Transcript How did it work? - SE2 Mathematics

SE2 Math FIT Project
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A Number Trick
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Your answer is 1!

How did it work?
Think of a number.
 Add 3.
 Double the result.
 Subtract 4.
 Divide the result by 2.
 Subtract the number
you first thought of.
 Aha! Your answer is 1!

The Plan
 Expressions
and Equality
 BREAK
 Problem
Solving Across the Grades
 Instructional Strategies
 Homework for Next Session
The Assessment Cycle
Review
Collect
Information
Implement
Analyze
Plan For
Improvement
The Patterning and Algebra Strand
Algebraic
Thinking
Patterns and
Relationships
Expressions and
Equality
What is Algebra Really?
Mathematicians view algebra as a system that allows one
to:
• represent mathematical relationships
• explain relationships among quantities
• analyze change
4s = p
Side
Length
P = 4s
Perimeter
1m
4m
2m
3m
8m
12m
Matching Game
1.
2.
3.
4.
5.
6.
expression
equation
inequality
variable
coefficient
constant
A.
B.
C.
D.
E.
F.
x
3<x+2
3x
3=x+2
4x +1
30n
What is a variable?
A variable is a letter that represents a
value that can change or vary.
1) 3 + ___ = 10
2) 6 +
= 9
3) 8 + x = 12
4) 5 +
= 8
These are all
variables
What is a Coefficient?
The coefficient is the number multiplied
by the variable.
Coefficient
Variable
Expressions
An expression contains at least one
or more variables.
5+x
variable
Primary EQAO Assessment (41%)
Junior EQAO Assessment (62%)
Grade 9 EQAO - Applied (52%)
Grade 9 EQAO - Academic (79%)
What is an Equation?
An equation is a statement where one
expression is equal to another.
Left
Side
Right
Side
5+x=8+3
variable
Primary EQAO Assessment (56%)
Junior EQAO Assessment (55%)
Grade 9 EQAO – Applied (72%)
Grade 9 EQAO – Academic (86%)
Expressions vs. Equations
Sentences
Expressions
Equations
Inequalities
Numerical
2+3
2+3=5
9
-5>3
Variable
X+7
11= 3 + 2m
6y
-4<8
Open sentences
Open sentences have solutions and can be solved.
Equality
8+4=
+5
What goes in the box?
8+4=
+5
Grade
#students
Ans: 7
Ans: 12
Ans: 17
Ans:
12 and 17
Other
Ans:
2
99
12
41
16
10
20
3
106
11
53
18
11
13
4
105
13
50
15
11
16
5
98
11
49
14
10
14
6
92
15
34
20
11
12
School
500
62
227
83
53
75
The Juggler ?
Video: Grade 4 Class
True/False
Statements
6=6
2+4=6
6=3+3
8 + 4 = 7 + 5
12
=
12
6 = 7
Expressions and Equality
Looking
Grade 2
Grade Back
3
Grade 4and
GradeForward
5
Grade Grade
Properties of
Numbers
Missing
Numbers
Relationships
6
Students
represent two
number
expressions that
are equal.
Students
investigate the
inverse
relationship of
addition and
subtraction.
Students
investigate the
inverse
relationship of
multiplication
and division.
Students find
missing
numbers in
equations.
(addition &
subtraction to
18)
Students find
missing
numbers in
equations.
(addition &
subtraction with
one/two digits)
Students find
missing
numbers in
equations.
(multiplication
with one/two
digits)
Commutative
Property of
Addition
Associative
Property of
Addition
Commutative
Property of
Multiplication
Properties of
Zero
Properties of
Zero and One
Distributive
Property of
Multiplication
Students
investigate
variables as
changing
quantities.
7
Grade
8
Students investigate variables as
changing quantities and as
unknown quantities as distinct from
a constant in an equation.
Students solve single-variable linear equations
(addition, subtraction, multiplication, division) using
a variety of strategies.
Is This True?
a + b = b + a
a x b = b x a
Commutitive Property
3+7
10
7+3
Is This True?
(a + b) + c = a + (b + c)
(a × b) × c = a × (b ×
c)
Associative Property
9+4+4+4+4
9+9+7
Distributive Property
25
10
10 x 25 = 250
4
4 x 25 = 100
25 (10 + 4) = 350
14 x 25
Another Look
From The Beginning
Kindergarten
More Than, Less Than, The Same As
Five
Six
Less
More
Comparing Handfuls
Symbol Sense
Equalities and Inequalities
Equalities and Inequalities
Missing Numbers - Unknowns
Why use letters to represent variables?
Developmental Continuum
nn
The Balance Model
2
3
4
5
6+7=
+5
25 – 4 = 15 +
-6=5+9
x 4 = 20 + 4
6
12 = 5 + s
8 = 32 ÷
2 x n + 3 = 11
7
5x + 7 = 12 + 5
Solving Equations
==
2X b = b + 6
2b - b
=b -b +6
B=6
How many in each bag?
Break Time
Next Steps - Using True/False Statements
15 + 20 = 16 + 19
12 + 25 = 13 + 36
75 - 19 = 74 - 18
Balance the Gobots
If


=6
Balance the seesaw..
Find as many solutions as
possible.
Balance the Gobots
6
1
5
6
2
4
6
3
3
6
4
2
6
5
1
Variable Rule
All symbols and/or letters in an equation
represent the same quantity!
+
= 5
= 10
+
= 10
Tug-of-War
Four acrobats, five grandmas, and a dog named Ivan
are having a Tug-of-War contest.
Your task is to decide who will win the final round of
the contest. The first two rounds will give you all the
information you need to make your decision!
Tug-of-War
Result: A Tie
Result: A Tie
Tug-of-War
Who will win the tug-of-War contest?
Tug-of-War
Result: Tied!
Result: Tied!!
Result: ???
Problem Solving Across the Grades
Use Logical Reasoning
Use Logical Reasoning (Algebra)
Look for a Pattern
The overall total for all the columns must be equal to the
overall totals for the rows. Find the difference to
determine the missing column.
Row total
28 + 30 + 20 + 16
94
94-69
25
=
=
=
=
=
Column total
? + 19 + 20 + 30
? + 69
?
?
What’s Missing?
28
30
18
20
?
30
23
22
Problem Solving Across the Grades
Patterning and Algebra All Year
How can you bring in
patterning and algebra in
your other units of study?
Homework for Next Time (January)
1. Continue the conversations with your grade team or
division about integration, explicit language, big
ideas etc. of Patterning and Algebra.
2. Administer the performance task to your students
(bring individual student samples to the next session
for moderated marking).
3. Visit the Math Lab folder on Tel for patterning
activities across the grades. Bring any interesting
samples to the next session to share.