Grade 6 Mathematics
Explore algebraic thinking through pattern recognition, coordinate graphing, and functional relationships. These activities bridge concrete experiences with abstract mathematical concepts.
By the end of these activities, students will be able to:
Different pattern types students will explore and analyze
Patterns that increase by a constant amount
an + b
Patterns involving area and perimeter relationships
Based on geometric formulas
Patterns where position determines value
f(n) = expression with n
Patterns visible on coordinate graphs
y = mx + b relationships
Students investigate growing patterns using concrete materials and develop algebraic thinking through pattern analysis.
Create a growing pattern using blocks (e.g., 3, 6, 9, 12... or L-shapes that grow). Build the first 4-5 terms physically.
Record pattern in a table showing term number and value. Look for relationships between term position and value.
Graph the pattern on coordinate plane with term number on x-axis and pattern value on y-axis.
Write the pattern rule algebraically (e.g., 3n for the pattern 3, 6, 9, 12...). Test the rule with known values.
Predict the 20th term using the algebraic rule and verify by extending the pattern or using the formula.
Students create and interpret coordinate art while developing understanding of coordinate systems and algebraic relationships.
Provide coordinate pairs that form a picture when plotted. Start with simple shapes to build confidence.
Students plot points accurately and connect in order to reveal the hidden picture (school mascot, seasonal theme, etc.).
Analyze the coordinate relationships. Look for patterns in x and y values, symmetry, and transformations.
Create their own coordinate picture for classmates. Plan design, determine coordinates, and write clear directions.
Display artwork with coordinate instructions. Students visit gallery and recreate each other's coordinate art.
Students explore functional relationships through hands-on function machine activities and algebraic expression building.
Introduce the concept of function machines that take inputs and produce outputs according to a rule.
Give students input-output pairs and challenge them to discover the hidden function rule through testing.
Write the discovered rule as an algebraic expression using variables (e.g., n + 5, 2n - 1).
Use the algebraic expression to predict outputs for new inputs, then verify with the function machine.
Design their own function machines with unique rules for other groups to solve and express algebraically.
Students explore connections between tables, graphs, and algebraic expressions through area and perimeter investigations.
Create rectangles with width 2 and varying lengths (1, 2, 3, 4, 5). Calculate perimeter for each rectangle.
Record length and perimeter data in table format. Look for patterns in how perimeter changes as length increases.
Graph the relationship with length on x-axis and perimeter on y-axis. Analyze the shape and slope of the line.
Develop algebraic expression for the pattern (P = 2l + 4). Test rule with table values.
Compare the same relationship shown in table, graph, and equation. Discuss advantages of each representation.
Key concepts and progressions for building algebraic understanding
