Modeling numbers: 3-digit numbers

Purpose

This unit uses one of the digital learning objects, Modeling Numbers: 3-digit numbers, to support students as they investigate the place value of numbers up to 999. The numbers are represented using a variety of place value equipment commonly used in classrooms.

Achievement Objectives
NA2-2: Know forward and backward counting sequences with whole numbers to at least 1000.
Specific Learning Outcomes
• Represent numbers in the range of 0-999 using place value equipment.
Description of Mathematics

The learning object has two main functions:

• Firstly, the learning object allows students to make their choice of number using the 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, the learning object provides students with a number that they are asked to represent using the place value equipment.  Feedback is provided to the students to help them.

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:

• Explore 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 work in pairs to form their 2 or 3-digit number
• Encourage students to work in pairs or small groups when using the learning object.
• Restrict numbers to two digits initially.
• Allow 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:

• 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.
Activity

The Learning Objects

The learning object, Modeling Numbers: 3 digit numbers, can be accessed from the link below.

Prior to using the Modeling Numbers: 3 digit numbers Learning Object

The knowledge lesson Show me the Number Level 2 unit helps students to understand place value for tens and ones using two digit numbers and equipment. It would be useful to do this lesson prior to using the Modeling Numbers: 3 digit numbers learning object. 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. 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 visualize the place value columns.

Working with the learning object with students (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. Ask the students what they think will happen if you count backwards 11, 10, 9. Watch the place value equipment change as you click back using the arrow in the ones place.
Ask the students how the number 250 will be represented. Use the learning object to show the number. Ask the students how the number 305 will be represented. Use the learning object to show the 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, or in standard form or represented on a 3-bar abacus. Using the left and right arrows the students can 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.

Working with the object with students (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 provides 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 modeling your own number.

Notes regarding working with place value equipment.

There are a number of ways to explore place value concepts. The learning object provides a variety of models to help students visualize the place value columns. 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.

Students working independently with the learning object

Because this learning object generates numbers for students to model, once they are familiar with how it works you could allow individual students or pairs of students to work with the learning object independently. 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.

Students working independently without the learning object

Using place value equipment students can work in pairs to represent numbers. Working in pairs provides students with the opportunities to work together to practice saying and representing numbers with equipment.