JUNIOR INFANTS
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Introduce numbers 0-5.
Recognise numbers 0-5.
Write numbers 0-5.
Combine sets of objects 0-5.
Children should understand the relationship between each number and the amount of objects they
represent.
Record pictorially what each number represents.
Order numbers 0-5.
Pictorially represent number stories up the five using the word “and”.
Example:
and
SENIOR INFANTS
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Revise numbers 0-5 as in junior infant programme.
Introduce numbers 6-10 using similar format as in junior Infants programme.
Introduction of number stories
1. Using unifix cubes introduce the term “is the same as”.
e.g. 3 cubes in one hand
3 cubes in the other
3 “is the same as” 3
2. Introduce the symbol = … “is the same as” (not “Equals”)
3. 2 and 3 = (“and” is a new term)
4. The next stage is to introduce the new symbol “+” but still refer to them as “and”.
5. After completing number 1 according to the junior infants format, the number stories can be introduced
beginning at 2 and working up to ten using unifix cubes, always working from left to right.
Story of 2 – ways of breaking up number 2
2+0=2
1+1+2
0+2+2
Language: +  “and”
=  “is the same as”
Always work from left to right.
1
Teacher records each line on the blackboard.
Follow a similar format for all stories up to 10.
SIMPLE ADDITION
Simple numbers sums based on the numbers that have been completed
i.e.
3+ 1= □
2 + 2 =□
1. Orally use unifix cubes to get the answer.
2. Record sums in their copies and complete the sums in their maths books using cubes.
3. Dots representing/under numbers in the sum e.g. 5 + 4 =
.....
. . . . Count the dots to get the answer.
4. Introduce the number line for addition to enable the children to count on the number line to get the answer
to the sums.
N.B. Tell the children to keep their left hand finger on the first number of the sentence and count with the right
hand.
FIRST CLASS
Revision of number stories 1-10
Revision of simple addition 1-10
6+4=
or
6
+4
using cubes
hopping on number line (1-10)
Use of “Friendly Numbers” (e.g. 1 + 9 = 10, 2 + 8 = 10 etc)
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Introduction of number 11-20 using dienes blocks (10’s and units)
Creation of numbers using 10’s and units. e.g. counting out 17 units,
renaming using 1 ten and 7 units etc.
Introduction of numbers 20-100 using dienes blocks.
Use of hundred square
Addition using “transition boards”. There is no renaming in first class.
Tens
3
+ 2
5
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Units
6
2
8
Start with the units first
Six units and two units equals eight units
2
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3 tens and 2 tens equals 5 tens
5 tens and 8 units – that number is 58
SECOND CLASS
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Counting on from a given number using the hundred square
Revise grouping of tens and units, eg 35 is 3 tens and 5 units.
Revision of simple addition.
Example
T
1
+
1
U
3
3
6
+
T
3
1
4
U
4
2
6
Steps for addition with renaming.
1. Grouping of ten with renaming e.g. 35 = 2 tens and 15 units
2. Using dienes blocks / notation boards and. Concrete materials are used first, this is followed by the written
concept.
+
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T
1
21
4
U
4
7
1
11
(11 = 1 ten + 1 unit)
Symbol + is now called “plus” instead of “adding on”.
Add tens and units from the top down.
THIRD CLASS
 Revision of tens and units
 Revision of addition of tens and units with and without renaming.
 Introduce “hundreds”.
 Place value up to 999 (dienes blocks and notation boards / abacus)
Example:
243 = 2 hundreds = 200
569 = 6 tens = 60
331 = 1 unit = 1
Simple addition of hundreds, tens, and units.
H
T
U
2
3
3
+
1
2
5
3
5
8
start adding units from top down, then tens, then hundreds.
3
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Addition with renaming using dienes blocks and notation boards.
