Virginia SOL 4.PFA.1.d
The Standard
Solve contextual problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules.
Virginia Standards of Learning for Mathematics · The student will identify, describe, extend, and create increasing and decreasing patterns (limited to addition, subtraction, and multiplication of whole numbers), including those in context, using various representations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read a situation and identify the one-step rule connecting each input to its output. They use addition, subtraction, or multiplication to complete missing values and extend the pattern. They use the results to answer the question in context.
What Mastery Looks Like
- Students choose addition, subtraction, or multiplication and name the fixed whole number used in the rule. They apply the same rule to every pair, extend the pattern, and answer the question with correct units.
Common Misconceptions
- Students often compare consecutive outputs instead of checking how each input maps to its output. They may reverse subtraction or add the multiplier instead of multiplying. Some choose a rule that fits one pair but not every pair.
How to Assess It
- Exit ticket: A player has 42 points and loses 6 after each penalty. Complete 42→36, 36→30, 30→__, state the rule, and write the next pair.
Lesson moves
Ways to Teach It
Give students input and output cards to match under +4, -3, and ×5 rules, then have them add one new pair.
Post the pairs 6→18, 8→24, and 11→33; ask students to name the rule and explain how each pair proves it.
Play Rule Detective: one partner chooses +7, -4, or ×3, gives three input-output pairs, and the other identifies and extends the rule.
Set up school-store price cards; students apply a $5 discount to each input price, list outputs, and predict the next discounted price.
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Printable 4.PFA.1.d Worksheet
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- 5.PFA.1.c
Solve contextual problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules (...
- 4.PFA.1.a
Identify, describe, extend, and create increasing and decreasing patterns using various representations (e.g., objects, pictures, numbers, number lines, input/o...
- 5.PFA.1.a
Identify, describe, extend, and create increasing and decreasing patterns using various representations (e.g., objects, pictures, numbers, number lines, input/o...
- 4.PFA.1.b
Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, or function machines and generalize the change to id...
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