Explaining the concepts of ‘trading’ or ‘renaming
Trading (or grouping) – grouping numbers into groups of 1s, 10s, 100s, 1000s (etc) in order to perform simple additions and
subtractions
For example, you get 10 of a particular unit and then trade it for one of the subsequent unit (i.e 10 ones are traded for 1 ten. 10 tens
are traded for 1 hundred). It is important for teachers to make sure the students understand the link between the blocks, the actions
and the words – than merely move the blocks as directed by the teacher without making the connections with the concept of trading
and the addition process.
A simple trading example is:
34 + 21 = ?
= 55
•
•
•
Renaming – Numbers need to be renamed in a varietyy of ways rather than being
understood in terms of counting or even place value (Booker et al, 2010, pg 81).
For example, 89 can be viewed as 8 tens and 9 ones, as well as 89 ones.
568 can be interpreted as 5 hundreds, 6 tens and 8 ones; or 56 tens, 8 ones; or 568
ones.
**** RENAMING AND TRADING GO HAND-IN-HAND ****
Explain why these understandings are
essential for children’s number learning.
• Renaming and trading numbers are crucial number processes in developing number sense (Booker et
al, 2010, pg 82). Renaming of numbers is used everyday.
• It is important that students understand trading and renaming in order to create meaningful
mathematical experiences.
• Renaming is a crucial way of understanding numbers. Booker et al state that understanding how
numbers can be renamed is important for comparison and rounding, counting on and back, and, later,
students will need an understanding of renaming in order to understand the algorithms for subtracting
and diving large numbers (2012, pg 119).
• These concepts lay the foundations to a students future mathematical education, for example, once
an understanding of renaming and trading has been gained, children can then extend this thought
process to counting on and back by hundreds, tens and by ones (especially with larger numbers) Booker
et al, 2010, pg 121).
• Students must understand when renaming is appropriate, for example, in Stage 1 Mathematics (NSW),
students may be shown that you only need to rename sometimes.
An example is: 65-32 = ? (show working and explain why you do/do not have to rename a number).
Answer: Renaming is the same thing as borrowing. In this particular problem, 32 can be subtracted from
65 without renaming (65-32=33). However, if the problem was 62-35, you would have to rename the 2 to
12, by borrowing from the 6, which would then become 5.
5 62 12 35
27
Examples
Activity 1: Using pop-sticks to rename
• Ensure that students are familiar with using popsticks and rubber bands to represent three-digit
whole numbers, as an extension of work with 2digit numbers. For example:
• 43 is made with 4 bundles of ten and 3 singles,
• 143 is made with 1 group of ten bundles of ten (i.e.
a hundred group), 4 bundles of ten and 3 singles.
• Then ask them to make 143 using only bundles of
ten and singles, (i.e. 14 bundles of ten and 3
singles). Give them practice with other three-digit
numbers. Students can make challenges for each
other to complete. The advantage of using the popsticks is that all the individual units are easily seen
and can be bundled and unbundled readily; a
disadvantage is that many sticks are required for
larger three-digit numbers. Students can prepare
bundles of ten and of ten tens (100) to keep for use
on many occasions.
Source: State Government of Victoria. (2009).
Department of Education and Early Childhood
Development. Mathematics Developmental Continuum.
Retrieved from
http://www.education.vic.gov.au/studentlearning/teach
ingresources/maths/mathscontinuum/number/N22501
P.htm#a1
Examples (cont’d)
Activity 2: Using MAB to rename
Ensure that students are familiar with using MAB to represent numbers. For example:
43 is made with 4 longs and 3 minis
43 can also be made with 43 minis
143 is made with 1 flat, 4 longs and 3 minis
Note to Teachers: Emphasise that 43 separate minis is cumbersome compared with the convenience of
using 4 longs and 3 minis instead. Highlight, that there are still the same number of blocks (really,
the total volume is still the same).
Then ask them to make 143 using only:
longs and minis (14 longs and 3 minis)
flats and minis (1 flat and 43 minis)
•
•
Make the point that while we could also use 143 separate minis, it is too cumbersome.
Give students practice with other three-digit numbers. Students can also make challenges for each
other to complete. MAB are useful because quite large numbers can be represented. A
disadvantage is that a long, for example, has to be exchanged for 10 separate minis, rather than
broken up into 10 minis. Teachers will need to highlight that the same number of blocks is present
after the exchange.
Source: State Government of Victoria. (2009).
Department of Education and Early Childhood
Development. Mathematics Developmental Continuum.
Retrieved from
http://www.education.vic.gov.au/studentlearning/teach
ingresources/maths/mathscontinuum/number/N22501
P.htm#a1
Examples (cont’d)
Number expanders are a common tool used in the classroom to help
explain the concept of renaming.
Blank, to show hundreds,
tens and ones.
236 = 2 hundreds + 3 tens + 6 ones
236 = 2 hundreds + 36 ones
236 = 23 tens + 6 ones
236 = 236 ones
Examples (cont’d)
Trading
Adding numbers
• Numbers of any size can be added together easily. When adding 2, 3
and 4 digit numbers using a written method, write the numbers in a
vertical list. You will need to properly line up the place value columns
so you get the correct total.
• Example:
• Step 1: Make sure each number is carefully listed in neat place value
columns to avoid errors.
• Step 2: Working from right to left, add each column, starting with the
units column. You may have to trade to the next column.
9 ones + 5 ones = 14 ones.
Trade ten ones for one ten
6 tens + 1 ten = 7 tens
2 hundreds + 7 hundreds = 9 hundreds
Answer = 974
Examples (cont’d)
Subtracting numbers
• When we subtract, we take away one of the two numbers from the other. Make
sure the same place value columns line up underneath each other.
6 ones cannot be taken away from 5 ones. We need to
add ten ones to make 15, and change the 3 at the top of
the tens column to 2. 15 ones less 6 ones, equals 9 ones.
Step 2: (Tens column)
4 tens cannot be taken away from 2 tens. Trade 1
hundred to make 12, and change the 4 at the top of the
next column to a 3. 12 less 4 equals 8.
Step 3: (Hundreds column)
3 hundreds less 2 hundreds leave 1 hundred.
Answer = 189