Beginning Fractions Lessons

If fractions are taught correctly, they are fun and easy to learn. Most texts move children far too quickly into adding with unlike denominators. I found that by using fraction circles (manipulatives) and spending plenty of time on like denominators and foundational concepts, children could move easily into unlike denominators. They understood how fractions work!

Fraction kits for each child or pair of children are essential. Kits are available commercially or you can make your own.

Fraction Kits

I kept 35 fraction kits, each in a laminated 6 x 9" manila envelope, in a box in my classroom and passed them out whenever necessary to teach or review a concept. Each kit contained:

2 Wholes (brown)	4 Halves (yellow)	6 Thirds (orange)	8 Fourths

12 Sixths (purple)	16 Eighths (blue)	18 Ninths (green)	24 Twelfths (pink)

Here are masters for reproducing your own fraction kits and smaller fraction circles that can be used to make your own worksheets.

All the lessons and worksheets I have (so far) are linked here. I haven't had time to write lessons and worksheets for every concept, though I hope to complete that someday (write to encourage me). Once you've solidly taught the basics, you can transition to commercially available materials. The first lessons are the most important, which is why I include scripted lessons for them, based on Madeline Hunter's lesson design. To hear me teaching the lesson on comparing fractions, watch the Principles of Good Teaching workshop.

Spend plenty of time on basic concepts, and the rest will fall quickly into place. Although my students were well "behind" initially, they finished fractions before all the other classes and remembered what they'd learned. They made up for lost time because they had mastered the foundational concepts.

Sequence of Objectives for Adding and Subtracting Fractions

Fractions 1: Introduction and diagnostic pretest: Lesson | Worksheet | Answer Key
Fractions 2: Concept of fractions: Lesson | Worksheet
Fractions 3: Identifying fractions: Lesson | Worksheet | Key
Fractions 4: Shading in fractions: Lesson | Worksheet
Fractions 5: Fractions of shapes other than circles: Lesson | Worksheet
Fractions 6: Parts to wholes: Lesson | Worksheet
Fractions 7: Comparing fractions: Lesson | Worksheet
Quiz on basic concepts of fractions

Reducing (simplifying answer to lowest terms): Worksheet 1 | Key 1 | Worksheet 2 | Key 2
Factors
Common factors, greatest common factor
Quiz on concepts of fractions and reducing

Adding like fractions with no reducing: Worksheet | Key
Adding like fractions with reducing: Worksheet | Key
Adding like fractions and identifying answers that need reducing: Worksheet | Key
Subtracting like fractions with reducing
Quiz on adding and subtracting like fractions with and without reducing

Concept of a mixed number, identifying mixed numbers
Reducing mixed numbers
Adding mixed numbers with like fractions and reducing
Quiz on adding and subtracting mixed numbers with and without reducing

Concept of improper fraction, identifying improper fractions
Reducing improper fractions
Reducing improper fractions in mixed numbers
Adding like fractions with reducing improper fractions
Adding mixed numbers with like fractions and reducing/regrouping
Quiz on adding like fractions with mixed numbers and improper fractions, regrouping
Test on all concepts and skills so far

Concept of equivalent fractions
Concept of multiples, generate chart of multiples
Common multiples, least common multiple
Equivalent fractions using least common multiple
Quiz on equivalent fractions

Adding unlike fractions when one denominator is the least common multiple; no reducing
Adding unlike fractions when one denominator is the least common multiple; include reducing of proper fractions
Adding unlike fractions when one denominator is the least common multiple; include reducing of improper fractions
Adding unlike fractions in mixed numbers when one denominator is the least common multiple; include reducing of improper fractions and regrouping
Subtracting unlike fractions when one denominator is the least common multiple; reducing of all kinds
Adding unlike fractions when neither denominator is the least common multiple; reducing of all kinds
Subtracting unlike fractions when neither denominator is the least common multiple; reducing of all kinds
Quiz on adding and subtracting unlike fractions with reducing of all kinds

Adding unlike mixed numbers; no reducing
Adding unlike mixed numbers; reducing of proper fractions
Adding unlike mixed numbers with and without regrouping
Quiz on adding unlike mixed numbers with and without carrying

Subtracting parts from wholes
Subtracting like mixed numbers with regrouping
Subtracting unlike mixed numbers with regrouping
Quiz on subtracting parts from wholes and mixed numbers with borrowing

Review, mixing like and unlike denominators, reducing of all kinds, mixed numbers with and without regrouping
Final test on adding and subtracting fractions