Saturday 21 June 2014

Math Lesson for Grade 5



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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