I'm currently taking an Additional Basic Qualification course so that I can teach the Junior grades (4-6), and below you'll find a Grade 5 Mathematics lesson plan that I created for the course.
Grade 5 Mathematics
Lesson Topic:
Multiplying Two Two-Digit Whole Numbers and Area
The
intention for this lesson is that students are introduced to multiplying two
two-digit whole numbers as an authentic problem with multiple entry
points. Students will not be given any
algorithms for multiplying these numbers, instead they will have to puzzle the
problem out by working in small groups, creating strategies, and documenting
these strategies in their math journals.
The teacher will circulate and asking guiding/leading questions. This instructional strategy was discussed at
length in The Report of the Expert Panel
on Mathematics Instruction, Grades 4-6 (2004).
The
problem might look something like this:
A rural school wants to
put grass seed on its schoolyard. The
schoolyard is shaped like a rectangle.
The schoolyard’s length is 42 metres, and its width is 37 metres. Grass seed costs $4.00 per metre
squared. How much will it cost to seed
the schoolyard?
Rationale for
Instructional Strategy
I’ve
picked this instructional strategy because it allows students to practice basic
math concepts, but it also connects these concepts to real-life scenarios and
situations. In theory, when students
understand how what they’re learning is relevant to their lives, then they are
more likely to be engaged and motivated to learn. This engagement and motivation are essential
to changing the prevailing attitude toward Math, which is that some people just
aren’t “good at Math” and that it’s “okay” not to be good at Math, both of
which are untrue.
TLCP and Bloom’s
Taxonomy
This lesson could be modified to
connect to a TLCP with an overall focus of field sports. For example, instead of calculating the area
of a schoolyard, students could calculate the area of a Soccer field (FIFA World
Cup).
This problem requires both higher- and
lower-ordering thinking skills because students are relying on their knowledge
and comprehension of key concepts, applying these concepts to a problem, and
reflecting upon the strategies they came up with to solve this problem.
Video Support
The
following video (link below) from Khan Academy would be an excellent tool to
consolidate student’s understanding of multiplying two two-digit whole numbers,
and ultimately to introduce or consolidate the strategy that I’m hoping
students will come to on their own: using an area model to multiply two
two-digit whole numbers.
This lesson/video deals with
multiplying two-digit numbers by two digit numbers (e.g. 78 x 65). Below is the process for how I was taught to
multiply two two-digit numbers:
·
Line
up the numbers in columns with the greatest number on top; draw a line and
multiplication sign underneath.
·
Multiply
the bottom right digit by the top right digit; write down the answer under the
line in the correct columns (e.g. ones, tens).
·
Move
down a space and put 0 in the ones column; multiply the bottom right digit by
the top left digit.
·
Move
down a space and put a 0 in the ones column; multiply bottom left digit by top
right digit.
·
Move
down a space and put a 0 in the ones column and a 0 in the tens column. Multiply bottom left digit by top left digit.
·
Add
up the four answers for the final answer.
This
way of teaching the multiplication of two two-digit numbers involves memorizing
a set of rules. The focus in on when and
where to place the 0’s so that the student gets the right answer.
The teacher in the video uses what’s
called the “Area Model” to associate the operations that the student is
completing in the multiplication exercise with a diagram or manipulative. Students can see the relationships between
the numbers that they’re multiplying, and the answer makes more sense.
Learning how to multiply in this way
also shows students that there are multiple ways to answer a math problem, even
a math problem that seems to have a simple algorithm or process for solving it.
More importantly, learning in this way
helps the student to visualize the problem and enables them to do it mentally
later on.
Connection to Ontario
Curriculum Expectations
|
Overall
|
Specific
|
|
Number Sense and
Numeration
|
|
|
·
Solve
problems involving the multiplication and division of multi-digit whole
numbers, and involving the addition and subtraction of decimal numbers to
hundredths, using a variety of strategies.
|
·
Multiply
two-digit whole numbers by two-digit whole numbers, using estimation,
student-generated algorithms, and standard algorithms.
|
|
Measurement
|
|
|
·
Estimate,
measure, and record perimeter, area, temperature change, and elapsed time, using
a variety of strategies.
|
·
Determine,
through investigation using a variety of tools and strategies, the
relationships between the length and width of a rectangle and its area and
perimeter, and generalize to develop the formulas
·
Solve
problems requiring the estimation and calculation of perimeters and areas of
rectangles.
|
Connection to the
Achievement Chart
·
Not
all categories and criteria have to be graded.
Which criteria and which categories the teacher chooses to assess and
evaluate will depend on what assessment tool is used (e.g. coming up with the solution
to the problem lends itself to Knowledge and Understanding or Application;
reflecting in the Math Journal lends itself to Thinking; and, sharing with
peers or conferencing with the teacher lends itself to Communication).
|
Criteria
|
Interpretation
|
|
Knowledge and
Understanding
|
|
|
Knowledge of content (e.g. facts, terms, procedural
skills, use of tools).
|
Lines up two two-digit numbers correctly to multiply
them.
|
|
Understanding of Mathematical Concepts
|
Understands, for example, that multiplying the bottom
right digit by the top left digit is multiplying a one-digit by a ten-digit,
not a one-digit by a one-digit.
