Place value- Counting with decimal numbers with 3 decimal places

General

Students are able to count forwards and backwards with decimal numbers with 3 decimal places.

Relevance

Students need this to be able to calculate with decimal numbers with 3 decimal places.

Introduction

Start by naming the numbers which indicate beak length for the birds. You can ask for the largest and smallest numbers.

Development

Discuss the term "decimal place". These are the places that come after the decimal point. There can be 1, but also many. Using the number line, show that you take 10 steps from 0.001 to 0.01. Show these steps using the tube with increase of water by 0.001 liter per step. Every line shows 0.001 liter, and when it is full, it contains 0.01 liters. You can also show this with a real tube in class. Do this to show that 0.001 is a very small portion of an object or number. It can still be very important though, like when weighing grams of gold. Show students the water tubes on the interactive whiteboard and ask them to fill in the missing numbers. Then practice counting with decimal numbers in a number sequence. Count forwards or backwards by 0.001. Spend time explaining what happens in the step between 5.999 and 6.000.

Check that students are able to count forwards and backwards with decimal numbers with 3 decimal places by asking the following questions:
- Which number changes when you add by 0.001 (the last one).
- When do you count on (and change the ones) when the number has 3 decimal places? (by 0.999)

Guided practice

Join the students to complete the number sequence. First counting with 0.001, and then with 0.002. They they count backwards with 0.001. Students are asked to write using 3 decimal places, writing for example 6.000.

Closing

Emphasize that it is important to know how to count forwards and backwards with decimal numbers because you need it to be able to calculate with these numbers. As an example name a doctor who needs to know how to count with decimals to give an accurate dosage of medicine. Ask your students where else they might see a decimal number with 3 decimals. Examples are with racing events, measuring weight at the post office, gymnastic scores, etc. Finish with a game. Ask the students to form a line (and become a snake). The head of the snake is given a decimal number, say 4.123. The next student must say the number that is 0.001 more, so 4.124- 4.125- 4.126, etc. Do this a few times with different numbers. Then do this again with a new "head" but ask students to count in steps of 0.100. Note with the class that you count much less "far" when you count in steps of 0.001. You can also ask students to count backwards.

Teaching tips

You can help visualize this for students who are having difficulty. Take a digital scale, or stopwatch with thousandths to help them see the difference between the numbers. Students who are comfortable with steps of 0.001 can be challenged with steps of 0.002 and 0.005, or even 0.020 and 0.050.