all together
Q. How
can we
use the
graph to
find
these?
4.5 x 5
3.6 x 5
85. .
0 1 2 3 4 5 6 7 8 9 10
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Write the
answers to
these:
1.4 x 5 =
2.5 x 5 =
4.8 x 5 =
6.6 x 5 =
5.6 x 5 =
7.2 x 5 =
8.1 x 5 =
9.4 x 5 =
86. .
0 1 2 3 4 5 6 7 8 9 10
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Graph
of the 5x
table
Which
other
tables
can we
put on
our
graph?
87. .
0 1 2 3 4 5 6 7 8 9 10
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
We can
draw these:
2x table
3x table
and
4x table
Put them on
your graph
using
colours
88. .
0 1 2 3 4 5 6 7 8 9 10
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Use these
graphs to
find:
4.5 x 2 =
4.5 x 3 =
4.5 x 4 =
4.5 x 5 =
89. .
0 1 2 3 4 5 6 7 8 9 10
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Tetrahedras
find
3.5 x 2 =
3.5 x 3 =
3.5 x 4 =
3.5 x 5 =
5.5 x 2 =
6.3 x 3 =
7.5 x 4 =
9.2 x 5 =
Spheres find
2.7 x 2 =
4.3 x 3 =
5.7 x 4 =
7.2 x 5 =
Prisms find
3.9 x 2 =
8.1 x 3 =
4.7 x 4 =
5.9 x 5 =
90. Q. Which
times table
does this
represent?
The
multiplication by
10 gives 25.
10 x ? = 25
Q. What
number x 10
gives 25?
91. 2.5 x 10 = 25
Find
estimates for
3 x 2.5
4 x 2.5
7 x 2.5
8 x 2.5
Which line
would we need
to draw to get
estimates of
multiplication by
3.8?
92. We would need
a line whose
coordinates are
0,0 and 10,38
Draw the line on
your graphs
Use the graph to
find estimates
for 5 x 3.8
3 x 3.8
7.5 x 3.8
93. What strategies did you use to obtain your
estimates?
Did you use approximations e.g.
5 x 3.8 ~ 5 x 4.0 = 20
Exact answers are: 5 x 3.8 = 19.0
3 x 3.8 = 11.4
7.5 x 3.8 = 28.5
What are the limitations of the graph method?
94. By the end of the lesson the children
should be able to:
Draw and interpret a line graph where
intermediate points have meaning.