Understands that l x w = area.
|
|
Thinking
|
|
|
Understanding the problem
|
Student understands that this is a multiplication
problem, not an addition, subtraction, or division problem.
|
|
Making a plan for solving the problem
|
Student comes up with own strategy for multiplying the
two two-digit whole numbers, written in math journal.
|
|
Carrying out a plan.
|
Student shows evidence of having implemented their
strategy in trying to solve the problem.
|
|
Looking back at the solution.
|
Student shows evidence of having verified that the
answer to the problem was correct.
|
|
Use of critical/creative thinking processes.
|
Student revises strategy if strategy fails, or reflects
upon strategy if successful.
|
|
Communication
|
|
|
Expression and organization of mathematical thinking.
|
Student’s process as written in Math journal is clear
and easy to follow.
|
|
Communication for different audiences and purposes in
oral, visual, and written forms.
|
Student communicates strategy for solving problem to
peers and to teacher.
|
|
Use of conventions, vocabulary, and terminology of the
discipline.
|
Student uses the terms “multiplication,” “ones,” “tens,”
“hundreds,” and “thousands,” “length,” “width,” and “area” correctly.
|
|
Application
|
|
|
Application of knowledge and skills in familiar context.
|
Applies knowledge how to calculate area to the problem.
|
|
Transfer of knowledge and skills to new contexts.
|
Transfers knowledge of multiplication tables and of
tens, ones, hundreds, and thousands to two-digit multiplication problems.
|
|
Making connection within and between various contexts.
|
Makes the connection between area of a rectangle and two-digit
multiplication.
|
What type of
learning is taking place?
Knowledge and
Understanding:
Students are practising and becoming more familiar with math terms, procedural
skills, tools, and concepts. Students
are reviewing and integrating such knowledge and skills as their times tables,
multiplication, place value, the difference between ones, tens, hundreds, and
thousands, length, width, and area.
Thinking: As students attempt to the solve the
problem given to them, they are becoming problem-solvers and critical thinkers,
but most importantly, they are learning to document their research in a way
that’s meaningful for both themselves and others.
Communication: As students collaborate and share
their answers, they are learning to express themselves clearly and for a
specific purpose. This collaboration and
sharing could occur in small groups, in pairs, or whole class. Students could
share their answers with either peers, or with the teacher who is assessing
them.
Application: Students are learning to connect what
they’ve learned in Measurement about the relationship between the length and
width of a rectangle and its area to the arithmetic that they are learning
now. By making this connection, students
will uncover a new way to understand the material, which in turn will make the
material more meaningful to them.
Supporting Learners
both Inside and Outside the Classroom
Inside the
Classroom
·
Show
the video either before or after the lesson; either way, the lesson will change
dramatically. Know your students and consider
which strategy would work best.
·
Use
diagrams; a simple explanation of the area model on the blackboard could help
many struggling students.
·
Use
manipulatives; having cubes, geoboards, and other such manipulatives available
could really help some students understand the problem in a more concrete way.
·
Group
students appropriately; some students prefer to work alone or in pairs; some
students work better in small groups; know your students and group them
accordingly.
·
Ensure
that students are writing in their Math Journals; it’s essential for students
to document their thinking process if you’re going to assess it later on. Otherwise, you must rely on observation.
Outside the
Classroom
·
In
the event that a student has to be absent, a link to the video from Khan Academy,
as well as the lesson’s main task/problem, can be posted to a classroom website
or blended learning platform.
·
Parents
can support their child’s learning by checking the website and working through
the problem with their child.
·
The
teacher needs to available and to communicate with the parents and student to
assess and evaluate learning.
·
Blended-learning
platforms provided by school boards sometimes have a feature that allows
students to chat or post to forums, and if this resource is available, then the
student wouldn’t even have to miss out on the collaborative part of the
project!
Flipping the Lesson
This
lesson could easily be flipped:
·
Post
a link to the video on your classroom website ahead of time, and have the
students watch the video at home, the night before the lesson, as preparation
for the lesson. That way, when the
students come to class, they can focus on solving the problem, rather than
grappling with the concepts. This
strategy frees up students’ time to collaborate, and it frees up the teacher’s
time to circulate, help, and observe.
·
If
students don’t have ready access to either a computer or the internet at home,
then give students time at the beginning of class to watch the video. Options for this include projecting the video
for the whole class to see, booking the computer lab so each student has a
computer (though for a five minute video, this option is rather redundant), or
if your school has access to iPads, give one iPad to each group and instruct
them to watch the video as a group before they begin solving the problem.
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