# Stage 1 whole numbers

Skill focus count forwards by ones from a given 3-digit number

Students can:

• count forwards by ones from a given three-digit number

## 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 – flip and see

• Provide each student with a large collection of popsticks and a base board divided into a 'tens' and a 'ones' column.
• Place numeral cards in the range zero to nine face down on the floor.
• The students take turns to flip over two numeral cards and place one card in the tens column and one card in the ones column on their base board.
• Students then bundle popsticks into tens and place the correct number of bundles and units onto their base board to match the numeral cards.
• Discuss how many tens and ones were made.

### Activity 2 – dice

Materials required:

• dice
• a collection of base 10 blocks or unifix cubes

### Race to 100

• place each student with a partner.
• each partner rolls the dice and the one who rolls the highest, goes first.
• players will take turns rolling the dice, adding each number rolled onto their previous total using base ten blocks, and racing to reach 100. For example, player 1 rolls the dice. Let's say this player rolls a 5, they will then take 5 units, showing what their score is.
• player 2 (partner) does the same.
• player 1 has their turn again and let's say they roll a 6. The 6 has to be added onto their previous number (5).

The goal is for students to use mental strategies by putting back their 5 units and trading for one ten and one unit. This shows they understand addition place value.

If they take 6 more units, count, and then realise that they have enough units to trade for a ten, this shows they are still developing an understanding of the concept.

Players continue adding and trading until they have enough tens to trade for a 100 block. The first player to reach 100 is the winner.

When students gain confidence in the activity, have students record their working out on paper as they go, representing the blocks with numbers. For example, 5 + 6 = ?. I know that 5 + 5 gives me 10 and 1 more makes 11

### Ordering – less than and greater than

Version 1: In pairs, students are given three dice of different colours, representing hundreds, tens and ones. Students take turns to throw the dice, record their three-digit number and writing the number before and after the number rolled.

Version 2: In pairs, students are given three dice of different colours, representing hundreds, tens and ones. Students take turns to throw the dice and record their three-digit number. Students nominate whether their number will be 'greater than' or 'less than' their partner's number.

They compare their numbers by showing the relationship between the two three-digit numbers they have made by using a < or > sign.

For example, student A rolls 431 and says 'greater than'. Student B rolls 146 which is 'less than'. Student B wins the point. The winner is the first to 20 points.

This activity could be repeated using four dice.

## References

### Australian curriculum

RACMNA027: Recognise, model, represent and order numbers to at least 1000;

ACMNA029: Explore the connection between addition and subtraction.

### NSW Syllabus

MA1-4NA: Applies place value, informally, to count, order, read and represent two and three digit numbers; MA1-5NA: Addition and Subtraction

## Numeracy app

OKTA: Oh, no! Okta and his friends need help. Help rescue them by transporting them to a safe ocean. How fast can you transport the Oktas? Use your counting skills to save as many as you can before the timer runs out. This app was developed for children in grades pre K–2 by Illuminations. It is also available as an online activity along with many other free math resources for children at National Council of Teachers of Mathematics.