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Comparing and ordering decimals can be a confusing topic with the introduction of new place values such as tenths, hundredths, and thousandths in addition to the whole number place values.
See the fact file below for more information on the comparing and ordering decimals can be a confusing topic with the introduction of new place values such as tenths, hundredths, and thousandths in addition to the whole number place values. or alternatively, you can download our 31-page Numbers And Operations In Base Ten: Comparing and Ordering CCSS 5.NBT.3b worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- At the end of the lesson, students will be able to compare two decimals to thousandths based on place values, using >, =, and < symbols. Students will also be able to order a set of decimals from least to greatest and vice versa.
A NOTE FOR THE TEACHER
- When comparing and ordering decimals, take note of the following:
- Place values that don’t have any digits written in them can be replaced with zero.
- Compare the values of each place value digit from LEFT to RIGHT.
- Always convert written/expanded forms of decimals into their numerical form for easier comparisons.
- Comparing and ordering decimals can be a confusing topic with the introduction of new place values such as tenths, hundredths, and thousandths in addition to the whole number place values. The first thing we always do when comparing two decimal numbers is to list their place values in a table. Take, for example, the number: 5.545 and 5.554
- We then start to compare the digits written in each value from left to right. If the digits are equal, then we move to the next place value to the right until one digit is eventually greater than the other. That way, we can then make a conclusion about the two numbers.
- In the example, for the one’s places, both numbers are 5, which means we have to move to the next place value. For the tenths place, notice how both numbers are again equal to 5, which means we move to the next place value. For the hundredths place, however, 5 is greater than 4, which means we can conclude that 5.554 is greater than 5.545. This can also be written as 554 > 5.545. Take note that once we conclude, we don’t need to take into consideration the comparisons in the next place values to the right to avoid confusion
- Take, for example, 10.56 and 9.99
- After writing the digits of these numbers in a place value table, right off the bat, we can conclude that 10.56 is greater than 9.99 because the former has a digit in the tens place, while the latter does not have any digit in the tens place.
- When ordering decimals, we still use the same concepts in comparing decimals. For example, we want to order the following decimals from least to greatest: 1.105, 134, 1.175. Like in comparing decimals, we always start by writing down the digits into a place value table.
- Based on the one’s digits, we can conclude that 0.134 is the smallest number because it has the least values. That leaves us with comparing 1.105 and 1.178. If you’ve noticed, the digits in the one’s place are equal for the two numbers. Furthermore, we can also see that the digits in the tenths place are also equal. However, in the hundredths place, we know that 7 is greater than 0. Thus, we can conclude that 1.175 is greater than 1.105.
- From the conclusions made, we can then write the decimal numbers in ascending order from left to right.
- 134, 1.105, 1.175
Numbers And Operations In Base Ten: Comparing and Ordering CCSS 5.NBT.3b Worksheets
This is a fantastic bundle that includes everything you need to know about Numbers And Operations In Base Ten: Comparing and Ordering across 31 in-depth pages. These are ready-to-use worksheets that align with the Common Core CCSS code5.NBT.3b for Numbers And Operations In Base Ten: Comparing and Ordering.
Table of contents
- A lesson plan
- Warm up activity
- Math theory explained
- Assisted learning activities
- Independent learning activities
- Extension activities and games
- Answer keys
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Use With Any Curriculum
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