Astor Academy Methods - Kindergarten Mathematics

Sample day 1 - October, Unit 2 (Week 8: one more, and first through tenth)

• Counting routine (5 min). Day 33 of school: show 3 tens and 3 ones on ten-frames; count by ones to 33.
• Warm-up (10 min). Flash a ten-frame with 6 dots for 2 seconds. 'How many? How did you see it?' ('5 and 1 more.')
• Activity 1 (15 min). Staircase towers: each pair builds cube towers 1 to 10. 'What do you notice?' Children see that each tower is one more than the last (NY-K.CC.4c).
• Activity 2 (15 min). Animal parade: line up ten toy animals. 'Who is first? Who is fifth? Who is right after the third?' (NY-K.CC.4d). Pairs take turns asking each other.
• Synthesis (5 min). 'If I add one more cube to the 7 tower, how tall is it? How do you know without counting all?'

Sample day 2 - January, Unit 5 (Week 17: ways to make 5)

• Counting routine (5 min). Count by tens to 100, then count on by ones from 75 to 85.
• Warm-up (10 min). Show 5 fingers as 3 and 2, then 4 and 1. 'Is it still 5?'
• Activity 1 (15 min). Shake and spill: put 5 two-color counters in a cup, shake, spill. Count red and yellow. Record with a drawing and, when ready, an equation (5 = 3 + 2) (NY-K.OA.3).
• Activity 2 / centers (20 min). Teacher group: the NYSED 'both addends unknown' story type ('Grandma has 5 flowers. How many can go in the red vase and how many in the blue vase?'). Other centers: cube trains, dot-card match, fluency game within 5.
• Synthesis (10 min). Make a class chart of every way we found to make 5. 'Did we find them all? How can we tell?' (MP7, MP8)

Sample day 3 - May, Unit 8 (Week 32: coins)

• Counting routine (5 min). Count on from 91 to 100; count by tens.
• Warm-up (10 min). Notice and Wonder with a large photo of a penny and a dime side by side.
• Activity 1 (15 min). Coin detectives: each pair gets pennies, nickels, dimes, and quarters and magnifying glasses. Sort them any way you like, then explain your sort (size, color, pictures, edges) (NY-K.MD.4, NY-K.MD.3).
• Activity 2 (15 min). 'Penny or dime?' game: a partner hides a coin in one hand; the other names it after looking. Count the pennies in a pile of 10 or fewer (NY-K.CC.5a).
• Synthesis (5 min). 'How can you tell a dime from a penny?' Record children's words on a chart.

NYC Reads names a citywide reading screener (Acadience) for K-2; Astor did not find a citywide kindergarten math screener in the NYC Solves pages it could check, so use your school's curriculum assessments if it has them. The tools below are Astor's.

1. Unit interviews

Each unit ends with a short one-on-one interview (listed under each unit). Kindergarten math is best checked with objects in hand and a conversation, not a worksheet.

2. Monthly classroom benchmarks (Astor targets)

These are Astor's planning targets, paced so every standard is reached by June. They are not NYSED numbers.

3. End-of-year interview checklist (every standard)

• Multilingual learners. Use gestures, real objects, and number words in the home language alongside English; post a picture word bank (more, fewer, same, add, take away, shape names).
• Students with disabilities. Use larger manipulatives, fewer objects at once, visual schedules for centers, and the supports in each child's IEP. NYSED notes that manipulatives and visual models should always be connected to written symbols and methods.
• Children ready for more. Same task, bigger numbers (count to 120, story problems to 20), and 'Is there another way?' prompts.

● = standard in focus (taught and checked); ○ = practiced. Every kindergarten standard is in focus in at least one unit, and every one appears in the end-of-year interview.

Standards for Mathematical Practice are used in every unit: MP1 Make sense of problems and persevere in solving them.; MP2 Reason abstractly and quantitatively.; MP3 Construct viable arguments and critique the reasoning of others.; MP4 Model with mathematics.; MP5 Use appropriate tools strategically.; MP6 Attend to precision.; MP7 Look for and make use of structure.; MP8 Look for and express regularity in repeated reasoning..

From NYSED, New York State Next Generation Mathematics Learning Standards (2017), Kindergarten pages.

