It is easy for students with poor understanding of decimals to mistakenly think locating say 2.4 on a number line is simply a matter of counting along 4 divisions from 2 towards 3.

I am demonstrating my number sense by showing the difference between decimal and fraction number lines.

Using Materials

Problem: “Jolene draws this number line on the board and adds an arrow where she reckons 2.4 is located (the black arrow). Explain Jolene’s reasoning. Why is Jolene wrong?” Draw Jolene’s number line on the board without the grey arrow for the moment.

Discuss why Jolene is wrong. (Answer: Counting along 4 divisions only works if there are 10 divisions  not 5 as in this case.)

Discuss where 2.4 actually is. (Answer: Imagine 10 divisions and add the grey arrow.)

Examples: Worksheet (Material Master 8–12).