# 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

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*Source: www.SusanCAnthony.com, ©Susan C. Anthony*