Unit Plan 1 (Grade K Math): Math Routines & Counting

Focus: Launch math talk, manipulative norms, and daily counting; connect number names to quantities 0–5 with one-to-one and cardinality.

Grade Level: K

Subject Area: Mathematics (Counting & Cardinality)

Total Unit Duration: 5 sessions (one week), 30–40 minutes per session

I. Introduction

This launch week builds classroom math culture and joyful counting. Students practice handling tools safely, talking about math, and matching number words to objects. They learn that the last number said tells “how many” and practice counting out a requested amount to 5.

Essential Questions

• How do we use and share math tools respectfully?
• What does it mean to count a set the right way?
• How do number words tell how many things are in a group?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Follow manipulative norms (get, use, return) and contribute to math talk routines.
2. Count objects to 5 with one-to-one correspondence and say the last number to tell how many (cardinality).
3. Recognize that the number of objects is the same regardless of order (if counted once each).
4. Count out a given number of objects (0–5) when asked.

Standards Alignment — CCSS Kindergarten (threaded across the unit)

• K.CC.4a–c: Understand counting principles (one-to-one, cardinality, each next number is one more).
• K.CC.5: Count to answer “how many?” up to 5; count out a given number.
• Mathematical Practices: MP.1–MP.6 threaded (perseverance, reasoning, argument, modeling, tools, precision).

Success Criteria — Student Language

• I can touch-count each object one time and say the last number to tell how many.
• I can count out a set of 0–5 when someone asks for a number.
• I can explain how I counted and show it with my finger/pointing.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Math journals, mini whiteboards; counters, linking cubes, two-color chips, ten frames (5-frame for this unit).
• Picture cards and small counting trays/circles; numeral cards 0–5; simple number path 0–5.
• Routine posters: Tool Norms, How We Count, My Turn–Your Turn.

Preparation

• Anchor charts: “One touch, one count”, “Last number tells how many”, “Count out a number”.
• Rehearse call-and-response sentence stems: “I counted ___.” “I touched each one.”

Common Misconceptions to Surface

• Double-counting or skipping objects.
• Saying a number list without pointing/matching to objects.
• Changing the answer after moving objects (if each was counted once, total stays the same).
• Confusing zero with “nothing to count” vs. still naming 0.

Key Terms (highlighted in lessons) count, number name, one-to-one, cardinality, set, match, how many, zero, more, fewer, same, count out

IV. Lesson Procedure

(Each day: Launch → Explore → Discuss/Consolidate → Reflect. Suggested timing for a 30–40 min block.)

Session 1 — Welcome to Math Tools & Counting Names (K.CC.4; MP.1, MP.5)

• Launch (6–8 min): Tour tool norms; chant 0–5 with fingers.
• Explore (15–18 min): Stations: (A) Touch-count picture dots to 5; (B) Build towers of 0–5 cubes to match numeral cards.
• Discuss (6–8 min): What helped you keep track? (pointing, moving into a “counted” circle).
• Reflect (2–3 min): “Today I counted ___ by ___.”

Session 2 — One-to-One with 5-Frames (K.CC.4a; MP.5, MP.6)

• Launch (5–6 min): Model placing one counter per square on a 5-frame while saying each number word once.
• Explore (15–18 min): Partner task: draw a numeral card (0–5), build it on the frame, then check partner’s count.
• Discuss (6–8 min): Share strategies for not skipping/doubling.
• Reflect (2–3 min): “One way I keep one-to-one is ___.”

Session 3 — Cardinality: The Last Number Tells How Many (K.CC.4b–c; MP.2, MP.6)

• Launch (6–8 min): Quick image (flash 4 dots); students say how many and explain.
• Explore (15–18 min): Mix-and-move: count scattered objects to 5, circle counted items, say “I have __.”
• Discuss (6–8 min): If we move them, do we have the same amount? Why?
• Reflect (2–3 min): “I knew it was __ because I said the last number and stopped.”

