1. Place value and numeration
Layout By PresenterMedia.com
By Maths Mates Group 2

2. Objective 1: Explain what place value is and why it is essential for developing
number sense and numeracy skills.
• Place value is a crucial mathematical element that children are unknowingly engaged in
from a young age; first using whole numbers and later, decimals.
• These early, authentic experiences will act as the foundation of one’s ability to
confidently read, write, calculate, correctly order, and discuss numbers, their
representations and systems, with accuracy (Johnson, 2013).
• A teacher must offer their learners a variety of individualised, authentic and
manipulative, counting activities, group and exchange activities, and the chance to
manipulate numbers in various ways. Reys, Lindquist, Lambdin and Smith (2009, p. 161)
explain, it is essential for students to “make sense of numbers” and the variety of ways
and contexts in which they can be used.
• A strong foundation of number sense; that is the mathematical language, symbols, and
patterns (Booker, Bond & Sparrow, 2010), will enable students to extend on their
knowledge, and use this to solve and understand more complex problems, later in life.
Contributor: Tori Robinson

3. Objective 2: Give examples of common problems and misconceptions children have
with place value and give examples of appropriate activities to support children’s
‘correct’ learning.
Contributor: Phillippa Corden
Common problems
• Renaming is neglected, and the significance of zero is not appreciated (Booker et al, 2010)
• Confusion when counting teen numbers due to the lack of pattern (Reys et al,2009).
• Bridging the decade or hundred (Reys et al, 2009), eg; 3010 instead of 40
• Reversing digits when writing number (Reys et al, 2009), eg: 52 /25 not recognising the
difference in value
• Writing numbers that were read aloud (Reys et al, 2009), eg: Hundred and sixty four as 100604
Activities to support learning
Large Collections
Have students collect a large quantity (e.g. 1000) of ring pulls, popsicle
sticks, bread tags. Then, ask students to list the ways they could check how
many. Ask: If we counted by 5s, then by 10s, would we get the same total?
Would the total be the same if we counted by 4s?
Which Number Is Bigger?
Ask students to say which of two numbers
(e.g. 26 and 27) is bigger. Then, invite them to
explain how they could convince someone
that this has to be so.
Counting On
Arrange some MAB materials or bundled materials so there are some ones, some tens, then some more ones, more tens, and
so on. Invite students to count on by 1s and 10s to say how many little blocks altogether. Cover the blocks with a piece of card
and gradually uncover the materials as the count proceeds. Ask: Does the total change if we start the count from the right
instead of the left? Extend the activity to include hundreds blocks (Department of Education Western Australia,2013).

4. Objective 3: Explain patterns and relationships in the place value system.
Contributor: Jacqueline Gibb
Tools for discovering patterns and relationships in the place value system.
•the role of 10’s:
Ten’s are swapped for ones. This
allows us to order and group our
numbers (Reys et al., 2009, p. 163).
We further swap 10 x 10 for 1 x
100 and so forth.
Composing and decomposing numbers:
Understanding that numbers can be made up of
several groups assists students in understanding
place value (Reys et al., 2009, p. 165). For
example, 14 can be thought of as:
Two key patterns and relationships in the place value system
•Hundreds chart – Allows students to visually explore patterns
•Place value models – Assist students to manipulate objects to represent and group
numbers in different ways
•Calculator – Use calculator to discover patterns

5. Objective 4: Give examples of learning activities to develop ‘trading’ or ‘renaming’
concepts and skills and explain why these understandings are essential for children’s
number learning.
Contributor: Kim Bullock
Children must understand that 78 is much more than the number after 77, that it is made up of
7 tens and 8 ones. Misunderstanding or gaps in children’s number understanding are proven to
be the major source of children’s difficulty with mathematics and numeracy (Booker et
al., 2010).
Renaming activity
Have students make a bicycle odometer (as per the image).
Ask the students to decide what changes after each 9 in a sequence. Have them use their
odometer to read a number sequence. For example: what number is 1 more than 99
(109, 189, 1099)? What is the pattern in these changes? (Department of Education and Training
of Western Australia [DETWA], 2004).
Trading Activity
Teacher designs images and prices on the interactive whiteboard (eg shoes $25). Students in a
small group are allocated the job of shopper, banker and shop keeper. The shopper begins with
a amount of counters and bundling sticks. He works tells the ‘banker’ what he wants to buy and
the banker trades the amount for a different configuration (25 counters for 2 bundling sticks of
10 plus 5 counters). The shopper then ‘purchases the item.
(Images from DETWA, 2004)

