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Examples
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.
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 =).
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- NA
Vertical Alignment
Previous Benchmarks
Next Benchmarks
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 expects students to justify their arguments when plotting, comparing and ordering (MTR.4.1).
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).
Strategies to Support Tiered Instruction
- Instruction includes the use of place value charts, number lines and relational symbols to compare numbers to the thousandths that have the same amount of digits but different values. It is imperative for students to develop a conceptual understanding of rounding, such as what the benchmarks are, using place value understanding to round numbers without instruction of mnemonics, rhymes or songs.
- For example, when comparing 7.468 and 23.15, students record 7.468 and 23.15 in a place value chart. The teacher asks students to compare these numbers, beginning with the greatest place value and explains that the number 23.15 has 2 tens and the number 7.468 does not have any tens so 7.468 < 23.15 and 23.15 > 7.468 even though both numbers have the same amount of digits. Also, students plot 7.468 and 23.15 on a number line to compare the magnitude of the numbers.
- For example, when comparing 12.3 and 9.57 students record 12.3 and 9.57 in a place value chart. The teacher asks students to compare these numbers, beginning with the greatest place value while explaining that the number 12.3 has one ten and the number 9.57 does not have any tens so 9.57 < 12.3 and 12.3 > 9.57 even though both numbers have the same amount of digits. Also, students plot 12.3 and 9.57 on a number line to compare the magnitude of the numbers.
Instructional Tasks
Instructional Task 1 (MTR.3.1)
- 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 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
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Educational Game
Formative Assessments
Lesson Plans
Original Student Tutorial
Tutorials
STEM Lessons - Model Eliciting Activity
In this MEA, the students will help a charitable organization select 5 snack items from a list to provide nutritious snacks for children in low-income communities. Students will practice using the four operations to solve real-world problems and use decimal notation to make calculations involving money. Additionally, they will be asked to compare multi-digit numbers to the thousandths.
Students work in teams to plan the contents of a covered wagon for a family relocating from Missouri to Oregon. Students must calculate the weight and cost of the wagon by adding, subtracting, and multiplying with decimals.
MFAS Formative Assessments
In the context of two word problems students are asked to compare decimals using the less than, equal to, and greater than symbols.
Students compare pairs of decimals, one in word form to one in expanded form.
Original Student Tutorials Mathematics - Grades K-5
Help out at the fishing tournament while comparing decimals through the thousandths place in this interactive tutorial.
Student Resources
Original Student Tutorial
Help out at the fishing tournament while comparing decimals through the thousandths place in this interactive tutorial.
Type: Original Student Tutorial
Educational Game
This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!
Type: Educational Game
Tutorials
In this Khan Academy tutorial video two decimals are compared using grid diagrams.
Type: Tutorial
This Khan Academy tutorial video presents using place-value to compare two decimals expressed to thousandths.
Type: Tutorial
