6th Grade Mathematics
Unit 3: Fractions

Unit 3 includes instruction on common factors and multiples, multiplying fractions, and dividing fractions. In grade 5, students learned about equivalent fractions and used that knowledge to add and subtract fractions. Now, in grade 6, we build on that knowledge. Students will learn to multiply and divide whole numbers, fractions, and mixed numbers. They will see concrete representations of multiplying and dividing fractions and learn the algorithm for each. In future units in grade 6, we will build on the students' more complete knowledge of fractions and apply it to thinking about and solving problems involving ratios.


Unit 3 has three cycles: Cycle 1 - GCF and LCM, Cycle 2 - Understanding Fraction Concepts, and Cycle 3 - Dividing Fractions.

Cycle 1 - GCF and LCM

In cycle 1, students will learn about both the Greatest Common Factor (GCF) of a pair of numbers as well as the Least Common Multiple (LCM). For each concept, students will put their knowledge to practice for given pairs of numbers and within word problems. The final lesson of cycle 1 includes complex real-world math scenarios that involve finding the GCF or LCM. The student will apply and practice their problem-solving strategies to determine if GCF or LCM will best help them find the solution.

Cycle 2 - Understanding Fraction Concepts

In cycle 2 of the fractions unit, students will continue to build on their fraction knowledge from grades 4 and 5. They will begin the unit by estimating the value of fractions. They will use fraction estimation and common denominators to compare and order fractions and mixed numbers. Finally, students will multiply whole numbers, fractions, and mixed numbers. Students will apply their computation skills with fractions to problem-solving and real-world math scenarios.

Cycle 3 - Dividing Fractions

Unit 3 finishes with a cycle of lessons on dividing fractions. Students will first divide whole numbers by fractions, then fractions and mixed numbers by other fractions and mixed numbers. They will then use fraction, decimal, and whole number computation to help them make sense of complex real-world math situations and to find the solution to math questions.

The final lesson of cycle 3 is a problem solving lesson that continues to build your students' problem-solving strategies. Previously, in the start-up unit, students learned the general problem solving process and also applied their knowledge of the structure of problems to aid in solving extraneous data problems and in completing problems with a missing part. This lesson introduces the Sort and List strategy to solve word problems.