SHIFTING FROM MATHEMATICAL
WORKSHEETS TO MEANINGFUL TASKS
FACILITATED BY: CYNTHIA BELL
NUMERACY SPECIALIST
LITERACY ASSISTANCE CENTER
OBJECTIVES
 Build understanding of the effects of meaningful tasks
 Understand the levels of cognitive demand as they relate to depth of knowledge and be able to identify
the levels in a task
 Discuss how the 8 Standard Mathematical Practices can be the focus when developing tasks
WHAT IS A MEANINGFUL TASK?
 A mathematical task is a problem or set of problems that focuses students’
attention on a particular mathematical idea and/or provides an opportunity to
develop or use a particular mathematical habit of mind
 Is engaging, relatable, and can maintain student interest
WHY ARE TASKS/ACTIVITIES IMPORTANT?
 Tasks and activities lead to prolonged retention
 Tasks help educators shift their instruction from how to get the answer to
understanding mathematics
IMPLEMENT TASKS THAT PROMOTE REASONING AND
PROBLEM SOLVING
 “Student learning is greatest in classrooms where the tasks consistently
encourage high-level thinking and reasoning and least in classrooms where
the tasks are routinely procedural in nature” (Boaler and Staples 2008; Hibert
and Wearne 1993; stein and Lane 1996)
 Tasks need to have a range of cognitive demand both low and high. They
should range from complex challenges to a routine exercise
ADDRESSING COGNITIVE COMPLEXITY
COMPARE THE TWO TASKS
Task # 1
You are trying to decide which of two
smartphone plans would be better.
Plan A charges a basic fee of $30 per
month and 10 cents per text message.
Plan B charges a basic fee of $50 per
month and 5 cents per text message.
How many text messages would you
need to send per month for plan B to
be the better option? Explain your
decision.
Task # 2
Solve each of the following systems.
4x + y =2
x–y=3
x + 7y = 0
2x – 8y = 22
-6x + 5y = 1
6x + 4y = -10
Adapted from Illustrative Mathematics Illustrations & Kutasoftware.com
WORKSHEET FOR TASK #2
LET’S TRY IT!
LET’S TRY IT!
(6x2 + 3x) - (2x2 + 8x)
This problem was simplified to
4x2 + 11x which is incorrect.
Explain why this is incorrect by citing any mathematical property or connecting
the concept to another mathematical skill.
CONNECTING THE PRACTICES
Effective teaching of mathematics engages students in solving and discussing tasks that promote
mathematical reasoning and problems solving and allow multiple entry points and varied solution
strategies.
Source: Principles to Actions – Ensuring mathematical success for all by the NCTM 2014
EXPERIENCES OF THE PRACTICES
Habits of Mind
Reasoning & Explaining
Modeling & Using Tools
Seeing Structure & Generalizing
EXAMPLE WORKSHEET
EXAMPLE TASK SMP #3
Is the statement
p – 1 = 5p + 3p – 8
Always, Sometimes or Never True
LET’S REVIEW
To build a meaningful task you should consider these two things:
Standard
Mathematical
Practices
Cognitive
Complexity
Meaningful
Task
THINGS YOU COULD TRY!
 Class discussion
 Create your own problems
 Game
 Fix someone’s homework
 Group task
 Tutor another
 Individual task
 Peer to peer tutoring
 Rotating partners
 Puzzle
CONTACT INFORMATION
Cynthia Bell
Numeracy Specialist
Literacy Assistance Center
Phone: 212-803-3306
Email: cynthiab@lacnyc.org