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activities to reinforce place value

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									Activities to Reinforce Place Value

Some activities which develop children’s understanding of place value are
outlined on the Layered Targets handout (See ‘Key questions’ column).

The activities below are additional ideas. Most can be adapted to reinforce the
curricular target for place value across a range of Year Groups. They are
deliberately structured to be short and focused, so that they can be carried out
during mental and oral starters, as well as in any spare minutes that you can
find (!)

The purpose of our place value work can be summarised as follows:

   1. We want children to have a sense of what the numbers that we use
      (whether it’s 3, 340 or 345000) actually mean.

   2. We want children to be able to represent collections of objects, and the
      numbers that they hear, using the appropriate digits, in the appropriate
      order.

   3. In addition, very importantly, we want children to be able to use their
      understanding of place value to help them identify relationships
      between numbers and to carry out calculations on those numbers.

Read and Write

Children work in pairs. They need to sit so that one person in the pair can see
the board, and the other can’t.

Write a number on the board. The child who is facing the board reads out the
number to their partner. Their partner writes down the number that they have
heard. Both children then compare the number that has been written down
with the number that was on the board. Is it the same?

This is a useful activity for bringing to light and addressing any difficulties and
misconceptions that the children may have. It can be carried out as a whole
class, or in smaller groups. Make sure each child gets the chance to be both
‘reader’ and ‘writer’!

As with all activities where children read out numbers, you will need to be very
strict about reading the numbers correctly- 537 is five hundred and thirty
seven, not five three seven. Make sure you always model this for them when
you are talking about numbers. The children might be interested to hear about
reasons why numbers are not always spoken correctly- particularly in TV
adverts, where missing out words like ‘thousand’ and ‘hundred’ make
products seem less expensive!

Zero in
If children are struggling with recording numbers, especially those which
include place holding zeroes, this activity may help.

Write up a collection of numbers on the board, which use different
arrangements of the same digits eg;

       10 053        10 503        10 530         15 030

Read out one of the numbers and ask the children to tell you which one you
chose. This activity will promote useful discussions about what difference it
makes when the zero in the number takes a different position.

Follow up: When the children have correctly identified the numbers that you
read out, they could be asked to put the numbers in order. This will help to
reinforce the key concepts that were covered in the discussions in the first
part of the activity, about the way that the position of a digit in a number
changes its value.

In the initial stages of working towards their place value target, children will
find it easier to work with a list of given numbers, as in this activity. They can
then move on to writing the numbers that they hear once their understanding
has developed.

Number Scramble

Children who struggle with place value often find it much easier if the
concepts are reinforced using the column headings (see below)

                           TTh    Th    H     T    U
                            2      3    5     1    7

In this activity the children work in groups. The group size will depend on the
number of digits in the numbers that you are practising. Each group needs its
own set of digit cards, and column headings.

The column headings for each group need to be up on the wall of the
classroom, so that they are just higher than the children’s heads. You might
want to get the children to put up the column headings as the first stage of the
activity- this will allow you to check whether they know the correct order.

Each child in the group needs a number card. You might want to include one
or more zeroes if the success criteria for your curricular target include a
reference to the role of place holding zeroes.

Say a number. Holding their cards, the children must arrange themselves into
a line underneath the column headings so that they are showing the number
that you said.

Variation- Decimal numbers
You can also use this game to reinforce the place value of decimal numbers
and the link between fractions and decimals. This will help children develop
the concept that when we say, for example, ‘seventy five hundredths’, we use
the equivalence of this number to seven tenths and five hundredths to record
it (see below).

                          U     Tenths Hundredths
                          0       7        5

NB It’s essential that we put the decimal point on the ‘line’ between the units
and the tenths column, rather than giving it its own column, as the children
often try to do. If it has its own column, the system falls apart when you try
and multiply or divide by 10!

Finish it off

This game helps children to use place value to identify relationships between
numbers. It uses the column headings described in the previous activity.

Put up the column headings on the board that you are working with. Then fill
in digits in some of the columns (see below):

                       HTh TTh        Th   H       T       U
                            3              5       2       8

In pairs, the children copy the number onto whiteboards and choose digits of
their own to fill in the empty columns. Each pair then says the number that
they have made.

