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
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. 
The learning object's second function is to provide students with a number that they are asked to represent using the place value equipment.  Feedback is provided to the students to help them.  
This unit is suitable for students working at Stage 5-Early Additive of the Number Framework.  It includes a sequence of problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

The knowledge section of the New Zealand Number Framework outlines the important items of knowledge that students should learn as they progress through the strategy stages. This unit of work and the associated learning object are useful for students at stage 5-Early Additive of the Number Framework.

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

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 bacus, 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.


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