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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?

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!

Double The Sum Subtract 4 Divide by 2 Subtract Start Number Add 3 Pick A Number 2n + 6 2n n + 3 n 2n The Algebraic Expression

Expressions and Equality BREAK Problem Solving Across the Grades Instructional Strategies Homework for Next Session The Plan

The Assessment Cycle Review Plan For Improvement Analyze Collect Information Implement

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 P = 4s 4s = p Side Length Perimeter 1m4m 2m8m 3m12m

Matching Game 1. expression 2. equation 3. inequality 4. variable 5. coefficient 6. constant A. x B. 3 < x + 2 C. 3x D. 3 = x + 2 E. 4x +1 F. 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

The coefficient is the number multiplied by the variable. CoefficientVariable What is a Coefficient?

An expression contains at least one or more variables. 5 + x variable Expressions

Primary EQAO Assessment (41%)

Junior EQAO Assessment (62%)

Grade 9 EQAO - Applied (52%)

Grade 9 EQAO - Academic (79%)

What is an Equation? 5 + x = variable LeftSideRightSide An equation is a statement where one expression is equal to another.

Primary EQAO Assessment (56%)

Junior EQAO Assessment (55%)

Grade 9 EQAO – Applied (72%)

Grade 9 EQAO – Academic (86%)

Expressions vs. Equations Numerical Variable ExpressionsEquationsInequalities X = 5 11= 3 + 2m > 3 6y - 4 < 8 Sentences Open sentences Open sentences have solutions and can be solved.

Equality = + 5 What goes in the box?

8 + 4 = + 5 Grade#studentsAns: 7Ans: 12Ans: 17Ans: 12 and 17 Other Ans: School The Juggler ?

Video: Grade 4 Class True/False Statements 6 = = 6 6 = = = =

Looking Back and Forward Expressions and Equality Grade 2Grade 3Grade 4Grade 5Grade 6 Grade 7 Grade 8 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 investigate variables as changing quantities. Students investigate variables as changing quantities and as unknown quantities as distinct from a constant in an equation. 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) Students solve single-variable linear equations (addition, subtraction, multiplication, division) using a variety of strategies. Commutative Property of Addition Properties of Zero Associative Property of Addition Properties of Zero and One Commutative Property of Multiplication Distributive Property of Multiplication Relationships Missing Numbers Properties of Numbers

Is This True? a + b = b + a a x b = b x a Commutitive Property

Is This True? (a + b) + c = a + (b + c) (a × b) × c = a × (b × c) Associative Property

x x 25 = x 25 = (10 + 4) = 350 Distributive Property

Another Look

From The Beginning Kindergarten More Than, Less Than, The Same As Five Six Less More

Comparing Handfuls Symbol Sense

Equalities and Inequalities

Missing Numbers - Unknowns

Why use letters to represent variables?

Developmental Continuum n n

The Balance Model = – 4 = = x 4 = = 5 + s 8 = 32 ÷ 62 x n + 3 = 11 75x + 7 =

Solving Equations B = 6 How many in each bag? = 2X b = b b 2b = b + 6 =

Break Time

Next Steps - Using True/False Statements = = =

Balance the seesaw.. Find as many solutions as possible. Balance the Gobots = 6 If

Balance the Gobots

All symbols and/or letters in an equation represent the same quantity! Variable Rule + = 10 + = 5

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

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 ========== Column total ? ? + 69 ?

What’s Missing? ?302322

Problem Solving Across the Grades

Patterning and Algebra All Year How can you bring in patterning and algebra in your other units of study?

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. Homework for Next Time (January)