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Level Four > Number and Algebra

Modeling Numbers: Decimals

Purpose: 

This unit uses one of the digital learning objects, Modelling Numbers: Decimals, to support students as they investigate the place value of numbers with three decimal places. The numbers are represented using a variety of place value equipment commonly used in classrooms.

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 7, Advanced Multiplicative Part Whole, of the Number Framework.

Achievement Objectives:

Achievement Objective: NA4-6: Know the relative size and place value structure of positive and negative integers and decimals to three places.
AO elaboration and other teaching resources

Specific Learning Outcomes: 

represent numbers with three decimal places 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 represent using the place value equipment. Feedback is provided to the students to help them. This unit is suitable for students working at stage 7 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: decimals, can be accessed from the link below:

Prior to using the Modeling Numbers: Decimals learning objects

The learning objects Modeling Numbers: 3-digits and Modeling Numbers: 6-digits are very similar but only have whole numbers. It would be useful for students to try one of these learning objects first. It would also be helpful if students had some understanding of decimals .

Working with the learning object with students (Choose your own Number)

1. Show students the learning object and explain that it provides a model for representing numbers using place value equipment. Zoom in by clicking on the magnifying glass icon to show the students the names of the columns for the places to the right of the decimal point. Use the magnifying glass to click back to the hundreds, tens, and ones place value equipment. Use the arrow keys to show students how to make a number. Start from the ones column and click through the numbers so the students can see the colour change for the 6th cube. Discuss how this makes it easier to immediately identify numbers between 6 and 9.


2. 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 11. Ask the students what they think will happen if you count backwards from 11. Watch the place value equipment change as you click back using the arrows

3. Zoom in to the decimal section using the magnifying glass. Show the students that the place value equipment behaves in the same way for the thousandths, hundredths and tenths columns. Use the arrow keys to make a number in the thousandths column and click through the numbers so the students can see the colour change happen for the 6th cube as it did in the ones column.

4. Ask the students to count as you click to arrows to make the numbers 6 thousandths, 7 thousandths, 8 thousandths, 9 thousandths, 10 thousandths. Watch as the 10 cubes join to make a rod and slide into the hundredths column. Ask the students what they think will happen when you make the 11 thousandths.
Ask the students what they think will happen if you count backwards from 11 thousandths. Watch the place value equipment change as you click back using the arrows.

5. Click the right arrow to see the number represented using words, a place value house, in standard form or represented on a three bar abacus. Show the students the words written in the form of three and eighty-four hundredths and in the form three point eight four. Usually decimals are read in the format three point zero eight four, but this learning object also provides it in the format of three and eighty-four hundredths to help develop students understandings of decimal place value. Again the colour of the place value equipment matches the colour of the columns in the text. Using the left and right arrows the students can choose how to represent the number.

6. You may wish to explain the other representations to the students. Using the magnifying glass zoom out to see the full number. Continue to make a number. Make sure students understand how a zero digit in the number is represented. Do enough examples together for students to see how the equipment shows the change between the columns.

7. If you have selected to show the number using written words below the place value equipment then a speaker icon is available to click. Click the speaker icon to hear the number being spoken. Ask the student if it is same as what they said. The speaker icon is available for both the format of zero point zero two, and zero and two hundredths.

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 format of the wording is either in the form zero point three or zero and three tenths. The format follows the same format shown before the die is clicked on. 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 choosing 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 model to help students visualize the place value columns. Students will benefit from exploring place value with a range of equipment ranging from place value blocks, decimats, pipe decimals, a three 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.