• NY-K.CC.1: Count to 100 by ones and by tens.
• NY-K.CC.2: Count to 100 by ones beginning from any given number (instead of beginning at 1).
• NY-K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
• NY-K.CC.4: Understand the relationship between numbers and quantities up to 20; connect counting to cardinality.
• NY-K.CC.4a: When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (1:1 correspondence)
• NY-K.CC.4b: Understand that the last number name said tells the number of objects counted, (cardinality). The number of objects is the same regardless of their arrangement or the order in which they were counted.
• NY-K.CC.4c: Understand the concept that each successive number name refers to a quantity that is one larger.
• NY-K.CC.4d: Understand the concept of ordinal numbers (first through tenth) to describe the relative position and magnitude of whole numbers.
• NY-K.CC.5a: Answer counting questions using as many as 20 objects arranged in a line, a rectangular array, and a circle. Answer counting questions using as many as 10 objects in a scattered configuration.
• NY-K.CC.5b: Given a number from 1-20, count out that many objects.
• NY-K.CC.6: Identify whether the number of objects in one group is greater than (more than), less than (fewer than), or equal to (the same as) the number of objects in another group. Note: Include groups with up to ten objects.
• NY-K.CC.7: Compare two numbers between 1 and 10 presented as written numerals.
• NY-K.OA.1: Represent addition and subtraction using objects, fingers, pennies, drawings, sounds, acting out situations, verbal explanations, expressions, equations, or other strategies.
• NY-K.OA.2a: Add and subtract within 10.
• NY-K.OA.2b: Solve addition and subtraction word problems within 10.
• NY-K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way. Record each decomposition with a drawing or equation.
• NY-K.OA.4: Find the number that makes 10 when given a number from 1 to 9. Record the answer with a drawing or equation.
• NY-K.OA.5: Fluently add and subtract within 5.
• NY-K.OA.6: Duplicate, extend, and create simple patterns using concrete objects.
• NY-K.NBT.1: Compose and decompose the numbers from 11 to 19 into ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
• NY-K.MD.1: Describe measurable attributes of an object(s), such as length or weight, using appropriate vocabulary.
• NY-K.MD.2: Directly compare two objects with a common measurable attribute and describe the difference.
• NY-K.MD.3: Classify objects into given categories; count the objects in each category and sort the categories by count. Note: Limit category counts to be less than or equal to 10.
• NY-K.MD.4: Explore coins (pennies, nickels, dimes, and quarters) and begin identifying pennies and dimes.
• NY-K.G.1: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
• NY-K.G.2: Name shapes regardless of their orientation or overall size.
• NY-K.G.3: Understand the difference between two-dimensional (lying in a plane, "flat") and three-dimensional ("solid") shapes.
• NY-K.G.4: Analyze, compare, and sort two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts, and other attributes.
• NY-K.G.5: Model objects in their environment by building and/or drawing shapes.
• NY-K.G.6: Compose larger shapes from simple shapes.

• Codes. All 30 kindergarten codes and sub-codes are copied from the NYSED standards document; NY-K.OA.6 and NY-K.MD.4 appear only on the Next Generation side of the NYSED crosswalk (no 2011 match).
• Curriculum mapping. Unit titles, section titles, and lesson counts come from Illustrative Mathematics' published K materials (the lesson counts come from IM's v1 scope and sequence, which says goals are "subject to minor changes"). IM is aligned to the Common Core, so the coin and pattern work in Unit 8 and earlier units is Astor's addition to cover the two NYS-only standards.
• NYC Solves in elementary school is new in 2026-27 and covers four districts so far; most NYC elementary schools are not yet on a mandated math curriculum. Districts 5 and 25 use i-Ready and Amplify Desmos, which have their own sequences.
• Astor's own choices: daily minutes, monthly targets, activities, centers, household swaps, and interview tasks. The "Grandma has 5 flowers" story is adapted from the 'Both Addends Unknown' example in NYSED's problem-type chart.
• No citywide K math screener was found in the NYC Solves pages checked.

All links were opened or downloaded on October 19, 2026 (America/New_York). Standard codes and wording were copied from the NYSED PDFs (copies kept in src-cache/).

New York State (standards) 1. New York State Education Department. New York State Next Generation English Language Arts Learning Standards (2017). Kindergarten section, pp. 15-21; Appendix A (Language Standards 1 and 2, P-2 band), pp. 94-95. https://www.nysed.gov/sites/default/files/nys-next-generation-ela-standards.pdf 2. NYSED. Crosswalk Between P-12 ELA Common Core Learning Standards (2011) and the revised NYS Next Generation ELA Learning Standards (2017) - Kindergarten. https://www.nysed.gov/sites/default/files/programs/standards-instruction/nys-ela-standards-kindergarten-crosswalk.pdf 3. NYSED. New York State Next Generation Mathematics Learning Standards (2017; PDF created 2019). Kindergarten Overview and standards, pp. 17-24 (including the NY-K.OA.2 problem-type chart on p. 20). https://www.nysed.gov/sites/default/files/programs/curriculum-instruction/nys-next-generation-mathematics-p-12-standards.pdf 4. NYSED. NYS Next Generation Mathematics Learning Standards Kindergarten Crosswalk. https://www.nysed.gov/sites/default/files/programs/curriculum-instruction/nys-math-standards-kindergarten-crosswalk.pdf

