Stage 2 whole numbers
- use place value to read, represent and order numbers up to four digits
- record numbers using expanded notation
Activities to support the strategies
Students in Stage 1 and 2 need to develop an understanding of place value. For example, in the number 3 450, the ‘four’ represents four hundred. Students need to understand how a number is constructed and the value each digit holds within the total number. We use expanded notation to show this. E.g. 3 450 = 3 000 + 400 + 50.
However, we also need students to understand that place value is more than just position value. For example, if I ask “How many hundreds are in 3 450?” some students may answer, “There are four, as there is a four in the hundreds column”. This is not entirely accurate, because there are 34 hundreds in 3 450 as 3 000 is made up of 30 hundreds. We need to focus on the whole number not just on column values. This is important for addition and subtraction as there are different ways to break up 3 450 depending on what we are adding it to.
If I need to solve:
3 450 + 1 400 =
I could use standard decomposition to split the thousands and hundreds,
3 000 + 1 000 + 400 + 400 + 50
But say I was asked to solve
3 450 + 2 450 =
I could see 3 450 as 2 450 + 1 000 (non-standard decomposition)
Therefore it may be easier to double 2 450 then add on the remaining 1 000
Students also need to have opportunities to create numbers using concrete materials. Students can build numbers using a variety of resources such as Base 10 Blocks, unifix cubes, ten strips or ten frames and bundles of pop sticks (for one- and two-digit numbers). Unifix cubes are particularly useful as students can build rows of ten and can break them up when necessary- this supports addition and subtraction skills.
Activity 1 – three and four digit numbers
In small groups, students use a pack of playing cards with the tens and picture cards removed. The aces are retained and count as 1.
- student A turns over the first 3 cards and each player makes a different three digit number.
- student A records the three numbers.
- student A then puts the cards at the bottom of the pile.
- students each take a turn in turning over three cards and recording the group's three digit numbers.
- When each student has had a turn they sort and order their numbers and write them in ascending order
- students can then check each other’s working out.
Students extend the game by making four digit numbers.
Possible questions include:
- Can you read each number aloud?
- Can you order the numbers in ascending and descending order?
- Can you state the place value of each numeral?
- What is the largest/smallest number you can make using three cards/four cards?
- What is the next largest/smallest number you can make using three cards/four cards?
- Can you identify the number before/after one of your three digit/four-digit numbers?
- Can you find a pattern? How can you describe your pattern? How can you continue the pattern?
- How many different ways can you represent each number? (expanded notation, in words)
- Can you count forwards/backwards by tens/hundreds from one of your three-digit/four-digit numbers?
- Can you round one of your three-digit or four-digit numbers to the nearest hundred? To the nearest thousand?
Activity 2 – how many ways?
The teacher selects a four digit number and records it on the board. Students express and present the number in as many ways as they can. A time limit may be imposed. Students can show the class what each variation looks like using concrete materials or drawings.
Activity 3 – highest number
Students play in pairs, sharing one score sheet. Players take turns to roll a die to try to make the highest number they can. Once a number has been placed in a column its position cannot be changed. The student who makes the higher number wins that game.
Students play several games to determine an overall winner.
The teacher ties the lesson together by asking:
- What is the largest possible number you can score? (9999 if you are using 0–9 dice and playing a 4-digit game)
- Who scored closest to this?
- What was your highest number?
- What was your lowest number?
Some of the results may be written on cards and pinned onto a “clothesline” to help students order 3-digit and 4-digit numbers.
Activity 4 – place value Bingo
Materials required: pen, A4 paper and place value cards (PDF 28.1KB)
- On the top of the card write 'ones' then write a '0'.
- On the next card write 'ones' and put a '1' on it. Continue this through to 9.
- Then start a set of cards for the 'tens' from 0 to 9, the 'hundreds' from 0 to 9 and the 'thousands' from 0 to 9. Alternately you can use different coloured paper to represent each value, e.g. red = thousands, green = hundreds, yellow = tens, orange = ones.
On a piece of paper the students draw a place value chart. On the chart they write a three- or four-digit number of their choice.
To play the game
The teacher calls out a number e.g. 9 hundreds. If the student has a 9 in the hundreds column they circle the number. The teacher places or writes the number on the board to keep track of past numbers. The teacher continues calling numbers e.g. 3 tens, and so on, until a student has all digits circled in one number. The student then calls out 'bingo' and says their numbers using place value.
The student reads read the whole number, e.g. two thousand, nine hundred and fifty-one. If they are correct, they win. A new game starts with the students writing another number on their bingo card.
ACMNA052: Recognise, model, represent and order numbers to at least 10 000
ACMNA054: Recognise and explain the connection between addition and subtraction
MA2-4NA: Applies place value to order, read and represent numbers up to five digits
MA2-5NA: Addition and subtractions. Uses mental and written strategies for addition and subtraction involving 2, 3.4 and 5 digit numbers
- Developing efficient numeracy strategies stage 1 (PDF 16.6MB) provides clear directions for supporting student learning in number. It builds on students' current methods of solving arithmetic problems.