Transcript Using a 3-part Lesson Model

3-Part Lessons
Jane Silva
Instructional Leader
Mathematics/Numeracy, K-8
SW
Teaching Through Problem Solving Using a
Three-Part Lesson Model
• allows teachers to develop rich and engaging tasks
• naturally embeds the mathematical processes
expectations
• leads to conceptual understanding and more
meaningful connections
Teaching Through Problem Solving
A good instructional problem:
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builds on students’ prior knowledge and skills;
considers a key concept or big idea;
has a meaningful context;
has multiple entry levels (differentiation);
solution is not immediately obvious;
may have more than one solution;
promotes the use of one or more strategies;
requires decision making;
may encourage collaboration.
Components of a 3-Part Lesson
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Part 1 (Before/Getting Started/Minds On)

Part 2 (During/Working On It/Action)
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Part 3 (After/Reflect and Connect)
Identify the Curriculum Expectations
What are/is:
• the content and process expectations this lesson
addresses for your grade level;
• the prior knowledge and skills students would have
learned in the previous grade;
• the overall and specific expectations this problem
addresses for the next grade level; and
• expectations/connections to other strands.
Ex: Gr. 8 - solve and verify linear equations involving a one-variable term
and having solutions that are integers, by using inspection, guess and
check, and a "balance" model
Determine the Big Ideas
Big Ideas
• The broad, important understandings that students
should retain long after they have forgotten many of
the details of something they have studied.
Ex:
Any pattern, algebraic expression, relationship, or equation can be
represented in many ways.
The principles and processes that underlie operations with numbers and
solving number equations apply equally to algebraic situations.
Determine the Learning Goal
Learning Goals:
• Consider the curriculum expectations and big ideas
• Describe what students are expected to learn
• Provide students with a clear vision of where they
are going
• Focus effective teacher feedback on learning
• Develop students’ self-assessment and selfregulation skills
Ex: I will be able to create equations and use different strategies and
representations to show that the equations are true.
3-Part Lesson – An Algebra Example
Part 1 - Before/Getting Started/Minds On
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relates to the day’s lesson goals and problem;
activates prior knowledge;
assesses students’ prior knowledge and skills;
engages students/develops a context;
checks for students’ understanding for ‘during’.
Part 1 - Before/Getting Started/Minds On
• 5-10 minutes
• Activating students’ mathematical knowledge and
experience that is directly related to the
mathematics in the lesson problem
• Use a smaller problem similar to the previous
known problem
• Use student work responses for class analysis and
discussion to highlight key ideas and/or strategies
Part 1
• Sort and sequence the equation strips.
Ex: Opportunity for Differentiation - Parallel Questions
– Only 1 equation in the envelope
– 2 equations in different colours
– 2 equations with different variables
– Partially completed solutions
– 3 or 4 equations in the same colour
Part 1
Part 2 – During/Action/Working On It
Students are:
• actively-engaged in problem solving;
• making hypotheses and conjectures;
• choosing methods, strategies, and manipulatives;
• discussing mathematical ideas with others;
• constructing their own knowledge; and
• developing perseverance.
Part 2 – During/Action/Working On It
Teacher is:
• scaffolding students’ learning;
• conferencing with small groups or individual
students;
• observing and noting student/group strategies,
mathematical language, and models of
representation;
• engaging in Assessment FOR Learning.
Part 2 – During/Action/Working On It
• 15-20 minutes
• Understand the problem, make a plan, carry out
the plan
• Students solve the problem individually, in pair, or
in small groups
• The teachers support student understanding and
assesses for learning
Part 2
Write an equation with 4 different numbers and the
variable x.
At least 2 numbers must be from this list:
4
13
100
Show that your equation is true.
1000
Assessment FOR Learning:
Observation and Interview Template
Part 3 – After/Reflecting and Connecting/
Consolidation and Debrief
Students are:
• reflecting on their own thinking (meta-cognitive
skills) and the thinking of other students;
• communicating problem solving strategies,
methods, and solutions to their peers;
• consolidating the learning of new concepts.
