M.6.R.NS.1

Finishes the fraction work that starts in Grade 3 and sets up dividing all rational numbers in Grade 7.

Not yet reviewed by a teacher

Builds on

Where to go for intervention

Grade 5

M.5.Q.NF.7PriorityThe step right before this one: dividing with a unit fraction, using the same fraction models and equations. Grade 6 takes away the "unit" limit.Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions using fraction models and equations to represent the problem.M.5.Q.NF.4PriorityA quotient is checked by multiplying back, and the rule for dividing fractions comes out of fraction multiplication, so a student needs this to make sense of either.Apply and extend previous understandings of multiplication to efficiently, flexibly, and accurately multiply a fraction or whole number by a fraction.M.5.Q.NF.3PriorityReading a fraction as division is what lets a quotient be written and understood as one number.Interpret a fraction as division, where a quantity (the numerator) is divided into equal parts (the denominator). Flexibly and efficiently solve real world word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Assess the reasonableness of answers using estimation strategies. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Grade 3

M.3.Q.OA.2The two meanings of division start here: how many in each share, and how many shares. "How many 3/4-cup servings are there?" is the second meaning with fractions.Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.M.3.Q.OA.6Division as an unknown-factor problem. The same thinking explains why a fraction quotient multiplies back to where it started.Demonstrate understanding of division as an unknown-factor problem.

M.6.R.NS.1

Priority

Interpret and efficiently, flexibly, and accurately determine quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Common Core: 6.NS.A.1

Resources2 thinking tasks14 IM tasksWIDAOSPI

Thinking tasks2

From the BTC Curricular Math Task Sheet, shared by Building Thinking Classrooms teachers

Illustrative Mathematics tasks14

10 more

From the Illustrative Mathematics task library, CC BY-NC-SA 4.0

WIDA language connections1

Explain · Interpretivelistening, reading and viewing

ELD-MA.6-8.Explain.Interpretive · Language for Mathematics, Grades 6-8

Interpret mathematical explanations by…

Identifying concept or entity

OSPI's example connections to the WIDA ELD Standards Framework. How to read these

From OSPI

Washington OER Hub · Free, openly licensed materials for M.6.R.NS.1

Smarter Balanced interim assessment

Grade 6: Divide Fractions by Fractions · Focused interim block, items 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13*, 14*

A star marks an item aligned to Smarter Balanced claims 2, 3 or 4: problem solving, reasoning or modeling on this content.

On the SBA

PRISM's read

OSPI lists every item on its own focused block here, so expect computing a quotient, reading a division expression as a story or a fraction model, and two items that ask for more than the procedure.

Smarter Balanced target

Claim 1 (Concepts and Procedures), Target B: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Major work of the grade, DOK 1, 2.

OSPI's interim connections

Grade 6: Divide Fractions by Fractions · items 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13*, 14*

A star marks an item aligned to Smarter Balanced claims 2, 3 or 4: problem solving, reasoning or modeling on this content.

Smarter Balanced publishes its claims and targets in its content specifications, written to the Common Core. A 2026 standard reaches them through OSPI's crosswalk. Check them before anything official.

Builds to

Where it goes next

Grade 6

M.6.R.EE.7Solving px = q when p and q are fractions takes a fraction quotient.Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p,q and x are all nonnegative rational numbers.

Grade 7

M.7.Q.NS.2PriorityGrade 7 divides all rational numbers, including negatives. Fraction division has to be solid before signs are added.Efficiently, flexibly, and accurately apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.M.7.R.RP.1A unit rate from a ratio of fractions is a fraction divided by a fraction.Efficiently, flexibly, and accurately compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Connects to

Taught alongside it, including its supporting standards.

M.6.SR.G.2PriorityFinding a missing edge of a prism from its volume, when the edges are fractions, is fraction division.Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.M.6.R.RP.3PriorityUnit rates and "how many groups" problems with fractional amounts use these quotients.Efficiently, flexibly, and accurately demonstrate understanding of ratio and rate reasoning by solving real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations to find different ways to express the same ratio.