This activity reinforces the way that we read numbers. Listening to each pair
read out their number will help children to see the patterns in the way that
numbers are said (eg bleep hundred and beepity thousand dash hundred
and blankity blank).

Variation (1): Place holding zeroes

As above, but when you fill in your chosen columns, use zeroes.

                          TTh    Th    H       T       U
                                  0            0

Again, the children should hear a pattern in the numbers that they have made,
even though each pair have come up with a different number.

It’s all relative!

You will need to choose a group of volunteers for this activity. Give each a
card with zero on one side and a non-zero digit on the other side.
Put the column headings described previously up on the board at the front of
the room. Then ask the children with cards to organise themselves under the
column headings to make a number. Initially they all need to show the non-
zero side of their card to the class.

                                 H     T    U
                                 3     2    6

The rest of the class work as talking partners. They tell their partner what
number is currently shown on the cards. A few pairs of children can then be
chosen to say the number.

Then choose one of the volunteers to turn their card over so that the zero is
showing instead of the digit. Ask the rest of the class what number is shown
now.

                                 H     T    U
                                 3     0    6

Continue in this way, making a different number each time. This activity is a
good starting point for questions such as:

      -   Do we still have units/ hundreds? How many?
      -   Do we still have any tens?
      -   So how do we say our new number?

Follow up- If you write up the original number and the ‘changed’ number, so
that children can see both, you will be able to discuss what sum was carried
out to change the old number into the new number.
       - What sum would we do to change it back again?

Number Doctor

(Apologies to Hilary, because I stole this idea from her sentence level work!)

This activity gives you another way of reinforcing those place holding zeroes
that children find so tricky. You will need some number cards, including some
zeroes.

Use the cards to put a number on the board.

                                  6         3


(Depending on the stage that your children are at, you might also want to
have the column headings up.)

The number is sick because there is something wrong with it. It should be six
hundred and three.
Ask the children to ‘cure’ the number. They can write down the ‘cured’ number
on whiteboards for you to see, and a volunteer can come and arrange the
cards correctly, including zeroes as appropriate.

Again, there is a lot of useful discussion that can be generated by this activity:
       - What was the number we could see?
       - What should it have been?
       - What was wrong with it? (It said it had 6 tens, but it should have
          had 6 hundreds)
       - How did we make it better? (We gave it zero tens, and put the 6 in
          the hundreds column)

Target numbers

The children will need calculators for this activity. Give them a number to type
into the calculator (eg 67 952).

The first child chooses which digit they want to change to a zero. They say the
sum that needs to be done to reduce their chosen digit to zero. (‘I want to
make the ‘hundreds’ into zero. I need to do 67 952 minus 900’). Their partner
carries out the calculation. Then change over, and choose another digit to
reduce to zero.

By taking part in this activity, the children will get practise both in reading
numbers which include place holding zeroes, and in seeing the relationships
between numbers.

Limit this game to subtraction initially. More able children might go on to
investigate how they can make digits zero by using addition. What effect does
this have on the other digits in the number? Will they ever be able to make
every digit zero if they use only adition?

Number Chains

This activity is quick to set up, and is the kind of thing that you could put up on
the board for children to work on as soon as they come into the classroom in
the morning, in the few minutes while you are getting ready to do the register.

Write up a starting number, and a sequence of operations which result in a
change to one digit of the number at a time.

    1 265    +30              -200            +4000               -3


The children use whiteboards to record what number they generate after each
operation. They can then discuss their number chain with a partner.
       - What number did they finish with?
       - Which digit did each operation change?

They can then set challenges for their partner-
      -   What operation would make the starting number into 1565?
      -   Write down 3 steps to change 1 265 into 3 219.

Resources to support Place Value work

As we have already seen, reinforcement of the concepts of place value is
often easier when a wide variety of practical resources are used. These allow
children to build up mental images which support their understanding. Useful
resources include:

Straws (for early place value work- see Layered targets handout)
Dienes equipment
Beadstrings
Place value arrows (including decimals)
Abacus
Place value flip books

The game ‘Sharkpool’ on the Mathszone website, is a fantastic way to
reinforce place value in two digit numbers.

								
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