New York City 5. NYC Public Schools. NYC Reads (approach, curricula options, launch timeline). https://www.schools.nyc.gov/learning/subjects/literacy/nyc-reads 6. NYC Reads. NYC Reads Family Guidance (2023-24; lists Fundations, Heggerty, Really Great Reading; HMH Into Reading, EL Education, Wit & Wisdom; Acadience Reading as the K-2 screener three times a year). Copy hosted on a school website: https://cdnsm5-ss20.sharpschool.com/UserFiles/Servers/Server_473288/File/%20Our%20School/Announcements/NYC%20Reads%20Supporting%20Families.pdf 7. NYCPS University Partnerships. Instructional Priority: NYC Reads (foundational skills: Fundations paired with Heggerty, or Really Great Reading). https://nycpsuniversitypartnerships.zendesk.com/hc/en-us/articles/36694996233755-Instructional-Priority-NYC-Reads 8. NYC Reads Learning Community. Resources for Core Instruction (phonics, decodable text, sound walls guidance). https://sites.google.com/schools.nyc.gov/nycpslc/resources-for-core-instruction 9. NYC Public Schools. NYC Solves (Math Shifts; launch timeline incl. Phase 1 Elementary SY 2026-27, Districts 5, 11, 12, 25). https://www.schools.nyc.gov/learning/subjects/math/nyc-solves 10. NYC Mayor's Office. Mayor Mamdani and Chancellor Samuels Announce Expansion of NYC Solves and NYC Reads (May 21, 2026). https://www.nyc.gov/mayors-office/news/2026/05/mayor-mamdani-and-chancellor-samuelsannounce-expansion-of-nyc-so 11. Chalkbeat New York. Mamdani launches elementary school math curriculum overhaul (May 22, 2026). https://www.chalkbeat.org/newyork/2026/05/22/nyc-elementary-school-math-curriculum-mandate-districts-mamdani/ 12. NYCPS Math Resources. Illustrative Mathematics (NYC implementation resources; Notice and Wonder routine). https://sites.google.com/view/nyc-math-resources/high-quality-instructional-materials-hqim/illustrative-mathematics 13. NYC Public Schools. 2026-2027 School Year Calendar. https://www.schools.nyc.gov/calendar/2026-2027-school-year-calendar (PDF: http://www.schools.nyc.gov/docs/default-source/sections/calendar/2026-27-school-year-calendar.pdf)

Curricula (NYC Reads and NYC Solves options) 14. EL Education. Grades K-2 Curriculum Plan (K modules Toys and Play, Weather Wonders, Trees Are Alive, Enjoying and Appreciating Trees; writing tasks; required trade books). https://el-education-production.s3.amazonaws.com/media/documents/CurriculumTools_CurriculumPlan-K-2_0419.pdf 15. EL Education. ELA K curriculum page (module titles; 1-hour K-2 Reading Foundations Skills Block). https://curriculum.eleducation.org/curriculum/ela/grade-k 16. Great Minds. Wit & Wisdom Core Texts. https://greatminds.org/hubfs/GM-%20Marketing%20Collateral%20Catalog/Collateral%20Catalog/Wit%20and%20Wisdom/WW_Core%20Texts_Final%20Web_2.10.23.pdf 17. Great Minds. Wit & Wisdom K-8 Modules at a Glance (K essential questions). https://core-docs.s3.amazonaws.com/documents/asset/uploaded_file/1669860/Wit___Wisdom_Scope_and_Sequence_K-5.pdf 18. Illustrative Mathematics / Kendall Hunt. Kindergarten scope and sequence and units (8 units, section titles). https://im.kendallhunt.com/K5/teachers/kindergarten/course-guide/scope-and-sequence.html and https://im.kendallhunt.com/k5/teachers/kindergarten/units.html 19. Illustrative Mathematics. IM K-5 Scope and Sequence (v1; lesson counts per K unit; "subject to minor changes in the final published version"). https://illustrativemathematics.org/wp-content/uploads/2021/02/v1-IM-K-5-Math-Scope-and-Sequence.pdf

Assessment and foundational skills 20. Acadience Learning. Acadience Reading K-6 Benchmarks and Composite Score (March 11, 2021), Kindergarten table. https://acadiencelearning.org/wp-content/uploads/2026/01/Acadience-Reading-K-6-Benchmark-Goals-handout_2021_color.pdf 21. UK Department for Education and Skills. Letters and Sounds: Principles and Practice of High Quality Phonics (2007), Phase Two and Three letter sets. https://assets.publishing.service.gov.uk/media/5a7aa7b6e5274a34770e630c/Letters_and_Sounds_-_DFES-00281-2007.pdf 22. Fry, Edward. First 100 Instant Words (list as published by SightWords.com). https://sightwords.com/wp-content/uploads/fry_1st_100_Updated-2.pdf

Book titles and authors 23. Every anchor text and read-aloud title/author pair was checked against Open Library search (https://openlibrary.org/search.json) on October 19, 2026; curriculum-listed titles were also matched to sources 14 and 16.