Place value- know the value of zero in decimal numbers
Place value- know the value of zero in decimal numbers
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General
Students learn the value of zero in decimal numbers.
Common core standard(s)
5.NBT.A
Relevance
It is important to know what the zero means in a decimal number, to be able to understand the numbers.
Introduction
The interactive whiteboard shows an image of bananas on a scale, which says 0.0, ask if this is possible. The answer is no- because 0.0 means it weighs nothing, and we know that bananas have weight.
Development
Explain that the places after the decimal point have names and tell students that first two places after the decimal point are called tenths, and hundredths. Practice saying these names out loud. Zoom in on what tenths are, and what hundredths are by showing how many times 0.1 and 0.01 fit into the number 1, and discuss the differences between tents and hundredths. Discuss the Decimal chart(tens, ones, tenths, hundredths) chart using a money amount. Next explain the Decimal chart with thousandths. Make sure that you explain that the 'th' stands for thousandths, and that one thousandth fits into 1, 1,000 times. The next slide shows a number without tenths, without hundredths, and without thousandths, one made entirely of the number 0. But it does show the place value of that zero. You can show that a 0, located in any of the boxes in the decimal chart indicates that this space has no number of that value. It is a placeholder, and makes sure that the other numbers stay in their correct places. Show the slide with the bananas again. This time it says 0.99. Ask if this image is correct, and also ask what the 0 stands for: it stands for 0 pounds. Discuss a few more examples like Dafne Schippers running a 100 meter dash and ask what the 0 on the stopwatch stands for. Then discuss the fastest lap ever by Max Verstappen, who drove his lap in 1 minute, 14 seconds, 2 tenths, 4 hundredths and 0 thousandths. Ask why they measure to the thousandths in Formula 1 racing, but not with running. Ask three students to come to the board to drag the given numbers to create numbers that have no tenth, no hundredth, and no thousandth (so a 0 in that space). Finally, three money amounts are given, and you can ask students to write down the amount and ask them to tell you what the 0 stands for in those numbers.
Check that students understand the value of 0 in decimal numbers by asking the following questions:
- Can you name a decimal number that has a 0 in it? What does the 0 mean?
- Can you name a decimal number that has 0 tenths?
- Can you name a decimal number that has 0 hundredths?
Guided practice
First look with students to discover what a number does not have. Then determine which numbers have no hundredths. Finally you determine what the 0 is a placeholder of in a number with tenths, hundredths, and thousandths.
Closing
Discuss with students what the importance of a zero in decimal numbers is and ask if they can come up with situations that have a 0 after the decimal point. Ask students to determine which number on the interactive whiteboard has a 0 as a placeholder for the hundredths. Have students form pairs and ask them to write numbers in which the 0 is a placeholder for tenths, hundredths, and thousandths. The first student writes a number, and the second must give the answer. Then they swap.
Teaching tips
Students who have difficulty determining the value of zero in decimal numbers can be supported by extra practice using the decimal chart.
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