Place value- decimal numbers with 1 or 2 decimal places on the number line
Place value- decimal numbers with 1 or 2 decimal places on the number line
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General
Students learn to place decimal numbers with 1 or 2 decimal places on the number line.
Common core standard
CCSS.Math.Content.4.NF.C.5
CCSS.Math.Content.4.NF.C.6
Relevance
It is important to be able to place numbers on the number line to be able to compare them and know their order. If you are able to place numbers on a number line, you are able to determine which numbers are less or greater than your given number.
Introduction
Start by matching activities to their speeds. It is in miles per hour. Ask them to say the numbers out loud. Then complete the number sequences. It starts with counting forward or backwards by 0.1, then by 0.01.
Instruction
Tell students that on a number line they always have to look at the staring number and the final number, so you know how big the number line is. Then you count the intermediate marks on the number line, so you can figure out what each mark represents. In this case, the number line goes from 0 to 1 and it has 10 marks. 1 :10 = 0.1, so every mark represents 0.1. When you know what the marks represent, you can place your number on the number line. Practice this with students. First with the number line from 0 to 1, and then with a number line from 4 to 5. Make sure students understand that each mark represents 0.1. Next, show a number line that has 100 intermediate marks, so each mark represents 0.01. Say that when you place a number on the number line, like 0.23, it is useful to think about its neighboring tens numbers. In this case, 0.2 and 0.3. Next you count the smaller marks to discover your number's exact location. Practice this with your students using different decimal numbers with 2 decimal places. First write the tenths under the number line, this helps to pinpoint where the numbers belong. 0.1, 0.2, 0.3, 0.4.....1.0. Next show a blank number line. They cannot count tenths or hundredths on a blank line. It is important that they imagine the lines, particularly the middle line. Then they can approximately place their number on the number line.
Check that students are able to place numbers with 1 or 2 decimal places on the number line by asking the following questions:
- What are the neighboring tens numbers of 0.34?
- What is exactly in the middle between 2.6 and 2.8?
- What is exactly in the middle between 2.6 and 2.7?
Guided practice
Practice identifying the number shown on a number line with number lines from 0.1 to 0.2 with intermediate marks. Then students must determine which number is in the middle. Finally students must determine which number is approximately shown with a number line only showing the middle mark.
Closing
Repeat with students the steps they should take in placing a number on the number line. First look at the starting and ending number of the number line. Then look if there are intermediate marks, or if they need to imagine them- so they know how much each mark is worth, or about where a mark belongs. Then they look to find the neighboring tens numbers and then place the number. Ask students to explain their thinking. Check with a final exercise in which students must place decimal numbers with 1 or 2 decimal places on the number line. Ask which number is shown by the question mark, which number is in the middle, and where 5.65 is on the number line. Ask them to explain their thinking.
Teaching tips
Students who are not as comfortable with the number line can be confused by the changes of starting and final numbers, as well as the changes in value of intermediate marks. Take time to review the steps with the students and emphasize the importance of determining the starting and final numbers of the number line, and taking the time to determine the value of the intermediate marks. You can also have them practice on a number line to 100, telling them that the only difference is that a decimal point is in the number.
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