 Review
addition and subtraction facts: pupils over-learn
the 100 addition and subtraction facts previously learned
with Experimenting with Numbers. Now they are ready
to learn to read and write equations. Because pupils
have already discovered the basic facts using concrete
materials, as they proceed to write the numerals 1 to
10, their learning will be reinforced and this knowledge
will fill the written symbols with meaning, giving the
pupils a wealth of understanding to transfer to the
numerals 1 to 10.
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The lessons: These begin with
sensori-motor exercises to develop the ability to
gauge the lengths of straight lines, vertical loops
and strings of anti-clockwise vertical loops, in preparation
for writing numerals 1 to 10.
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Learning to read and write equations: This
programme has an accompanying Pupil’s Workbook
which enables the teacher to assess a pupil’s
understanding of each lesson as pupils complete the
written exercises. A key strength of Workbook 2 is
in the continuous support provided by the 2-d images
of the number blocks and pattern boards. ( see
illustration).
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Discovering addition and subtraction facts
with sums of 10 and less: When combinations
of blocks are placed in the 10-box in sequence, pupils
can use this organisation to reason that if 9 needs
1 to make 10, then 8 needs 2 and 7 needs 3 to make
10 and so on. They will measure these combinations
of blocks with the 10-block. Next, a pupil will put
two other blocks in the box that, together, make 10
and ‘tell the story’. Encourage pupils
to use their own words; if they do it shows that they
understand what they are doing. Teach the pupils to
record an addition fact from the 10-box with the number
markers and signs. Step by step the pupil records
each move with the number markers. Then they read
back the newly formed equation: 8 plus 2 equals 10.
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Commutativity of addition: Although
pupils do not use the term commutative property, they
show they understand it by changing the order of the
blocks in a pair.
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Pupils Workbook: Teachers elicit
that each pair of blocks measures (or equals) 10 by
going over the combinations orally first, then pupils
complete the equations by writing the numbers in the
boxes provided. You will see the level of support
given in the workbook from the 2-d illustrations next
to the written equations to be completed. This provides
secure transfer of concrete understanding to the abstract
form. Some pupils will benefit from using graph-paper
as the boxes may be too small for their handwriting
abilities.
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Related ‘family groups’ of
facts: The relationship between addition
and subtraction is one of ‘doing’ and
‘undoing’ like wrapping a parcel and unwrapping
it. The plus sign stands for putting two blocks together;
now the minus sign stands for diminishing the total
by taking one of the blocks away. The pupil will say
“10 minus 1,” “10 take away 1”,
or “10 less 1.” When acting out an addition
story, pupils understand there will be more in the
end. When acting out a subtraction story, they will
see that there is less in the end. The experiments
dramatise the opposite character of addition and subtraction.
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Solve word problems: To solve
word problems, pupils must be able to determine which
operation is required - addition or subtraction. The
teaching presents pictured problems that pupil’s
state in their own words and then record in symbols.
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Learning about money - The value of coins: The
value of a coin cannot be discovered by looking at
its size. Children often think the larger coins are
worth more than smaller coins which causes much confusion.
Pupils work through experiments with the support of
the relevant number blocks. Coins, pasted on top of
unit cubes, 2-blocks, 5-blocks and 10-blocks, draws
on a level of existing understanding, with which to
apply to learning about money.
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