6.3.E
The Standard
multiply and divide positive rational numbers fluently
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students calculate products and quotients involving positive fractions, decimals, whole numbers, and mixed numbers. They use reliable procedures and estimate to decide whether answers are reasonable.
What Mastery Looks Like
- Students accurately solve fraction and decimal multiplication and division problems without prompts. They choose an efficient method, estimate a reasonable range, and check their result.
Common Misconceptions
- Students often misplace the decimal point or treat decimal multiplication like addition. They may invert the first fraction instead of the divisor. Some cancel factors across addition or fail to rewrite mixed numbers as improper fractions.
How to Assess It
- Exit ticket: Solve 3/4 × 2.6 and 5.04 ÷ 0.8. Estimate each answer and show enough work to justify the decimal placement.
Lesson moves
Ways to Teach It
Use fraction strips to model 3/4 × 2/3 and 3/4 ÷ 1/8, then match each model to a numerical procedure.
Ask students to explain why dividing 6 by 1/2 gives a result greater than 6, using words, pictures, or equations.
Play Operation Match with fraction and decimal problem cards, answer cards, and estimate cards that students sort into matching sets.
Give a recipe for four servings and have students scale it to six servings using fraction and decimal ingredient amounts.
Keep exploring
Related Standards
- 4.4.H
solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders
- 7.3.A
add, subtract, multiply, and divide rational numbers fluently
- 6.3.D
add, subtract, multiply, and divide integers fluently
- 5.3.K
add and subtract positive rational numbers fluently
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