6.3.A
The Standard
recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the reciprocal of a nonzero divisor. They rewrite division expressions as multiplication expressions and confirm that both forms have the same value.
What Mastery Looks Like
- A student correctly changes 2/3 ÷ 4/5 into 2/3 × 5/4 and finds the value. The student can explain why only the divisor is inverted.
Common Misconceptions
- Students may invert the first number, invert both numbers, or keep the division sign after finding the reciprocal. Some think zero has a reciprocal or forget that zero cannot be a divisor.
How to Assess It
- Give the exit ticket: Rewrite and solve 3/4 ÷ 2/5 using multiplication. Explain why the new expression has the same value.
Lesson moves
Ways to Teach It
Use fraction strips to model 3/4 ÷ 1/2, then compare the model with 3/4 × 2.
Ask, "Why does 2/3 ÷ 4/5 match 2/3 × 5/4?" Students explain with words or a drawing.
Run a card sort where students pair each division expression with its reciprocal multiplication form, then calculate to verify each match.
Pose a recipe problem: How many 3/4-cup servings fit in 4 1/2 cups, then rewrite the calculation using a reciprocal.
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