H
T
U
2
9
9
16
+
11
16
5
14
4
6
4
1. Add units, then rename to tens and units
2. Add tens, then rename to hundreds and tens
3. Add the hundreds.
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Symbols used : + plus
= equals
FOURTH CLASS
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Use the same steps as 3rd, except numbers are now up to 9999
FIFTH AND SIXTH CLASS
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At this level, tens of thousands are introduced. The same addition method is applied.
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JUNIOR INFANTS and SENIOR INFANTS
Only in informal ways i.e. noticing/observing “the difference” (Partitioning of sets of objects 10 in the set, 6 are girls.
How many are boys?).
Colour the girls one colour, the boys another (as in story of 8, 9, 10 etc.).
Vocabulary: Count backwards, less than, what number comes before.
FIRST CLASS
Develop an understanding of subtracting as deducting, as complementing and as difference (0-20).
Deducting:
Complementing:
I had 10 sweets, I ate 3. How many have I left?
There are 10 stickers in a set. I have 4. How many do I need to make a
full set?
I have 12 crayons. Mary has 6 crayons.
How many more have I? How many fewer has she?
Difference
-
-
develop and recall mental strategies (0-20) (counting back/on, using doubles/near doubles, using zero, using
‘10’ facts, adding to check results).
(tell number story – record pictorially, as a number sentence or as a written story).
solve problems involving subtraction. Devise problems for each other.
estimate differences within 99.
(by subtracting the tens; checking estimates using manipulatives).
subtract numbers without renaming (within 99) (estimate difference first; then use concrete materials,
number lines and hundred squares).
use mental calculations, record using number lines, number sentences and algorithms.
use the symbols + -,=
(formal introduction of symbols only occurs after sufficient oral and exploratory work has been completed,
emphasis on the equals sign as signifying “the same as’ or equivalent.
exploring using a number-balance.
solve one-step problems involving subtraction.
subtract without renaming, tens and units
“Minus” is introduced in 1st class
Example
-
T
6
4
2
U
7
3
4
5
1. Read the units first. 7 take away 3 = 4
2. 6 take away 4 = 2
3. Answer = 24
SECOND CLASS
As with first Class, the emphasis is on subtracting as deducing, complementing, difference.
 mental strategies (0-20) emphasis on different strategies to subtract numbers (doubles, near
doubles, ’10 facts, adding to check results).
 construct number sentences involving subtraction.
 estimation of difference within 99 (use of rounding strategies)
 subtraction of numbers within 99 (with and without renaming): Estimate using tens, write
calculations only after plenty of practical and mental calculations, check answers using hundred
square, number line or by adding.
 use of symbols +,-,=(<= less than,>= greater than)
 solve one-step and two-step problems involving addition and subtraction.
Example
T
U
23
14
1
6
1
8
1. Read the units first. 4 take away 6, I cannot do, I must rename. I go over to my tens. I cross out my 3 and
rename it to 2.
I bring my 10 over to my units. I add the 10 and 4 together. I now have 14 units. I change it to 14. Read the
units again. 14 take away 6 = 8.
2. I go to my tens, 2 take away 1 = 1.
3. Answer = 18
THIRD CLASS
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subtract without and with renaming within 999 (estimating differences, rounding where necessary,
checking estimates, record using horizontal and vertical presentation).
 know and recall subtraction facts.
 Solve word problems involving subtraction.
Example:
H
7
2
4
6
+
T
4
8
5
13
U
5
7
8
1
1. Read the units first, 5 minus 7, I cannot do, I must rename. I go over to the tens. I cross out my 4 and rename
it to 3. I bring over my 10 to my units. I add the 10 and 5 together, I now have 15 units. I change it to 15.
Read the units again: 15 minus 7 = 8.
6
2. I go to my tens: 3 minus 8 I cannot do. I must rename. I go over to my hundreds. I cross out my 7 and
rename it to 6. I bring my hundred (100 = 10 tens) over to my tens. I add the 10 tens and the 3 tens. I now
have 13 tens. 13 minus 8 = 5.
