Play explorations: set up stations with loose parts for students to explore number sense using these suggestions. Polypad is a virtual manipulative tool that could be used for these activities.
Emerging/Developing
Instructional focus:
Use concrete manipulatives (cubes, counters) and drawings; describe numbers in everyday language (“I have 3 hundreds, 2 tens, and 5 ones”).
Core competency connections:
Communication – orally describe using visuals.
Critical/Creative Thinking – match symbols to quantities
Personal Responsibility – practice describing in partner work.
Developing/Proficient
Instructional focus:
Represent numbers with standard/base ten notation and written words; compare numbers using <, >, =
Core competency connections:
Communication – explain reasoning for comparisons.
Critical/Creative Thinking – sort numbers into categories (odd/even, size).
Personal Responsibility – check accuracy of own representations.
Proficient/Extending
Instructional focus:
Explore multiple representations (e.g., 823 as 800+20+3, tally, money); justify why they are equivalent
Core competency connections:
Communication – share representations with others.
Critical/Creative Thinking – find creative/alternative ways to show numbers.
Social Responsibility – support peers by demonstrating flexible thinking.
Emerging/Developing
Instructional focus:
Hands-on modeling with 1s, 10s and 100s; build and trade to reinforce place value
Practice breaking numbers into hundreds, tens, ones with teacher modeling (452 → 400 + 50 + 2).
Core competency connections:
Communication – point to/label “hundreds, tens, ones”; read expanded form aloud
Critical/Creative Thinking – group and regroup blocks; connect blocks to expanded notation
Personal Responsibility – take care of materials, follow steps; use charts/checklists to stay on track
Developing/Proficient
Instructional focus:
Represent multi-digit numbers with blocks; connect block models to written numerals and words
Write expanded form independently; connect to place value strategies for addition and subtraction
Core competency connections:
Communication – describe models; explain reasoning using math vocabulary
Critical/Creative Thinking – connect models to equations; analyze different decompositions (700+20+5 vs. 600+120+5)
Personal Responsibility – self-monitor accuracy of builds; reflect on which strategy is helpful
Proficient/Extending
Instructional focus:
Use blocks to model addition/subtraction with regrouping; explore beyond 1000 and the relationships between 100, 1000 and 10000; Use expanded form flexibly to solve problems; explore non-standard decompositions (e.g., 452 = 300 + 100 + 40 + 12)
Core competency connections:
Communication – present multi-step block strategies; teach peers how different forms work
Critical/Creative Thinking – compare models to mental math; evaluate efficiency of strategies
Social Responsibility – coach peers using block models; invent new decompositions
Emerging/Developing
Instructional focus:
Use concrete objects to build simple addition/subtraction; draw pictures to represent
Core competency connections:
Communication –share “story problems” orally
Critical/Creative Thinking –identify when to add vs. subtract
Personal Responsibility – check answers with manipulatives
Developing/Proficient
Instructional focus:
Write equations for real-world situations; solve using place value strategies
Core competency connections:
Communication –explain solution steps
Critical/Creative Thinking – choose efficient, descriptive strategies
Personal Responsibility – track steps and reflect on how mistakes help you learn
Proficient/Extending
Instructional focus:
Create multi-step problems; explore patterns in addition/subtraction
Core competency connections:
Communication – present and defend multiple strategies
Critical/Creative Thinking – evaluate efficiency of methods
Social Responsibility – design original math puzzles
Emerging/Developing
Instructional focus:
Use numbers in daily contexts (counting snacks, school supplies, kitchen tools)
Core competency connections:
Communication – talk about “how many” in daily life
Critical/Creative Thinking – decide which numbers matter in a context
Personal Responsibility – notice numbers outside, at the library, at the store...
Developing/Proficient
Instructional focus:
Solve contextual problems (shopping, time, distance)
Core competency connections:
Communication – explain connections to personal life
Critical/Creative Thinking – decide how to represent a problem
Personal Responsibility – track strategies in a math journal
Proficient/Extending
Instructional focus:
Extend to abstract connections (population, sports statistics, environment)
Core competency connections:
Communication – share data with others
Critical/Creative Thinking – analyze trends in real-world data
Social Responsibility – consider how numbers reflect community/global issues
Emerging/Developing
Instructional focus:
Place numbers on a visual line with support; use jumps of 5s, 10s and/or 100s
Core competency connections:
Communication – explain position of a number
Critical/Creative Thinking – count intervals
Personal Responsibility – find "mistakes" in number lines (on purpose)
Developing/Proficient
Instructional focus:
Estimate and accurately place numbers; use number lines for addition/subtraction
Core competency connections:
Communication – describe thinking aloud
Critical/Creative Thinking – justify estimation
Personal Responsibility – reflect on accuracy of placements
Proficient/Extending
Instructional focus:
Explore open number lines (without benchmarks); use them to solve multi-step problems
Core competency connections:
Communication – explain strategy with open lines
Critical/Creative Thinking – compare multiple placements/paths
Social Responsibility – invent their own number line scales
Emerging/Developing
Instructional focus:
Skip-count with songs, movement; start with 1s, 2s, 5s and 10s
Core competency connections:
Communication – chant/count
Critical/Creative Thinking – notice patterns in counting
Personal Responsibility – practice daily with visuals
Developing/Proficient
Instructional focus:
Count by 25s, 50s, 100s; start from random numbers
Core competency connections:
Communication – explain strategies used for counting
Critical/Creative Thinking –predict next/previous numbers
Personal Responsibility – self-correct when errors occur
Proficient/Extending
Instructional focus:
Work with challenging intervals (count by 7s, 9s); connect to multiplication/division
Core competency connections:
Communication – articulate reasoning with complex patterns
Critical/Creative Thinking – find shortcuts for efficient counting
Social Responsibility – design skip-counting games and activities to share with others