3.4.J
The Standard
determine a quotient using the relationship between multiplication and division
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a known multiplication fact to solve a division problem. They rewrite division as a missing-factor equation and find the unknown factor.
What Mastery Looks Like
- A student can rewrite 42 ÷ 7 as 7 × ? = 42 and find 6. The student explains how the multiplication fact proves the division answer.
Common Misconceptions
- Students may switch the divisor and quotient when writing the related multiplication equation. They may also confuse equal groups with the total number of objects. Some rely on repeated subtraction without connecting it to a multiplication fact.
How to Assess It
- Give students 35 ÷ 5. Ask them to find the quotient and write a multiplication equation that proves their answer.
Lesson moves
Ways to Teach It
Have students arrange 24 counters into 6 equal groups, then record the related multiplication and division equations.
Ask students to explain in writing how knowing 8 × 4 helps them solve 32 ÷ 8.
Play a fact-family match game where students pair division cards with related multiplication cards.
Give 32 pencils to 8 table groups, and have students find the equal share and prove it with multiplication.
Keep exploring
Related Standards
- 6.3.B
determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than ...
- 3.5.D
determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product
- 6.3.A
recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
- 4.4.E
represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations
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