Level 2: Placevalue
Materials
Instructions
Bold type indicates what should be said.
Empty container of counters in front of student and ask:
“Can you count these as quickly as possible and write down the number please?” Note how the count is organised and what is recorded.
If not 26, ask,
“Are you sure about that? How could you check?”
Once student has recorded 26, circle the 6 in 26 and ask,
“Does this (point to the 6)
have anything to do with how many counters you have there?” Indicate the collection. Note student’s response.
Circle the 2 in 26 and repeat the question. Note student’s response. Place counters back in the container.
Place bundles and sticks in front of the student and ask,
“Can you make 34 using these materials please?” Note student’s response. If student asks or moves to unbundle a ten, say,
“Before you do that, is there any way you could use these (pointing to the bundles of ten)
to make 34?” Note student’s response. Remove sticks.
Tip out the container of 26 counters and ask student to count these again and record the number. Note response, then ask,
“Can you put these into groups of four please?” Once this is completed, point to the 26 that has been recorded and circle the 6. Ask:
“Does this have anything to do with how many counters you have?” Circle the 2 in 26 and repeat the question. Note student responses.
If counter task handled reasonably well, place the 099 Number Chart in front of the student. Cover the numbers 33 to 66 with the Masking Card and ask,
“Can you count on by ones from 41 please?” If done easily, point to 57 and ask,
“Can you count back by ones from here please?” Note student’s response.
Run your finger down the column headed by 5 and ask,
“What are we counting on by now?” If student says “fives”, remove mask and try to find out what he/she is thinking by asking,
“Do you still think we are counting by fives … Why?” Proceed to next question. If student answers “ten or tens” to initial question, leave mask in place and ask ,
“Can you count on from 15 by tens until I say ‘stop’?” If student stops at 95, encourage him/her to continue. Say “stop” when student no longer continues or at 135 (whichever comes sooner). Note response and whether or not student can proceed beyond 95.
2.1 Advice rubric
This tool has four different elements, the kidney bean task, the bundling sticks task, the regrouping task, and the number chart task. The observations and advice associated with each task are presented in turn below.
Kidney beans
Student responses to this task indicate the meanings they attach to 2digit numerals. A version of this task was originally employed by Ross (1989) who identified five stages in the development of a sound understanding of placevalue, each of which appears in some form in the advice below.
Observed response  Interpretation/Suggested teaching response 

Little/no response  May not understand task 
Response given but not indicative of strong placevalue knowledge, eg, refers to 6 ones or physical arrangement such as “2 groups of 3” for circled 6, and “twenty” for circled 2. 
Suggests 26 is understood in terms of ones, or 20 (ones) and 6 ones, may not trust the count of 10 or see 2 as a count of tens  Check extent to which child trusts the count for 10 by counting large collections (see
Tool 2.2 )
 Practice
making, naming and
recording tens and ones, emphasising the count of tens in the tens place and the count of ones in the ones place

Says 6 ones and 2 tens fairly quickly 
Appears to understand the basis on which 2digit numbers are recorded  Consolidate 2digit placevalue by
comparing 2 numbers (materials, words and symbols),
ordering/sequencing (by ordering 5 or more 2digit numbers or placing in sequence on a rope from 0 to 100),
counting forwards and backwards in placevalue parts starting anywhere (eg, 27, 37, 47 (clap), 46, 45, 44, 43, …), and by
renaming (eg, 45 is 4 tens and 5 ones or 45 ones)
 Consider introducing 3digit placevalue

Bundling sticks
Student responses to this task indicate their understanding of placevalue and the extent to which they trust the count of 10, that is, they can treat 10 as a countable unit.
Observed response  Interpretation/Suggested teaching response 

Little/no response, incorrect or insists on using/counting by ones only  May not understand task, does not trust the count of 10  Check extent to which child
trusts the count for 10 by counting large collections (see
Tool 2.2 ) and review
subitising and
partpartwhole ideas for 10 (see
Level 1 )
 Practice
making, naming and
recording tens and ones, emphasising the count of tens in the tens place and the count of ones in the ones place

Counts ones, attempts or asks to unbundle tens in order to continue count of ones, after prompt may check count of bundle then uses either 2 tens and 14 ones or 3 tens and 4 ones 
Suggests placevalue ideas not well established, may not trust the count of 10 if student checks the number in a bundle  Check
trust the count, review
subitising and
partpartwhole ideas for 10 and
making, naming and recording tens and ones (see
Level 1 Advice )
 Consolidate 2digit placevalue by
comparing 2 numbers (materials, words and symbols),
ordering/sequencing (by ordering 5 or more 2digit numbers or placing in sequence on a rope from 0 to 100),
counting forwards and backwards in placevalue parts starting anywhere (eg, 27, 37, 47 (clap), 46, 45, 44, 43, …), and by
renaming (eg, 45 is 4 tens and 5 ones or 45 ones)

Uses 3 tens and 4 ones to make 34 without any hesitation 
Suggests sound understanding of placevalue, particularly if combined with ability to recognise 6 as 6 ones and 2 as 2 tens in 26.  Consolidate 2digit placevalue by
comparing 2 numbers (materials, words and symbols),
ordering/sequencing (by ordering 5 or more 2digit numbers or placing in sequence on a rope from 0 to 100),
counting forwards and backwards in placevalue parts starting anywhere (eg, 27, 37, 47 (clap), 46, 45, 44, 43, …), and by
renaming (eg, 45 is 4 tens and 5 ones or 45 ones)
 Consider introducing 3digit placevalue

