Understanding Place ValueIntervention Booklet 3
– Hundreds to a Million
TARGET GROUP: Year 7/8 – AC / EA
FOCUS: To secure student understanding of place value from hundreds to a million.
SUGGESTED APPROACH
Alongside effective classroom teaching the students will receive additional small group teaching focused on connecting key understandings of place value from hundreds to a million assuming they have an understanding of place value to 100. Timeframe will vary depending on progress of the student/s. Therefore knowledge and strategy checks (see below) must be carried out regularly during the sessions.
Tasks (word problems, number problems, problem solving) should be used to support understanding of place value when solving addition, subtraction, multiplication and division problems.
Key Point: The rule of place value – only digits from 0-9 may be placed in any Place Value column – should be reinforced throughout all place value tasks e.g. the process of exchange and /or trade of ten ones for one ten and ten, ten dollar notes for a one hundred dollar note. DLO link eg. ‘Wish Ball’.
Connections must be made between the place value equipment used, the language and the symbols e.g. 12 tens – to 120 – to one hundred and twenty.
SUPPORT READINGS
Recommended Professional readings on and about place value:
Van de Walle - Chpt 11
Numeracy ‘Pink Book’ Book 5 ‘Teaching Place Value, Addition and Subtraction’.
Place Value Intervention Booklet 2
DIAGNOSTIC ASSESSMENTS
Knowledge and strategy checks to be asked at start of support and end of each teaching session.
1)49 recorded in modelling book, ask how many bags of ten there are in 49.
If there is an incorrect response refer to Place Value Intervention Booklet 2.
2)Record 164 in modelling book. Ask how many bags of ten could you make?
3) 4 hundreds, six tens, five ones and three thousands – what is the number?
4) 13 tens and 9 tens – what is the sum?
ON GOING INFORMATION COLLECTION
- Modelling books
- Anecdotal notes
- Photographs
- ICT presentations
- Students work books including goal setting, record of work, reflections.
- NUMPa, IKAN, PAT and GLOSS
- National Standards placements
- OTJs
WHAT TO DO
Programme Structure
Personnel:specialist teache/classroom teacher
Location: flexible according to individual schools and situations
Time: 20 mins-half hour sessions daily. Two weeks or alter depending on progress of students. Eg. If they ‘get it’ early select another group to work with.
Size of Group: 6-8, need a few students to have thinking conversations.
Lesson Structure:
Addition example
Equipment – play money, Arrow cards, and Place Value houses
Bina saved $74 and her grandmother gave her $ 57 for her birthday. How much did Bina have all together?
Students make 74 and 57 using play money then discuss how to solve the problem. Teacher records the solutions using the following notation: e.g. 7 tens + 5 tens –> 12 tens –> 1 hundred and 2 tens
4 ones + 7 ones –> 11 ones –> 1 ten and 1 one = 1 hundred and 3 tens and 1 one -> 100 +30+1 (expanded form) =131 Emphasis on the language of place value - trading, swapping, exchanging (not borrowing) e.g. I am trading 10 ten dollar notes for a single one hundred dollar note Relating to the place value houses – 12 tens and 11 ones – what does this look like in the columns of the houses?
Subtraction example
Same equipment as mentioned in Addition example
There are 83 dollars in the piggy bank.
Linda spends 29 dollars on a DVD. How many dollars left?
Children make 83 using money – Student explains: e.g. – I have 8 ten dollar notes and 3 one dollar notes, I will take 3 one dollar notes away to leave 8 ten dollar notes. And I will swap / trade one ten dollar note at the bank for ten singles because I still need to take away 6 dollars. I am left with 7 tens and 4 ones -> 74 Now I have to take away 2 tens from 7 tens – which leaves me with 5 tens Answer – 5 tens and 4 ones which is 54 Similar processes can be used to solve multiplication and division problems using play money equipment or canisters and beans
Multiplication example
Equipment: Film canisters with beans, or play money, PV houses, Arrow cards
e.g- 4 x 45 – 4 groups of 4 tens, and 4 groups of 5 ones record student solutions: e.g. 16 tens + 20 ones = ? 16 tens = 1 hundred and 6 tens – same as 160
20 ones – two tens – 20
160+20 = 180 – how many tens?
Division example
Equipment= As stated in the Multiplication example.
e.g. 550 – how many tens are there? (in the whole number)
record student solutions :
e.g.in 1 hundred there are 10 tens so in 5 hundred there are 50 tens
in 50 there are 5 tens
so 55 tens altogether in 550
Using the answers to problems continue to make links to the place value houses as in addition model
After consolidation of these values – problems can be extended to include thousands and beyond. Eg. ten hundreds for one thousand etc.
Extend to larger numbers by:
introducing the idea of rolling over – eg. $999,999 + one dollar – using money and linking to place value houses
Students’ work in pairs – one student takes on the role of banker and the other requests the money during the trade.
This activity is designed for students to practice naming the place value columns, and to record the number linking the use of commas with the separation of the place value houses.
Then the idea of rolling back – e.g.$100,000 -25=?
Trade $100,000 for 10 ten thousand dollar notes,
Trade 1 ten thousand dollar note for 10 one thousand dollar notes
Trade 1 thousand dollar note for 10 hundred dollar notes
Trade 1 hundred dollar note for 10 ten dollar notes
Trade 1 ten dollar note for 10 one dollar notes
Now take away twenty five dollars – how much have you left?
Read, write and say the number that
As a follow up – without using the place value houses write in words these numbers:
45 906 e.g. forty five thousand, nine hundred and six
215 052
4 532 867
eighty thousand and twenty six
Expanded form and as a number:
800+6 = (806)
6 + 5000 + 30000 = (3506)
500000 + 30000 + 4000 + 50 + 2 = (?)
use arrow cards as support equipment if needed
Progression of problems – if 3+4=7, then 30+40=70, 3 tens and 4 tens is 7 tens
Using appropriate materials to scaffold understanding of PV
Links between strategy and knowledge – identify specific knowledge required for specific strategies
Issues / Misconceptions /Suggestions /Checklists/things to note:
The canon of place value – make it explicit
Home links
Information sheet explaining key Concepts and language involving place value, sent home outlining key ways parents can support their child.
place value games - online
mathsgames4children.com
Developers: Linda, Christine, Robyn and Bobby