This unit uses one of the digital learning objects, Modeling Numbers: 3-digit numbers, to support students in investigating the place value of numbers up to 999. The numbers are represented using a range of standard place value materials.
- Represent numbers in the range of 0-999 using place value equipment.
The learning object has two main functions:
- Firstly, it allows students to make their choice of number using place value equipment. They can listen to that number being read using the speaker function. The learning object also represents the number using place value equipment, written words, place value houses, standard forms and an abacus.
- Secondly, it provides students with a number that they are challenged to represent using the place value equipment. Feedback is provided to the students to help them.
The Level 2 Number Unit, Show me the Number, is a useful starting point for developing the prior knowledge necessary for engagement in this unit, as it helps students to understand place value for tens and ones using two digit numbers and equipment. Some prior experience with representations and materials used in the learning object would also be beneficial.
There are a number of ways to explore place value concepts. Students will benefit from exploring place value with a range of equipment including place value blocks, beans and canisters, bundles of sticks, 3-bar abacus, and number flip charts. Avoid starting immediately with wooden place value blocks and the three-pronged abacus. They are restrictive in building children’s understanding of place value. Bundling popsicle sticks is a good place to start so that children can see what makes one ten and how many bundles of 10 will give 100. A next step would be to make groupings using small plastic bags of ten beans as well as loose beans, moving onto cannisters of beans (opaque) and loose ones. Using a Place Value House divided into columns for hundreds, tens and ones with counters reinforces the positional property of place value. The counters represent ones, tens and hundreds depending on the position they hold. Place value blocks (interlocking plastic ones) and place value houses can be introduced here. The base ten property needs to be emphasised throughout so that children grow to understand the increase in powers from right to left. The learning object then provides practise to help students visualise the place value columns.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
- exploring 2- or 3-digit numbers using a variety of place value material (threading beads, beans in bags, arrow cards, slavonic abacus, number lines, 10 frames, bundling sticks, Animal strips, magnetic board and counters, money, interlocking base 10 sets, base 10 flip stands). Children can work in pairs to form a 2 or 3-digit number
- encouraging students to work in pairs or small groups when using the learning object
- strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
- working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities
- restricting numbers to two digits initially, and extending numbers to three or more digits (where appropriate)
- allowing students to explore the Modeling Numbers: 6-digit numbers learning object, if appropriate.
The context for this unit can be adapted to suit the interests and experiences of your students. For example, you might apply real life contexts to explore the numbers. A good example could be Polyfest which can have 150 or more groups performing and very large numbers of students involved.
Te reo Māori kupu such as ine tatau (count) and uara tū (place value) could be introduced in this unit and used throughout other mathematical learning.
You could also encourage students, who speak a language other than English at home, to share the words related to counting and place value that they use at home.
- Access to the internet and Modeling Numbers: 3-digit numbers
- A range of place value materials, such as threading beads, beans in bags, arrow cards, slavonic abacus, number lines, 10 frames, bundling sticks, Animal strips, magnetic board and counters, money, interlocking base 10 sets, base 10 flip stands
There are two components to this unit - modelling your own number and modelling a given number. You should model both of these components for students and provide ample time for students' exploration of these. Consider how you will provide opportunities for students to engage with the learning object, either alongside or after your modelling. You could allow individual students or pairs of students to work with the learning object independently (perhaps they could think of a number for their partner to model or create). They could be encouraged to complete a given number of examples. Students can also explore making their own number, saying it aloud and then checking using the speaker icon. As an extension, you could provide students with a familiar context (e.g. quantities of resources in the sports shed) and ask students to use the place value equipment or the learning object to represent a model of the relevant quantities (e.g. there are 39 tennis balls in the sports shed - can you show this with the learning object?).
If the number of devices is a barrier to engagement with this learning object, consider having some students work with place value equipment to represent numbers, whilst the others work with the digital representation (then switch). Working in pairs provides students with the opportunities to work together to practice saying and representing numbers with equipment.
Model your own number
- Show students the learning object and explain that it provides a model for representing numbers using place value equipment.
- Use the up and down buttons at the top of the screen to show students how to make a number. Start from one and click through the numbers so the students can see the colour change at the 6th cube. Discuss how this makes it easier to immediately recognise numbers between 6 and 9.
- Ask the students to count as you click the arrows to make the numbers 6, 7, 8, 9, 10. Watch as the 10 cubes join to make a rod and slide into the tens column.
- Ask the students what they think will happen when you make the number 11 and if you count backwards 11, 10, 9. Demonstrate how the place value equipment changes as you click back using the arrow in the ones place.
- Ask the students how the numbers 250 and 305 (for example, you could explore others as well) will be represented. Use the learning object to show each number. Make sure students understand a how a zero digit in a number is represented. Do enough examples together for students to see how the equipment shows the change between the ones, tens and hundreds column.
- Click the right arrow at the bottom of the screen to see the number represented using a place value house, in standard form, or on a 3-bar abacus. Use the left and right arrows to choose how to represent the number. You may wish to explain these different representations to the students. If you have selected to show the number using written words then below the place value equipment a speaker icon is available to click. If you click the speaker icon you will hear the number being spoken.
Model a given number
- Click on the die at the bottom left of the screen. A number will appear in words in the box for the student to build using the place value equipment. The student can click on the speaker icon to hear the number being spoken.
- Ask a student to use the arrow keys to build the number. The learning object will provide feedback to the student. Ensure that you try enough examples that students see that the second feedback provided by the computer indicates which column their error is in.
- Clicking the down arrow at the bottom of the screen will return you to modelling your own number.
Dear family and whānau,
This week we have been using the Modeling Numbers: 3-digit numbers learning object. This enables us to represent numbers up to 999 using place value material. Ask your child to read numbers up to 999, for example letter box numbers, 3-digit licence plates, numbers in the newspaper.