Unit Title:
Name:
Rational Numbers
Derek Glover
Number of Lessons:
Subject(s):
8
Mathematics
Time: (in weeks)
~2
Grade(s):
9
Rationale: The purpose of this unit is to provide students with a fun and applicable approach towards the use of rational numbers. Rational numbers are
used frequently in Mathematics and the Sciences, and as such, it is crucial that students not only understand what rational numbers are, but know how to
solve problems involving rational numbers.
Overview: The applications of Rational Numbers are the focus of this unit. Students will have been introduced to the notion of a rational number in Grade
8, and thus defining rational numbers will come almost immediately in this unit. The bulk of the unit will be devoted to the solving of problems involving
rational numbers (in both fraction and decimal form). Key concepts include the multiplication, division, addition, and subtraction of fractions and decimals,
as well as finding common denominators and simplifying fractions. At the end of the unit, there is a chapter which develops the notion of a square root. In
this section, students will solve problems involving perfect squares as well as develop estimation strategies for non-perfect squares. This section leads
directly into the next unit which deals with exponentiation.
Prescribed Learning Outcomes from IRPs:
• A3 – Demonstrate an understanding of rational numbers by:
Ø Comparing and ordering rational numbers.
Ø Solving problems that involve arithmetic operations on rational numbers.
• A5 – Determine the square roots of positive rational numbers that are perfect squares.
• A6 – Determine an approximate square root of positive rational numbers that are non-perfect squares.
Prerequisite Concepts and Skills:
By the end of Grade 8 students should have the ability to:
Ø Demonstrate an understanding of multiplication and division of integers, concretely, pictorially, and symbolically. (A7)
Ø Demonstrate an understanding of multiplication and division of positive fractions and mixed numbers concretely, pictorially, and
symbolically. (A6)
Ø Solve problems that involve rates, ratios, and proportional reasoning. (A4)
Ø Demonstrate an approximate square root of numbers that are not perfect squares (limited to whole numbers). (A2)
Ø Demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers).
(A1)
Teacher Preparation Required: Creation of tests, quizzes, worksheets and problems to solve. Acquisition of required materials.
Cross-Curricular Connections: As previously stated rational numbers are used frequently in many areas of mathematics as well as the sciences and even
in the humanities. Because life is not always explained using whole numbers understanding how decimals and fractions work is pivotal for understanding
trends in geography and business. Additionally, rational numbers are used extensively in the calculations students will be expected to do in Chemistry,
Physics, and Biology. Square roots are also often present in scientific formulae.
Extensions to Unit: There are many simple hands-on activities in the text, which would not require much more than cards or dice. If time permits, these
activities could be both fun and educational for the students, as they would allow for problem-solving practice in the form of a game. Additionally, these
activities would encourage students to verbalize their knowledge of fractions, which is beneficial for both the speaker and the listener.
Universal Design for Learning (UDL) and Differentiated Instruction (DI): The diversity of learners will be important in the delivery of subject matter
in this unit. To accommodate for diversity, I would like to include hands-on activities such as games in my lessons. These activities would not only be
educational, but they would allow for a break from the monotony of problem-solving that is often unavoidable in math classes. Additionally, I would like
to include visual representations in problems wherever possible because this may allow students to make the connections between the abstract
mathematical concepts to the concrete.
Resources: Class text (Math Links 9), Cards (15-16 decks), Dice (30-32)*, Candy(M&Ms)*, Snap Cubes, Scissors Glue, Document Viewer, Projector.