Part 3 – After/Reflecting and Connecting/
Consolidation and Debrief
Teacher is:
• deciding which group’s strategies, methods, or
solutions should be presented to highlight the
mathematical thinking and to develop the
mathematical understanding of all students related
to the problem and lesson goals;
• facilitating the learning by annotating and labeling
work samples;
• asking for clarification or having students summarize
for partners or the whole group the thinking of the
presenting group; and
• engaging in Assessment FOR Learning.
Part 3 – After/Reflecting and Connecting/
Consolidation and Debrief
• 20-25 minutes
• Teacher selects 2 or more solutions for class
discussion and decides which solution to share
• Teacher organizes solutions to show math
elaboration from one solution to the next, towards
the lesson goal
• Student authors explain and discuss their solutions
with their peers
• Teacher mathematically annotates solutions to
make mathematical ideas, strategies, tools explicit
Part 3
What thinking did you use to create your
equation?
Which strategies did you use to show that your
equation is true?
Teachers Can Differentiate
Content
Process
Product
According to Students’
Readiness
Interest
Adapted from The Differentiated Classroom: Responding to the Needs of All Learners (Tomlinson, 1999)
Learning
Profile
Differentiation Strategies
Goal
The goal is to meet the needs of a broad range of
students, but all at one time– without creating
multiple lesson plans and without making students
who are often labelled as strugglers feel inferior.
Differentiated Instruction
Structures and Strategies
Structures
• Cubing
• Menus
• Choice Boards
• RAFTs
• Tiering
• Learning Centers
• Learning Contracts
• Open Questions
• Parallel Tasks
Strategies
• Anticipation Guide
• Think-Pair-Share
• Exit Cards
• Venn Diagrams
• Mind Maps
• Concept Maps
• Metaphors/Analogies
• Jigsaw
Cube
Powers
Face 1: Describe what a power is.
Face 2: How are powers like multiplying? How are they
different?
Face 3: What does using a power remind you of? Why?
Face 4: What are the important parts of a power? Why
is each part needed?
Face 5: When would you ever use powers?
Face 6: Why was it a good idea (or a bad idea) to invent
powers?
Menu
Fractions, Percent and Decimals
Appetizer (Everyone):
• What does the denominator and numerator tell you?
Main dish (Choose 1):
• You want to estimate 20/30 as a percent. Describe your thinking.
• You want to estimate 0.3 as a fraction. Describe your thinking.
Side dishes (Choose 2):
• Draw a picture to show why 0.4 and 6/15 are equivalent.
• Draw a flow chart to show how someone should proceed to convert a
fraction to a percent.
Dessert(if you wish)
• A decimal begins 0.24…. but then it continues. What do you know about
the fraction it could represent.
• Alicia says that the only fractions that are whole numbers of percents
have denominators of 2, 4, 5, 10, 20, 25, and 50. Do you agree? Explain.
Choice Board
Fractions
Complete question # …. on
page …. in your text.
Choose the pro or con side
and make your argument:
The best way to add mixed
numbers is to make them
into equivalent improper
fractions.
Think of a situation where
you would add fractions in
your everyday life.
Make up a jingle that would
help someone remember
the steps for subtracting
mixed numbers.
Someone asks you why you
have to get a common
denominator when you add
and subtract fractions but
not when you multiply. What
would you say?
Create a subtraction of
fractions question where the
difference is 3/5.
•
Neither denominator you
use can be 5.
• Describe your strategy.
Replace the blanks with the
digits 1, 2, 3, 4, 5, and 6 and
add these fractions:
[]/[] + []/[] + []/[]
Draw a picture to show how
to add 3/5 and 4/6.
Find or create three fraction
“word problems”. Solve
them and show your work.
R.A.F.T.
