# Common Misunderstandings - Level 2.4 Renaming and Counting Tool

## Level 2: Place-value

### Instructions

Bold type indicates what should be said.

Place 3 hundreds, 17 tens and 6 ones in front of the student. Make sure student understands that they are hundreds, tens, and ones. Ask: “Can you write down the number shown by these blocks please?” Note student’s response. If number is incorrect, ask student to explain their answer then move on to the Card A task.

If correct, that is, 476 is recorded, remove materials to one side and ask: “If you could only use tens and ones to make that number, how many tens would you need?” Note student’s response and/or strategies. If student appears hesitant, try to find out what he/she is thinking by asking, “Can you tell me what you are thinking about?” or “What are you trying to do?”

Place Card A in front of the student and ask: “Can you read that number please?” … Note response, then ask, “Can you think of a number that is smaller than this but larger than 50?” … Note student’s response, then point to Card A again and ask, “Now, can you write down a number that is 2 tens larger than this?” … Note student’s response. If student experiences some difficulty with this, try to find out why. Either stop at this point or proceed to Card B if appropriate.

Present Card B and ask: “Can you read that number please?” … Note response, then ask, “Can you think of a number that is smaller than this but bigger than 517?” … Note response. If correct, ask, “This time, can you write down a number that is at least 1 hundred more than this but smaller then 968?” … Note response. If student hesitates, remove card and proceed to Card C.

Present Card C and ask: “Can you read that number for me please?” … If correct, ask, “Can you count on by ones from that number please? If student counts on by ones fairly easily, point to Card C again and say: “Thank you, now what if I asked you to count backwards by tens, what number do you think would be ten less than this number?” … Note student’s response, explore their thinking if appropriate.

This tool has two different elements, the MAB task and a card-based task. The observations and advice associated with each task are presented in turn below

### MAB materials

This task would only be used with students who had demonstrated a sound understanding of 2-digit place-value (see Tool 2.1) and are familiar with the MAB materials. Student responses to this task indicate the extent to which they understand 3 and 4-digit place-value.

Observed response Interpretation/Suggested teaching response

Little/no response, counts actual blocks (26), or says something like “3 flats, 17 longs and 6 minis”

May not understand task and/or is unfamiliar with MAB materials, does not recognise significance of units

Number recorded does not indicate that tens need to be regrouped as hundreds, eg, says” 3 hundreds, 17 tens and 6 ones”, or records 3176 or 376

Suggests hundreds not understood as 10 tens, may not fully appreciate the role of position in recording numbers

• Review and consolidate 2-digit place-value (see above)
• Play Trading Game to given 3 digit numbers to reinforce that 10 tens is 1 hundred

Number recorded correctly as 476, but unable to say how many tens would be needed, may attempt to count the number of tens by counting all (eg, 10, 20, 30 …) and keeping track of the count or by formally dividing 476 by 10

May not appreciate that numbers can be renamed in terms of place-value parts in a variety of ways, may interpret task in terms of quotition division (how many tens in 476?)

• Review and consolidate 2 and 3-digit numbers, that is, make, name, record, compare, order/sequence, count forwards and backwards in place-value parts and rename numbers in more than one way
• Model and practice renaming in particular using MAB and Number Expanders

476 recorded, indicates 47 tens needed fairly quickly or by counting tens in a way that shows an understanding of 10 tens in 1 hundred (eg, “10 tens in 1 hundred so 40 tens and 7 more

Demonstrates a relatively sound understanding of 3-digit place-value

• Consolidate 3-digit place-value (see above)
• Consider introducing or review and consolidate 4-digit numeration as appropriate

Observed response Interpretation/Suggested teaching response

Reads 86 correctly, provides an appropriate smaller number for Card A, may or may not provide a number that is 2 tens larger for Card A and experiences some difficulty with Card B

Suggests 2 and/or 3–digit number knowledge not very well established

• Review and consolidate 2-digit place-value knowledge (see Advice for Tools 2.1)
• Consider introducing and/or reviewing and consolidating 3-digit place-value as appropriate

Able to provide appropriate numbers for Cards A and B, but tends to provide numbers such as 520, 600 or 670 for a number smaller than 673 and 800 or 900 for a number at least 1 hundred more than 673 but smaller than 968, may not be able to read 5308 or count on by ones from 5308

Suggests 3 and/or 4-digit place-value knowledge not very well established

• Review and consolidate 3-digit place-value knowledge (see above)
• Consider introducing and/or reviewing and consolidating 4-digit place-value as appropriate

Able to read and count on by ones from 5308, may have difficulty counting back by tens

Suggests 4-digit place-value knowledge not very well established, may not be aware that renaming can be used to support counting back by tens

• Review and consolidate 4-digit place-value knowledge (see above)
• Illustrate the use of renaming in situations like this by using a Number Expander, eg, show 5308 as 5 thousands 30 tens and 8 ones, this facilitates counting backwards in tens as 1 ten is taken from 30 to give 5 thousands 29 tens 8 ones or 5298

Identifies 5298 as 1 ten less than 5308

Suggests a sound understanding of 4-digit place-value

• Consider introducing and/or reviewing and consolidating 5-digit place-value as appropriate