6. Objective 5: Use the First Steps Maths documents as a resource to select learning
activities suitable for students of particular achievement levels.
Contributor: Sophie Adams
Activity 1 (Level 1): Jack in a Box
Activity 2 (Level 3): Magnets on the Board
Activity 3 (Level 4): Spinner

7. Objective 6: Outline how to design learning experiences to support students in
developing a growing understanding of place value.
Contributor: Michelle Sheridan
•Use concrete models to create a hands on experience. There are two types of
materials which can be used in a lesson including: ungrouped materials and
grouped materials (Reys et al., 2009).
•Marbles, beans, cubes or straws are ungrouped materials which
can be used by the students to form their own groups.
•Base 10 blocks or straws that were previously grouped prior to the
students using them, are a pre-grouped material (Reys et al., 2009).
• Begin by using large numbers and skip the teens from 11-19 (Reys et al., 2009). These
number names may confuse the students while they are establishing an understanding for
place value because their names do not suggest their place value, example, 437 suggests
that there is 4 hundred and 3 tens and 7 ones, whilst 17 when said aloud does not suggest
its place value.
•Give the students experience with decomposing numbers in various ways such as
30 can be decomposed into 3 tens, 30 ones, 2 tens and 10 ones etc. Money is a real life
object that can be incorporated into decomposing numbers and learning place value. Using
real life situations is essential for preparing students for their future and makes learning
more meaningful.
(Images from Primary Concepts, 2008)

8. Objective 7: Identify important principles for teaching place value ideas.
Contributor: Phillippa Corden
• Composing and decomposing numbers is important in
developing place value (Booker et al, 2010).
• Recognition that zero represents nothing of
something.
• Conservation of number irrespective of spacial
arrangement.
• The ability to subitise , classifying, comparing ordering
and patterning.
• Recognising and demonstrating that the place-value
pattern is built on the operations of multiplication or
division of tens (ACARA, 2013)
• Place value provides an organisational structure for
counting(Reys et al., 2009).

9. Objective 8: Outline important learning in place value for children to develop
Contributor: Annalise Wilkinson
Booker et al., 2010; Reys et al., 2009)

10. Additional Objective: Awareness of relationships and patterns in decimal place value
Decimals create great confusion for many students. The misconception that a decimal can
be treated like a whole number is very common for primary students (Roche, 2010).
Introducing place value ideas with decimals:
• Begin with 1 as the unit
• Instead of grouping by tens: group by one-tenth
• use a decimal place after the ones place
• Explain that 10 of the tenths make a 1, just as 10 of any unit make the next larger unit
• Hundredths, and thousandths can be introduced in a similar way
(Reys et al., 2009)
Tools for introducing place value ideas with decimals:
Contributor: Jodie Dobbs
Place value grid
Hundred square
Decipipes
Linear Arithmetic Blocks
Multibase Arithmetic Blocks
Decimat

11. Decimals relationship to place value
Contributor: Alyson Redding
Considering a number children know what
ones, tens, hundreds and thousands. They
know what a value of 4 in 3457 is 4 hundreds.
When introducing place value ideas with
decimals again start with the unit. Instead
grouping then in one tenth (Reys et al , 2009)
Decimal numbers O.7981, have three digits after the
decimal point, each digit has different place value.
The first digit after the decimal point is called the
tenths place value. There are seven tenths in the
number O.7981. The second digit tells you how many
hundredths there are in the number. The number
O.7981 has four hundredths. The third digit is the
thousandths place. The fourth digit is the ten-
thousandths place which is five in this example.
Therefore, there are seven tenths, nine
hundredths, eight thousandths, and one ten-
thousandths in the number 0.7981 (Booker et
al, 2010).

12. Reference List
Australian Curriculum, Assessment and Reporting Authority. (2013).The Australian Curriculum v5.0 Year 4
Retrieved from http://www.australiancurriculum.edu.au/Year4
Booker, G., Bond, D., Sparrow, L. & Swan, P. (2010). Teaching primary mathematics (4th Ed.). Forest, NSW: Pearson.
Department of Education and Training of Western Australia. (2004). First Steps in mathematics: Number –
Understanding whole and decimal numbers; Understanding fractions. Port Melbourne: Rigby Heinemann. Pages
40-45.
Primary Concepts. (2008). Active learning for Pre K-3 and special needs. Retrieved from
http://www.primaryconcepts.com/meas/plastic-base-ten-flats.asp
Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping Children
Learn mathematics (1st Australian Edition). Australia: John Wiley and Sons
Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). Helping children learn mathematics (9th Ed.). New York:
John Wiley & Sons.
Roche, A. (2010). Decimals: Helping students to make sense of decimal place value. Mathematics
Classroom, 15(2), pp. 4-12.