### Clarifications

*Clarification 1:*Instruction emphasizes conceptual understanding through the use of manipulatives, visual models, number lines or equations.

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

**Grade:**4

**Strand:**Fractions

**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 to have students begin connecting fractions with decimals. This benchmark will connect fractions and decimals by writing equivalent fractions with denominators of 10 or 100 (decimal fractions). Decimal fractions are defined as fractions with denominators of a power of ten.- For students to have a concrete foundation for future work with decimals (MA.4.NSO.1.5, MA.4.FR.1.2, MA.4.FR.1.3), plan experiences that allow students to use 10 by 10 grids, base-ten blocks, and other place value models (MTR.2.1) to explore the relationship between fractions with denominators of 10 and denominators of 100.
- This work lays the foundation for performing decimal addition and subtraction in MA.4.NSO.2.7.

### Common Misconceptions or Errors

- Students often confuse decimals such as 0.6 and 0.06. Students need to have a conceptual understanding of the visual representations for tenths and hundredths. Students should use models and explain their reasoning to develop their understanding of the connections between fractions and decimals.

### Strategies to Support Tiered Instruction

- Instruction includes concrete models and drawings to solidify the conceptual understanding of fraction place value.
- For example, students create a model for $\frac{\text{2}}{\text{10}}$. The teacher then asks students to model a fraction that is equivalent to a denominator of 100 and explain what they notice about the models. Conversation involves connections to the value of the fractions.

- Instruction includes building fractions and their equivalents with base ten blocks.
- For example, students build $\frac{\text{2}}{\text{10}}$ “two-tenths” and $\frac{\text{20}}{\text{100}}$“ twenty hundredths” with base ten blocks while using vocabulary that will help students see the decimal connection as well. Students will realize that the numbers have the same value.

- Instruction includes opportunities to use concrete models and drawings to solidify understanding of fraction equivalence.
- For example, students use models to describe why fractions are equivalent or not equivalent when referring to the same size whole.

- When looking at $\frac{\text{1}}{\text{4}}$ and $\frac{\text{2}}{\text{8}}$, discussion includes that both fraction models are the same size. So, when comparing them, we are comparing the same size whole. Students see that 1 out of the 4 are shaded in the first model and 2 out of the 8 are 2 are shaded in the second model, making the $\frac{\text{1}}{\text{4}}$ equal $\frac{\text{2}}{\text{8}}$. Students use this understanding to move into fractions with larger denominators.

### Instructional Tasks

*Instructional Task 1* (MTR.4.1)

### Instructional Items

*Instructional Item 1 *

**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

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Tutorial

## Student Resources

## 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

## Problem-Solving Tasks

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Type: Problem-Solving Task

Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways.

Type: Problem-Solving Task

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

## Tutorial

In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Type: Problem-Solving Task

Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways.

Type: Problem-Solving Task

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task