Overview of Lessons:
Lesson
#
1
Time
70 Min
Topic
Intro /
Prerequisite skills
PLOs
In
Lesson
A3
Instructional
Objectives
• To differentiate
between review
terminology
• To express rational
numbers in
fraction form in
lowest terms
• To construct a
rational numbers
foldable
Teaching
Strategies
Direct
Instruction,
Guided
Practice,
Hands-On
Instruction
Lesson Activities
• Overview of rules
and expectations
• Review of basic
terminology and
required skills
• Foldable Activity
Assessment
Strategies
Materials
(Specific to
This Lesson)
• Formative
assessment of
Grade 8 skills
during review
• Foldable activity
will be collected
at the end of the
unit and graded
• Expectations
handout
• Foldable
printout
• Scissors
• Glue
• Lined paper
2
60 Min
2.1: Comparing
and Ordering
Rational
Numbers
A3
• To compare and
order rational
numbers in
decimal and
fraction form
• To convert rational
numbers from
fractions to
decimals and viceversa
• To independently
solve problems
involving the
comparing and
ordering of
rational numbers
Direct
Instruction,
Guided
Practice, and
Independent
Practice (with
circulation)
• Warm-up activity
• Terminology
worksheet (handout)
• Short lesson and
guided problem
solving
• Assignment 2.1
• Warm-up
activity will be
graded by
students then
submitted
•Formative
assessment of
students during
lesson and group
problem solving
and during
independent
practice
circulation
• Assignment 2.1
will be collected
and graded
•Warm-Up
problem
• Terminology
worksheet
• Calculator
• Class notes
handout
• Lined paper
3*
70 Min
Math Link
Activity /
Problem Solving
A3
• To verbalize the
skills learned last
class in a game
setting
• To analyze the
breakdown of
colors in a typical
candy box*
• To independently
solve problems
involving the
comparing and
ordering of
rational numbers
Guided
Practice,
Independent
Practice (with
circulation),
and
Cooperative
Learning
• Warm-up activity
• Math-link game
(card fractions)
• Candy counting
group activity*
• Problem solving
with class
• Time to work on
homework (2.1)
•Warm-up activity
will be graded
by students then
submitted
• Formative
assessment of
students during
group activities
and during
independent
practice
circulation
• Assignment 2.1
will be collected
and graded
• Warm-up
problem
• Cards (15
packs)
• Candy*
(probably
M&Ms)
• Calculator
• Lined paper
4
70 Min
2.2: Problem
Solving with
Rational
Numbers in
Decimal Form
A3
• To solve problems
involving the
addition,
subtraction,
multiplication, and
division of rational
numbers in
decimal form (both
positive and
negative)
Direct
Instruction,
Guided
Practice, and
Independent
Practice (with
circulation)
•Warm-up activity
• Short lesson and
guided problem
solving
• Assignment 2.2
• Warm-up
activity will be
graded by
students then
submitted
• Formative
assessment of
students during
lesson and group
problem solving
and during
independent
practice
circulation
•Assignment 2.2
will be collected
and graded
• Warm-up
problem
• Calculator
• Class notes
handout
• Lined paper
5
70 Min
2.3: Problem
Solving with
Rational
Numbers in
Fraction Form
A3
• To solve problems
involving the
addition,
subtraction,
multiplication, and
division of rational
numbers in
fraction form (both
positive and
negative)
Direct
Instruction,
Guided
Practice, and
Independent
Practice (with
circulation)
• Warm-up activity
• Short lesson and
guided problem
solving
• Assignment 2.3
• Warm-up
activity will be
graded by
students then
submitted
• Formative
assessment of
students during
lesson and group
problem solving
and during
independent
practice
circulation
• Assignment 2.3
• Warm-up
problem
• Calculator
• Class notes
handout
• Lined paper
will be collected
and graded
6
70 Min
Quiz / 2.4:
Determining
Square Roots of
Rational
Numbers
A3, A5,
A6
• To differentiate
between perfect
and non-perfect
squares
• To find square
roots of perfect
squares
• To estimate square
roots of nonperfect squares
Direct
Instruction,
Guided
Practice, and
Independent
Practice (with
circulation)
• Quiz (2.1-2.3)
• Lesson (using snap
cubes to introduce
the idea of squares)
and guided problem
solving
• Assignment 2.4
7
60 Min
Chapter Review
A3, A5,
A6
• To increase
understanding of
the preceding
Chapter 2 skills in
preparation for the
unit test
Guided
Practice and
Independent
Practice
•Warm-up activity
• Guided problem
solving
• Review problems
for students
(assignment)
• Quiz will be
submitted and
graded
• Formative
assessment of
students during
lesson and group
problem solving
and during
independent
practice
circulation
• Assignment 2.4
will be collected
and graded
• Warm-up
activity will be
graded by
students then
submitted
• Formative
assessment of
students during
group problem
solving and
during
independent
practice
circulation
• Review
assignment will
be collected and
graded
• Quiz
• Calculator
• Class notes
handout
• Lined paper
• Warm-up
problem
• Problems
(notes)
handout
• Lined paper
8
75 Min
Chapter 2 Test
A3, A5,
A6
• To write a unit test
involving the
preceding Chapter
2 skills
Test
Invigilation
• Unit Test
(Cumulative)
• Test will be
submitted and
graded
(Summative
assessment)
• Unit test
Reflections/Revisions (if necessary, continue on separate sheet):
*In lesson 3, if the Math Link card game takes too long, I may not do the candy counting game. This activity will be discretionary. All warm-up problems
will be to do with material that was covered in the previous class. Lesson 6 may take longer than anticipated (especially since the snap blocks will be used)
so I may have to add in an extra day to fully cover this topic before the test. There are a number of Math Link activities that I could do with the class to
reinforce content taught in sections 2.2 through 2.4. These activities would not require many resources (cards, dice, and coins) and could be done if there is
an abundance of time in any particular lesson. Also, I can vary the number of problems that I go over with the class during guided practice to allow for a
reasonable (but not too lengthy) amount of time for independent practice at the end of each lesson