Grouping task
Student responses to this task indicate the strength of their understanding of placevalue by exploring the extent to which they can be distracted by the regrouping and the perceptual image it presents (6 groups of 4 and 2 ones remaining). Interestingly, some students who referred to the 2 in 26 as “twenty” in the first instance are prompted to refer to the 2 in 26 as “2 tens” after the grouping exercise.
Observed response  Interpretation/Suggested teaching response 

Little/no response or refers to 6 as the number of groups of 4 and 2 as the 2 remaining ones  Distracted by the visual arrangement to override whatever else they may know about what ‘26’ means, suggests little/no placevalue knowledge. May not understand task, does not trust the count of 10  Check extent to which child
trusts the count for 10 by counting large collections (see
Tool 2.2 ) and review
subitising and
partpartwhole ideas for 10 (see
Level 1 )
 Practice
making, naming and
recording tens and ones, emphasising the count of tens in the tens place and the count of ones in the ones place

Is not distracted by visual image or regrouping, but refers to 2 as “twenty” 
Suggests placevalue ideas not well established, may not trust the count of 10  Check
trust the count, review
subitising and
partpartwhole ideas for 10 and
making, naming and recording tens and ones (see above)
Consolidate 2digit placevalue by
comparing 2 numbers (materials, words and symbols),
ordering/sequencing (by ordering 5 or more 2digit numbers or placing in sequence on a rope from 0 to 100),
counting forwards and backwards in placevalue parts starting anywhere (eg, 27, 37, 47 (clap), 46, 45, 44, 43, …), and by
renaming (eg, 45 is 4 tens and 5 ones or 45 ones) 
Says 6 ones and 2 tens fairly quickly 
Appears to understand the basis on which 2digit numbers are recorded  Consolidate 2digit placevalue by
comparing 2 numbers (materials, words and symbols),
ordering/sequencing (by ordering 5 or more 2digit numbers or placing in sequence on a rope from 0 to 100),
counting forwards and backwards in placevalue parts starting anywhere (eg, 27, 37, 47 (clap), 46, 45, 44, 43, …), and by
renaming (eg, 45 is 4 tens and 5 ones or 45 ones)
 Consider introducing 3digit placevalue

Number chart task
Student responses to this task indicate their understanding of the placevalue pattern and the extent to which they recognise the count of 10 and treat 10 as a countable unit.
Observed response  Interpretation/Suggested teaching response 

Little/no response or hesitant to count hidden numbers on from 41 or back from 57  Unlikely response but may not understand task, needs to see the numbers to generate the count, and/or is unsure about the number naming sequence  Check extent to which child can accurately count a physical collection (see
Tool 2.2 )
 Practice
making, naming and
recording tens and ones, emphasising the count of tens in the tens place and the count of ones in the ones place
 Draw attention to the patterns inherent in the 099 Number Chart by talking about the 1 ten family, 2 ten family, 3 ten family etc and how each number is represented, eg, 34 is in the 3 ten family, it is made up of 3 tens and 4 ones. Discuss what remains the same and what changes in each row (tens remain the same, ones change).
 Rehearse oral counting sequence and counting larger collections efficiently (see
Tool 2.2 )

Manages to count on/back by ones fairly easily but says “fives” when asked to identify column count. May count on by tens once mask removed.  May not understand task but more likely to be distracted by visual perception suggesting understanding of placevalue pattern not very robust, may only understand count of tens in terms of multiplies of ten and ones (ie, 10, 20, 30, 40, …)  Practice
making, naming and
recording tens and ones, emphasising the count of tens in the tens place and the count of ones in the ones place
 Draw attention to the patterns inherent in the 099 Number Chart (see above). Discuss what remains the same and what changes in each row (tens remain the same, ones change) as well as each column (ones remain the same, tens change).
 Practice counting on/back in placevalue parts starting from anywhere using Number Charts that extend beyond 100

Recognises count of tens and can count on by tens to 95 but hesitates or counts on by ones or fives to arrive at 105  May not appreciate that tens can be counted as countable units in the same way that any other ‘object’ might be counted, or that numbers can be renamed in terms of their placevalue parts  Practice
renaming hundreds, tens and ones, using MAB materials (eg, 124 can be shown as 1 hundred 2 tens and 4 ones, as 12 tens and 4 ones, or as 124 ones). Record in words as in example given. Discuss which is the easiest way to remember or think about these numbers
 Practice counting on/back in placevalue parts starting from anywhere using Number Charts that extend beyond 100

Recognises count of tens and counts to 135 with little difficulty 
Suggests a sound understanding of the basis on which 2digit numbers are recorded  Introduce 3digit placevalue
 Use MAB and Number Expanders to consolidate 3digit placevalue by
comparing 2 numbers (materials, words and symbols),
ordering/sequencing (by ordering 5 or more 3digit numbers or placing in sequence on a rope from 0 to 1000),
counting forwards and backwards in placevalue parts starting anywhere (eg, 327, 337, 347 (clap), 346, 345, 344, 343, …), and by
renaming (eg, 845 is 8 hundreds 4 tens and 5 ones, 84 tens and 5 ones, or 845 ones)
 Use
Number Chart activities(pdf  27.6kb) to reinforce counting patterns
