Expanded form: Writing a number to show the value of each digit separately. For example, 34 = 30 + 4
Place value: The value of a digit based on its position in a number.
- Identify each digit in the number
- Determine the place value of each digit
- Write each digit with its place value
- Join them with addition signs
In 34, we have digit 3 and digit 4
The 3 is in the tens place, so its value is 3 × 10 = 30
The 4 is in the ones place, so its value is 4 × 1 = 4
34 = 30 + 4
34 in expanded form is 30 + 4
• Correct tens value: 3 × 10 = 30 (2 points)
• Correct ones value: 4 × 1 = 4 (2 points)
• Proper format: Addition sign and equation (1 point)
Expanded form: Writing a number to show the value of each digit separately. For example, 78 = 70 + 8
In 78, we have digit 7 and digit 8
7 tens = 7 × 10 = 70
8 ones = 8 × 1 = 8
78 = 70 + 8
78 in expanded form is 70 + 8
• Correct tens value: 7 × 10 = 70 (2 points)
• Correct ones value: 8 × 1 = 8 (2 points)
• Proper format: Addition sign and equation (1 point)
Expanded form: Shows place value breakdown (56 = 50 + 6)
Verification: Checking that expanded parts equal original number
5 tens = 50, 6 ones = 6, so 56 = 50 + 6
50 + 6 = 56 ✓
56 in expanded form is 50 + 6, verified by adding 50 + 6 = 56
• Correct tens value: 5 × 10 = 50 (2 points)
• Correct ones value: 6 × 1 = 6 (2 points)
• Verification: Adding expanded parts equals original number (1 point)
• Understands tens vs ones
• Recognizes base ten system
• Uses proper notation
• Follows step-by-step process
• Adds expanded parts
• Confirms accuracy
• B: 10-11 points
• C: 8-9 points
• D: 6-7 points
• F: Below 6 points
Place value misunderstanding: Confusing face value with place value
Student treats 4 as 4 ones instead of 4 tens
Use base ten blocks to show 47 as 4 tens and 7 ones
Practice with visual representations before abstract numbers
Focus on tens place value understanding with concrete materials
• Scoring: Incorrect tens value results in lost points
• Diagnosis: Indicates foundational place value gap
• Intervention: Targeted instruction needed
Systematic place value error: Consistent misunderstanding across multiple problems
Student consistently treats tens digit as ones
Review base ten concept with manipulatives
Track improvement over multiple assessments
Systematic remediation focusing on tens place value with visual aids
• Concrete materials: Base ten blocks and visual aids
• Repetitive practice: Daily reinforcement activities
• Progress tracking: Regular assessment monitoring
Objective 1: Students will identify the place value of digits in two-digit numbers
Objective 2: Students will write two-digit numbers in expanded form
Objective 3: Students will verify expanded form by adding parts
Objective 4: Students will understand the base ten number system
CCSS.MATH.CONTENT.1.NBT.B.2: Understand that the two digits of a two-digit number represent amounts of tens and ones
CCSS.MATH.CONTENT.1.NBT.B.2.A: 10 can be thought of as a bundle of ten ones
CCSS.MATH.CONTENT.1.NBT.B.2.B: The numbers 11-19 are composed of a ten and some ones
CCSS.MATH.CONTENT.1.NBT.B.2.C: The numbers 10, 20, 30... refer to one, two, three... tens
Strategy 1 - Formative: Ongoing observation during guided practice
Strategy 2 - Summative: Formal assessment at unit completion
Strategy 3 - Diagnostic: Pre-assessment to identify gaps
Strategy 4 - Remedial: Targeted intervention for struggling students
For Struggling Learners: Use manipulatives, visual aids, and step-by-step guidance
For On-Level Learners: Standard practice with verification requirements
For Advanced Learners: Challenge with three-digit numbers and word problems
For English Language Learners: Visual representations and bilingual vocabulary support
Indicator 1: 80% accuracy on basic expanded form exercises
Indicator 2: Ability to explain place value relationships
Indicator 3: Consistent verification of answers
Indicator 4: Transfer of knowledge to new problems
For Proficient Students: Advance to comparing numbers using place value
For Developing Students: Additional practice with concrete materials
For Struggling Students: Intensive intervention and small group instruction
For All Students: Integration with addition and subtraction concepts
Assessment Questions & Answers
Question: How should I score expanded form assessments fairly when students make minor calculation errors?
Answer: Use a rubric-based scoring system that separates conceptual understanding from computational accuracy:
- Conceptual understanding (place value recognition): 2 points
- Computational accuracy (correct calculations): 2 points
- Proper format and notation: 1 point
This allows you to identify whether students understand the concept but struggle with computation, or vice versa.
Focus on the place value understanding as the core skill being assessed!
Question: My child got a C on the expanded form assessment. What does this mean and how can I help?
Answer: A C indicates your child demonstrates average understanding but needs additional practice:
- They may understand the concept but need more practice with application
- They might benefit from visual aids and hands-on materials
- Additional repetition with different numbers would be beneficial
- Focus on verification by adding expanded parts to check answers
Work with your child using base ten blocks or drawings to reinforce the concept at home.
Consistent daily practice with small numbers will build confidence!
Question: Why do we need to assess expanded form? Isn't regular math enough?
Answer: Assessing expanded form is crucial because it tests your understanding of how numbers work!
- It shows whether you understand that 34 means 30 + 4, not just 3 + 4
- It builds the foundation for bigger math problems later
- It helps you understand money, time, and measurements
- It prepares you for addition and subtraction with regrouping
Expanded form assessment ensures you truly understand numbers, not just memorize them!
It's like checking that you understand how a car engine works, not just how to drive!