Modeling numbers: 6-digit numbers

Purpose

This unit uses one of the digital learning objects, Modeling Numbers: 6-digit numbers, to support students as they investigate the place value of numbers up to 999 999.

Achievement Objectives
Specific Learning Outcomes
  • represent numbers up to 999 999 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 form 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 6 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.

Activity

The Learning Objects

The learning object, Modeling Numbers: 6-digit numbers, can be accessed from the link below:

Prior to using the Modeling Numbers: 6 digit numbers Learning Objects

The learning object Modeling Numbers: 3-digit numbers is very similar but only has 3 digits. It would be useful to review this object with students first. If place value knowledge to 100 is secure move onto working with the 6 digit object. 

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.

Show the students how it is possible to zoom in and out by clicking on the magnifying glass icon. Zoom in to show only the ones, tens and hundreds columns using the magnifying glass. 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 identify 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. 

Repeat this by zooming out and using the same procedure with the thousands, ten thousands and hundred thousands. Encourage students to make the connections between the place value houses while appreciating the power of multiplying by ten to create a new place. 

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 columns .

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 three bar abacus. Again the colour of the place value columns matches the colour of the columns in the chosen representations. 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 then written words then below the place value equipment a speaker icon is available to click. Ask a student to read the number you have made. Click the speaker icon to hear the number being spoken. Ask the student if it is same as what they said.

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 models to help students visualize the place value columns. Students will also benefit from exploring place value with a range of equipment including place value blocks, numeracy money, and a place value abacus. 

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. You can also create dice that students roll to increase or decrease their number by a place value amout such as : 10, 1000, 100 000 etc. They create a number with equipment, roll the die and then describe what will change in the digits and nin the model when it increases by the rolled amount. This activity can be expnaded by including two dice one with place value amounts and one with addition and subtraction signs so that a student creates a number rolls an operation and a place value amount and adjusts their model to reflect the new amount. 


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