3. I go to my hundreds. 6 minus 2 = 4.
4. Answer = 458.
Example involving zero
-
H
34
2
1
T
910
8
1
U
16
7
9
1. Read the units first: 6 minus 7 I cannot do. I must rename. I go over to my tens. There is no 10 there.
Therefore I must go to my hundreds. I cross out the 4 and rename it to 3. I put a small 1 beside my 0 in the
tens. I now have 10 tens.
2. I must start again, 6 minus 7 I cannot do. I must rename. I go over to my tens. There are 10 tens there. I cross
out my 10 and rename it to 9, I bring my ten to the units and I add my 10 and 6 together, I now have 16
units.
3. 16 minus 7 = 9
4. 9 minus 8 =1
5. 3 minus 2 = 1
6. Answer = 119
Example involving 2 zeros:
H
T
45
910
3
4
1
5
U
0
6
4
1
1. Read the units first: 0 minus 6 I cannot do. I must rename. I go over to my tens. There is no 10 there. I go to
my hundreds, I cross out my 5 and rename to 4. I put a small 1 beside the 0 in the tens (100 = 10 tens).
2. I start to read the units again, 0 minus 6 I cannot do. I must rename. I go over to by tens. I cross out my 10
and rename it to 9. I bring my 10 over to my units.
3. I start again, 10 minus 6 = 4
4. Subtract my tens. 9 minus 4 =5
5. Subtract my hundreds, 4 minus 3 = 1
6. Answer = 154
FOURTH CLASS
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subtract without and with renaming (within 999)
estimate difference, checking estimates without and with a calculator.
know and recall subtraction facts.
Solving word problems involving subtraction (using a calculator to develop problem – solving strategies and
to verify estimations).
the same subtraction method is applied for 4th, 5th and 6th class.
FIFTH AND SIXTH CLASS
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estimate differences (using strategies i.e. front-end estimation, rounding, clustering, special numbers).
estimate and compute answers with a calculator.
Subtract without and with a calculator.
THIRD CLASS
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Multiplication is introduced as repeated addition using unifix cubes.
Example :
Three groups of two equals six.
a) 3 times 2 equals six 3 x 2 =6
b) 3 twos, six
3
x2
6
Simple Long Multiplication
T.
1
x
2
1.
2.
3.
4.
U.
3
2
6
Multiply units first.
Write your answer in the units.
Multiply your tens next.
Write your answer in the in the tens.
Renaming using Tens and Units
T
U
1
6
1 x
2
3
2
1. Multiply units first, rename your answer by putting units down and carrying over your tens
2. Multiply your tens then add on any extra tens.
3. Put your answer underneath.
Renaming using Hundreds, Tens and Units
1. Multiply units first, rename your units answer, carry tens to your tens.
2. Multiply your tens, rename your tens, carry hundreds to your hundreds
FOURTH CLASS
Follow the sequence of 3rd class as revision.
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Multiplication of 1000’s
The same as multiplication of 100’s but carrying over to the thousands as needed.
Long Multiplication of tens
T
U
2
5
X
2
6
T
2
is the same as x
U
5
6 plus
x
T
2
2
U
5
0
So 25 x 6 = 150
and to multiply anything by a multiple of ten, you first multiply by the tens figure, then add a zero, meaning
25 x 20 = 25 x 2 = 50 and add a zero = 500
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Add both lines to get 650.
T
U
2
5
X
2
3
6
1
15
0
+
5
0
0
Magic Zero
6
5
0
Break your sum into multiplication of tens and multiplication of units.
Multiply the units first as per third class.
To multiply the number by the tens, you first multiply by the ten part (add your magic zero), then multiply by
the tens figure. When writing the sum, put down the magic zero, then continue by multiplying by the
number in the tens place.
Add your two answers
FIFTH CLASS
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The same multiplication method is applied for
multiplication of whole numbers including units, tens hundreds and thousands.
Multiplication of a whole number by a decimal.
SIXTH CLASS
Multiplication of a decimal by a decimal is introduced. In this case, the sum is done without decimal points first, then
you count the number of digits after decimal points in the question – this will tell you how many digits come after
the decimal point in the answer.
