1 · Adding two-digit numbers
1
Adding two-digit numbers
This session is designed to enable learners to:
앫 add tens to a given two-digit number;
앫 add units to a given two-digit number;
앫 add two two-digit numbers correctly.
앫 Sheet 2 – Solution, large enough to show the whole group
the completed hexagon and the shaded triangles.
앫 Card set E – Digits 0 to 9.
For each learner you will need:
앫 mini-whiteboard, marker and cloth.
For each pair or small group of learners you will need:
앫 Card set A – Numbers ending in 4;
앫 Card set B – Numbers ending in 1;
앫 Card set C – Numbers ending in 8;
앫 Card set D – Making a hexagon (three pages);
Print each card set on a different colour of card.
앫 Sheet 1 – Template for sums or sheets of squared paper;
Optional:
앫 number line from 0 to 100 (not supplied).
Ask learners to work in pairs or small groups of three or four.
Share out Card set A – Numbers ending in 4 between the
groups. It does not matter if each group gets a different
number of cards.
Write the number ‘14’ on the board. Ask learners to add 10 to
this number and explain that the group that has the card with
the answer ‘24’ should hold it up and call out ‘24’. Ask them to
add on 10 again and find who has the card. Continue until all
the cards have been used.
Repeat the activity using Card set B – Numbers ending in 1 and
and Card set C – Numbers ending in 8.
Continue until learners are answering fluently.
Note that the numbers on the cards go up nearly to 200 since,
when pairs of two-digit numbers are added, the answer can be
up to 198. If learners become very confident, you may wish to
continue past 200, without cards but writing numbers on the
board.
Ask learners to spread all the cards they have, from all three
sets, in front of them. Then repeat the activity with a different
start number (for example 4, 21, 38) and adding 20, 30, and so
on. If learners find this difficult, encourage them to add in lots
of 10, for example add two lots of 10 as equivalent to adding
20.
Alternatively, you may wish to start by sharing out all the cards
from Card sets A, B and C so that learners have a wider choice
and have to think more about their answers.
Ask learners to work in pairs. Give each pair of learners a
mini-whiteboard and marker. Write a two-digit number (for
example 64) and a single-digit number (for example 2) on the
board. Ask learners to add the two numbers together and write
the answer on their mini-whiteboard. Ask them to write down
anything that helps them do the calculation – for example,
some may like to draw part of the number line to help them
count on:
64
65
66
Alternatively, you can provide each pair of learners with a
number line from 0 to 100, or display it at the front of the
room.
Repeat for other additions of a single digit until learners are
answering fluently.
Now ask learners to work in pairs or small groups (up to four
per group). Give each pair or group Card set D – Making a
hexagon. Point out that each triangle has at least two sides
with either a number or an addition sum. Explain that the task
is to fit the triangles together to form a hexagon such that
adjacent sides of the triangles show the same value.
Show Sheet 2 to demonstrate the completed hexagon. Explain
that learners should aim to complete the shaded (inner)
triangles first, then the outer triangles. Do not show Sheet 2
long enough for learners to ‘spot’ some of the triangles!
Learners should work together to complete the hexagon,
helping each other through discussion. They can use a
mini-whiteboard or a number line if they need to.
They may find it helpful to write the answers on the cards,
rather than have to remember them, but this will mean that
you cannot re-use this set of cards.
As you move round the room, listen to learners’ explanations
and make a note of any obvious misconceptions that emerge,
for whole group discussion at the end of the session. If you
notice any mistakes, ask learners to show you how they
calculated the answer.
Discuss any problems that arose in the hexagon activity. In
particular, ask learners to explain how they dealt with ‘53 + 65’
and the other pairs of two-digit numbers. It may be that they
ignored them and matched the sides by default, in which case
ask them to explain how they think the answer could be
reached. Show that there are various possible strategies. If
learners cannot work out a strategy for themselves, encourage
them to split the second number into two, for example 53 + 65
= 53 + 60 + 5
Practise more examples, using mini-whiteboards.
Ask learners to work in pairs. Give each pair of learners Sheet
1 – Template for sums, or some squared paper on which they
can draw boxes as follows:
+
=
Using Card set E – Digits 0 to 9, select cards one at a time at
random. Call out the digit on each card as you select it.
Learners have to write each digit as it is called, in one of the
four boxes. The aim is to make the total of the two two-digit
numbers as close to 100 as possible. When four digits have
been chosen and learners have written their numbers in the
boxes, ask learners to add up the total of a neighbouring pair
of learners. The pair with the answer closest to 100 is the
winner.
You can repeat this activity several times, shuffling the pack of
cards each time. You may wish to invite learners to select the
cards, which you offer fanned out with only the backs of the
cards visible.
You can repeat the activity with a different target total.
If learners find this activity easy, you could extend it by using
three digits.
앫 Using mini-whiteboards, ask learners to give an example of
two numbers that add up to 67. Write the numbers on the
board and discuss them. Ask for more pairs of numbers to
make the same total, particularly if learners have ‘played
safe’ with answers such as 66 + 1. Alternatively, make some
restrictions to encourage the use of two-digit numbers by
stating conditions such as ‘Both numbers have to be
between 10 and 50’.
앫 Repeat the activity using other target numbers.
앫 If learners find this activity easy:
– ask them to find three or more numbers that add up to
the given number;
or
– give a three-digit target number.
앫 All these activities can be adapted to give learners practice
in subtraction.
Card set A – Numbers ending in 4
24
34
44
74
84
94
124
134
144
174
184
194
54
64
104
154
164
114
Card set B – Numbers ending in 1
21
31
41
51
61
71
81
91
101
111
121
131
141
151
161
171
181
191
Card set C – Numbers ending in 8
28
38
48
58
68
78
88
98
108
118
128
138
148
158
168
178
188
198
Card set D – Making a hexagon (page 1 of 3)
+
4
3
8=
31
28
+1
115
64
=
31 + 5 =
28
8=
=
1
+
+3
=
61
42
+
37
=
48 + 1 =
+
2
3
8
=
2
6
+
8
3
=
0
4
29
73 + 7 =
10
104
+
12
32
11
Card set D – Making a hexagon (page 2 of 3)
30
40
35 + 80 =
91
43
41 + 50 =
+
3
6
29
1=
+6
0=
+
1
2
=
0
4
49
80
+
3
8
=
0
5
14 + 10 =
+
4
1
=
6
1
24
25 + 10 =
65
31
96
22
Card set D – Making a hexagon (page 3 of 3)
83
25 + 7 =
=
=
5
6
=
45
64
+
3
5
77
+6
+8
23 + 54 =
78
26 + 2 =
37
=
0
1
51
25
21 + 30 =
+
3
3
29
50
1=
3
=
8
+
89
+2
34
36
35
13
–
0
1
2
3
4
5
6
7
8
9
Sheet 1 – Template for sums
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Sheet 2 – Solution