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# Stage 3 whole numbers

## Strategies

Students can:

• round numbers when estimating
• understand where negative numbers are used
• locate negative numbers on a number line

## Activities to support the strategies

In mathematics, students are required to round numbers to the nearest ten, hundred or thousand when estimating. There is an emphasis on number sense, confidence and competence in using mental, written and calculator techniques. It is important that students can approximate and estimate successfully when dealing with problems in everyday life, especially involving money.

### Activity 1

When learning to estimate, it is important that students clearly know their number facts and relationships. In teaching students to round numbers, students must understand place value and the meaning 'close to'. It is important that students develop a sense of number and what it 'looks' like.

The following activities will allow students to develop their skills in approximating, estimating and rounding.

1. Ask students to give estimates in practical situations, such as:

• How many counters will fill this large container?
• How many students could sit comfortably in our classroom, without any chairs and desks in the room?
• How many steps would it take to reach the school library from our classroom?
• How many textbooks could fit on the floor in our school hall?

Students make the number cards 0 to 9 and select four, five or six cards. a) Students use the cards selected to:

• place them in ascending or descending order
• make the largest/smallest possible number
• make the next largest/smallest number
• make the largest/smallest even/odd number.

b) Students use the cards to create four-, five- or six-digit numbers then:

• identify and write the number before and after some of the numbers made
• state the place value of each numeral
• count forwards and backwards by tens/hundreds/thousands from some of the numbers made
• represent the number in as many different ways as possible (using expanded notation, in words).

c) Working in pairs, students randomly allocate cards to each place value column, for example: View/print (PDF 113.64KB)

Students:

• round each number they have generated to the nearest ten, then
• round each number to the nearest hundred, then
• round each number to the nearest thousand.

Repeat these steps with another random allocation of cards.

### Activity 2 – rounding numbers

Give the following cards to students View/print (PDF 71.22KB)

• In small groups students write the headings Number, Number rounded to the nearest 100 and Number rounded to the nearest 1000 and place at the top of their working space. The students then sort through the cards, placing each one under the appropriate heading.
• Students use the media or internet to look for real-life situations where large numbers are used. Use these numbers to practise rounding to the nearest hundred, thousand, etc.
• This activity can be repeated with six-digit cards.
• As numbers are displayed and read aloud by the teacher, students locate the correct written form and write the matching number in the space provided. View/print (PDF 580.98KB)

### Matching numbers to words

Students in pairs/groups cut up the numbers and paste them onto the correct words as below. View/print (PDF 74.57KB)

### Activity 3 – negative numbers

Display a number line from 0 to 19. Discuss:

• Starting from the zero on the number line, the numbers are in ascending order towards the right end of the number line.
• What happens to the numbers at the left end of the number line?
• Are there any numbers less than zero?

Students discuss what negative numbers are and when they are used. Collect examples from books, newspapers or the internet, such as:

• temperatures that are below zero
• facts that have negative numbers, e.g. elevations below sea level, such as the Dead Sea which has an elevation of approximately - 420 metres.

Discuss each example.

Hang a 'washing line' across the classroom. As a class activity, students use the following cards to correctly position numbers, including negative numbers, on a number line. Stage 3 – whole numbers – washing line activity (PDF 65.33KB)

• Put the card with -15 at the left end and the card with 15 at the right end of the line.
• The teacher randomly chooses a card and asks a student to hang the card in its approximate position on the number line.
• The student must give reasons to justify the chosen position.
• Repeat with other students until all the cards have been positioned on the number line.

These steps can be repeated using cards with negative fractions, decimals and mixed numerals.

## References

### Australian curriculum

ACMNA107: Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction

ACMNA124: Investigate everyday situations that use integers. Locate and represent these numbers on a number line

### NSW syllabus

MA3-4NA: Orders, reads and represents integers of any size and describes properties of whole numbers.

### NSW numeracy continuum

Aspect 4: Place Value – System Place Value.

### NSW literacy continuum

VOCC12M2: Vocabulary knowledge, Cluster 12, Marker 2: Increasingly uses appropriate content vocabulary when creating spoken and written texts about specific topics.

### Other literacy continuum markers

VOCC12M4: Vocabulary knowledge, Cluster 12, Marker 4: Draws on knowledge of word origins to work out meaning of new words.

## Numeracy app

Greater Than is a children’s app that is meant to help them learn which numbers are bigger than others. It tests their knowledge of greater than and less than for numbers up to 10 in a fun, game-like manner in order to keep the children's interest. The app uses fun sounds in response to the child's selection and encourages them as they go along. The app has a status bar at the bottom which graphically shows the child how well they’re doing!