ROLE
AUDIENCE
FORMAT
TOPIC
Coefficient
Variable
Email
We belong together
Algebra
Principal of a school Letter
Why you need to
provide more
teaching time for
me
Variable
Students
Instruction manual
How to isolate me
Personal ad
How to find a life
partner
Equivalent fractions Single fractions
Tiers
Fractions
Tier 1: all fractions are proper; have common
denominators; and can be modeled
Tier 2: fractions are proper and improper; have
different denominators, but all can be modeled
with pattern blocks
Tier 3: fractions are proper and improper and not all
can easily be modeled
Learning Centers
Surface Area
Station 1: Simple “rectangular” or cylinder shape
activities
Station 2: Prisms of various sorts
Station 3: Composite shapes involving only prisms
Station 4: Composite shapes involving prisms and
cylinders
Station 5: More complex shapes requiring invented
strategies
Open Questions
Strategies for Creating Open Questions
Start with the Answer
Closed:
√64 =
8
Open:
An irrational number is about 8. What
might it be?
√65
√64
2π + 2
8/3 π
Strategies for Creating Open Questions
Ask for similarities and differences
Closed:
Describe each term in the equation
y = 3x - 2
Open:
How are these two equations alike?
How are they different?
y = 3x – 2 y = 6x - 4
Strategies for Creating Open Questions
Replace a number with a blank
Closed:
A rectangle has a length 3cm and a
width 4cm. What algebraic expression
can describe features of the
rectangle?
Open:
A rectangle has a length __cm and a
width 4cm. What algebraic expression
can describe features of the
rectangle?
Parallel Tasks
The idea is to use two similar tasks that meet different
students’ needs, but make sense to discuss together.
Parallel Tasks - Examples
• Cell phone Plans
Per
month
Per
minute
Plan 1
$27
200
free;
then
35¢
Plan 2
0
30¢
• Choose Plan 1 or Plan 2.
• How much would 250
minutes cost?
• Provide an equation.
Parallel Tasks - Examples
Numeration and Number Sense
• Task A: 1/3 of a number is 24. What is the number?
• Task B: 2/3 of a number is 24. What is the number?
• Task C: 40% of a number is 24. What is the number?
Parallel Tasks - Examples
Task 1:
Find the equation
of a line to
complete this
parallelogram:
y=8
y = -3x + 12
y=2
Task 2:
Find the equation
of a line to
complete this
right triangle
y = -2x + 8
y = 1/3 x
How to Create Parallel Tasks
Think about the underlying big idea. Think about how it
can be made more accessible to struggling students.
Alter your original task to allow for that accessibility.
Resources
Leading Math Success (Grades 7-9)
The Leading Mathematics Search Tool for Instructors,
Parents and Students (or LMSTIPS for short) was
developed as part the Leading Math Success project
in order to assist Teachers, Parents and Students in
finding quality, relevant math resources on the
Internet.
Edugains
A dynamic site where Ontario educators involved in
Grades K-12 teaching and learning can access a wealth
of resources and information to support mathematics.
http://www.edugains.ca/newsite/math2/index.html
Balanced Assessment in Mathematics
• From 1993 to 2003, the Balanced Assessment in
Mathematics Program existed at the Harvard
Graduate School of Education. The project group
developed a large collection of innovative
mathematics assessment tasks for grades K to 12,
and trained teachers to use these assessments in
their classrooms.
National Council Of Teachers Of Mathematics
Designed to "illuminate" the new NCTM Principles
and Standards for School Mathematics. (Activities,
Lessons, Standards and Web Links)
Wired Math
Free math games and resources for Grades 7, 8, 9
from the Department of Mathematics at the
University of Waterloo.
National Council of Teachers of Mathematics
Access to elementary to high school resources that
include: articles, rich tasks and activities,
problems, technology tips, and more.
Ontario Education Resources Bank
Supported by the Education Ministry of Ontario. Includes
lessons, units, assessments and more. Note: The content
of the website is available to teachers and students.
Teacher userid: tdsbteacher
Teacher password: oerb
Gizmos
ExploreLearning.com offers the world's largest library
of interactive online simulations for math and science
education in grades 3-12.
In order to receive an username and password, email:
[email protected].