Counting and Composing Numbers

Overview

This 12-week kindergarten unit develops counting, numeral writing, quantity, comparison, and early addition and subtraction. Students use concrete objects, drawings, movement, and the Progress in Math text where available. Each class meets for 45 minutes with 14 students, using a consistent routine that supports repetition, language development, and hands-on practice.

Learning intentions

Students will be able to:

• Count, read, and write numbers in sequence from 0 to 20 and count to 100 by ones and tens.
• Start counting from a given number and connect the last number counted to the total quantity.
• Represent quantities to 20 with objects, drawings, and written numerals.
• Compare numbers and quantities and use addition and subtraction to describe joining, separating, and making 10.

Success criteria

• I can count forward from a number and tell how many objects there are.
• I can write a numeral to show a quantity from 0 to 20.
• I can compare two numbers and say which is greater, less, or equal.
• I can model and solve addition and subtraction problems within 10, including facts within 5.

Curriculum links

• Counting and Cardinality: know number names and the count sequence; count to 100 by ones and tens.
• Counting and Cardinality: write numerals from 0 to 20 and represent quantities with written numerals.
• Counting and Cardinality: connect counting to cardinality, count organized and scattered collections, and compare written numbers from 1 to 10.
• Operations and Algebraic Thinking: model addition and subtraction situations, make 10, and add and subtract fluently within 5.

Lesson structure (45 minutes)

Use this structure each day. Change the number range and task according to the 12-week sequence below.

1. 0–7 min · Counting warm-up. Open with the counting routine slides and lead students in counting chants, movement counting, number identification, or counting forward from a number. Students count aloud, whisper-count, clap, and respond to quick “What comes next?” prompts.

2. 7–15 min · Mini-lesson and modeling. Use the teaching and modeling slides and model the day’s concept with a ten-frame, counters, numeral cards, or the Progress in Math lesson. Students explain what they notice, help build a quantity, and practice the language “There are ___ because the last number tells how many.”

3. 15–28 min · Partner hands-on practice. Place students in seven pairs and distribute the guided counting and number practice sheet when recording is needed. Students count, build, compare, or solve with counters while partners take turns as Builder and Checker; the teacher circulates and questions individuals.

4. 28–38 min · Small-group application. Revisit the partner game and problem-solving slides and give each pair a short task matched to need. Students represent a quantity or story problem with objects, draw it, and record a numeral or equation; the teacher works with a focus group of four students.

5. 38–43 min · Share and correct. Display the discussion and error-analysis slides and select two strategies to discuss. Students show models, compare solutions, and explain how they know the answer is reasonable.

6. 43–45 min · Exit check. Use the exit-question slide for one oral or written prompt. Students respond individually by drawing, writing a numeral, selecting a comparison symbol, or solving a fact.

12-week sequence

• Week 1: Number names and sequence. Count forward and backward within 10, match spoken numbers to numeral cards, order numbers 0–10, and practice writing 0–5. Use songs, floor-number walks, and Progress in Math counting activities.
• Week 2: Quantities and cardinality. Count collections arranged in lines and circles, touch each object once, answer “How many?” and explain why the final count gives the total. Extend to 20.
• Week 3: Numerals 0–10. Build quantities with counters, match collections to numerals, write 0–10, and investigate zero as “no objects.”
• Week 4: Numerals 11–20. Build teen numbers with ten-frames and ones, read and write 11–20, and represent each number with objects, drawings, and numerals.
• Week 5: Count to 100. Count by ones using a hundred chart and by tens using bundled straws or ten-frames. Begin counting forward from numbers other than 1.
• Week 6: Counting from any number. Practice “start at ___ and count on,” missing-number games, number-path movement, and counting out a given number of objects.
• Week 7: Compare quantities and numerals. Compare numbers 1–10 using objects, drawings, and written numerals. Use the language greater than, less than, and equal to before introducing symbols as appropriate.
• Week 8: Addition as putting together. Act out and model joining stories, combine two groups within 10, draw the action, and write equations with a box or blank for an unknown.
• Week 9: Addition as adding to. Solve “start, change, result” stories within 10 using counters, drawings, fingers, and equations. Include unknowns in different positions.
• Week 10: Subtraction as taking apart and taking from. Separate groups, remove objects, act out stories, and record subtraction equations within 10.
• Week 11: Make 10. Find the missing part for numbers 1–9 using ten-frames, counters, drawings, and equations such as 6 + __ = 10. Encourage multiple representations.
• Week 12: Fluency and application. Develop fluent addition and subtraction within 5 through games, story problems, quick images, and mixed review. Assess counting, numeral writing, quantity, comparison, make-10, and operation understanding.

Resources

• the counting routine slides
• the guided counting and number practice sheet
• Progress in Math kindergarten text and teacher materials
• Counters, linking cubes, and ten-frames
• Numeral cards 0–20 and a floor number line
• Hundred chart and craft sticks bundled in tens
• Whiteboards, markers, pencils, and crayons
• Small bags of organized and scattered objects
• Ten-frame cards and simple story-problem picture cards

Assessment

• During counting, ask individual students to start at a given number, count forward, count a collection, and state the total without recounting.
• Review models and worksheets for accurate numeral formation, one-to-one counting, quantity-to-numeral matching, comparison language, and equations.
• Use the final exit check each day; in Week 12, record individual performance on counting to 20, counting from a given number, writing numerals, comparing numbers, making 10, and solving addition/subtraction within 5.

Differentiation

• Support students with a reduced range, enlarged numerals, ten-frames, touch-counting, number lines, hand-over-hand modeling when appropriate, and sentence frames such as “I counted ___, so there are ___.”
• Pair students thoughtfully and assign roles so every child handles materials and explains thinking; provide repeated oral directions, gestures, and picture models for multilingual learners.
• For students ready for more challenge, begin counting from larger numbers, use scattered collections to 20, include unknowns in all positions, and ask for two different representations or equations.
• Provide pencil grips, adapted counters, extra response time, and teacher-led practice for students with fine-motor, attention, speech-language, or working-memory needs.