### Examples

The numbers 3.2; 3.24 and 3.12 can be arranged in ascending order as 3.12; 3.2 and 3.24.### Clarifications

*Clarification 1:*When comparing numbers, instruction includes using an appropriately scaled number line and using place values of the ones, tenths and hundredths digits.

*Clarification 2:* Within the benchmark, the expectation is to explain the reasoning for the comparison and use symbols (<, > or =).

*Clarification 3: *Scaled number lines must be provided and can be a representation of any range of numbers.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**4

**Strand:**Number Sense and Operations

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## 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 plot, order, and compare decimals using place value. Grade 4 contains the first work with decimals. During instruction make connections to decimal fractions (e.g.,$\frac{\text{1}}{\text{10}}$, $\frac{\text{1}}{\text{100}}$) (MA.4.FR.1.2).- For instruction, teachers should show students how to represent these decimals on scaled number lines. Students should use place value understanding to make comparisons.
- Students learn that the names for decimals match their fraction equivalents (e.g., 2
*tenths*is equivalent to 0.2 which is equivalent to $\frac{\text{2}}{\text{10}}$). - Students build area models (e.g., a 10 × 10 grid) and other models to compare decimals.

### Common Misconceptions or Errors

- Students treat decimals as whole numbers when making a comparison of two decimals. They think the longer the number, the greater the value.
- For example, they think that 0.04 is greater than 0.4.

### Strategies to Support Tiered Instruction

- Instruction includes the use of place value understanding, decimal fractions, and decimal
grids to compare decimals.
- For example, students compare 0.14 and 0.2 using decimal fractions. The teacher begins instruction by having students write each decimal as a fraction, $\frac{\text{14}}{\text{100}}$ and $\frac{\text{2}}{\text{10}}$. The teacher explains that $\frac{\text{2}}{\text{10}}$ is equal to $\frac{\text{20}}{\text{100}}$ because if we multiply the numerator and denominator of $\frac{\text{2}}{\text{10}}$ by 10, we generate the equivalent fraction $\frac{\text{2}}{\text{10}}$ = $\frac{\text{2x10}}{\text{10x10}}$. Next, the teacher compares the fractions to determine that $\frac{\text{14}}{\text{100}}$ < $\frac{\text{20}}{\text{100}}$ , so 0.14 < 0.2.
- For example, students use place value understanding and a place value chart to compare 0.14 and 0.2. The teacher explains that when comparing decimals, we start with the digit to the far left because we want to compare the greatest place values first. Both values have a 0 in the ones place, so we will move to the tenths place. One-tenth is less than two-tenths, so 0.14 < 0.2.

- For example, students compare 0.3 and 0.03 using decimal fractions. The teacher begins instruction by having students write each decimal as a fraction, $\frac{\text{3}}{\text{10}}$ and $\frac{\text{3}}{\text{100}}$. The teacher then explains to students that $\frac{\text{3}}{\text{10}}$ is equal to $\frac{\text{30}}{\text{100}}$, because if we multiply the numerator and denominator of $\frac{\text{3}}{\text{10}}$ by 10, we generate the equivalent fraction $\frac{\text{3}}{\text{10}}$ = $\frac{\text{3x10}}{\text{10x10}}$. Next, the teacher compares the fraction to determine that $\frac{\text{30}}{\text{100}}$ > $\frac{\text{3}}{\text{100}}$, so 0.3 > 0.03.
- For example, students compare 0.3 and 0.03 using decimal grids, representing each value, and explain that 0.3 covers a greater area of the decimal grid than 0.03, so 0.3 is greater than 0.03. that 30 > 3 , so 0.3 > 0.03.

### Instructional Tasks

*Instructional Task 1 *(MTR.3.1)

- a) 3
*tenths*+ 5*hundredths*_____ 3*tenths*+ 11*hundredths* - b) 4
*hundredths*+ 5*tenths*_____ 1*tenths*+ 33*hundredths* - c) 4
*hundredths*+ 1*tenths*_____ 1*tenth*+ 4*hundredths* - d) 5
*hundredths*+ 1*tenth*_____ 15*hundredths*+ 0*tenths* - e) 5
*hundredths*+ 1*tenth*_____ 0*tenths*+ 15*hundredths*

### Instructional Items

*Instructional Item 1*

- a. 0.06
- b. 0.70
- c. 0.8
- d. 0.5
- e. 0.4

**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

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Task

## Tutorial

## STEM Lessons - Model Eliciting Activity

Students will determine what cell phone would be the best phone for their teacher to purchase for science class. Factors to consider are price, touch screen, camera, voice command, weight and display size. Students will need to compare decimals to determine how to order and rank the phone brands.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies. Students will use multiplication and division of whole numbers to plan for how many packages to order.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

Students are asked to compare four pairs of decimals using the *less than*, *greater than*, or *equal to* symbols.

Students are asked to compare two pairs of decimals in the context of word problems and to record a comparison using an inequality symbol.

Students are asked to consider two grids with different sized wholes and determine if both models show four-tenths.

Students are asked to compare decimals by drawing a visual model and record the comparison using the *less than*, *greater than*, or *equal to* symbol.

## Original Student Tutorials Mathematics - Grades K-5

Learn how to locate decimals on a number line and compare decimals to save the Decis from a wizard's spell in this interactive tutorial.

## Student Resources

## Original Student Tutorial

Learn how to locate decimals on a number line and compare decimals to save the Decis from a wizard's spell in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Task

Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

Type: Problem-Solving Task

## Tutorial

In this Khan Academy tutorial video two decimals are compared using grid diagrams.

Type: Tutorial

## Parent Resources

## Problem-Solving Task

Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

Type: Problem-Solving Task