Unit 1 — Connecting Counting to Cardinality
Description
Unit 1 establishes foundational counting skills and introduces the relationship between counting and quantity. Students learn number names and the count sequence up to 10, develop one-to-one correspondence, and understand that the last number counted tells how many objects are in a set. Students also begin to identify and describe basic shapes and represent quantities with numerals. Addition is introduced as putting together and adding to, while subtraction is presented as taking apart and taking from. Throughout the unit, students work with objects up to 10 in various arrangements and configurations.
Essential Questions
- How can numbers be represented?
- How can we show numbers in different ways?
- Why do we need to be able to count objects?
- How do we use numbers every day?
Learning Objectives
- Count orally by ones up to 10
- Write numbers from 0 to 10
- Understand one-to-one correspondence when counting
- Identify that the last number named tells the quantity
- Count objects arranged in different configurations
- Represent addition as putting together and adding to
- Create addition events with objects, drawings, and sounds
- Classify objects into categories and count objects in each category
Supplemental Resources
- Index cards for flash cards for number names and numerals
- Chart paper for recording counting patterns and number lines
- Counters or manipulatives for modeling addition situations
- Ten frames printed on paper or plastic page protectors for dry-erase use
- Dice for counting and number recognition games
Counting and Cardinality
Digital Literacy
Geometry
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to strengthen understanding of mathematical terms. Students utilize reading comprehension skills by acting out or drawing the order of important events in story problems. Students create mathematical stories using numbers, pictures, and words in interactive student notebooks and read alouds.
Students work with data and make calculations involving measurements and other data across all modules. Students develop understanding through observing patterns and analyzing information related to physical and natural phenomena.
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, developing economic literacy.
Formative Assessments
- Classwork on counting and numeral identification
- Exit tickets observing one-to-one correspondence
- Whiteboards for quick number writing checks
- Individual observations during counting activities
- Math journals recording addition events with drawings
Summative Assessment
Chapter tests assessing counting sequences, numeral recognition, cardinality, and basic addition representation
Benchmark Assessment
— not configured —
Alternative Assessment
Students may demonstrate counting and cardinality understanding through one-to-one pointing or touching objects while an adult records responses, or by selecting the correct quantity from two or three options presented visually. Number formation may be modified to include tracing numerals, matching numerals to sets, or verbal identification of written numbers with visual supports such as number cards or ten-frames.
IEP (Individualized Education Program)
During counting and cardinality activities, provide physical manipulatives and number lines taped to the student's workspace to support one-to-one correspondence and numeral recognition. Allow students to demonstrate understanding through oral counting, pointing, or moving objects rather than requiring written responses, and accept dictated or verbally narrated explanations of addition events in place of independent written work. Directions for multi-step counting tasks should be broken into single steps and paired with visual cues, such as picture-supported number cards, to reduce cognitive load and support processing.
Section 504
Ensure preferential seating during whole-group counting instruction to minimize distraction and support focus during oral counting sequences and numeral identification tasks. Provide extended time on number writing checks and chapter assessments, and allow the use of a personal number line or manipulative set during any independent counting or addition work.
ELL / MLL
Support vocabulary development around counting language — such as 'how many,' 'total,' 'add,' and number names — by pairing spoken words with visual number cards, fingers, and grouped objects so meaning is made concrete. Simplified, consistent verbal directions paired with physical demonstration will help students access counting routines, and home language counting sequences may be honored during informal practice to build conceptual bridges to English number names.
At Risk (RTI)
Begin with smaller sets of objects (within 5) to build confident one-to-one correspondence before extending to 10, ensuring students experience early success with counting and cardinality. Connect number quantities to personally meaningful contexts, such as counting classroom items or snack pieces, and use frequent brief check-ins during counting activities to catch and address emerging misconceptions before they become entrenched.
Gifted & Talented
Invite students who have demonstrated secure counting and cardinality within 10 to explore quantities and addition combinations beyond 10 or to investigate how the same quantity can be arranged in different ways while still representing the same number. Encourage students to explain their reasoning about why the last number counted tells 'how many,' pushing toward the conceptual understanding of cardinality rather than procedural counting alone, and offer opportunities to represent and communicate addition stories in multiple ways, including self-created drawings or arrangements.