Eg
25.6 x 3.4 (There are 2 digits after the decimal points – 6 and 4)
So your answer is 256 x 34 = 8704, but put the decimal point two places from the end giving you an answer of 87.04
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THIRD CLASS
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Division is introduced as a understanding of sharing and repeated substraction.
This is recorded using number sentences e.g.20 – 4 =20 -4-4 -4 -4-4 = 0
It is developed as the reverse of multiplication.
Unifix Cubes are used in the explanation.
e.g 21 ÷ 3 = 7
1.
21 is shared among 3 people or
2.
21 is placed in groups of 3 or
3.
How many 3’s in 21?
Introduce various ways of writing a division sentence
2
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5
2
1
8
9
Step 1. 2 goes into 5 2 times (twice) with a remainder of 1. Put your remainder up over the next number.
Step 2 2 goes into 18 9 times evenly. Write down 9.
Answer = 29
Tens and units are divided by one digit numbers with remainders.
FOURTH CLASS
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Division with remainders are introduced
2
Step 1
Step 2.
Step 3.
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5
2
1
3
6
1
5
7 R1
2 goes into 5 two times (twice) remainder 1
Write down 2 and carry 1
2 goes into 13 6 times remainder 1. Write down 6 and carry 1.
2 goes into 15 7 times remainder 1. Write down 7 r 1.
Overall answer = 267 r l
Hundreds, tens and units are divided by one-digit number in 4th class.
FIFTH CLASS
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The concept of long division is introduced. Hundreds, tens and units are divided by two-digit number.
This is developed as repeated subtraction.
10
Method
1. Estimate
2. Divide into the first digits
3. Subtract
4. Bring down next digit
5. Repeat if necessary
0
26 5
-2
2
-2
0
1
1
6
5
3
2
9
5
R 21
5
4
1
Rough Work (RW)
26 x 1 = 26
26 x 9 = 234
Step l:
Estimate how many times does 26 go into 0? Answer = 0
Write up 0
Step 2:
Estimate how many times does 26 go into 51? Answer = 1
Check answer in R.W. Write up 1. Subtract 26 from 51. Answer = 25
Step 3:
Bring down 5.
Step 4:
Estimate how many times does 26 go into 255. Answer = 9. Check in R.W.
Write up 9. Subtract 234 from 255. Answer = 21.
Step 5:
Have I anything to bring down? No.
Over all answer = 19 with a remainder of 21 or 19 R 21
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Division is extended to division of a decimal number by a whole number.
e.g. 75.6 ÷ 4
(This is short division as the divisor is a one digit not a two digit)
7 35 . 36
1 8 . 9
Step 1:
4 goes into 7 once remainder 3. Write down 1 and carry 3.
Step 2:
4 goes into 35 8 times remainder 3. Write down 8 and carry 3 beside the 6.
Step 3:
Put decimal point under the decimal point.
Step 4:
4 goes into 36 9 times evenly. Write down 9. Overall answer = 18.9.
4
SIXTH CLASS
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Long division is extended using thousands, hundreds, tens and units
e.g. 7852 ÷ 26. The same method as 5th class is used.
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Eg.
Division of a decimal number by a decimal is also taught. In this case, you multiply the divisor by either
10, 100 or 1000 to make it a whole number. Then multiply the number being divided by the same
multiple (10, 100 or 1000). Continue as a normal long division sum.
29.12 ÷ 5.2
5.2 x 10 gives a whole number = 52
29.12 x 10 gives 291.2
So your new sum is 291.2 ÷ 52 = 5.6
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Problem Solving Strategy
1. Read the problem carefully
2. Underline the important words
Altogether
Less than
More than
Share
Groups of
3. Decide what you are going to do and how many parts there
are.
4. Write down your work, don’t do it in your head.
5. Draw a picture that illustrates the problem.
+
=4
6. Reread the question and check you have it done correctly.
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