Download 1 Grade Level: 6th Grade An Introduction to Algebra Standards for

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Grade Level: 6th Grade
An Introduction to Algebra
Standards for Mathematical
Practice:
1. Make sense of problems and
persevere in solving them.
5. Use appropriate tools
strategically.
6. Attend to precision.
Common Core Standard:
Objective:
Students will verbalize
verbal expressions.
Students will find unknown
numbers in addition,
subtraction, and
multiplication sentences.
Students will model
expressions with variables.
Students will write variable
expressions for models.
Students will solve one
variable equation.
Students will solve multistep equations.
Students will solve
problems using Algebra
Tiles to model equations.
Students will model and
solve problems using
part/part whole to model
equations.
6.EE.2 Write, read, and evaluate expressions in which
letters stand for numbers.
a. Write expressions that record operations with numbers
and with letters standing for numbers. For example,
express the calculation “Subtract y from 5” as 5 – y.
b. Identify parts of an expression using mathematical terms
(sum, term, product, factor, quotient, coefficient); view one
or more parts of an expression as a single entity. For
example, describe the expression 2 (8 + 7) as a product
of two factors; view (8 + 7) as both a single entity and a
sum of two terms.
c. Evaluate expressions at specific values of their variables.
Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including
those involving whole- number exponents, in the
conventional order when there are no parentheses to
specify a particular order (Order of Operations). For
example, use the formulas V = s3 and A = 6 s2 to find the
volume and surface area of a cube with sides of length s =
½.
Key Words & Definitions:
Algebraic Expression
A mathematical phrase involving a variable or variables,
numbers, and operations. Ex: n-2
Variable
A letter such as n, that represents a number in an
expression or an equation.
Order of Operations
The order in which operations are done in calculations.
Work inside parentheses is done first. Then multiplication
and division are done in order from left to right, and finally
addition and subtraction are done in order from left to
right.
Distributive Property
Multiplying a sum (or difference) by a number is the same
as multiplying each number in the sum (or difference) by
that number and adding the products. Example: 3x (10 + 4)
= (3 x10) + (3x4)
Term
a part of a sum in an algebraic expression.
Coefficient
a constant that multiplies a variable. In Ax + By = C, A and B
are coefficients
2
of x and y.
Factor
one of two or more expressions that are multiplied
together.
Product
the result of two numbers being multiplied.
Quotient
the answer to a division problem.
Sum
the result of adding.
Equation- a mathematical statement that says that two
expressions have the same value.
Equality- two values are not equal. a ≠ b says that a is not
equal to b
Lesson
Teacher Preparation:
 Pull up Algebra Page(Appendix 1)
Background Knowledge:
Students should have background knowledge in the
areas of knowing what a symbol is. Students should
know how to solve for the unknown. Lesson should
build on prior knowledge of solving one step
addition, subtraction, multiplication, and division
equations.
Introduction:
Fill out a KWL chart for Algebra on the
smart board.
First:
At the beginning of the lesson,
start a discussion by asking, “I am
thinking of a number. Now, I am
going to add three to my number.
My total will be 12. How can I
represent this?”
Tell students they will need to be
detectives and figure out a way to
represent the unknown.
Ask students to draw a picture of
what this expression represents.
(Take note as to how students
chose to visually represent
equation as a formative
assessment)
Tell the students they just
completed their first Algebra
problem in the 6th grade.
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Teacher Preparation:
 Students Notebooks
 Appendix 1-5
Background Knowledge:
Second:
Ask students to pull out their math
notebooks.
Shows slides 1-5 and allow
students to take notes in their
math journals.
Teacher Preparation:
 Algebra Tiles/ Students
 Appendix 6
Background Knowledge:
Students more than likely will not be familiar
with algebra tiles. They will need to get used to
transitioning from thinking about tens and ones,
to thinking in terms of x & units. Lower students
may struggle to transition from seeing tiles as
base ten to algebraic form.
Teacher Preparation:
Third:
Distribute Algebra tiles. (Appendix
6)
Inform students what each tile
stands for. (Appendix 6) Long tile is
the unknown number, while the
small 1cm squares are unit tiles.
(Unit tile = 1)
Prompt: Can you use the algebra
tiles to represent the equation we
just discussed? Let students work
independently to use algebra tiles
to represent equation.
Fourth:
Pair students up.
 Pair students up ( Appendix 7)
Each group should receive Algebra
Tiles & Appendix 8, Simplifying
 Algebra Tiles/ Group
Expressions. Appendix 9 is the
answer key.
 Copy of Appendix 8 for every student
Have students work in pairs to
 Answer Document ( Appendix 9)
complete the page.
Goal is to see students understand
Background Knowledge/Notes:
that they can put like terms
together.
Students will have background knowledge in
As pairs finish, pair groups up to
working together to solve problems. If students have
compare answers. Each group
trouble, respond by prompting them with a
should explain why they think their
question. Try to refrain from helping Students
answers are correct, and how they
chose to work their problem.
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Teacher Preparation:
Fifth:
As a whole group, have students
discuss appendix ten. (Zero Pair)
Let students share reasonable
ways to solve problem.
Introduce them to the term “Zero
Term”
Have students take notes in their
math journal.
 Appendix 10
 Student Math Journals
Background Knowledge/Notes:
Students should be familiar with how to balance an
equation by “canceling out”. “Zero pair” will be a
new vocabulary term. Have students explain why it
is called a zero pair.
Teacher Preparation:
Sixth:
Pair students back up.
Each pair should receive algebra
tiles, and Appendix 12, Solving
Equations. (Appendix 13 is an
answer key)
 Pair Students up (Appendix 11)
 Copy of Appendix 12 for everyone.
 Answer Document (Appendix 13)
Background Knowledge:
Students will be using their math journals as a
resource for background knowledge.
Teacher Preparation:
 Appendix 16 should be pulled up on board
Background Knowledge:
Seventh:
Review Balancing an Equation
(Appendix 16)
Watch short video
Play algebra tile game.
Students will be relying on previous days inquiry
about solving equations.
Teacher Preparation:
 Appendix 18 should be displayed on board.
 Student Math Journals.
Background Knowledge:
Students will have background knowledge in
part/part whole method of thinking. They will just
need to see how it applies to algebra.
Eighth:
Introduce students to new
part/part whole strategy.
(Appendix 18)
Have students get out math journal
and take notes.
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Teacher Preparation:
 Pair students up
 Copy of Appendix 20 for every students
 Answer Document ( Appendix 21)
Background Knowledge:
Students will be depending on whole group
discussion and math journal as source for
information.
Teacher Preparation:
 Copy of Assessment for every student
(Appendix 22 & 24
 Answer Document (Appendix 23 & 25)
Background Knowledge: Students will be
depending on understanding of previous lessons
as a source of knowledge.
Ninth:
Pair students up.
Each pair should receive Appendix
20. (Appendix 21 is an answer key)
Have students explore solving
equations using Maps.
Once students are finished, have
each pair write a step by step guide
explaining how to use the method.
Students should explain what to
look at first, what needs to be
created, and how to solve the
problem.
Tenth:
Give students an assessment
on two strategies learned.
(Appendix 22 & 24) (Appendix
23 & 25 is an answer key.)
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