Session 4 — Count Out a Number (K.CC.5; MP.1, MP.4)

• Launch (5–6 min): Teacher asks, “Please count out 3 bears.” Model taking exactly that many.
• Explore (15–18 min): Partner play: one asks for a number (0–5), the other counts out that many into a tray; switch roles.
• Discuss (6–8 min): What did you do when you had too many or not enough?
• Reflect (2–3 min): “When asked for __, I counted out by ___.”

Session 5 — Counting Celebration Stations (K.CC.4–5; MP.3, MP.6)

• Task (18–22 min): Rotations: (A) Build & Tell (5-frame + numeral), (B) Count & Match (sets ↔ cards), (C) Count Out station (teacher asks).
• Peer Review (5–7 min): Read & Point: partner points and repeats the count; TAG mini: Tell a strength, Ask a question, Give a suggestion.
• Discuss (6–8 min): What helped your counting be clear to others?
• Reflect (2–3 min): Sticker check: “I can count to 5 with one-to-one.”

V. Differentiation and Accommodations

Advanced Learners

• Compose/decompose within 5 (e.g., 2 and 3 make 5); represent on two-color counters.
• Quick images with masked counts (brief flashes) to reinforce cardinality.

Targeted Support

• Use number paths and counting cups (move each counted item).
• Start with to 3 then extend to 5; echo-count with teacher finger-pointing.

Multilingual Learners

• Picture/word bank: count, how many, more, fewer, same, zero.
• Gestures for touch-count and stop at last number; choral responses.

IEP/504 & Accessibility

• Larger manipulatives and high-contrast 5-frames; tactile counters.
• Option to verbalize while an adult/peer moves objects.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Follows tool norms; participates in math talk.
• S2: Places one object per space while counting to 5.
• S3: States the last number to tell how many without recounting.
• S4: Counts out a requested number (0–5).
• S5: Communicates process clearly to a partner.

Summative (end of week; 0–2 per criterion, total 10)

1. One-to-One Correspondence (K.CC.4a)

• 2: Consistently touches/matches once per object to 5.
• 1: Minor skips/doubles; corrects with prompt.
• 0: Frequent mismatches.

2. Cardinality & “How Many?” (K.CC.4b–c)

• 2: Says the last number to tell how many; answer stable if items move.
• 1: Sometimes recounts or changes answer.
• 0: Does not use last number to determine total.

3. Count Out a Given Number (K.CC.5)

• 2: Accurately counts out 0–5 on request.
• 1: Needs a prompt/reminder to adjust.
• 0: Cannot produce requested amount.

4. Representation & Clarity (MP.6)

• 2: Organizes objects/frames to make counting clear to others.
• 1: Partially clear; labels or order occasionally confusing.
• 0: Disorganized; hard to verify.

5. Routines & Collaboration (MP.1, MP.5)

• 2: Uses tools safely; listens/takes turns; persists.
• 1: Inconsistent routines or turn-taking.
• 0: Needs frequent redirection.

Feedback Protocol (Math Talk)

• Read & Point (1 min): Partner points to each object as the counter counts.
• TAG (2–3 min): Tell a strength (clear pointing), Ask a question (“How did you know to stop?”), Give a suggestion (use a tray/circle).
• Author Response (1–2 min): Student restates count and makes one improvement.

VII. Reflection and Extension

Reflection Prompts

• What helps you remember to touch each object one time?
• How do you know when to stop counting?
• What can you do if you lose your place?

Extensions

• Count & Cover: Roll a 0–5 die; count out and cover a frame.
• Build the Number: Choose a card 0–5; show it with cubes, chips, or drawings.
• Math Story: “I counted out __ snacks for a friend.”

Standards Trace — When Each Standard Is Addressed

• K.CC.4a — Sessions 1–3 (one-to-one matching).
• K.CC.4b–c — Sessions 2–3 (cardinality; last number; one more).
• K.CC.5 — Sessions 4–5 (count out a number; answer “how many?”).
• MP.1–MP.6 — All sessions (perseverance, reasoning, argument, modeling, tools, precision).