MA.5.NSO.1 Number Sense and Operations
Understand the place value of multi-digit numbers with decimals to the thousandths place.
Plot, order and compare multi-digit numbers with decimals up to the thousandths. Example: The numbers 4.891, 4.918 and 4.198 can be arranged in ascending order as 4.198, 4.891 and 4.918. Example: 0.15 < 0.2 because 𝑓𝑖𝑓𝑡𝑒𝑒𝑛 ℎ𝑢𝑛𝑑𝑟𝑒𝑑𝑡ℎ𝑠 is less than 𝑡𝑤𝑒𝑛𝑡𝑦 ℎ𝑢𝑛𝑑𝑟𝑒𝑑𝑡ℎ𝑠, which is the same as 𝑡𝑤𝑜 𝑡𝑒𝑛𝑡ℎ𝑠.
Clarification 1: When comparing numbers, instruction includes using an appropriately scaled number line and using place values of digits.
Clarification 2: Scaled number lines must be provided and can be a representation of any range of numbers.
Clarification 3: Within this benchmark, the expectation is to use symbols (<, > or =).
Purpose and Instructional Strategies
The purpose of this benchmark is for students to use place value understanding to plot, order and compare multi-digit numbers with decimals to the thousandths. In Grade 4 (MA.4.NSO.1.5), decimals were plotted to the hundredths, and in Grade 6 (MA.6.NSO.1.1) rational numbers, including negative numbers, will be plotted.
During instruction, students should apply understanding of flexible representations from MA.5.NSO.1.3 to help them reason while plotting, ordering and comparing.
During instruction, teachers should show students how to represent these decimals on scaled number lines. Students should use place value understanding to make comparisons.
Instruction should expect students to justify their arguments when plotting, comparing and ordering.
Common Misconceptions or Errors
Students may be confused when comparing numbers that have the same digits (but different values). For example, when comparing 2.459 and 13.24, a student may not consider the magnitude of the numbers and only look at their digits. That student may claim that 2.459 is greater than 13.24 because the digit 2 is greater than the digit 1 (though they are actually comparing 2 and 10).
Instructional Task 1
Part A. Plot the numbers 1.519, 1.9, 1.409 and 1.59 on the number line below.
Part B. Choose two values from the list and compare them using >, < or =.
Part C. Choose a number between 1.519 and 1.59 and plot it on the number line.
Part D. Use evidence from your number line to justify which number is greatest.
Instructional Item 1
Select all the statements that are true.
a. 13.049 < 13.49
b. 13.049 < 13.05
c. 2.999 > 28.99
d. 1.28 < 1.31
e. 5.800 = 5.8