# Expressing Fractions

## Number & Operations – Fractions – 4th Grade

**Understand decimal notation for fractions, and compare decimal fractions.**

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

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*For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100*.

Use decimal notation for fractions with denominators 10 or 100.

*For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram*.

**Teacher Notes**

Understanding that decimals are a continuation of the place value system and numbers tho the right of the decimal represent numbers that are less than one is an important foundational understanding. Students need to understand that fractions and decimals are related; decimals have the same name as the fraction name in tenths and hundredths, and every fraction can be written as a decimal and every decimal can be written as a fraction.

Knowing the relationship between a fraction with a denominator of 10 to another fraction with a denominator of 100 is very important.

**Student Knowledge Goals**

I know that decimals can be written as fractions and fractions can be written as decimals.

I know that fractions with a denominator *10 *or *100* are called *decimal fractions.*

I can generate equivalent decimal fractions.

I can properly name fractions and decimals (e.g., 7/10 and .7 are "seven tenths").

I can add fractions with like denominators.

I can add decimal fractions.

I know that fractions with a denominator *10 *or *100* are called *decimal fractions.*

I can write decimal fractions as decimals in a variety of situations.

I can show that I understand decimal fractions using a variety of models.

**Vocabulary**

decimal fraction

hundredths

tenths

convert

**Lessons**

Engage NY Module 6 A-1 – Use metric measurement to model the decomposition of one whole into tenths.

Engage NY Module 6 A-2 – Use metric measurement and area models to represent tenths as fractions greater than 1 and decimal numbers.

Engage NY Module 6 A-3 – Represent mixed numbers with units of tens, ones, and tenths with number disks, on the number line, and in expanded form.

Engage NY Module 6 B-4 – Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.

Engage NY Module 6 B-5 – Model the equivalence of tenths and hundredths using the area model and number disks.

Engage NY Module 6 B-6 – Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.

Engage NY Module 6 B-7 – Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.

Engage NY Module 6 B-8 – Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.

**Student Video Lessons**

Virtual Nerd - 4.NF.C.6 - Express a fraction with denominator 10 as an equivalent fraction with denominator 100

Virtual Nerd - 4.NF.C.6 - Decimal notation for fractions with denominators 10 or 100.

Study Jams – Place values for decimals

**Online Problems and Assessments**

Khan Academy – Questions and Video Lessons

Fractions with denominators of 10, 100, and 1000

Add up to 4 fractions with denominators of 10 and 100

Add and subtract fractions with denominators of 10, 100, and 1000

Graph decimals on number lines

Graph fractions as decimals on number lines

Convert decimals between standard and expanded form using fractions

Convert fractions and mixed numbers to decimals

Convert decimals to fractions and mixed numbers

**Online Games**

Decimals & Fractions

**Printables**

Decimals & Fractions

Assessment Task 1

Assessment Task 2

Assessment Task 3

Assessment Task 4

Assessment Task 5

Assessment Task 6