# Teaching 4.NF.C.5 .6 – Express a Fraction with Denominator 10 as an Equivalent Fraction with Denominator 100 & Decimal Notation with Denominators 10 or 100

## Number & Operations – Fractions – 4th Grade

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

CCSS.Math.Content.4.NF.C.5
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 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
CCSS.Math.Content.4.NF.C.6
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 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
Learn Zillion – 4.NF.C.5 – Express fractions with a denominator of 10 as equivalent to fractions with denominators of 100
Learn Zillion4.NF.C.6 – Decimal notation for fractions with denominators 10 or 100
Virtual Nerd4.NF.C.6 – Express a fraction with denominator 10 as an equivalent fraction with denominator 100
Virtual Nerd4.NF.C.6 – Decimal notation for fractions with denominators 10 or 100.
Study Jams – Place values for decimals

Online Games
Decimals &  Fractions