• MA.5.NSO.1 Number Sense and Operations

Understand the place value of multi-digit numbers with decimals to the thousandths place.

MA.5.NSO.1.4

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.

Benchmark Clarifications:
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).

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 Items
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

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