Number Sense Activities
Grade 6 Mathematics
Develop deep understanding of number concepts through hands-on investigations of place value, special number sets, and number relationships. These activities build foundational skills for advanced mathematical thinking.
Learning Outcomes
By the end of these activities, students will be able to:
- Read and write numbers in words and figures up to 1,000,000 (seven digits)
- State the face value, place value and total value of any digit in a whole number up to 999,999,999
- Identify and describe special sets of numbers (square, prime and composite)
- Compare and order large numbers using place value understanding
- Represent numbers using multiple formats and visual models
Place Value Detective
Students become mathematical detectives to investigate and identify place values in large numbers.
Materials Needed
- Place value charts
- Digit cards (0-9)
- Base-ten blocks
- Detective badges (optional)
- Mystery number cards
- Recording sheets
Assessment Strategies
Formative Assessment:
- • Observe learners' ability to correctly identify place values
- • Listen to mathematical explanations and reasoning
- • Check accuracy of concrete representations
Summative Assessment:
- • Mystery number creation and solution accuracy
- • Written explanations of place value concepts
- • Peer assessment of detective presentations
Step-by-Step Instructions
Step 1: Setup Detective Agency
Give learners cards with 7-digit numbers written on them. Distribute detective materials and explain their mission.
Step 2: Investigate Numbers
For each mystery number, learners identify face value, place value, and total value of specified digits using detective skills.
Step 3: Build Evidence
Using base-ten blocks, represent the number concretely to verify their detective work.
Step 4: Create Mystery Cases
Students create their own 'mystery number' where they give clues about place values for others to solve.
Step 5: Detective Presentation
Present findings to the class, explaining their detective reasoning and mathematical evidence.
Real-World Connections
Extension Activities
- Investigate place values in different number systems (binary, base-5)
- Create place value word problems using real-world contexts
- Design a place value board game for younger students
Square Number Garden
Students explore square numbers through hands-on tile arrangements and create artistic representations.
Materials Needed
- Square tiles (at least 100 per group)
- Graph paper
- Calculators
- Colored pencils or markers
- Art supplies for decoration
- Recording templates
Assessment Strategies
Formative Assessment:
- • Observe tile arrangement accuracy
- • Check pattern recognition and extension
- • Listen to mathematical vocabulary usage
Summative Assessment:
- • Square number garden artwork with mathematical annotations
- • Written explanation of square number patterns
- • Problem-solving accuracy in finding new square numbers
Step-by-Step Instructions
Step 1: Tile Exploration
Provide learners with square tiles to form actual squares. Start with 1 tile, then 4, then 9, observing the pattern.
Step 2: Pattern Discovery
Count tiles to discover square numbers (1, 4, 9, 16, 25...) and discuss what makes them 'square'.
Step 3: Mathematical Recording
Record findings on graph paper showing the visual pattern and the numerical sequence.
Step 4: Challenge Investigation
Find the next three square numbers and verify with tiles. Explore the pattern: 1², 2², 3², 4², 5²...
Step 5: Artistic Garden Creation
Create an art piece showing the first 10 square numbers as decorated squares, incorporating mathematical labels.
Real-World Connections
Extension Activities
- Investigate cube numbers using 3D materials
- Explore triangular numbers and other figurate numbers
- Research historical uses of square numbers in architecture
- Create digital animations showing square number growth
Prime & Composite Investigation
Students investigate prime and composite numbers through systematic exploration and pattern analysis.
Materials Needed
- Number grids (1-100)
- Colored pencils or markers
- Factor cards
- Calculators
- Investigation recording sheets
- Prime number reference charts
Assessment Strategies
Formative Assessment:
- • Check factor-finding accuracy
- • Observe systematic investigation approaches
- • Listen to pattern discussions and mathematical reasoning
Summative Assessment:
- • Classification accuracy on number grids
- • Mathematical report quality and insights
- • Understanding demonstration through examples
Step-by-Step Instructions
Step 1: Number Classification Setup
Introduce the concepts of prime and composite numbers. Provide number grids and classification criteria.
Step 2: Systematic Investigation
Students systematically test numbers 1-100, identifying factors and classifying as prime or composite.
Step 3: Pattern Analysis
Color-code prime numbers on the grid and look for patterns. Discuss observations about prime distribution.
Step 4: Factor Exploration
For composite numbers, find all factors and explore relationships between factors and the original number.
Step 5: Mathematical Reporting
Create a report summarizing findings, including patterns observed and mathematical reasoning.
Real-World Connections
Extension Activities
- Explore twin primes and prime gaps
- Investigate the Sieve of Eratosthenes method
- Research historical significance of prime numbers
- Connect to modern cryptography applications
Large Number Representation Challenge
Students master reading, writing, and representing numbers up to 1,000,000 using multiple formats.
Materials Needed
- Large number cards
- Place value charts (up to millions)
- Base-ten blocks or drawings
- Number word cards
- Expanded form templates
- Real-world number examples
Assessment Strategies
Formative Assessment:
- • Monitor conversion accuracy between formats
- • Observe place value understanding in explanations
- • Check visual representation correctness
Summative Assessment:
- • Multi-format number representation portfolio
- • Comparison and ordering task accuracy
- • Real-world application problem solving
Step-by-Step Instructions
Step 1: Number Format Introduction
Present the same large number in different formats: standard form, word form, and expanded form.
Step 2: Conversion Practice
Students practice converting between different number representations using place value understanding.
Step 3: Real-World Applications
Use actual examples from population data, distances, and measurements to practice with authentic numbers.
Step 4: Visual Representation
Create visual models using base-ten concepts to represent large numbers concretely.
Step 5: Number Comparison Challenge
Compare and order large numbers, explaining reasoning using place value concepts.
Real-World Connections
Extension Activities
- Explore scientific notation introduction
- Research world populations and geographical distances
- Create number stories using large numbers
- Investigate historical large numbers (ancient civilizations, etc.)
Key Mathematical Vocabulary
Essential terms students should understand and use correctly
Place Value
The value of a digit based on its position in a number
Face Value
The actual value of a digit regardless of its position
Total Value
The face value multiplied by the place value
Prime Number
A number greater than 1 with exactly two factors: 1 and itself
Composite Number
A number greater than 1 with more than two factors
Square Number
A number that can be expressed as n × n for some integer n
Standard Form
Numbers written using digits (e.g., 456,789)
Word Form
Numbers written in words (e.g., four hundred fifty-six thousand)
Expanded Form
Numbers written showing place value (e.g., 400,000 + 50,000 + 6,000 + 700 + 80 + 9)