Locating decimals on a scale

1. Show students the number line to 2, that is divided into tenths, from the Copymaster. Give each student their own copy of the number line. Write a number with ones and tenths, like 1.4, in a space that students can see.
   Where would this number be located on the number line?
   What does the 4 in 1.4 refer to?
   Establish that 1.4 means one and four tenths. Locate 1.4 on the number line and write it in the correct position.
   
   
   Provide students with other ones and tenths decimals to locate on the tenths number line, such as 0.3, 1.9, and 0.8. This could be done in pairs or small groups. As you work, you might introduce relevant te reo Māori kupu, such as the words for numbers and words related to decimals (e.g. tau ā-ira - decimal number).
    
2. Ask students to predict where numbers that cannot be displayed on this number line, such as those larger than 2, would be located if the number line was continued.
    
3. Draw students' attention to numbers located between 0 and 1, such as 0.75.
   Where is 0.75 located?
   What do 7 and 5 refer to in 0.75? (tenths and hundredths respectively)
   Establish that 0.75 means zero ones, seven tenths, and five hundredths.
   How will we add on five hundredths to 0.7?
   Establish that the space between 0.7 and 0.8 will need to be equally partitioned into ten parts. Ask students to draw in hundredths marks between 0.7 and 0.8 and locate 0.75.
   
   
    
4. Provide students with a number line from zero to one divided into tenths and hundredths.
   Support them to practise locating further decimals to two places. Examples might be:

• 0.27                    
• 0.86                   
• 0.54                    
• 0.05
  
  
   

5. Extend this task to include decimals outside the shown range.
   Where is 3.81 located? Where is 5.06 located? Where is 1.11 located?
   Be sure to discuss the place value structure of each decimal, such as 3.81 is made up of three ones, eight tenths, and one hundredth. 
    
6. Extend this task to include decimals to three places. For example:
   Write the number 0.482.
   Where is this decimal located?
   What do four, eight, and two refer to in the number? 
   Establish the place value of each digit, before working through from tenths to thousandths to find the location. It is physically difficult to partition the space between 0.48 and 0.49 into ten equal parts so approximation should be expected. Look for students to demonstrate understanding of the process, and to recognise the need for approximation.
   
   

Next steps

1. Progress to beginning with an empty number line between two whole numbers, such as 2 and 3. Successively build up the decimal places and ask students locate the decimal with increased precision, such as 2.7 to 2.74 to 2.749. At each step, ask student to partition the number line themselves.
    
2. Develop ideas about rounding using ‘closest to’ criteria on the number line. Such as, round 0.36 to the nearest tenth. 0.36 is closer to 0.4 than 0.3 so rounds up.