7.3.A
The Standard
add, subtract, multiply, and divide 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 with positive and negative integers, fractions, and decimals using all four operations. They select efficient methods, manage signs correctly, and write answers in simplified form.
What Mastery Looks Like
- Students solve mixed sets accurately without relying on a calculator for every step. They choose efficient forms, track signs, simplify fractions, and check whether answers are reasonable.
Common Misconceptions
- Students may apply multiplication sign rules to addition, such as claiming two negatives always make a positive. They may miss a changed sign when subtracting a negative, use common denominators incorrectly, or divide by zero.
How to Assess It
- Give this exit ticket: solve −3.5 + 1.8, 2/3 − (−5/6), (−4/7)(21/8), and −1.2 ÷ 0.3, then explain one sign decision.
Lesson moves
Ways to Teach It
Use red and black counters to model signed addition and subtraction, then connect each model to a numerical equation.
Ask students to explain why subtracting a negative changes the value differently from adding a negative.
Deal rational-number cards, roll an operation die, and award a point for each correct simplified result.
Give students a checking account ledger with deposits, withdrawals, and shared expenses, then have them calculate the final balance.
Keep exploring
Related Standards
- 6.3.D
add, subtract, multiply, and divide integers fluently
- 5.3.K
add and subtract positive rational numbers fluently
- 6.3.E
multiply and divide positive rational numbers fluently
- 7.3.B
apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers
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