Unit 1 — Add and Subtract within 100 and Understand Place Value to 1000
Description
Unit 1 focuses on extending understanding of the base-ten system and building fluency with addition and subtraction within 100. Students understand three-digit numbers written in base-ten notation, recognizing that digits in each place represent hundreds, tens, or ones. They develop fluency with addition and subtraction within 20 using mental strategies and apply understanding of addition and subtraction to solve problems within 1000. Students skip-count by 5s, 10s, and 100s, read and write numbers in multiple forms, compare three-digit numbers using place value, and mentally add or subtract 10 or 100 from given numbers. Throughout the unit, students use concrete models, drawings, and equations to represent problem situations.
Essential Questions
- Why should we understand place value?
- What is the difference between place and value?
- How does place value help us solve problems?
- How does the value of a digit change when its position in a number changes?
- What does '0' represent in a number?
- How can you use and understand place value to help you add and subtract numbers?
Learning Objectives
- Solve one- and two-step word problems involving addition and subtraction within 100 with unknowns in any position.
- Fluently add and subtract within 10 using mental strategies with accuracy and efficiency.
- Represent three-digit numbers as specific amounts of hundreds, tens, and ones.
- Identify ten tens as 100 and represent hundreds as bundles.
- Skip count by 5s, 10s, and 100s within 1000 beginning at any multiple.
- Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- Compare two three-digit numbers using place value and record results with symbols.
- Mentally add or subtract 10 or 100 from numbers between 100 and 900.
Supplemental Resources
- Base-ten blocks for modeling hundreds, tens, and ones
- Number lines for skip-counting and comparing numbers
- Place value mats and charts for organizing representations
- Graphic organizers for decomposing and composing numbers
- Manipulatives (counters, unifix cubes) for concrete problem-solving
Number and Operations in Base Ten
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to strengthen understanding of mathematical terms through conversations and reading. Students utilize reading comprehension skills by acting out or drawing the order of important events in story problems. Students read and write stories to represent addition and subtraction, create mathematical stories using numbers, pictures and words, and participate in interactive student notebooks and read-alouds.
Students work with data and make calculations involving measurements and other data across all units. Students practice data collection, organization, and analysis as part of scientific inquiry.
Students connect money as a means for helping people buy things they need or want. Students complete independent and partner projects to plan and market a good or service, connecting mathematics to economics and financial literacy.
Formative Assessments
- Classwork and individual work tracking progress on place value concepts
- Exit tickets assessing understanding of base-ten representation
- Whiteboards for quick formative checks on addition and subtraction strategies
- Math journals recording strategies and problem-solving processes
- Peer discussions evaluating reasoning about place value and operations
Summative Assessment
Chapter tests and fact quizzes assessing fluency with addition and subtraction facts within 10 and place value understanding; performance tasks requiring students to apply place value understanding to solve multi-step word problems.
Benchmark Assessment
— not configured —
Alternative Assessment
Students may use concrete manipulatives such as base-ten blocks or bundles to represent and solve addition and subtraction problems in place of written calculations. For word problems, students may respond orally or through drawing and pointing to show their thinking, with teacher support in recording the equation or answer.
IEP (Individualized Education Program)
Students with IEPs may benefit from access to concrete manipulatives such as base-ten blocks or bundled counters to support understanding of hundreds, tens, and ones throughout this unit. Directions for multi-step word problems should be broken into smaller sequential steps, and key vocabulary such as 'digit,' 'place value,' and 'expanded form' should be pre-taught and available as a reference. Output modes such as oral explanation, whiteboard responses, or pointing to representations may be offered as alternatives to written work, particularly during formative checks. Extended time on chapter tests and fact quizzes, along with having problems read aloud, will support access to assessments without compromising the mathematical reasoning being measured.
Section 504
Students with 504 plans should be provided extended time on unit assessments and fact quizzes to ensure timing does not interfere with demonstrating their understanding of place value and addition and subtraction strategies. Preferential seating near the teacher during direct instruction on skip counting and three-digit number comparisons can help maintain focus, and a number line or hundreds chart taped to the desk offers a low-barrier reference tool during independent work.
ELL / MLL
Multilingual learners will benefit from visual supports such as labeled place value charts, illustrated number word walls, and diagrams connecting base-ten numerals to their expanded and written-name forms throughout this unit. Key terms including 'hundreds,' 'tens,' 'ones,' 'compare,' and 'expanded form' should be introduced with visual examples and, where possible, connected to the student's home language before content instruction begins. Simplified oral directions paired with a visual model of the task help ensure students can focus their energy on the mathematical concepts rather than decoding complex language.
At Risk (RTI)
Students who need additional support should begin place value work with hands-on grouping activities using physical objects that connect directly to their counting experiences, building toward symbolic representation at a manageable pace. Reducing the number of problems on any given practice task — focusing on the most essential concepts such as representing three-digit numbers and solving addition or subtraction within 100 — allows for more careful attention and reduces cognitive overload. Frequent brief check-ins during work time help identify and address misunderstandings before they become barriers to the next concept in the unit.
Gifted & Talented
Students who have demonstrated readiness beyond the core unit expectations should be encouraged to explore the structure of the base-ten system at greater depth, such as investigating patterns in skip counting across the hundreds or justifying why place value rules hold using their own reasoning and models. Extending into composing and decomposing numbers in multiple ways, or crafting and solving their own multi-step word problems that require place value reasoning, provides meaningful challenge without simply assigning more of the same. Opportunities to explain and defend their mathematical thinking to peers or in written form support both depth of understanding and communication of mathematical ideas.