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Lessons
Supreme Court Welcome
Discipline
Mathematics
Grade
6
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Professional Commentary

This two-lesson unit allows students to investigate the triangular numbers in an interesting, real-world context, the Supreme Court. Beginning with the classic handshake problem, students generate geometric and algebraic representations for the patterns they encounter and conclude with a formula for the nth triangular number. Activity sheets, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included. (author/sw)


Common Core State Standards for Mathematics
Standards for Mathematical Practice
CCSS.Math.Practice.MP1 
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP7 
Look for and make use of structure.
CCSS.Math.Practice.MP8 
Look for and express regularity in repeated reasoning.
Grade 6
Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2 
Write, read, and evaluate expressions in which letters stand for numbers.
  1. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
  2. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
  3. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
6.EE.A.3 
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.A.4 
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Reason about and solve one-variable equations and inequalities.
6.EE.B.6 
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9 
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (5–7)
B.
Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.
Benchmarks (8–10)
A.
Generalize and explain patterns and sequences in order to find the next term and the nth term.
Grade Level Indicators (Grade 6)
1.
Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.
2.
Use words and symbols to describe numerical and geometric patterns, rules and functions.
Grade Level Indicators (Grade 7)
1.
Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.
2.
Generalize patterns by describing in words how to find the next term.
Grade Level Indicators (Grade 8)
2.
Generalize patterns and sequences by describing how to find the nth term.
Principles and Standards for School Mathematics
Algebra Standard
Understand patterns, relations, and functions
Expectations (6–8)
represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
relate and compare different forms of representation for a relationship;
Use mathematical models to represent and understand quantitative relationships
Expectations (6–8)
represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
relate and compare different forms of representation for a relationship;
model and solve contextualized problems using various representations, such as graphs, tables, and equations.