Unit 2 — Add and Subtract within 20
Description
Students extend addition and subtraction strategies to within 20, developing fluency with multiple strategies including counting on, making ten, decomposing and composing numbers, using the relationship between addition and subtraction, and creating equivalent but easier sums. Students work with two-digit numbers from 10 to 99, developing place value understanding by recognizing that two-digit numbers are composed of tens and ones. Students learn to compare two-digit numbers using symbols >, =, and <. Data work includes organizing, representing, and interpreting data with up to three categories through graphs and data tables. Counting extends to 120, and students extend their understanding of the base-ten system.
Essential Questions
- How can patterns help us understand numbers?
- How can we organize and display data we collected into three categories to create a graph?
- How can we use counting to compare objects in a set?
- What do the numerals represent in a two or three digit number?
- What patterns can be found on the 0-99 chart?
- How does a graph help us better understand the data collected?
- How can large quantities be counted efficiently?
Learning Objectives
- Use addition and subtraction within 20 to solve problems, including word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions.
- Determine if addition and subtraction equations within 20 are true or false.
- Solve addition and subtraction equations within 20 by finding the missing whole number in any position.
- Apply properties of operations (associative property) as strategies to add or subtract within 20.
- Add and subtract whole numbers within 20 using various strategies: counting on, making ten, composing, decomposing, relationship between addition and subtraction, creating equivalent but easier or known sums.
- Solve addition word problems with three whole numbers with sums less than or equal to 20.
- Organize, represent, and interpret data with up to three categories, compare the number of data points among the categories, and find the total number of data points.
- Compose and decompose numbers to 20 to identify the value of the number in the tens and ones place.
- Use the meaning of tens and ones digits to record comparisons of 2 two digit numbers using >, =, and < symbols.
- Count to 120 orally, read and write numerals, and write numerals to represent the number of objects (up to 120).
Supplemental Resources
- Base-ten blocks or place value manipulatives for tens and ones representation
- Number cards (0-20) for comparison activities and sorting
- Graph paper and printed data collection templates for organizing categorical data
- Printed numeral cards for building two-digit numbers
- Hundreds chart or 0-99 chart for pattern recognition activities
Digital Literacy
Number and Operations in Base Ten
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to mathematical terms, utilize reading comprehension skills by acting out or drawing the order of important events in story problems, and create mathematical stories using numbers, pictures, and words through interactive student notebooks and read-alouds.
Students work with data and make calculations involving measurements and other data across all mathematical modules, engaging in investigations and observations related to patterns and phenomena.
Students connect money as a means for helping people buy things they need or want and complete independent or partner projects to plan and market a good or service, exploring economic concepts and community responsibilities.
Formative Assessments
- Exit tickets assessing fluency with making ten and other addition strategies within 20
- Whiteboard problems for quick computation and strategy sharing
- Individual problem-solving tasks with two-digit number composition and decomposition
- Group data collection activities and graphing representations
- Math journals documenting comparison strategies and problem-solving reasoning
- Place value activities using base-ten blocks and drawings
Summative Assessment
Unit 2 chapter tests and performance tasks assessing fluency with addition and subtraction within 20, place value understanding, and data interpretation skills.
Benchmark Assessment
Benchmark assessment within adopted programs and Mad Minute fluency assessments for addition and subtraction within 10.
Alternative Assessment
Students may demonstrate understanding through manipulatives, drawings, or number lines instead of written equations, with teacher-led questioning to explain their thinking. Visual supports such as ten-frames, number bonds, or partially completed problems may be provided to reduce cognitive load while assessing core concepts of addition, subtraction, and place value.
IEP (Individualized Education Program)
For students with IEPs, provide physical manipulatives such as counters, linking cubes, and base-ten blocks to support hands-on exploration of addition, subtraction, and place value concepts. A number line taped to the desk and a reference chart showing the making-ten strategy can reduce cognitive load while students build fluency within 20. Allow students to demonstrate understanding through oral explanations or by pointing to representations rather than requiring written responses, and provide graph templates and comparison sentence frames to support data and comparison tasks. Break multi-step word problems into smaller parts and read them aloud, highlighting key numbers and action words to help students identify the operation needed.
Section 504
Students with 504 plans should be provided extended time on computation tasks and assessments, particularly those involving multi-step addition and subtraction within 20 or two-digit number comparisons. Preferential seating near direct instruction reduces distraction during strategy modeling, and reducing the number of problems on practice tasks allows students to demonstrate mastery without fatigue. Access to a number line or hundreds chart during independent work supports accuracy without replacing the development of mathematical reasoning.
ELL / MLL
Multilingual learners benefit from visual anchor charts that illustrate addition and subtraction strategies, place value concepts, and comparison symbols alongside simple labels in both English and, when possible, the student's home language. Pre-teaching key vocabulary such as 'compare,' 'tens,' 'ones,' 'more than,' and 'less than' before a lesson begins helps students access the mathematical content more confidently. Graphs and data tasks should be introduced with concrete objects before moving to pictorial representations, and directions for problem-solving activities should be given in short, clear steps with visual support to reinforce meaning.
At Risk (RTI)
Students who need additional support should begin addition and subtraction tasks using concrete manipulatives and connect new strategies, such as making ten, to counting strategies they already know and trust. Offering entry points through smaller number ranges within 20 before increasing complexity allows students to build confidence and fluency gradually. During place value work, using physical bundles of objects to represent tens and ones helps make the abstract concept tangible, and frequent check-ins with brief, focused feedback during practice keep students on track before errors become habits.
Gifted & Talented
Students who have demonstrated early fluency with addition and subtraction within 20 can be challenged to justify why strategies such as making ten or decomposing numbers are mathematically efficient, moving beyond computation into reasoning and proof. Extending place value work to three-digit numbers or exploring patterns in the base-ten system up to and beyond 120 provides meaningful depth rather than repetition. These students can also design their own data collection questions with more than three categories, analyze the results, and craft written or oral arguments comparing data sets, integrating mathematical communication with higher-order thinking.