- Level 3
- Number and Algebra
- Number and place value
- Recognise, model, represent and order numbers to at least 10 000
Number and place value • Level 3
Recognise, model, represent and order numbers to at least 10 000
At level 2 students will have experienced making their own bundles of 10 using materials such as unifix cubes or icy-pole sticks. It is imperative that these types of materials are used before MAB are introduced so students clearly know that 10 bundles of 10 really is 100. MAB has the groups already established and, while they are great once the notion of groups of 10 is understood, they are the second step. Many students at level 3 will need a refresher on using bundling materials before modelling numbers using MAB.
Use a place value chart to help students see the pattern of place value. Students can use these to write numbers in words and numbers written in words into the numerical representation. Students often find it difficult to write numbers like fifty thousand and twelve in digits as they may not fully understand the meaning of each place in a number. The place value chart helps with placing the zeros in the correct place. Place value charts can also be used to help students order numbers.
Recognise, model, represent and order numbers to at least 10 000 (VCMNA130)
VCAA Sample Program: A set of sample programs covering the Victorian Curriculum Mathematics.
VCAA Mathematics glossary: A glossary compiled from subject-specific terminology found within the content descriptions of the Victorian Curriculum Mathematics.
Students count and order numbers to and from 10 000. They recognise the connection between addition and subtraction, and solve problems using efficient strategies for multiplication with and without the use of digital technology.
Students recall addition and multiplication facts for single-digit numbers. They represent money values in various ways and correctly count out change from financial transactions.
Students model and represent unit fractions for halves, thirds, quarters, fifths and eighths, and multiples of these up to one. They classify numbers as either odd or even, continue number patterns involving addition or subtraction, and explore simple number sequences based on multiples.
Wishball whole number
This activity, Wishball whole number, tests students’ understanding of place value with whole numbers. Students receive a starting number, such as 3786. They work towards turning this number into the given target number. Students spin a digit and then choose the place value to move to the target number in a few moves as possible. You can use a ‘Wish ball’ to help you reach the target number. Try to achieve the target with as few additions or subtractions as possible.
Play the game with the whole class first. Pointing out the multiple representations of the number: the abacus, the numerical and the vertical number line. Once the class has the idea, students can work in pairs and play the game on a laptop or tablet. Pairs record the starting number, target number and the number of turns it took to achieve the goal. They should also record their strategies and share these with the class once all pairs have had time to play at least 5 games.
Provide students with a place value chart where whole numbers to 10,000 can be recorded and a ten-face dice. The students roll the dice and write the digit in the column of their choice with the aim of making the largest number possible.
This is best completed in small groups where 4 or 5 students record on their own chart from the same set of digits. A laminated place value chart and a marker makes it easy to repeat the game. After several games have been played, ask students to share their strategies for making the largest number.
Ask students to write a four-digit number on an A4 piece of paper so that it is easy to see.
The first step is for the students to arrange themselves in order from smallest to largest. At this stage don’t worry about the scale. Use blutack or magnets to place the numbers in order on the white board for use later in the activity.
Once the numbers are in order, show the students a numberline, a long piece of clothesline is good. Make sure it’s at least 5 metres long. This is an activity for outside or in the corridor.
Challenge the students to decide how they are going to mark the numberline so that their numbers can be correctly placed. Have markers written on large coloured sticky notes or kindergarten squares. Have a discussion about whether the number line needs to start from 0 and of course the answer is no. They can choose the smallest number which is likely to be around 1000 and the largest which is likely to be around 9999. Folding the clothes line or using another piece as a ruler are both good ways. Encourage the students to come up with the idea of marking the 1000’s and possibly the mid-points.
Once the students have placed the markers on the numberline they then collect their numbers from the board. Do this in stages: all the numbers between 1000 and 1999 and so on. Students use pegs to attach their numbers to the numberline. Some may need assistance to place their numbers: Is it closer to the beginning of the section, bigger than the middle and so on.
Once all the numbers have been placed the students can then be challenged to place additional numbers.
Learning from home
This activity, Wishball whole number, will test children's understanding of place value with whole numbers. Students receive a starting number, such as 3786. They work towards turning this number into the given target number. They spin a digit and then choose the place value to move to the target number in a few moves as possible. They can use a ‘Wish ball’ to help them reach the target number. The aim of the game is to try to achieve the target number with as few additions or subtractions as possible.
Play the game together to begin with. As you play, discuss the multiple representations of the number: the abacus, the numerical and the vertical number line. Once your child understand the game they may play on their own. Encourage your child to record the starting number, target number and the number of turns it took to achieve the goal. Discuss with them the strategies they used along the way. Did they improve as they played more games? Why?