Two Ten Frames Two ten frames may be used to help children understand teen numbers. Teen numbers present particular problems for young children. The choice of single-digit number names is quite arbitrary, however, once the single-digit number names have been established, they are used to generate further numbers. The two-digit such as sixty, seventy, eighty . . . . all derive from the single-digit number names and add ‘ty’ to the end. However, many anomalies occur. Consider the spelling of twenty, thirty, forty, fifty. These words bear some resemblance to their single digit counterparts, but not in the same way that sixty and seventy do. Teen numbers present their own particular difficulty. Most numbers are read from left to right, however, 18 is read as eighteen. The one ten is read as ‘teen’. Some children who hear eighteen will write 81 because the eight is said first. The first two-digit numbers that children experience are eleven and twelve, which do not follow any pattern at all. Two ten frames placed side by side may be used to model teen numbers.
1 ten 8 ones – eighteen Ten frames may be joined to model larger two-digit numbers, although bundling sticks are less cumbersome for larger two-digit numbers.
2 tens 8 ones – twenty-eight Games that involve filling ten frames will aid in the development of thinking in tens and emphasise what happens when a decade is bridged. Note how adding 9 and 6 may be modelled using two different colours.
9 and 6
becomes 10 and 5 1 ten 5 ones – fifteen
Playing with Place Value
12
© P. Swan
Base Ten Blocks
Large Cube
Flat
Long
Mini
Originally, these manipulative materials were called Multibase Arithmetic Blocks/MAB (Not MABs.) The blocks were in various bases. Base Four blocks were made in groupings of four.
Nowadays, only the Base Ten versions are used. They are sometimes referred to as Place Value Blocks or Deines Blocks (after Z. P. Deines, who promoted their use). Base Ten Blocks are an example of a proportional material. That is, ten of the single small cubes (mini) fit along the long. Ten longs fit over the flat and ten flats may be layered to form the large cube.
10 tens make 1 hundred
10 ones make 1 ten
If the small cube is given a value of one, THEN the long has a value of ten, the flat one hundred and the large cube one thousand.
Playing with Place Value
20
Š P. Swan
5 Spin a spinner and recreate the number shown on arrow cards
1 0 0 6 0
1 6 8
8 6. Show the number on a Gattegno Grid.
4 0 0 2 0
4 2 3
3 33 Š P. Swan
Playing with Place Value
Place Value Number Expanders Number expanders are folded and then unfolded to reveal the place values of each digit. There are three typical questions that students need to be able to answer which relate to place value. These are: • What is in the ... place? • In what place is the ...? • How many ... in the number? A number expander helps students to answer these questions.
5
Thousands
7
Hundreds
4
Tens
6
Ones
The number expander also may be folded to explain the renaming. For example:
5 7 4 6 57 hundreds, 46 ones - or 5 thousands, 74 tens and 6 ones.
If the number expander is made from paper, then once a number is written on the expander a new one would be required for each number. Laminating the section where the digits are written means that the number expander may be re-used. Alternately, a series of digits and paperclips may be used to create a re-useable number expander. The number expander may be altered to help students with larger numbers and decimal fractions all you need to do is change the words. The design of the number expander means that when folded, it displays the sequence of digits in place value positions, but when progressively unfolded reveals the value of the digits. The unfolding can be done in different ways. For example:
5 7 4 6 Playing with Place Value
5
Ones
36
Thousands
7 4 6 © P. Swan